TWI452283B - A method of calibrating a system that obtains reflectance data and a method of calibrating a reflectometer - Google Patents

Description

校準一獲得反射率資料之系統的方法及校準一反射計之方法Method for calibrating a system for obtaining reflectance data and method for calibrating a reflectometer

本發明係關於光學計量學領域。更明確地說，本發明提供一種方法，藉由該方法可精確校準反射率資料。在一實施例中，本發明提供一種方法，藉由該方法可精確校準寬頻真空紫外(VUV)反射率資料。另外，本發明亦提供一種方法，藉由該方法可執行高度精確的薄膜量測。The invention relates to the field of optical metrology. More specifically, the present invention provides a method by which the reflectance data can be accurately calibrated. In one embodiment, the present invention provides a method by which to calibrate broadband vacuum ultraviolet (VUV) reflectance data. In addition, the present invention also provides a method by which highly accurate film measurements can be performed.

光學反射量測技術由於其非接觸、非破壞性且通常高通量的性質已長期應用於半導體製造工業中之過程控制應用中。此等工具中的大多數在光譜區的某部分中操作，該光譜區跨越深紫外波長及近紅外波長(DUV－NIR通常為200－1000 nm)。朝較薄層的推近及複雜新材料的引入已挑戰此等儀器之靈敏度。結果，此已迫使努力研發使用較短波長(在200 nm以下)之光學反射量測儀器，於其中可實現對材料特性之微小改變的較大靈敏度。在美國申請案第10/668,642號(於2003年9月23日申請)中描述一種執行此等量測之方法，該申請案揭示用於真空紫外(VUV)反射計之系統及方法，其揭示內容以引用方式併入本文中。Optical reflectometry has long been used in process control applications in the semiconductor manufacturing industry due to its non-contact, non-destructive and generally high throughput properties. Most of these tools operate in a portion of the spectral region that spans the deep ultraviolet and near infrared wavelengths (DUV-NIR is typically 200-1000 nm). The approach to thinner layers and the introduction of complex new materials have challenged the sensitivity of such instruments. As a result, this has forced efforts to develop optical reflectance measuring instruments using shorter wavelengths (below 200 nm) in which greater sensitivity to small changes in material properties can be achieved. A method of performing such measurements is described in U.S. Patent Application Serial No. 10/668,642, filed on Sep. 23, 2003. The content is incorporated herein by reference.

為了自反射量測資料獲得有意義的定量結果，需要正規化或校準經量測之反射率值以便產生絕對反射光譜。在DUV－NIR區中的較長波長處，傳統上已利用各種技術完成此。In order to obtain meaningful quantitative results from the reflectance measurements, it is necessary to normalize or calibrate the measured reflectance values to produce an absolute reflectance spectrum. At longer wavelengths in the DUV-NIR region, various techniques have traditionally been accomplished using various techniques.

歸因於絕對反射計系統之複雜性，商用反射計通常量測經反射之強度，按照已知的絕對反射率標準對該強度予以校準。在DUV－NIR波長範圍中，因為在此波長範圍內光學特性為熟知的且反射率相當穩定，所以通常利用矽晶圓(其具有原生SiO₂ 層)。Due to the complexity of the absolute reflectometer system, commercial reflectometers typically measure the intensity of the reflection and calibrate the intensity according to known absolute reflectance criteria. In the DUV-NIR wavelength range, since the optical characteristics are well known and the reflectance is relatively stable in this wavelength range, a germanium wafer (which has a native SiO ₂ layer) is usually used.

對於不同儀器，精密校準步驟不同，但是本質上，通常所量測之數量為 其中，I_r 為自樣本反射且由偵測器量測到之強度，且I₀ 為入射強度。I₀ 通常未知。另外，I₀ 將由於環境變化、由環境變化引起之光學系統偏移及光源之強度輪廓偏移而隨時間流逝變化。在任何給定時間處，由校準程序確定I₀ ： 其中I_cal 為校準標準之經量測強度，且R_cal 為校準標準之假設反射率。若已知關於校準樣本之足夠資訊，例如，光學特性、表面粗糙度等，則可利用標準薄膜模型產生R_cal 。利用此I₀ 經由方程式1執行、校準後續量測。The precision calibration steps are different for different instruments, but in essence, the amount usually measured is Where I _r is the intensity reflected from the sample and measured by the detector, and I ₀ is the incident intensity. I ₀ is usually unknown. In addition, I ₀ will change over time due to environmental changes, optical system offsets caused by environmental changes, and intensity profile shifts of the light source. At any given time, I ₀ is determined by the calibration procedure: Where I _cal is the measured intensity of the calibration standard and R _cal is the assumed reflectance of the calibration standard. If sufficient information about the calibration sample is known, such as optical properties, surface roughness, etc., a standard film model can be used to generate R _cal . With this I ₀ , the subsequent measurements are performed via Equation 1 .

在通常實施時，此程序假設I_cal 之變化僅是由於以上所述之環境或燈強度變化，且不是由於校準標準本身的變化。實際上，利用以上方法通常不可偵測校準標準隨時間流逝之變化，因為此等變化被簡單地"校準掉"。顯然，隨時間流逝，所有後續反射率量測之精確性及穩定性高度取決於用以產生R_cal 之假設的精確性以及校準樣本本身的穩定性。In normal practice, this procedure assumes that the change in I _cal is due only to the environmental or lamp intensity variations described above and is not due to changes in the calibration standard itself. In fact, it is generally not possible to detect changes in calibration standards over time using the above methods, as these changes are simply "calibrated out". Clearly, over time, the accuracy and stability of all subsequent reflectance measurements is highly dependent on the accuracy of the assumptions used to generate R _cal and the stability of the calibration sample itself.

一些校準技術涉及併入有移動面鏡之複雜光學配置。在美國專利第4,368,983號(及併入本文中之參考文獻)中提供此等方法之實例，該專利描述利用多程反射計來量測樣本之絕對反射率的裝置及方法。Some calibration techniques involve complex optical configurations incorporating a moving mirror. Examples of such methods are provided in U.S. Patent No. 4,368,983, the disclosure of which is incorporated herein by reference.

雖然此等方法提供獲得經校準之反射率資料之方法，但是其通常遭受耗時之事實，涉及相當多的機械運動且不能容易地整合於適合供半導體製造環境中利用的系統中。此外，許多此等方法經設計以供單一波長反射計中利用，其中結合波長選擇預單色器利用單一波長偵測器。While these methods provide a means of obtaining calibrated reflectance data, they typically suffer from time consuming facts involving considerable mechanical motion and cannot be easily integrated into systems suitable for use in semiconductor manufacturing environments. In addition, many of these methods are designed for use in a single wavelength reflectometer that incorporates a single wavelength detector in conjunction with a wavelength selective pre-monochromator.

理想地，將需要提供一種技術，藉由該技術可同時快速且簡單地且以使其本身適合供半導體製造環境中利用之方式校準寬頻反射量測資料。Ideally, it would be desirable to provide a technique by which broadband reflectance measurements can be calibrated simultaneously, quickly and simply, and in a manner suitable for use in a semiconductor fabrication environment.

美國專利第RE 34,783提出一種校準方法，其中描述一種方法，該方法包括：自絕對反射率為熟知之校準樣本量測反射率，用絕對值除經量測值以獲得一系統效率係數，及接著，在不改變照明或光學器件之情況下量測未知材料之反射率且將該係數應用於經量測值以獲得其絕對值。U.S. Patent No. RE 34,783 teaches a calibration method in which a method is described which includes measuring the reflectance from a known calibration sample of absolute reflectance, dividing the measured value by an absolute value to obtain a system efficiency factor, and then The reflectivity of the unknown material is measured without changing the illumination or optics and the coefficient is applied to the measured value to obtain its absolute value.

實務上，單晶矽晶圓常用作校準樣本，因為其易於獲得、在製造上可控制且在DUV－NIR區中的光學特性已經良好特徵化。此方法在~250 nm以上的波長處相當好地工作，在該波長處單晶矽之反射率既穩定又可預測。In practice, single crystal germanium wafers are often used as calibration samples because they are readily available, controllable in manufacturing, and have been well characterized in the DUV-NIR region. This method works reasonably well at wavelengths above ~250 nm, where the reflectivity of single crystal germanium is both stable and predictable.

在較短波長(<250 nm)處，單晶矽晶圓之反射率既不穩定又不可預測。存在於晶圓上之自然(或"原生")形成之二氧化矽層的厚度的微小變化可顯著影響經量測之反射率。另外，已知超薄濕氣層及/或烴層(在文獻中有時稱作空浮分子污染物或AMC)將被吸附至表面上，進一步修改在此光譜區中之樣本反射率。由於在VUV計量工具中的重複利用，污染物膜亦可產生於校準樣本上。此等膜之存在及生長會改變校準標準之反射率。結果，將單晶矽晶圓在<250 nm的波長處之反射率視作"已知"特性通常是不合理的。At shorter wavelengths (<250 nm), the reflectivity of single crystal germanium wafers is both unstable and unpredictable. Small changes in the thickness of the natural (or "native") cerium oxide layer present on the wafer can significantly affect the measured reflectance. Additionally, it is known that ultra-thin moisture layers and/or hydrocarbon layers (sometimes referred to in the literature as airborne molecular contaminants or AMCs) will be adsorbed onto the surface, further modifying the sample reflectance in this spectral region. Contaminant films can also be produced on calibration samples due to reuse in VUV metrology tools. The presence and growth of such films can alter the reflectivity of the calibration standard. As a result, it is generally unreasonable to regard the reflectance of a single crystal germanium wafer at a wavelength of <250 nm as a "known" characteristic.

美國專利第5,798,837號中提出一種克服此問題之方法，該專利描述一種光學量測系統，該光學量測系統包括一參考橢圓偏光計(ellipsometer)及至少一非接觸光學量測設備，諸如反射計。參考橢圓偏光計用來確定校準樣本之光學特性。接著，藉由將來自光學量測設備之經量測光學特性與來自參考橢圓偏光計之經確定光學特性相比較來校準光學量測設備。A method for overcoming this problem is proposed in U.S. Patent No. 5,798,837, which describes an optical measuring system comprising a reference ellipsometer and at least one non-contact optical measuring device, such as a reflectometer. . A reference ellipsometer is used to determine the optical properties of the calibration sample. The optical metrology device is then calibrated by comparing the measured optical properties from the optical metrology device to the determined optical properties from the reference ellipsometer.

將單獨的參考橢圓偏光計整合於光學量測系統中以便校準第一光學量測設備是既複雜又昂貴的。此外，若參考橢圓偏光計要產生精確結果，則必須恰當對準並校準參考橢圓偏光計本身。Integrating a separate reference ellipsometer into an optical metrology system to calibrate the first optical metrology apparatus is both complicated and expensive. In addition, if an accurate result is to be produced with reference to an ellipsometer, the reference ellipsometer itself must be properly aligned and calibrated.

其後，將非常需要研發一種方法，該方法快速且精確地校準來自以<250 nm的波長操作之光學反射計之寬頻資料而不會有與將第二參考儀器併入系統中相關聯的複雜性及費用。Thereafter, it would be highly desirable to develop a method that quickly and accurately calibrates broadband data from optical reflectometers operating at wavelengths <250 nm without the complexity associated with incorporating a second reference instrument into the system. Sex and expenses.

另外，若此方法特別使精確校準在包含VUV光譜區之波長處之反射量測資料成為可能，則其將為有利的，其中第三方檢定標準之特性之小的不確定性可導致相當大的誤差。若此方法能夠獨立確定此等標準之特性以便減少或完全消除其採購及維護需要，則其將更為理想。In addition, it would be advantageous if this method specifically enabled accurate calibration of reflectance measurements at wavelengths including the VUV spectral region, where small uncertainties in the characteristics of third party assays can result in considerable error. It would be more desirable if the method was able to independently determine the characteristics of these standards in order to reduce or completely eliminate their procurement and maintenance needs.

除了提供一種使精確校準反射量測工具成為可能的技術之外，需要提供一種技術，藉由該技術，可執行高度精確之薄膜量測。在寬範圍之薄膜應用中利用光學反射率量測。通常，利用數學模型記錄並隨後分析樣本之絕對反射率，以便確定物理特性之種類。In addition to providing a technology that enables accurate calibration of reflectometry tools, there is a need to provide a technique by which highly accurate film measurements can be performed. Optical reflectance measurements are utilized in a wide range of film applications. Typically, a mathematical model is used to record and subsequently analyze the absolute reflectivity of the sample to determine the type of physical property.

通常，當定量指標(通常被稱作"適合度"參數)達到特定值時，認為分析完成。不幸的是，利用習知"適合度"參數可達到之量測精確性有限。因此，其後，將需要研發更靈敏的"適合度"量測以便在薄膜量測中可獲得較高精確性等級。Typically, when a quantitative indicator (often referred to as a "fitness" parameter) reaches a certain value, the analysis is considered complete. Unfortunately, measurement accuracy is limited by the use of conventional "fitness" parameters. Therefore, it will be necessary to develop a more sensitive "fitness" measurement to achieve a higher level of accuracy in film measurement.

本發明之一實施例提供一種方法，藉由該方法，可快速且精確地校準VUV反射率資料。在一實施例中，該方法使同時校準涵蓋寬範圍波長之反射率資料成為可能。另外，該技術以非常適合供半導體製造環境中利用的方式操作。One embodiment of the present invention provides a method by which VUV reflectance data can be quickly and accurately calibrated. In one embodiment, the method makes it possible to simultaneously calibrate reflectance data covering a wide range of wavelengths. Additionally, the technology operates in a manner that is well suited for use in semiconductor manufacturing environments.

該方法可為獨立的，因為其可能不需要利用第二參考儀器。其可提供一種方法，藉由該方法可自動驗證校準結果以使得將減少及/或完全消除對第三方檢定標準之利用。This method can be independent as it may not require the use of a second reference instrument. It can provide a method by which the calibration results can be automatically verified such that the use of third party verification criteria will be reduced and/or eliminated altogether.

在一實施例中，技術包括使用一標準("校準")樣本，即使標準樣本由於標準樣本特性的微小變化而在感興趣的波長處展示出顯著的反射率變化，該樣本仍允許在該等波長中的校準。因此，即使在預期將碰到在使用者感興趣之波長區中傳統上顯著的校準誤差的情況下，仍可達成校準。關於此點，技術可利用某一校準誤差量的存在，該校準誤差量可被稱作校準誤差函數。In one embodiment, the technique involves the use of a standard ("calibration") sample, even though the standard sample exhibits a significant change in reflectance at the wavelength of interest due to minor variations in the characteristics of the standard sample, the sample is still allowed to be Calibration in wavelength. Thus, calibration can be achieved even in the event that it is expected to encounter a conventionally significant calibration error in the wavelength region of interest to the user. In this regard, the technique may utilize the presence of a certain amount of calibration error, which may be referred to as a calibration error function.

在另一實施例中，校準過程可包括一種技術，該技術使用第一樣本及第二樣本。第一樣本可包括感興趣之光譜區中作為樣本特性變化之函數之顯著的反射率變化且第二樣本在同一光譜區中可具有相對無特點的反射光譜。第一樣本可視作標準或校準樣本，且第二樣本可視作參考樣本。在一實施例中，光譜區可包括VUV光譜區。In another embodiment, the calibration process can include a technique that uses a first sample and a second sample. The first sample may include significant reflectance changes in the spectral region of interest as a function of sample property change and the second sample may have a relatively uncharacteristic reflectance spectrum in the same spectral region. The first sample can be considered a standard or calibration sample and the second sample can be considered as a reference sample. In an embodiment, the spectral region can include a VUV spectral region.

在另一實施例中，提供一種校準技術，其中標準或校準樣本可具有相對未知之特性，例外情況為：可假設在感興趣之光譜區中具有顯著校準誤差函數。因此，若可假設標準樣本由於樣本特性變化而展示出急劇的反射率變化，則無需已知標準樣本之確切特性。In another embodiment, a calibration technique is provided in which a standard or calibration sample can have relatively unknown characteristics, with the proviso that a significant calibration error function can be assumed in the spectral region of interest. Therefore, if it can be assumed that the standard sample exhibits a sharp change in reflectance due to changes in sample characteristics, the exact characteristics of the known standard sample are not required.

在本發明之另一實施例中，提供一種技術，藉由該技術可執行非常精確的薄膜量測。該方法可為數學擬合演算法提供更靈敏的"適合度"指標，該指標對原始資料中存在的雜訊較不敏感。擬合程序可為光譜驅動擬合程序而不是僅依賴於振幅驅動程序(其通常併入有差異計算)。在此實施例中，藉由使用急劇、窄的光譜特點之存在可獲得該等量測。In another embodiment of the invention, a technique is provided by which very precise film measurements can be performed. This method provides a more sensitive "fitness" indicator for the mathematical fitting algorithm, which is less sensitive to the noise present in the original data. The fitting program can be a spectrally driven fitting program rather than relying solely on amplitude drivers (which typically incorporate difference calculations). In this embodiment, the measurements can be obtained by using the presence of sharp, narrow spectral features.

在一實施例中，藉由光譜驅動擬合程序(其使用被量測樣本之預期反射光譜與被量測樣本之實際反射光譜的比率)獲得該等量測。因此，本文所提供之技術使用該等值之比率而不是基於預期值與實際值之間的差異。該等技術在含有急劇光譜特點(例如，對於薄膜樣本通常在VUV區中展示出的急劇特點)之光譜區中尤其有用。因此，提供一種資料收斂技術，其可有利地使用所揭示材料之吸收邊緣效應。以此方式，有利地使用急劇光譜特點(例如，由干涉或吸收效應引起的光譜特點)以更好確定指示實際量測值之資料最小值。In one embodiment, the measurements are obtained by a spectrally driven fitting procedure that uses the ratio of the expected reflectance spectrum of the measured sample to the actual reflected spectrum of the sample being measured. Therefore, the techniques provided herein use the ratio of the equivalents rather than the difference between the expected and actual values. Such techniques are particularly useful in spectral regions that contain sharp spectral features (e.g., sharp features that are typically exhibited in VUV regions for film samples). Accordingly, a data convergence technique is provided that can advantageously use the absorption edge effects of the disclosed materials. In this way, sharp spectral characteristics (eg, spectral characteristics caused by interference or absorption effects) are advantageously used to better determine the minimum value of the data indicative of the actual measurement.

在另一實施例中，資料縮減技術可使用兩步驟方法。在此實施例中，諸如振幅驅動擬合程序之低解析度步驟可首先用於提供"粗略"量測。接著，諸如光譜驅動擬合程序之有利地使用急劇光譜特點之存在的高解析度步驟可用於提供"精細"量測。在一實施例中，藉由利用以差異為基礎的技術(如在"卡方"優點函數中)，低解析度步驟可獲得粗略量測值。高解析度步驟可為光譜驅動步驟，其包括在最初由低解析度技術識別之感興趣之區中的以比率為基礎的技術。In another embodiment, the data reduction technique can use a two-step approach. In this embodiment, a low resolution step such as an amplitude driven fitting procedure may first be used to provide a "rough" measurement. Next, high resolution steps such as spectrally driven fitting procedures that advantageously use the presence of sharp spectral features can be used to provide "fine" measurements. In an embodiment, a coarse measurement may be obtained by a low resolution step by utilizing a difference based technique (as in the "chi-square" merit function). The high resolution step can be a spectrally driven step that includes a ratio based technique in the region of interest that was originally identified by the low resolution technique.

在另一實施例中，提供一種反射計校準技術，該技術可包括在校準過程中利用兩個校準樣本。另外，即使在校準樣本中之至少一或多者的實際特性與假設特性之間存在變化的情況下，該技術仍允許校準。另外，該技術使用來自第一校準樣本之量測與來自第二校準樣本之量測的比率來確定校準樣本中之至少一者的實際特性。接著，可使用已確定之實際特性來輔助校準反射計。In another embodiment, a reflectometer calibration technique is provided that can include utilizing two calibration samples during a calibration process. In addition, the technique allows calibration even if there is a change between the actual and hypothetical characteristics of at least one or more of the calibration samples. Additionally, the technique uses the ratio of the measurements from the first calibration sample to the measurements from the second calibration sample to determine the actual characteristics of at least one of the calibration samples. The determined actual characteristics can then be used to assist in calibrating the reflectometer.

在利用兩個校準樣本之另一實例中，可使用自第一校準樣本發射之強度與自第二校準樣本反射之強度的比率。樣本可在所要波長處展示出相對不同的反射特性。在此技術中，接著，可認為每一樣本之反射率資料已自另一者相對去耦合，且可計算校準樣本中之一或多者的實際特性。接著，可使用已確定之實際特性來輔助校準反射計。In another example utilizing two calibration samples, the ratio of the intensity emitted from the first calibration sample to the intensity reflected from the second calibration sample can be used. The sample can exhibit relatively different reflection characteristics at the desired wavelength. In this technique, then, the reflectance data for each sample can be considered to have been relatively decoupled from the other, and the actual characteristics of one or more of the calibration samples can be calculated. The determined actual characteristics can then be used to assist in calibrating the reflectometer.

在另一實施例中，提供一種校準一獲得反射率資料之系統的方法。該方法可包括自第一校準樣本獲得反射率資料及自第二校準樣本獲得反射率資料，其中第一校準樣本及第二校準樣本中之至少一者的確切特性可不同於校準樣本之假設特性，且其中第一校準樣本與第二校準樣本之反射特性不同。該方法可進一步包括使用一基於自第一校準樣本獲得之資料與自第二校準樣本獲得之資料的比率以便輔助校準該系統。In another embodiment, a method of calibrating a system for obtaining reflectance data is provided. The method can include obtaining reflectance data from a first calibration sample and obtaining reflectance data from a second calibration sample, wherein an exact characteristic of at least one of the first calibration sample and the second calibration sample can be different from a hypothetical characteristic of the calibration sample And wherein the first calibration sample and the second calibration sample have different reflection characteristics. The method can further include using a ratio based on data obtained from the first calibration sample and data obtained from the second calibration sample to assist in calibrating the system.

在又一實施例中，揭示一種校準一反射計之方法。該方法可包括提供第一校準樣本及第二校準樣本，其中第一校準樣本與第二校準樣本之反射特性不同。該方法進一步包括自第一校準樣本收集第一組資料且自第二校準樣本收集第二組資料。該方法亦包括使用第一組資料之至少一部分與第二組資料之至少一部分的比率來確定第一校準樣本及第二校準樣本中之至少一者的特性，以使得可校準來自未知樣本的反射率資料。In yet another embodiment, a method of calibrating a reflectometer is disclosed. The method can include providing a first calibration sample and a second calibration sample, wherein the first calibration sample is different from the second calibration sample in reflective characteristics. The method further includes collecting a first set of data from the first calibration sample and collecting a second set of data from the second calibration sample. The method also includes determining a characteristic of at least one of the first calibration sample and the second calibration sample using a ratio of at least a portion of the first set of data to at least a portion of the second set of data such that the reflection from the unknown sample can be calibrated Rate information.

在另一實施例中，揭示一種校準一反射計之方法，其中該反射計在包括深紫外(DUV)波長以下之至少一些波長的波長處操作。該方法可包括提供第一校準樣本及第二校準樣本，其中第一校準樣本及第二校準樣本之反射特性不同。該方法進一步包括自第一校準樣本收集第一組資料，該第一組資料包括對於DUV波長以下之波長收集的至少一些強度資料。該方法亦包括自第二校準樣本收集第二組資料，該第二組資料包括對於DUV波長以下之波長收集的至少一些強度資料。另外，該方法可包括使用一基於第一組資料與第二組資料之比率來確定第一校準樣本及第二校準樣本中之至少一者的反射率，以在包括至少一些DUV波長的波長處輔助校準該反射計。In another embodiment, a method of calibrating a reflectometer is disclosed, wherein the reflectometer operates at a wavelength that includes at least some wavelengths below a deep ultraviolet (DUV) wavelength. The method can include providing a first calibration sample and a second calibration sample, wherein the first calibration sample and the second calibration sample have different reflection characteristics. The method further includes collecting a first set of data from the first calibration sample, the first set of data comprising at least some intensity data collected for wavelengths below the DUV wavelength. The method also includes collecting a second set of data from the second calibration sample, the second set of data comprising at least some intensity data collected for wavelengths below the DUV wavelength. Additionally, the method can include determining a reflectance of at least one of the first calibration sample and the second calibration sample based on a ratio of the first set of data to the second set of data to be at a wavelength comprising at least some DUV wavelengths Auxiliary calibration of the reflectometer.

在又一實施例中，揭示一種分析反射計資料之方法。該方法可包括提供第一反射計樣本及至少一第二反射計樣本，其中第一校準樣本之光學回應特性及第二校準樣本之光學回應特性不同。該方法可進一步包括自第一反射計樣本收集第一組光學回應資料及自第二反射計樣本收集第二組光學回應資料。該方法進一步包括藉由以獨立於在收集第一組光學回應資料及第二組光學回應資料時所使用的入射反射計強度之方式使用第一組光學回應資料及第二組光學回應資料來確定第一反射計樣本及第二反射計樣本中之至少一者的至少一特性。In yet another embodiment, a method of analyzing reflectometer data is disclosed. The method can include providing a first reflectometer sample and at least a second reflectometer sample, wherein the optical response characteristics of the first calibration sample and the optical response characteristics of the second calibration sample are different. The method can further include collecting a first set of optical response data from the first reflectometer sample and collecting a second set of optical response data from the second reflectometer sample. The method further includes determining by using the first set of optical response data and the second set of optical response data independently of the intensity of the incident reflectometer used in collecting the first set of optical response data and the second set of optical response data At least one characteristic of at least one of the first reflectometer sample and the second reflectometer sample.

在審閱以下描述及相關聯之圖式之後，可實現對本發明之優點之性質的進一步理解。A further understanding of the nature of the advantages of the present invention can be realized after a review of the following description and the accompanying drawings.

在圖1之流程圖102中大致提出通常使用標準樣本來校準反射計之方式。如圖中顯而易見，校準過程中第一步驟104是假設對標準樣本之反射特性的認識。掌握此資訊後，在步驟106中可將自樣本反射之光強度記錄為波長的函數且校準反射計。隨後，接著可在步驟108中用設備完全確定未知樣本之反射率。The manner in which the reflectometry is typically calibrated using standard samples is generally presented in flowchart 102 of FIG. As is apparent from the figure, the first step 104 in the calibration process assumes an understanding of the reflection characteristics of the standard sample. With this information in hand, the intensity of the light reflected from the sample can be recorded as a function of wavelength and the reflectometer is calibrated in step 106. Subsequently, the reflectivity of the unknown sample can then be completely determined by the device in step 108.

在圖2之流程圖202中概述此校準程序之更詳細描述，其中呈現在計算未知樣本之絕對反射率時所涉及的數學關係。圖2說明校準程序之流程圖202。在第一步驟204中，假設對標準樣本之反射特性的認識。接著，在步驟206中，記錄標準樣本之強度。接下來，在步驟208中，利用對標準樣本之假設反射特性的認識來計算源強度輪廓。在步驟210中，記錄未知樣本之強度。接著，如步驟212中展示，可計算未知樣本之反射率。接著，可根據步驟214之方程式表示未知樣本的反射率。檢查該過程之最後步驟，顯然未知樣本之經量測反射率與校準樣本之假設反射率成正比例。因此，若假設反射率不精確，則後果為經量測之反射率亦將不精確。A more detailed description of this calibration procedure is outlined in flowchart 202 of FIG. 2, which presents the mathematical relationships involved in calculating the absolute reflectivity of an unknown sample. Figure 2 illustrates a flow chart 202 of the calibration procedure. In a first step 204, an understanding of the reflection characteristics of the standard samples is assumed. Next, in step 206, the intensity of the standard sample is recorded. Next, in step 208, the source intensity profile is calculated using knowledge of the assumed reflection characteristics of the standard samples. In step 210, the strength of the unknown sample is recorded. Next, as shown in step 212, the reflectivity of the unknown sample can be calculated. Next, the reflectance of the unknown sample can be expressed according to the equation of step 214. Checking the final step of the process, it is clear that the measured reflectance of the unknown sample is directly proportional to the assumed reflectance of the calibration sample. Therefore, if the reflectivity is assumed to be inaccurate, the consequence is that the measured reflectance will also be inaccurate.

單晶矽晶圓已長期用作在DUV－NIR中操作之反射計的校準標準。單晶矽晶圓已證明其係理智的選擇，因為其為普遍存在的、在製造上可控制且在此光譜區中在光學上經良好特徵化。實務上，利用菲涅耳方程式(Fresnel Equation)及對原生二氧化矽表面層之光學特性及厚度以及對矽本身之光學特性的假設認識來計算矽晶圓的假設反射特性。Single crystal germanium wafers have long been used as calibration standards for reflectometers operating in DUV-NIR. Single crystal germanium wafers have proven to be a sensible choice because they are ubiquitous, controllable in manufacturing, and optically well characterized in this spectral region. In practice, the assumed reflection characteristics of the germanium wafer are calculated using the Fresnel equation and the assumption of the optical properties and thickness of the native ceria surface layer and the optical properties of the crucible itself.

當用於校準在比約250 nm長之波長處操作的反射計時，矽晶圓良好工作，因為關於其物理特性之基本假設在此波長區中對誤差相對不靈敏。換言之，晶圓表面上原生氧化物層之假設厚度的誤差不會顯著影響樣本之預期反射率且因此不會消極影響校準過程之精確性。When used to calibrate reflectances operating at wavelengths longer than about 250 nm, germanium wafers work well because the underlying assumptions about their physical properties are relatively insensitive to errors in this wavelength region. In other words, the assumed thickness error of the native oxide layer on the wafer surface does not significantly affect the expected reflectivity of the sample and therefore does not negatively impact the accuracy of the calibration process.

在圖3中進一步說明此點，圖3中呈現具有自10變化至30之SiO₂ 厚度之一系列SiO₂ /Si樣本的經計算反射光譜。舉例而言，反射光譜302說明具有10的SiO₂ 層之Si樣本，而反射光譜304說明具有30的SiO₂ 層之Si樣本。雖然在250 nm以上光譜之間的差異相當小，但是其在較短波長處變得非常顯著。因此，若假設原生氧化物層之厚度為10且其實際為20，則在低於250 nm之波長處將引入相當大的校準誤差。This point is further illustrated in Figure 3, which is presented in Figure 3 with 10 Change to 30 Calculated reflectance spectra of a series of SiO ₂ /Si samples of SiO ₂ thickness. For example, the reflectance spectrum 302 is illustrated as having 10 Si sample of SiO ₂ layer, while reflection spectrum 304 indicates that there are 30 Si sample of SiO ₂ layer. Although the difference between the spectra above 250 nm is quite small, it becomes very significant at shorter wavelengths. Therefore, if the thickness of the native oxide layer is assumed to be 10 And its actual is 20 , a considerable calibration error will be introduced at wavelengths below 250 nm.

圖4更好地說明此等誤差之效應。此圖中描繪對應於反射光譜對之比率的一系列曲線。每一對中的第一光譜對應於自具有"假設"原生氧化物厚度(其自10變化至30)的SiO₂ /Si樣本預期之光譜，而每一對中的第二光譜對應於具有20之"實際"原生氧化物厚度的SiO₂ /Si樣本。因此，圖4之曲線302對應於10假設原生氧化物厚度之反射光譜與20原生氧化物厚度之反射光譜的比率。類似地，圖4之曲線304對應於15假設原生氧化物厚度之反射光譜與20原生氧化物厚度之反射光譜的比率。以類似方式，曲線306、308及310分別說明20、25及30之假設原生氧化物厚度與20之原生氧化物厚度之反射光譜的比率。在此意義上，該比率基本上被視作對校準誤差的量測，此處稱作校準誤差函數(CEF)。CEF越接近一，與校準相關聯之誤差越低。如曲線306所示，在"假設"厚度等於20之"實際"厚度之情況下，CEF在所有波長處等於一，且校準完全精確。在"假設"厚度為25(僅5誤差)之情況下，CEF在短波長處達到大於1.3之值，而在250 nm以上的波長處維持小於1.002之值。此表示在VUV中誤差大於30%且在較長波長處誤差小於~0.2%。因此，雖然在大於250 nm之波長處矽晶圓容易用於校準反射計，但是其不會提供在VUV中精確校準反射計之實用方式。Figure 4 better illustrates the effects of these errors. A series of curves corresponding to the ratio of the reflection spectrum pairs are depicted in this figure. The first spectrum in each pair corresponds to a "hypothetical" native oxide thickness (from 10 Change to 30 The expected spectrum of the SiO ₂ /Si sample, and the second spectrum in each pair corresponds to having 20 The "actual" SiO ₂ /Si sample of native oxide thickness. Therefore, the curve 302 of FIG. 4 corresponds to 10 Assume the reflection spectrum of the native oxide thickness with 20 The ratio of the reflectance spectrum of the native oxide thickness. Similarly, curve 304 of Figure 4 corresponds to 15 Assume the reflection spectrum of the native oxide thickness with 20 The ratio of the reflectance spectrum of the native oxide thickness. In a similar manner, curves 306, 308, and 310 illustrate 20, 25, and 30, respectively. Assume the native oxide thickness with 20 The ratio of the reflectance spectrum of the native oxide thickness. In this sense, the ratio is essentially considered as a measure of the calibration error, referred to herein as the calibration error function (CEF). The closer the CEF is to one, the lower the error associated with the calibration. As shown by curve 306, the "hypothetical" thickness is equal to 20 In the case of the "actual" thickness, the CEF is equal to one at all wavelengths and the calibration is completely accurate. The "hypothesis" thickness is 25 (only 5 In the case of an error, the CEF achieves a value greater than 1.3 at short wavelengths and a value less than 1.002 at wavelengths above 250 nm. This means that the error is greater than 30% in VUV and less than ~0.2% at longer wavelengths. Therefore, while germanium wafers are easily used to calibrate reflectometers at wavelengths greater than 250 nm, they do not provide a practical way to accurately calibrate reflectometers in VUV.

另外，通常已知原生SiO₂ /Si系統在正常的製造或實驗室環境中將產生超薄(~1 nm或更小)的有機烴層。另外，在VUV工具的操作期間，有機材料可累積在膜表面上。藉由在酸中清洗此類型之污染物層或甚至利用VUV源本身，可移除此類型之污染物層。然而，波動的有機層在工具利用期間可使VUV區中之反射特性顯著波動。Additionally, it is generally known that a native SiO ₂ /Si system will produce an ultrathin (~1 nm or less) organic hydrocarbon layer in a normal manufacturing or laboratory environment. Additionally, organic materials can accumulate on the surface of the film during operation of the VUV tool. This type of contaminant layer can be removed by washing this type of contaminant layer in acid or even by utilizing the VUV source itself. However, the fluctuating organic layer can significantly fluctuate the reflective properties in the VUV region during tool utilization.

由於在典型製造環境中存在基於矽氧烷之化合物，另一誤差源係在曝露於VUV輻射之表面上基於聚矽氧之污染物的累積。此"經烘烤"層更難移除。隨時間流逝，此污染物層累積在原生SiO₂ /Si標準樣本之表面上，從而使標準樣本之絕對反射率(尤其是在VUV區中)減小。此意謂總是在假設原生SiO₂ /Si結構的情況下產生R_cal 的校準程序在VUV中常會產生錯誤結果。Since a oxoxane-based compound is present in a typical manufacturing environment, another source of error is the accumulation of polyoxo-based contaminants on the surface exposed to VUV radiation. This "baked" layer is more difficult to remove. Over time, this contaminant layer accumulates on the surface of the native SiO ₂ /Si standard sample, thereby reducing the absolute reflectance of the standard sample (especially in the VUV region). This means that the calibration procedure that always produces R _cal assuming a native SiO ₂ /Si structure often produces erroneous results in VUV.

此等變化通常會影響每一量測且對VUV反射率資料之可靠性有顯著影響。需要一種區別校準標準本身中發生之變化與由系統變化引起之I₀ 變化且在此等變化發生時校正絕對校準程序的方法。These changes typically affect each measurement and have a significant impact on the reliability of the VUV reflectance data. There is a need for a method of distinguishing between changes occurring in the calibration standard itself and I ₀ changes caused by system changes and correcting the absolute calibration procedure when such changes occur.

本發明之實施例提供一種解決此等問題之替代方法。圖5中所描繪之流程圖502對過程中所包括的步驟提供全面綜述。自該圖顯而易見，該技術要求利用兩個樣本，一標準樣本及一參考樣本。選擇標準樣本以使得預期其在某光譜區內展示出顯著的且在光譜上急劇的CEF。另一方面，選擇參考樣本以使得預期其在同一光譜區上展示出相對無特點的反射光譜。Embodiments of the present invention provide an alternative method of solving such problems. Flowchart 502, depicted in Figure 5, provides a comprehensive overview of the steps involved in the process. As is apparent from the figure, the technique requires the use of two samples, a standard sample and a reference sample. The standard sample is selected such that it is expected to exhibit a significant and spectrally sharp CEF in a certain spectral region. On the other hand, the reference sample is selected such that it is expected to exhibit a relatively uncharacteristic reflection spectrum over the same spectral region.

該過程之前兩個步驟504及506實際上與圖1之習知方法中所描述的步驟相同。亦即，假設對標準樣本特性的認識，接著，將自樣本反射之光強度記錄為波長函數且利用其來校準反射計。此時，如步驟508所描述，利用經校準之反射計來量測參考樣本且確定其反射率。一旦已完成此，便在步驟510中經由評估參考樣本之經量測反射特性及CEF來確定標準樣本之"實際"特性。掌握對標準樣本之"實際"特性之認識後，接著可在步驟512中精確重新校準反射計，藉此在該過程之第二步驟中移除由與標準樣本之"假設"特性相關聯之誤差引起的不精確性。如步驟514中所示，一旦已重新校準儀器，便可精確確定未知樣本之絕對反射率。The first two steps 504 and 506 of the process are substantially the same as those described in the conventional method of FIG. That is, assuming an understanding of the characteristics of the standard samples, the light intensity reflected from the sample is then recorded as a function of wavelength and used to calibrate the reflectometer. At this point, as described in step 508, the reference sample is measured using a calibrated reflectometer and its reflectivity is determined. Once this has been done, the "actual" characteristics of the standard sample are determined in step 510 by evaluating the measured reflectance characteristics of the reference sample and the CEF. Once the knowledge of the "actual" nature of the standard sample is mastered, the reflectometer can then be accurately recalibrated in step 512, thereby removing the error associated with the "what if" characteristic of the standard sample in the second step of the process. The inaccuracy caused. As shown in step 514, once the instrument has been recalibrated, the absolute reflectance of the unknown sample can be accurately determined.

在一實施例中，校準技術視對標準樣本之選擇而定。如上文所論述，標準需要在反射計之某光譜區內展示出顯著且在光譜上急劇的CEF光譜。在很大程度上，樣本之光學性質將指定此能力。具體言之，由標準樣本產生之CEF信號預期會在對應於包含該標準樣本之材料的一或多者的光學吸收邊緣附近增加。在此光譜區中，樣本特性的小變化可在經反射信號中產生顯著變化且因此產生大的CEF影響。其後，反射計因此需要具有足夠的光譜解析度才能確保偵測到並解決CEF信號之急劇特點。In one embodiment, the calibration technique depends on the choice of standard samples. As discussed above, the standard requires a significant and spectrally sharp CEF spectrum to be exhibited in a spectral region of the reflectometer. To a large extent, the optical properties of the sample will specify this ability. In particular, the CEF signal produced by the standard sample is expected to increase near the optical absorption edge of one or more of the materials comprising the standard sample. In this spectral region, small changes in sample characteristics can produce significant changes in the reflected signal and thus produce large CEF effects. Thereafter, the reflectometer therefore needs to have sufficient spectral resolution to ensure that the sharp characteristics of the CEF signal are detected and resolved.

在經設計以校準VUV反射計之本發明之較佳實施例中，標準樣本包含沈積於矽基板上之相對厚(~10000)的SiO₂ 層。圖6呈現此標準之CEF曲線，其中對於9990、10000及10010之"假設"SiO₂ 厚度，繪製三對反射光譜的比率。如自圖表顯而易見，對應於9990假設之光譜602及對應於10010假設之光譜604皆展示出實質的且在光譜上急劇的CEF特點(在"假設"厚度等於10000之"實際"厚度的情況下，CEF在所有波長處等於一)。實際上，圖中之資料指示10的誤差(僅表示千分之一份)在VUV反射率結果中將引入大於200%之不精確性。In a preferred embodiment of the invention designed to calibrate a VUV reflectometer, the standard sample comprises a relatively thick deposit on the germanium substrate (~10000 SiO ₂ layer. Figure 6 presents the CEF curve for this standard, for 9990, 10000, and 10010 The "hypothetical" SiO ₂ thickness is plotted against the ratio of the three pairs of reflectance spectra. As apparent from the chart, corresponding to 9990 Hypothetical spectrum 602 and corresponding to 10010 The assumed spectrum 604 exhibits a substantial and spectrally sharp CEF characteristic (in the "hypothetical" thickness equal to 10,000 In the case of the "actual" thickness, the CEF is equal to one at all wavelengths. In fact, the information in the figure indicates 10 The error (only one in a thousand) will introduce an inaccuracy of greater than 200% in the VUV reflectance results.

與圖4中所呈現之20的SiO₂ /Si樣本之CEF曲線(在圖4中，比250 nm長之波長處的CEF值顯示很少誤差(由於即使假設厚度與實際厚度不同，CEF仍全部接近一的事實)相反，當假設厚度與實際厚度不同時，圖6中所繪製之10000的SiO₂ /Si樣本之CEF值實際上在所有波長處展示出可量測的誤差。然而，重要的是注意CEF中的最急劇且最強烈的特點再次發生在VUV中(其係此區中存在SiO₂ 吸收邊緣的直接結果)。With 20 presented in Figure 4 The CEF curve of the SiO ₂ /Si sample (in Figure 4, the CEF value at a wavelength longer than 250 nm shows little error (due to the fact that even if the thickness is different from the actual thickness, the CEF is all close to one)) Assuming that the thickness is different from the actual thickness, the 10000 drawn in Figure 6 The CEF value of the SiO ₂ /Si sample actually exhibits a measurable error at all wavelengths. However, it is important to note that the sharpest and most intense feature in CEF occurs again in VUV (which is a direct result of the presence of SiO ₂ absorption edges in this region).

雖然10000的SiO₂ /Si樣本為本發明提供例示性標準，但是由於該樣本由於"假設"厚度的小誤差而產生之顯著CEF信號，熟習此項技術者將顯而易見許多其他樣本亦可同樣起作用。通常，可使用由於"假設"厚度或某其他假設樣本特性的小誤差而產生顯著CEF信號的任何樣本。Although 10000 The SiO ₂ /Si sample provides an exemplary standard for the present invention, but since the sample produces significant CEF signals due to small errors in "hypothetical" thickness, it will be apparent to those skilled in the art that many other samples may also function. In general, any sample that produces a significant CEF signal due to a small error in the "hypothetical" thickness or some other hypothetical sample characteristic can be used.

如本揭示案之範疇內所定義，CEF基本上為標準(或"校準")樣本之"假設"反射光譜與"實際"反射光譜的比率。若關於標準樣本之假設完全精確，則CEF在所有波長處假設值為一。相反，若該等假設在某程度上有缺陷，則CEF將展示出大於或小於一之值。假設的不精確性越大，CEF值偏離一越多。As defined in the scope of this disclosure, CEF is essentially the ratio of the "hypothetical" reflectance spectrum to the "actual" reflectance spectrum of a standard (or "calibrated") sample. If the assumptions about the standard sample are completely accurate, the CEF assumes a value of one at all wavelengths. Conversely, if the assumptions are to some extent defective, the CEF will exhibit a value greater or less than one. The greater the imprehension of the hypothesis, the more the CEF value deviates from one.

雖然CEF清楚提供對校準精確性之靈敏指標，但是其本身為不可觀察的。因此，一使用CEF之態樣係利用參考樣本來使CEF特點明顯。因為在初始校準之後對樣本執行的所有量測實際上為被研究之樣本之CEF與"實際"反射光譜的乘積，所以如此。因此，若量測具有大體上平滑且無特點之反射光譜之參考樣本，且若CEF不等於一，則在自參考樣本記錄之反射光譜中CEF的強烈、急劇的特點將非常明顯。因此，即使先前沒有對參考樣本之"實際"反射特性的詳細認識(除非參考樣本在感興趣之光譜區中相對無特點)，有可能容易地評估CEF之特徵，且因此測得關於標準樣本特性之初始假設的精確性。Although CEF clearly provides a sensitive indicator of calibration accuracy, it is itself unobservable. Therefore, a model using CEF uses a reference sample to make the CEF characteristics obvious. This is because all measurements performed on the sample after the initial calibration are actually the product of the CEF of the sample being studied and the "actual" reflectance spectrum. Therefore, if a reference sample having a substantially smooth and uncharacteristic reflection spectrum is measured, and if the CEF is not equal to one, the strong, sharp characteristic of the CEF in the reflection spectrum recorded from the reference sample will be very significant. Thus, even if there is no prior detailed understanding of the "actual" reflection characteristics of the reference sample (unless the reference sample is relatively uncharacteristic in the spectral region of interest), it is possible to easily evaluate the characteristics of the CEF and thus measure the characteristics of the standard sample. The accuracy of the initial hypothesis.

雖然具有大體上平滑且無特點之反射光譜之任何樣本可用作參考樣本，但是特別好適合的選擇可為寬頻VUV面鏡，如由美國Acton Research公司製造的具有#1200塗層之寬頻VUV面鏡。圖7中呈現此類型面鏡之典型反射光譜702。如自該圖顯而易見，此寬頻面鏡將整個VUV區中之高反射率與非常無特點的光譜相組合。自圖7可注意到，參考樣本在諸如VUV之光譜區(其中標準樣本可展示出顯著的CEF)中不會展示出急劇特點。用於參考樣本之樣本無需提供在不同樣本之間為一致的反射光譜。舉例而言，來自同一製造商的具有同一塗層之同一類型寬頻VUV面鏡在不同面鏡之間可展示絕對反射率的差異。然而，若為任何給定面鏡提供相對平滑且無特點的反射光譜(至少在感興趣之光譜範圍中)，則面鏡可適合用作參考樣本。此外，即使參考樣本(諸如，以上所述之面鏡)隨時間流逝展示出絕對反射率變化，樣本仍適合作為參考樣本。因此，製造參考樣本之可重複性及隨時間流逝的特性變化不如所要光譜範圍中樣本之無特點特性重要。While any sample having a substantially smooth and uncharacteristic reflectance spectrum can be used as a reference sample, a particularly well-suited choice can be a wideband VUV mirror, such as a broadband VUV surface with #1200 coating manufactured by Acton Research, USA. mirror. A typical reflection spectrum 702 of this type of mirror is presented in FIG. As is apparent from this figure, this wide-band mirror combines the high reflectivity in the entire VUV region with the very uncharacteristic spectrum. It can be noted from Figure 7 that the reference sample does not exhibit sharp features in a spectral region such as VUV where the standard sample can exhibit significant CEF. Samples for reference samples do not need to provide a consistent reflectance spectrum between different samples. For example, the same type of broadband VUV mirrors from the same manufacturer with the same coating can exhibit a difference in absolute reflectivity between different mirrors. However, if a given mirror is provided with a relatively smooth and uncharacteristic reflection spectrum (at least in the spectral range of interest), the mirror can be suitably used as a reference sample. Furthermore, even if a reference sample, such as the mirror described above, exhibits a change in absolute reflectance over time, the sample is still suitable as a reference sample. Therefore, the repeatability of manufacturing reference samples and the change in characteristics over time are not as important as the uncharacteristic nature of the samples in the desired spectral range.

熟習此項技術者將認識到，在諸如VUV之感興趣光譜區中相對無特點的一類型樣本為在樣本上具有原生氧化物之矽樣本。當與具有諸如1000的SiO₂ /Si之厚氧化物的矽樣本相比時，此等樣本相對無特點。因此，如本文所描述，在一替代性實施例中，標準樣本可為1000的SiO₂ /Si樣本且參考樣本可為具有原生氧化物層之矽樣本。Those skilled in the art will recognize that a relatively type of sample that is relatively uncharacteristic in a region of interest such as VUV is a ruthenium sample having native oxide on the sample. When with with such as 1000 When compared to bismuth samples of SiO ₂ /Si thick oxides, these samples are relatively uncharacteristic. Thus, as described herein, in an alternative embodiment, the standard sample can be 1000 The SiO ₂ /Si sample and the reference sample can be a ruthenium sample with a native oxide layer.

因此，提供一種技術，該技術包括使用一標準樣本，即使該標準樣本由於標準樣本特性的微小變化而在感興趣之波長處展示出顯著的反射率變化，該標準樣本仍允許在該等波長中進行校準。即使在預期將在使用者感興趣之波長區中碰到傳統上顯著的校準誤差的情況下，仍可達成校準。關於此點，該技術可利用某一校準誤差量的存在，該校準誤差量可被稱作校準誤差函數。Accordingly, a technique is provided that includes the use of a standard sample, even though the standard sample exhibits a significant change in reflectance at a wavelength of interest due to small changes in the characteristics of the standard sample, the standard sample is still allowed in the wavelengths Perform calibration. Calibration can be achieved even in the event that it is expected that a conventionally significant calibration error will be encountered in the wavelength region of interest to the user. In this regard, the technique may utilize the presence of a certain amount of calibration error, which may be referred to as a calibration error function.

因此，校準過程可包括一種技術，該技術使用第一樣本及第二樣本。第一樣本可包括在感興趣之光譜區中作為樣本特性變化之函數的顯著反射率變化，且第二樣本在同一光譜區內可具有相對無特點的反射光譜。第一樣本可視作標準樣本或校準樣本，且第二樣本可視作參考樣本。藉由首先利用標準樣本來校準系統且接著量測參考樣本，可假設自參考樣本觀察到之反射率的任何急劇變化是關於校準樣本之假設的不精確性的函數。掌握此認識後，接著可重新校準系統。Thus, the calibration process can include a technique that uses a first sample and a second sample. The first sample can include a significant reflectance change as a function of sample property change in the region of interest, and the second sample can have a relatively uncharacteristic reflectance spectrum in the same spectral region. The first sample can be considered as a standard sample or a calibration sample, and the second sample can be regarded as a reference sample. By first calibrating the system with standard samples and then measuring the reference samples, it can be assumed that any sharp change in reflectance observed from the reference sample is a function of the imprecision of the hypothesis of the calibration sample. Once you know this, you can recalibrate the system.

另外，校準技術可使用一標準樣本，該標準樣本可具有相對未知的特性，其中例外情況為可假設準樣本在感興趣之光譜區中具有顯著的校準誤差函數。因此，若可假設標準樣本由於樣本特性變化而展示出急劇的反射率變化，則無需已知標準樣本之確切特性。In addition, the calibration technique can use a standard sample that can have relatively unknown characteristics, with the exception that the quasi-sample can be assumed to have a significant calibration error function in the spectral region of interest. Therefore, if it can be assumed that the standard sample exhibits a sharp change in reflectance due to changes in sample characteristics, the exact characteristics of the known standard sample are not required.

在參考樣本量測可用於評估校準過程之結果之前，需要以數學方式建構一種根據CEF與參考樣本反射光譜之耦合而可量化地評估CEF的方法。在本發明之一實施例中，通常以以下方式完成此。Before the reference sample measurement can be used to evaluate the results of the calibration process, a method of quantitatively evaluating the CEF based on the coupling of the CEF to the reference sample reflectance spectrum needs to be mathematically constructed. In an embodiment of the invention, this is typically accomplished in the following manner.

首先，計算經量測反射光譜之導數。此用以減少CEF與參考樣本之"實際"反射光譜之間的耦合且更強調"急劇"的反射率結構(可能是CEF的貢獻)而不是強調(自參考樣本預期的)緩慢變化之特點。接下來，計算導數之絕對值且對所得函數積分。需在積分之前得到導數之絕對值，以便積極地獲取函數之正值及負值且避免抵消由參考樣本反射光譜引起的對導數的貢獻。在完成積分後，可定量地評估初始校準程序之結果。First, the derivative of the measured reflectance spectrum is calculated. This is used to reduce the coupling between the "actual" reflection spectrum of the CEF and the reference sample and to emphasize the "rapid" reflectance structure (which may be a contribution of CEF) rather than to emphasize the slow variation (as expected from the reference sample). Next, the absolute value of the derivative is calculated and the resulting function is integrated. The absolute value of the derivative is obtained before integration to actively obtain positive and negative values of the function and to avoid counteracting the contribution to the derivative caused by the reference sample reflection spectrum. After the integration is completed, the results of the initial calibration procedure can be quantitatively evaluated.

以此方式，可將積分值反饋給一演算法，該演算法迭代地調整關於標準樣本特性之初始假設、重新計算CEF且重新確定積分值，以期最小化其值。當已達成最小值時，已確定標準樣本之"實際"特性且因此已確定其"實際"反射率。此時，可精確校準反射計且執行對未知樣本的量測。In this way, the integral value can be fed back to an algorithm that iteratively adjusts the initial hypothesis about the characteristics of the standard samples, recalculates the CEF, and re-determines the integral value to minimize its value. When the minimum has been reached, the "actual" characteristics of the standard sample have been determined and thus their "actual" reflectivity has been determined. At this point, the reflectometer can be accurately calibrated and the measurement of the unknown sample performed.

在審閱圖8至圖11中所所呈現之資料之後，可實現對此方法中所涉及之步驟的進一步理解。圖8介紹在利用10010的"假設"厚度來校準10000的SiO₂ /Si標準樣本之後，對適當參考樣本執行之量測的結果。參考樣本(其經調整以用於校準)之經量測光譜中顯而易見之急劇結構為校準過程期間引入之10誤差的結果。圖8所示之信號802為自參考樣本獲得之經量測光譜。此信號為參考樣本之反射率與由不精確校準引起之CEF光譜的乘積。在該過程中，此時CEF信號與參考樣本反射率信號基本上耦合，且顯而易見主要存在於VUV中較短波長處。在本實例中，因為CEF信號主要存在於VUV區中且在此同一區中參考反射率實質上無特點，所以此會發生。A further understanding of the steps involved in this method can be achieved after reviewing the materials presented in Figures 8-11. Figure 8 shows the use of 10010 "hypothetical" thickness to calibrate 10000 After the SiO ₂ /Si standard sample, the results of the measurements performed on the appropriate reference samples. The apparent sharp structure in the measured spectrum of the reference sample (which was calibrated for calibration) was introduced during the calibration process. The result of the error. Signal 802 shown in Figure 8 is a measured spectrum obtained from a reference sample. This signal is the product of the reflectivity of the reference sample and the CEF spectrum caused by the inaccurate calibration. In this process, the CEF signal is now substantially coupled to the reference sample reflectance signal and is apparently present primarily at shorter wavelengths in the VUV. In this example, this occurs because the CEF signal is predominantly present in the VUV region and the reference reflectance is substantially non-characteristic in this same region.

在圖9中呈現此光譜之導數。不足為奇，CEF/參考反射率乘積導數信號902之主體仍駐留於光譜之VUV區中。接著，在積分之前計算跡線之絕對值，其最終產生對校準精確性之定量量測。接著，將此積分和傳回給一迭代程序，該迭代程序調整標準樣本之"假設"厚度且重新計算CEF/參考反射率乘積積分，直至最小化此值。The derivative of this spectrum is presented in Figure 9. Not surprisingly, the body of the CEF/reference reflectance product derivative signal 902 still resides in the VUV region of the spectrum. Next, the absolute value of the trace is calculated prior to integration, which ultimately produces a quantitative measure of calibration accuracy. This integral is then passed back to an iterative procedure that adjusts the "what if" thickness of the standard sample and recalculates the CEF/reference reflectance product integral until the value is minimized.

對於10000的SiO₂ /Si標準樣本(有或無雜訊添加至系統)，圖10之靈敏度曲線呈現作為"假設"厚度之函數的CEF/參考反射率乘積積分的值。曲線1002說明包括0.5%的雜訊成份之存在的CEF/參考反射率乘積積分的值，而曲線1004展示無雜訊之資料。自對資料之檢查顯而易見，即使原始反射率資料中存在0.5%的雜訊成份，積分對SiO₂ 層之"假設"厚度的小誤差仍非常靈敏。不用說，當"假設"厚度值匹配標準樣本之"實際"厚度時，達成CEF/參考反射率乘積積分的最小值。在迭代過程完成後，標準樣本之"實際"特性得以確定且儀器得以精確校準。此時，如圖11中所說明，CEF函數在所有波長處假設為值一，且對參考樣本之後續量測產生其真實的反射光譜1102。For 10000 The SiO ₂ /Si standard sample (with or without noise added to the system), the sensitivity curve of Figure 10 presents the value of the CEF/reference reflectance product integral as a function of "hypothetical" thickness. Curve 1002 illustrates the value of the CEF/reference reflectance product integral including the presence of 0.5% of the noise component, while curve 1004 shows no noise. Since the inspection of the data is obvious, even if there is 0.5% of the noise component in the original reflectance data, the integral is still very sensitive to the small error of the "hypothetical" thickness of the SiO ₂ layer. Needless to say, the minimum value of the CEF/reference reflectance product integral is achieved when the "assumed" thickness value matches the "actual" thickness of the standard sample. After the iterative process is completed, the "actual" characteristics of the standard samples are determined and the instrument is accurately calibrated. At this point, as illustrated in Figure 11, the CEF function is assumed to be a value of one at all wavelengths, and subsequent measurements of the reference sample yield its true reflected spectrum 1102.

在圖12之流程圖1202中概述此校準程序的例示性詳細描述，其中呈現在計算未知樣本之絕對反射率時所涉及的數學關係。如圖12之步驟1204所示，首先利用對預期會在給定光譜區中展示出顯著校準誤差特點之標準樣本的假設認識來計算標準樣本的假設反射率。在步驟1206中記錄來自標準樣本之強度。在步驟1208中，利用標準樣本之假設反射率來計算源強度輪廓。接著，在步驟1210中記錄來自預期會在同一光譜區中展示出實質上平滑之反射特性之參考樣本的強度。接下來，在步驟1212中計算參考樣本之反射率。接著，可根據步驟1214之方程式表示參考樣本之反射率。接著可在步驟1216中計算參考樣本反射光譜之導數的絕對值。接下來，在步驟1218中計算導數絕對值之積分。接下來，在步驟1220中執行對關於標準樣本特性之假設的迭代調整且重新計算標準樣本之假設反射率。自步驟1220傳回控制至步驟1214，直至最小化積分值且因此在自步驟1220進行至步驟1222過程中獲得標準樣本之實際特性。在步驟1222中，利用標準樣本之實際反射率來計算源強度輪廓。接著，在步驟1224中記錄未知樣本之強度。最後，可根據步驟1226之方程式計算並表示未知樣本的反射率。An illustrative detailed description of this calibration procedure is outlined in flowchart 1202 of Figure 12, which presents the mathematical relationships involved in calculating the absolute reflectivity of an unknown sample. As shown in step 1204 of Figure 12, the hypothetical reflectance of the standard sample is first calculated using hypothetical knowledge of a standard sample that is expected to exhibit significant calibration error characteristics in a given spectral region. The intensity from the standard sample is recorded in step 1206. In step 1208, the source intensity profile is calculated using the assumed reflectance of the standard sample. Next, the intensity of the reference sample from the expected spectral properties that would exhibit substantially smooth reflection in the same spectral region is recorded in step 1210. Next, the reflectance of the reference sample is calculated in step 1212. Next, the reflectance of the reference sample can be expressed according to the equation of step 1214. The absolute value of the derivative of the reference sample reflectance spectrum can then be calculated in step 1216. Next, the integral of the absolute value of the derivative is calculated in step 1218. Next, an iterative adjustment to the hypothesis regarding the characteristics of the standard samples is performed and the assumed reflectance of the standard samples is recalculated in step 1220. Control is passed back from step 1220 to step 1214 until the integral value is minimized and thus the actual characteristics of the standard samples are obtained during the process from step 1220 to step 1222. In step 1222, the source intensity profile is calculated using the actual reflectance of the standard samples. Next, the intensity of the unknown sample is recorded in step 1224. Finally, the reflectivity of the unknown sample can be calculated and expressed according to the equation of step 1226.

熟習此項技術者將認識到，存在許多其他方法用於以此方式量化CEF信號以使其可用於反饋回給迭代程序，迭代程序經設計以經由調整標準樣本之"假設"特性而最小化其值。另外，雖然以上論述已將標準樣本之厚度視作將於校準過程期間予以精確確定之"假設"特性，但是熟習此項技術者將進一步瞭解，標準樣本之許多其他特性亦可被視作"假設"特性且以相同方式予以確定。此等特性可包括(但不限於)複折射率、組合物、孔隙率及表面或界面粗糙度。在校準程序期間，可獨立確定此等特性，或在一些實例中，可同時確定此等特性以及其他特性。Those skilled in the art will recognize that there are many other ways to quantify the CEF signal in such a way that it can be used for feedback back to the iterative process, which is designed to minimize its "hypothetical" characteristics by adjusting the standard samples. value. In addition, although the above discussion has considered the thickness of the standard sample as a "hypothetical" characteristic that will be accurately determined during the calibration process, those skilled in the art will further appreciate that many other characteristics of the standard sample can also be considered as "hypothesis". "Characteristics and determination in the same way. Such characteristics may include, but are not limited to, complex refractive index, composition, porosity, and surface or interface roughness. These characteristics can be determined independently during the calibration procedure, or in some instances, these and other characteristics can be determined simultaneously.

在某些情況下，可執行額外的數學步驟以增強校準程序之效能。在自參考樣本所記錄之經量測反射率資料中存在顯著雜訊時，有利之舉可為在得到原始資料的導數之前或之後過濾原始資料。雖然先前技術中存在許多適當的平滑化濾波器，但是Savitzky－Golay濾波器特別適合此應用，因為其通常保留原始資料中光譜特點之寬度及位置。另外，在一些情況下，限制波長範圍(在該波長範圍內執行積分)從而進一步強調CEF信號之貢獻經證明為有益的。In some cases, additional mathematical steps can be performed to enhance the performance of the calibration procedure. In the presence of significant noise in the measured reflectance data recorded from the reference sample, it may be advantageous to filter the original data before or after the derivative of the original data is obtained. Although there are many suitable smoothing filters in the prior art, the Savitzky-Golay filter is particularly suitable for this application because it typically preserves the width and position of the spectral features in the original data. Additionally, in some cases, limiting the wavelength range (in which the integration is performed) to further emphasize the contribution of the CEF signal has proven to be beneficial.

熟習此項技術者將顯而易見，本發明容易地有助於許多實施模式。一種特別有利的方法將是，將參考樣本整合於反射計中以致可不費力地使用參考樣本。在美國申請案第10/668,644號(在2003年9月23日申請，其揭示真空紫外參考反射計)及美國申請案第10/909,126號(在2004年7月30日申請)中詳細描述此方法，該等揭示案以引用方式併入本文中。在圖12A中說明結合上述先前申請之美國申請案中所描述的系統利用本文所提供之校準技術的實例。圖12A提供如參考美國申請案第10/909,126(2004年7月30日申請)號中的圖34更詳細描述的寬頻反射計系統3400。系統3400可視需要包括多個源3201、3203及3302以及對應之多個光譜儀3214、3216及3304。內翻式面鏡FM－1至FM－4及對應視窗W－3至W－6可用於選擇各種源及光譜儀。如圖所示，面鏡M－1至M－5用於引導射束。樣本3206可定位在樣本射束3210中。亦提供參考射束3212。提供射束分離器BS且擋板S－1及S－2選擇使用哪個射束。在環境密封腔室3202及3204中可包括各種光學器件及樣本，以致可獲得在VUV頻寬中之量測。It will be apparent to those skilled in the art that the present invention readily facilitates many modes of implementation. A particularly advantageous method would be to integrate the reference sample into the reflectometer so that the reference sample can be used without difficulty. This is described in detail in U.S. Patent Application Serial No. 10/668,644, filed on Sep. 23, 2003, the disclosure of which is incorporated herein by reference. Methods, such disclosures are incorporated herein by reference. An example of utilizing the calibration techniques provided herein in conjunction with the system described in the above-referenced U.S. Application is illustrated in FIG. 12A. Figure 12A provides a broadband reflectometer system 3400 as described in more detail in Figure 34 of the U.S. Application Serial No. 10/909,126, filed on Jul. 30, 2004. System 3400 can include a plurality of sources 3201, 3203, and 3302 and corresponding plurality of spectrometers 3214, 3216, and 3304 as desired. Inverted mirrors FM-1 to FM-4 and corresponding windows W-3 to W-6 can be used to select various sources and spectrometers. As shown, mirrors M-1 through M-5 are used to direct the beam. Sample 3206 can be positioned in sample beam 3210. A reference beam 3212 is also provided. The beam splitter BS is provided and the baffles S-1 and S-2 select which beam to use. Various optics and samples can be included in the environmental sealed chambers 3202 and 3204 such that measurements in the VUV bandwidth can be obtained.

如圖12A中所展示，提供樣本射束(或通道)3210以自樣本3206獲得量測。提供參考射束(或通道)3212以參考該系統。通常，參考射束經組態以提供指示環境或其他系統條件之機制。參考射束可經組態以提供與樣本射束之射束長度及環境條件類似的射束路徑，然而，參考射束不會遇到樣本3206。在用本文所描述之校準技術操作的情況下，可將標準樣本置放於圖12A之樣本3206位置處。然而，單獨的參考樣本無需被置放在樣本3206位置處(雖然可使用對被置放在樣本3206位置處的單獨參考樣本的此種利用)。實情為，整個參考射束3212路徑可被視作"參考樣本"。舉例而言，射束分離器BS、面鏡M－4、視窗W－2及面鏡M－5(亦即，樣本路徑與參考路徑之間不同的元件)之累積效果可被視作一起形成"參考樣本"。若光學元件之組合效應在感興趣之光譜範圍中提供相對平滑的無特點之反射光譜，則通常可獲得對參考樣本之整個射束路徑的此種利用。將認識到，熟習此項技術者將瞭解使用校準技術之許多其他方法且本文所描述之校準技術不限於本文所參考的機械組態。雖然未圖示，但是反射計系統3400可包括處理器、電腦、其他電子器件及/或軟體，其用於根據本文所提供之校準技術來校準該系統。處理器、電腦、其他電子器件及/或軟體可與反射計光學硬體一體式建構或可為單獨的獨立單元，該單元與反射計光學硬體一起形成經組態以允許校準之反射計系統。As shown in FIG. 12A, a sample beam (or channel) 3210 is provided to obtain measurements from sample 3206. A reference beam (or channel) 3212 is provided to reference the system. Typically, the reference beam is configured to provide a mechanism to indicate environmental or other system conditions. The reference beam can be configured to provide a beam path similar to the beam length and environmental conditions of the sample beam, however, the reference beam does not encounter the sample 3206. In the case of operation with the calibration techniques described herein, a standard sample can be placed at the location of sample 3206 of Figure 12A. However, a separate reference sample need not be placed at the location of sample 3206 (although such utilization of a separate reference sample placed at the location of sample 3206 can be used). The truth is that the entire reference beam 3212 path can be considered a "reference sample." For example, the cumulative effect of the beam splitter BS, the mirror M-4, the window W-2, and the mirror M-5 (ie, the elements that differ between the sample path and the reference path) can be considered to be formed together. "Reference sample". Such utilization of the entire beam path of the reference sample is typically obtained if the combined effect of the optical elements provides a relatively smooth, uncharacteristic reflection spectrum in the spectral range of interest. It will be appreciated that those skilled in the art will appreciate many other methods of using calibration techniques and the calibration techniques described herein are not limited to the mechanical configurations referenced herein. Although not shown, the reflectometer system 3400 can include a processor, a computer, other electronics, and/or software for calibrating the system in accordance with the calibration techniques provided herein. The processor, computer, other electronics, and/or software may be integrally constructed with the reflectometer optical hardware or may be a separate stand-alone unit that, together with the reflectometer optical hardware, forms a reflectometer system configured to allow calibration .

本發明提供許多優點。一優點為其提供一種技術，藉由該技術，根據與市售薄膜標準樣本相關聯之不確定性可能太大而不能使利用習知方法精確校準成為可能的事實，可精確校準VUV反射量測資料。結果，可完全消除反射計工具使用者購買、維護並重新校準昂貴的標準樣本的需要。The present invention provides a number of advantages. One advantage is that it provides a technique by which the VUV reflectance measurement can be accurately calibrated based on the fact that the uncertainty associated with a commercially available film standard sample may be too large to enable accurate calibration using conventional methods. data. As a result, the need for reflectometer tool users to purchase, maintain, and recalibrate expensive standard samples is completely eliminated.

此外，本發明允許在對標準樣本或參考樣本之確切特性無先前認識的情況下達成非常精確的校準結果。此能力特別有用，因為實際上可預期所有樣本均會經歷作為時間之函數的微小特性變化(由於自然生長機制或污染物)。Furthermore, the present invention allows for very accurate calibration results to be achieved without prior knowledge of the exact characteristics of a standard or reference sample. This ability is particularly useful because virtually all samples are expected to experience small changes in properties (due to natural growth mechanisms or contaminants) as a function of time.

雖然本發明特別適合校準VUV反射量測資料之目的，但是本發明亦可用於校準來自其他光譜區之反射量測資料。在此等實例中，使用其他標準樣本(可預期該等其他標準樣本在感興趣之光譜區中會產生顯著的CEF信號)可為有利的。While the present invention is particularly well suited for calibrating VUV reflectance measurements, the present invention can also be used to calibrate reflectance measurements from other spectral regions. In these examples, it may be advantageous to use other standard samples (which may be expected to produce significant CEF signals in the spectral region of interest).

本發明之另一優點為其不需要利用次級參考儀器，藉此極大降低系統成本及複雜性。Another advantage of the present invention is that it does not require the use of a secondary reference instrument, thereby greatly reducing system cost and complexity.

一旦已自經校準之反射計記錄反射率資料，便通常發送該反射率資料至處理器單元，隨後在處理器單元處經由分析演算法縮減該資料。此等演算法通常將樣本之諸如反射率之光學資料與樣本之其他特性(如膜厚度、複折射率、組合物、孔隙率、表面或界面粗糙度等)相聯繫，接著可量測及/或監控該等特性。Once the reflectance data has been recorded from the calibrated reflectometer, the reflectance data is typically sent to the processor unit, which is then reduced at the processor unit via an analysis algorithm. These algorithms typically relate the optical data of the sample, such as reflectivity, to other characteristics of the sample (eg, film thickness, complex refractive index, composition, porosity, surface or interface roughness, etc.), which can then be measured and/ Or monitor these features.

通常利用某種形式之菲涅耳方程式結合一或多個模型描述包含樣本之材料的光學特性來完成資料縮減。不管在縮減資料集時利用的特定模式如何，較大目標一般是利用數學表達式來描述經量測資料以致可經由迭代最佳化過程獲得與樣本特性(如以上所論述)相關之某些參數。亦即，將經量測資料集與利用一視與樣本性質相關的一組參數而定的表達式計算出的資料集相比較。藉由迭代地調整參數值直至在兩個資料集之間達成充分一致時，最小化經量測資料集與經計算資料集之間的差異。通常根據"適合度"(GOF)參數來量化此差異。Data reduction is typically accomplished using some form of Fresnel equation in combination with one or more models describing the optical properties of the material containing the sample. Regardless of the particular mode utilized in reducing the data set, larger targets typically use mathematical expressions to describe the measured data so that certain parameters related to sample characteristics (as discussed above) can be obtained via an iterative optimization process. . That is, the measured data set is compared to a data set calculated using an expression determined by a set of parameters related to the nature of the sample. The difference between the measured data set and the calculated data set is minimized by iteratively adjusting the parameter values until a sufficient agreement is achieved between the two data sets. This difference is usually quantified based on the "fitness" (GOF) parameter.

先前技術中存在眾多用於計算GOF之數學表達式。大多數此等技術在某種程度上基於對經量測光譜與經計算光譜之間的差異的確定。雖然此等方法通常可適用且在參數空間中合理地定位絕對最小值之一般區，但是其通常在收斂時在彼最小值處展示出缺點，特別是在經量測資料中的雜訊位準增加的情況下。There are numerous mathematical expressions used in the prior art for calculating GOF. Most of these techniques are based in part on the determination of the difference between the measured and calculated spectra. While these methods are generally applicable and reasonably locate the general region of the absolute minimum in the parameter space, they typically exhibit shortcomings at the minimum at convergence, especially in the measured data. Increased circumstances.

如對於10000的SiO₂ /Si測試樣本所計算，圖13呈現先前技術GOF表達式(熟習此項技術者已知其為"卡方"優點函數)之靈敏度曲線1302。顯而易見，此標準優點函數提供一種定位膜"實際"厚度之一般區的有效方式，因為其展示出具有經良好定義之最小值的相對平滑的線形狀。然而，在更仔細檢查時，可見在最小值附近函數之靈敏度顯著降級。圖14中更好地說明此點，圖14呈現在經量測反射率資料中存在1%的雜訊的情況下圖13之靈敏度曲線1302之展開圖1402。Such as for 10000 Calculated by the SiO ₂ /Si test sample, FIG. 13 presents a sensitivity curve 1302 of a prior art GOF expression (known to those skilled in the art as a "chi-square" merit function). It will be apparent that this standard advantage function provides an efficient way to position the general region of the "actual" thickness of the film as it exhibits a relatively smooth line shape with a well defined minimum. However, when examined more closely, it can be seen that the sensitivity of the function near the minimum is significantly degraded. This is best illustrated in Figure 14, which shows an expanded view 1402 of the sensitivity curve 1302 of Figure 13 in the presence of 1% of the noise in the measured reflectance data.

在檢查圖14中之資料時顯而易見，駐留於原始反射率資料中之1%的雜訊會顯著減小優點函數使最小化程序能夠收斂於測試樣本之"實際"厚度上的能力。因此，需要研發一種在程序已大致定位在答案的附近時便確定"實際"厚度之優良方法。It is apparent from examining the data in Figure 14 that 1% of the noise residing in the original reflectance data significantly reduces the ability of the merit function to minimize the program's ability to converge on the "actual" thickness of the test sample. Therefore, there is a need to develop an excellent method of determining the "actual" thickness when the program has been roughly positioned near the answer.

本發明之另一較佳實施例提供此能力。亦即，該實施例提供高度靈敏的收斂量測，該量測可結合適當的最小化程序利用，以有效縮減經量測反射率資料，從而產生展示比較高精確性等級、接著可僅利用習知技術來達到之結果。雖然本發明經設計成結合傳統優點函數利用，但是本發明在一些實例中完全代替此等方法之利用。Another preferred embodiment of the present invention provides this capability. That is, this embodiment provides a highly sensitive convergence measurement that can be utilized in conjunction with an appropriate minimization procedure to effectively reduce the measured reflectance data, resulting in a display of a relatively high level of accuracy, which can then be utilized only. Know the technology to achieve the results. Although the present invention is designed to be utilized in conjunction with conventional merit functions, the present invention completely replaces the utilization of such methods in some instances.

在圖15之流程圖1502中呈現本文所描述之資料縮減技術之一實施例的一般綜述，其中呈現在與使用反射計來量測未知樣本相關聯的迭代資料擬合程序中所涉及的數學關係。過程中的第一步驟1504是利用經精確校準之反射計來獲得未知樣本的絕對反射光譜。在步驟1506中，一旦已記錄此光譜，便利用關於樣本物理特性之初始假設來計算樣本之"預期"反射特性。在掌握此等兩個光譜後，如步驟1508之方程式所示，確定"預期"光譜與"經量測"光譜之比率。A general overview of one embodiment of the data reduction technique described herein is presented in flowchart 1502 of Figure 15, in which the mathematical relationships involved in an iterative data fitting procedure associated with the use of a reflectometer to measure unknown samples are presented. . A first step 1504 in the process is to obtain an absolute reflectance spectrum of the unknown sample using a precisely calibrated reflectometer. In step 1506, once this spectrum has been recorded, it is convenient to calculate the "expected" reflection characteristics of the sample with an initial hypothesis regarding the physical properties of the sample. After mastering these two spectra, as shown by the equation of step 1508, the ratio of the "expected" spectrum to the "measured" spectrum is determined.

本文中稱作量測誤差函數(MEF)之此比率本質上與先前所論述之CEF類似。雖然兩個函數係關於"假設"資料集與"實際"資料集之比率，但是MEF稍微更易於評估，因為其未與參考樣本之反射率耦合。亦即，在最小化期間，經由檢查參考樣本反射光譜來評估CEF，而經由檢查未知樣本本身的反射率來評估MEF。This ratio, referred to herein as the Measurement Error Function (MEF), is essentially similar to the previously discussed CEF. Although the two functions are about the ratio of the "what if" data set to the "real" data set, the MEF is slightly easier to evaluate because it is not coupled to the reflectance of the reference sample. That is, during minimization, the CEF is evaluated by examining the reference sample reflectance spectrum, while the MEF is evaluated by examining the reflectance of the unknown sample itself.

在MEF(或反射光譜比率)可用於評估最小化程序的結果之前，必須再次建構適合的優點函數。在先前CEF所採取之方法之後，流程圖1502中下一步驟是如步驟1510中所示計算MEF之導數之絕對值。此用以強調MEF中急劇的光譜特點，該等光譜特點主要由包含未知樣本之一或多種材料的吸收邊緣附近的波長引起。此時，如步驟1512中所示，計算導數之絕對值且接著對所得函數進行積分。如之前一樣，需要在積分之前得到導數之絕對值，以便積極地獲取正值及負值。一旦完成積分，便有可能定量地評估縮減過程之結果。更明確地說，如步驟1514所示，可發生調整關於未知樣本之特性的假設及重新計算未知樣本之預期反射光譜的迭代過程。在重新計算預期反射光譜之後，控制再次轉至步驟1508且重複步驟1508－1514，直至最小化積分值，此時確定已獲得未知樣本之實際特性且控制轉至步驟1516，在步驟1516中提供未知樣本之實際特性作為輸出。Before the MEF (or reflectance spectral ratio) can be used to evaluate the results of the minimization procedure, the appropriate merit function must be constructed again. Following the method taken by the previous CEF, the next step in flowchart 1502 is to calculate the absolute value of the derivative of the MEF as shown in step 1510. This is used to emphasize the sharp spectral characteristics of the MEF, which are mainly caused by wavelengths near the absorption edge of one or more materials containing unknown samples. At this point, as shown in step 1512, the absolute value of the derivative is calculated and then the resulting function is integrated. As before, you need to get the absolute value of the derivative before the integration in order to actively obtain positive and negative values. Once the points are completed, it is possible to quantitatively evaluate the results of the reduction process. More specifically, as shown in step 1514, an iterative process of adjusting the hypothesis about the characteristics of the unknown sample and recalculating the expected reflection spectrum of the unknown sample may occur. After recalculating the expected reflectance spectrum, control passes again to step 1508 and steps 1508-1514 are repeated until the integral value is minimized, at which point it is determined that the actual characteristics of the unknown sample have been obtained and control passes to step 1516 where an unknown is provided. The actual characteristics of the sample are used as outputs.

注意，此技術對"假設"反射光譜與"經量測"反射光譜之間的固定偏移不靈敏。亦即，其不能有效用於縮減自包含極薄的膜(亦即，足夠薄而不會引起顯著的干涉效應)之樣本收集到之長波長反射量測資料，因為此等資料集不可能含有由此方法獲得之急劇光譜特點。幸運的是，在VUV區中，實際上所有薄膜樣本在其反射光譜中展示出某種形式的急劇結構，該結構由干涉或吸收效應引起。Note that this technique is insensitive to a fixed offset between the "hypothetical" reflectance spectrum and the "measured" reflectance spectrum. That is, it cannot be effectively used to reduce long-wavelength reflectance measurements collected from samples containing very thin films (ie, thin enough without causing significant interference effects) because such data sets are unlikely to contain The sharp spectral characteristics obtained by this method. Fortunately, in the VUV region, virtually all film samples exhibit some form of sharp structure in their reflection spectrum that is caused by interference or absorption effects.

為了更好地證明此方法之效能相對於習知卡方方法之效能的優越性，圖16呈現對於圖14之同一10000的SiO₂ /Si測試樣本利用本發明之實施例計算出之展開靈敏度曲線1602。比較此等兩個圖中之結果，其展示：本發明受存在於原始反射率資料中1%的雜訊位準的影響比卡方方法所受的影響小。此證實：本發明為最佳化程序提供對擬合最小值及因此對膜之"實際"厚度的更有效量測。此改良的效能證明：至少當"假設"厚度值大體在"實際"厚度附近時，本發明能夠比利用習知方法可能達成的結果更精確且可重複的結果。To better demonstrate the superiority of the performance of this method over the performance of the conventional chi-square method, Figure 16 presents the same 10000 for Figure 14. The SiO ₂ /Si test sample was calculated using the embodiment of the present invention to develop a sensitivity curve 1602. Comparing the results in these two figures, it is shown that the present invention is less affected by the chi-square method by the 1% noise level present in the original reflectance data. This confirms that the present invention provides a more efficient measurement of the minimum of the fit and thus the "actual" thickness of the film for the optimization procedure. This improved performance demonstrates that the present invention is capable of more accurate and repeatable results than would be possible with conventional methods, at least when the "assumed" thickness values are generally near the "actual" thickness.

對較大參數空間之研究證明在一些情況下最佳結合先前技術方法使用本發明的原因。在檢查圖17後，其原因變得顯而易見，圖17呈現在較寬之"假設"厚度值範圍內繪製之利用本發明對於10000的SiO₂ /Si樣本計算出的靈敏度曲線1702。雖然在"實際"厚度處之MEF積分值可清楚地與在所有其他"假設"厚度處之積分值區分，但是MEF積分之線形狀的急劇特點使其在計算上難以擬合。因此，更有效之舉是利用基於卡方之優點函數開始搜尋最小值，然後一旦達成明顯收斂，便轉變並利用本發明繼續搜尋"實際"最小值。在此理念上，本發明之利用表示反射計操作之高解析度模式。Studies of larger parameter spaces have demonstrated the best use of the present invention in some cases in combination with prior art methods. After examining Figure 17, the reason becomes apparent, and Figure 17 is presented for drawing within a wider "hypothetical" thickness value range using the present invention for 10,000 The sensitivity curve 1702 was calculated for the SiO ₂ /Si sample. Although the MEF integral value at the "actual" thickness can be clearly distinguished from the integral value at all other "what if" thicknesses, the sharp nature of the line shape of the MEF integral makes it computationally difficult to fit. Therefore, it is more efficient to start searching for the minimum value using the merits based on the chi-square, and then, once the apparent convergence is reached, transition and use the present invention to continue searching for the "actual" minimum. In this concept, the utilization of the present invention represents a high resolution mode of reflectometer operation.

在其他情況下，可認識到本發明提供之益處而無需亦使用習知之卡方方法。此一情況下之實例為在經量測反射率資料中存在1%的雜訊的情況下量測100的SiO₂ /Si樣本。在此情況下，本發明之全域搜尋效能與標準卡方方法之效能相當。圖18中所呈現之靈敏度曲線比較提供其證據。如圖18所示，比較標準卡方方法之靈敏度曲線1802與使用根據本發明之MEF技術的靈敏度曲線1804。雖然兩個函數展示出相對平滑的線形狀，但是注意到，反射率資料中1%的雜訊之影響在卡方結果中已顯而易見。In other instances, the benefits provided by the present invention may be appreciated without the use of conventional chi-square methods. An example of this case is to measure 100 in the presence of 1% of noise in the measured reflectance data. SiO ₂ /Si sample. In this case, the global search performance of the present invention is comparable to the performance of the standard chi-square method. A comparison of the sensitivity curves presented in Figure 18 provides evidence. As shown in FIG. 18, the sensitivity curve 1802 of the standard chi-square method is compared to the sensitivity curve 1804 using the MEF technique according to the present invention. Although the two functions exhibit a relatively smooth line shape, it is noted that the effect of 1% of the noise in the reflectance data is already evident in the chi-square results.

圖19及圖20呈現分別利用本發明之MEF技術(圖19之靈敏度曲線1902)及卡方方法(圖20之靈敏度曲線2002)計算出的覆蓋100的SiO₂ /Si樣本之"實際"厚度附近的4區之展開靈敏度曲線。對此等兩個圖的比較證明在此情況下本發明之有利效能。19 and 20 present coverage 100 calculated using the MEF technique of the present invention (sensitivity curve 1902 of FIG. 19) and the chi-square method (sensitivity curve 2002 of FIG. 20), respectively. 4 of the "actual" thickness of the SiO ₂ /Si sample The expansion sensitivity curve of the zone. A comparison of these two figures demonstrates the advantageous performance of the invention in this case.

因此，藉由使用擬合程序可獲得資料量測，該擬合程序包括為光譜驅動擬合程序之程序的至少一部分而不是僅依賴於振幅驅動程序(其通常併入差異計算)。更明確地說，藉由使用急劇、窄的光譜特點之存在可獲得該等量測。在使用光譜驅動程序之實施例中，被量測之樣本之預期反射光譜與被量測之樣本之實際反射光譜的比率。本文所提供之技術使用預期值與實際值的比率而不是基於預期值與實際值之間的差異。此比率之導數可用於強調急劇光譜特點。Thus, data metrics can be obtained by using a fitting program that includes at least a portion of the program that is a spectrally driven fit program rather than relying solely on amplitude drivers (which typically incorporate difference calculations). More specifically, these measurements can be obtained by using the presence of sharp, narrow spectral features. In an embodiment using a spectral driver, the ratio of the expected reflectance spectrum of the sample being measured to the actual reflectance spectrum of the sample being measured. The techniques provided herein use a ratio of expected values to actual values rather than based on differences between expected and actual values. The derivative of this ratio can be used to emphasize sharp spectral characteristics.

此等光譜驅動技術在含有急劇光譜特點(例如，薄膜樣本通常在VUV區中展示出的急劇特點)之光譜區中尤其有用。因此，提供一種收斂技術，其可有利地使用所揭示材料之吸收邊緣效應。以此方式，有利地使用急劇光譜特點(例如，其由干涉或吸收效應引起)以更能確定指示實際量測值的資料最小值。本揭示案中所呈現的優點函數可因此由被量測之材料之吸收特性予以驅動，其中強調由於樣本特性的小的變化而包含大的吸收(吸收邊緣)變化之區域。Such spectral drive techniques are particularly useful in spectral regions that contain sharp spectral features, such as the sharp features typically exhibited by thin film samples in the VUV region. Accordingly, a convergence technique is provided that can advantageously use the absorption edge effects of the disclosed materials. In this way, sharp spectral characteristics (eg, caused by interference or absorption effects) are advantageously used to more accurately determine the minimum value of the data indicative of the actual measurement. The merit function presented in the present disclosure can thus be driven by the absorption characteristics of the material being measured, emphasizing areas that contain large absorption (absorption edges) variations due to small variations in sample characteristics.

資料縮減技術可使用兩步驟方法。在此種實施例中，可首先利用諸如振幅驅動擬合程序之低解析度步驟來提供"粗略"量測。接著，可利用諸如光譜驅動擬合程序之有利地使用急劇光譜特點之存在的高解析度步驟來接著提供"精細"量測。在用於此技術之一方法中，藉由利用基於差異之技術(諸如"卡方"優點函數中)，可使用低解析度方法來獲得大略量測值，且接著藉由在該低解析度技術最初識別的重點區中使用基於光譜驅動比率之技術可獲得對實際量測值的更精確確定。Data reduction techniques can use a two-step approach. In such an embodiment, a "roughly" measurement may be provided first using a low resolution step such as an amplitude driven fitting procedure. Next, a high resolution step, such as the spectrally driven fitting procedure, advantageously using the presence of sharp spectral features, can be utilized to provide "fine" measurements. In a method for use in this technique, by utilizing a difference-based technique (such as in a "chi-square" advantage function), a low-resolution method can be used to obtain a rough measure, and then at the low resolution A more precise determination of actual measurements can be obtained using techniques based on spectral drive ratios in the key areas initially identified by the technology.

本文所提供之技術可視作對於存在急劇光譜特點之區動態加權結果。舉例而言，關於VUV範圍中存在之急劇光譜邊緣，可將此等技術視作應用一加權函數，該加權函數極力強調VUV而對DUV及較長波長資料(其中對於給定樣本，可能無法預期急劇光譜特點)蓄意忽視。另外，可加權該過程以致可僅包括可經合理預期含有有用資訊的經量測資料。此加權方法可為動態的，因為在每一迭代之後可重複決策過程(應考慮哪一經量測資料)。The techniques provided herein can be viewed as dynamic weighted results for regions where sharp spectral features are present. For example, regarding the sharp spectral edges present in the VUV range, these techniques can be viewed as applying a weighting function that strongly emphasizes VUV and DUV and longer wavelength data (which may not be expected for a given sample) Sharp spectral characteristics) deliberately ignored. Additionally, the process can be weighted such that only measured data that can be reasonably expected to contain useful information can be included. This weighting method can be dynamic because the decision process can be repeated after each iteration (which one should be considered).

雖然本文所呈現之實例已使用該技術以有助於精確量測膜厚度，但是熟習此項技術者將顯而易見，在量測其他材料特性(其包括但不限於複折射率、組合物、孔隙率、表面或界面粗糙度等)時可同樣使用本發明之其他較佳實施例。另外，雖然本文所提供之實例已特定地處理對SiO₂ /Si樣本之量測，但是顯而易見，可同樣利用所描述方法來量測許多其他類型之樣本。舉例而言，當分析更複雜的薄膜堆疊時可使用本文所提供之技術。此等堆疊之實例包括基板上之薄膜SiO₂ /SiN堆疊或基板上之薄膜SiN/SiO₂ /SiN堆疊。While the examples presented herein have used this technique to aid in accurate measurement of film thickness, it will be apparent to those skilled in the art to measure other material properties including, but not limited to, complex refractive index, composition, porosity. Other preferred embodiments of the invention may be used in the same manner as surface, interface roughness, and the like. Additionally, while the examples provided herein have specifically addressed the measurement of SiO ₂ /Si samples, it will be apparent that many other types of samples can be measured using the methods described as well. For example, the techniques provided herein can be used when analyzing more complex thin film stacks. Examples of such stacks include a thin film SiO ₂ /SiN stack on a substrate or a thin film SiN/SiO ₂ /SiN stack on a substrate.

如先前所論述，本發明所提供之高靈敏度等級主要由以下事實引起：當在包含此等樣本之材料中的一或多者的光學吸收邊緣附近時，本發明使用伴隨樣本特性之小變化的反射信號之實質變化。雖然此等特點通常位於VUV光譜區中，但是由於被研究之樣本之物理特性的微小變化而在MEF中預期有實質上急劇的特點的情況下，在較長波長處通常可應用該技術。As previously discussed, the high sensitivity levels provided by the present invention are primarily caused by the fact that the present invention uses small variations accompanying sample characteristics when in the vicinity of the optical absorption edge of one or more of the materials comprising such samples. The substantial change in the reflected signal. While these features are typically located in the VUV spectral region, this technique is typically applied at longer wavelengths where slight variations in the physical properties of the sample being studied are expected to be substantially acute in the MEF.

熟習此項技術者將認識到，存在用於以此方式量化MEF信號以便使其可用於反饋給迭代程序的許多其他方法，該迭代程序經設計以經由調整經量測樣本之"假設"特性而最小化其值。此外，亦將容易明白，在一些情況下，可執行額外的數學步驟以增強量測程序之效能。Those skilled in the art will recognize that there are many other methods for quantizing the MEF signal in this manner to make it available for feedback to an iterative procedure that is designed to adjust the "what if" characteristic of the measured sample. Minimize its value. In addition, it will be readily apparent that in some cases additional mathematical steps can be performed to enhance the performance of the metrology program.

將認識到，如上所述，提供一種校準技術，該技術可包括在校準過程中利用兩個校準樣本。另外，即使在校準樣本中之至少一者的實際特性與假設特性之間存在變化，該技術仍允許校準。另外，上述技術包括一種校準技術，其中使用來自第一校準樣本之經反射強度量測與來自第二校準樣本之經反射強度量測的比率(舉例而言，如圖12中所示之I_ref /I_cal )。It will be appreciated that, as described above, a calibration technique is provided that can include utilizing two calibration samples during the calibration process. In addition, the technique allows for calibration even if there is a change between the actual and hypothetical characteristics of at least one of the calibration samples. Additionally, the above techniques include a calibration technique in which the ratio of the reflected intensity measurements from the first calibration sample to the reflected intensity measurements from the second calibration sample is used (for example, I _ref as shown in FIG. 12) /I _cal ).

即使在校準樣本及系統變化及偏移中可存在變化的條件下，仍可以各種方式使用多個校準樣本及自該等樣本反射之強度之比率來達成校準。舉例而言，如上所述，利用兩個校準樣本，其中第一校準樣本在感興趣波長中具有急劇光譜特點且第二樣本與第一樣本相比在感興趣波長區中相對無特點。在使用兩個校準樣本的另一實例中，可使用自第一校準樣本反射之強度與自第二校準樣本反射之強度的比率，其中兩個校準樣本中的任一者需要為相對無特點。在此實施例中，如以下更詳細描述，僅需要樣本在所要波長處之反射特性相對不同。在此技術中，接著可認為每一樣本之反射率資料已自另一者相對去耦合。以上參考第一樣本及相對無特點之第二樣本所描述的技術為使用反射特性相對不同的兩個校準樣本的一實例，然而，如以下所描述，可使用無一校準樣本需為光譜無特點的技術。Even in the presence of variations in calibration samples and system variations and offsets, calibration can be achieved using a plurality of calibration samples and the ratio of the intensities reflected from the samples in various ways. For example, as described above, two calibration samples are utilized, wherein the first calibration sample has sharp spectral characteristics in the wavelength of interest and the second sample is relatively uncharacteristic in the wavelength region of interest as compared to the first sample. In another example in which two calibration samples are used, the ratio of the intensity reflected from the first calibration sample to the intensity reflected from the second calibration sample can be used, wherein either of the two calibration samples need to be relatively uncharacteristic. In this embodiment, as described in more detail below, only the reflection characteristics of the sample at the desired wavelength are required to be relatively different. In this technique, the reflectance data for each sample can then be considered to have been relatively decoupled from the other. The technique described above with reference to the first sample and the relatively uncharacterized second sample is an example of using two calibration samples having relatively different reflection characteristics, however, as described below, none of the calibration samples may be used for the spectrum. Features the technology.

更明確地說，即使在無絕對反射率校準的情況下，仍可經由經量測強度來量測來自兩個樣本之反射率的比率，因為 若在彼此短時間內自每一樣本量測強度，則環境或儀器偏移不會起顯著作用，因此，方程式3由以下事實引起：在兩次量測期間，入射強度I₀ 不會改變。利用標準薄膜回歸分析可分析此比率以提取由單一樣本之絕對反射率確定的相同膜參數(n、k、厚度、界面粗糙度等)。然而，與單一強度之情況不同，不同量測之間經量測比率的變化係由於樣本本身的變化，而不是環境或燈偏移。因此，可以不同時間間隔量測方程式3之比率以獨立於I₀ 的變化確定樣本的變化。接著，此資料可用於校準反射計且確定I₀ 。More specifically, even in the absence of absolute reflectance calibration, the ratio of reflectance from two samples can be measured via the measured intensity because If the intensity is measured from each sample in a short time from each other, the environmental or instrumental offset will not play a significant role, therefore, Equation 3 is caused by the fact that the incident intensity I ₀ does not change during the two measurements. This ratio can be analyzed using standard film regression analysis to extract the same film parameters (n, k, thickness, interfacial roughness, etc.) as determined by the absolute reflectance of a single sample. However, unlike the case of a single intensity, the change in the measured ratio between different measurements is due to changes in the sample itself, rather than environmental or lamp offsets. Thus, different time intervals can be measured independent of Formula 3 in a ratio of I ₀ variations determined sample variation. This data can then be used to calibrate the reflectometer and determine I ₀ .

為了獲得對此等技術之更好理解，可關於校準樣本變化是由於變化的氧化物厚度或由於污染物層(藉由假設SiO₂ 光學特性予以充分描述)的假設展示一實例。將認識到，本文所描述之實例校準樣本僅經提供以輔助理解所揭示技術且可使用其他校準樣本及厚度。In order to obtain a better understanding of these techniques, an example may be shown regarding the calibration sample change due to a varying oxide thickness or due to the assumption of a contaminant layer (sufficiently described by assuming SiO ₂ optical properties). It will be appreciated that the example calibration samples described herein are provided only to aid in understanding the disclosed techniques and other calibration samples and thicknesses may be used.

因此，為了提供對校準技術之例示性描述，可利用裸Si校準樣本結合1000的SiO₂ /Si校準樣本來建構經修改之校準程序。藉由量測兩個樣本之強度，可分析強度之比率以提取兩個樣本之氧化物厚度。可將對於裸Si校準樣本所確定之厚度反饋至方程式2之校準程序中以得到更精確的絕對反射率。Therefore, in order to provide an illustrative description of the calibration technique, a bare Si calibration sample can be used in conjunction with 1000 The SiO ₂ /Si calibration sample was used to construct a modified calibration procedure. By measuring the intensity of the two samples, the ratio of the intensities can be analyzed to extract the oxide thickness of the two samples. The thickness determined for the bare Si calibration sample can be fed back into the calibration procedure of Equation 2 to obtain a more accurate absolute reflectance.

圖21A、圖21B、圖22A及圖22B展示原生SiO₂ /Si校準樣本(樣本1，對應於R₁ )與標稱的1000的SiO₂ /Si校準樣本(樣本2，對應於R₂ )之間的模擬反射率比率的比較。圖21A及圖21B展示增加原生SiO₂ 厚度對比率R₂ /R₁ 的效應。如圖21A所展示，對於高達1000 nm之波長提供反射率比率R₂ /R₁ ，而圖21B為對於100 nm與400 nm之間的波長之同一比率的展開圖。在圖21A及圖21B中，分別在曲線2106、2104及2102中對於10、20及30的SiO₂ 展示原生氧化物的變化對樣本1(R₁ )之影響的曲線。增加原生SiO₂ 厚度之主要效應是增加VUV中的比率，因為反射率R₁ 減小。21A, 21B, 22A, and 22B show a native SiO ₂ /Si calibration sample (sample 1, corresponding to R ₁ ) and a nominal 1000 A comparison of the simulated reflectance ratio between the SiO ₂ /Si calibration samples (sample 2, corresponding to R ₂ ). 21A and 21B show the effect of increasing the native SiO ₂ thickness against the ratio R ₂ /R ₁ . As shown in Figure 21A, the reflectance ratio R ₂ /R ₁ is provided for wavelengths up to 1000 nm, while Figure 21B is an expanded view of the same ratio for wavelengths between 100 nm and 400 nm. In Figures 21A and 21B, for curves 10106, 2104, and 2102, for 10, 20, and 30, respectively. SiO ₂ shows a plot of the effect of changes in native oxide on sample 1 (R ₁ ). The main effect of increasing the thickness of the native SiO ₂ is to increase the ratio in VUV because the reflectivity R _{1 is} reduced.

與之相比，增加1000的SiO₂ 厚度之效應是改變針對較長波長之干涉最大值及最小值。更明確地說，圖22A及圖22B對於恆定樣本1(20的原生氧化物)說明樣本2(1000的SiO₂ /Si、1010的SiO₂ /Si及1020的SiO₂ /Si)之變化的效應。更明確地說，曲線2202、2204及2206分別展示樣本2(1000的SiO₂ /Si、1010的SiO₂ /Si及1020的SiO₂ /Si)之變化的影響(圖22A展示自100－400 nm波長之展開圖)。因此，可認為兩個樣本之厚度(一樣本厚且一樣本薄)已去耦合，且可自對比率量測之標準分析提取每一者之厚度。此外，可在不利用絕對反射率標準之情況下自比率資料提取此等厚度。因為不管系統或燈偏移如何此比率均相同(假設相當快速、連續地量測強度或樣本1及樣本2)，所以隨時間流逝在比率中觀察到的差異將對應於實際樣本之變化。圖21及圖22說明，若所述樣本特性為SiO₂ 厚度，則可確定每一樣本上之厚度變化量。接著，以此方式在樣本2上偵測到的原生氧化物層之厚度可用於利用彼樣本改良絕對校準之品質。Compared with it, increase 1000 The effect of the SiO ₂ thickness is to change the interference maximum and minimum for longer wavelengths. More specifically, Figures 22A and 22B for a constant sample 1 (20 Primary oxide) Description Sample 2 (1000 SiO ₂ /Si, 1010 SiO ₂ /Si and 1020 The effect of the change in SiO ₂ /Si). More specifically, curves 2202, 2204, and 2206 show sample 2 (1000, respectively) SiO ₂ /Si, 1010 SiO ₂ /Si and 1020 The effect of the change in SiO ₂ /Si) (Fig. 22A shows an unfolded view from the wavelength of 100-400 nm). Therefore, it can be considered that the thicknesses of the two samples (the same thickness and the same thickness) have been decoupled, and the thickness of each can be extracted from the standard analysis of the contrast ratio measurement. In addition, these thicknesses can be extracted from the ratio data without using the absolute reflectance standard. Since this ratio is the same regardless of the system or lamp offset (assuming a fairly fast, continuous measurement of intensity or sample 1 and sample 2), the difference observed in the ratio over time will correspond to the change in the actual sample. 21 and 22 illustrate that if the sample characteristic is SiO ₂ thickness, the amount of thickness change on each sample can be determined. Next, the thickness of the native oxide layer detected on sample 2 in this manner can be used to improve the quality of the absolute calibration using the sample.

注意，若校準樣本之一者確實保持恆定，則可直接自比率變化推斷其他樣本之反射率變化。然而，實務上，用於校準樣本偏移之機制通常是污染物層在兩個樣本上的累積，因此，通常將不是此種情況。Note that if one of the calibration samples does remain constant, the reflectance change of the other samples can be inferred directly from the ratio change. However, in practice, the mechanism used to calibrate the sample offset is usually the accumulation of the contaminant layer on both samples, so this will usually not be the case.

本文所描述之技術提供一種校準技術，即使污染物層不僅為生長氧化物層(其包括，例如，有機污染物或基於矽之污染物)，仍可使用此技術。對於以上所述之Si校準樣本，可足以說明生長污染物會減小絕對反射率的事實，因此對污染物之精密描述並非確實必要。然而，最精確的校準模型可包括兩個樣本上之不同的污染物層。The techniques described herein provide a calibration technique that can be used even if the contaminant layer is not only a growing oxide layer that includes, for example, organic contaminants or antimony-based contaminants. For the Si calibration samples described above, it is sufficient to demonstrate the fact that growing contaminants will reduce the absolute reflectivity, so a precise description of the contaminants is not really necessary. However, the most accurate calibration model can include different layers of contaminants on both samples.

相對反射率量測可用於確定對校準樣本上之污染物層累積的更好光學描述，且將資訊併入校準程序中。在以上實例中的膜結構可為樣本1之污染物層/原生SiO₂ /Si及樣本2之污染物層/1000的SiO₂ /Si，在相對反射率量測期間確定污染物層厚度。此將不僅產生更穩定的絕對反射率校準，而且首先產生更精確的絕對反射率。Relative reflectance measurements can be used to determine a better optical description of the accumulation of contaminant layers on a calibration sample and incorporate information into the calibration procedure. The film structure in the above examples may be the contaminant layer of sample 1 / the native SiO ₂ /Si and the contaminant layer of sample 2 / 1000 SiO ₂ /Si, the thickness of the contaminant layer is determined during relative reflectance measurements. This will not only result in a more stable absolute reflectance calibration, but will first produce a more accurate absolute reflectivity.

在圖23A及圖23B中提供對污染物層累積對於不同的污染物量可能如何影響反射率比率的說明。膜結構為樣本1之污染物層/10的SiO₂ /Si及樣本2之污染物層/1000的SiO₂ /Si。圖23A分別在曲線2302、2304及2306中展示對於10、20及30之三個不同污染物層厚度的R₂ /R₁ 比較。可注意，因為污染物層光學特性實際上不同於SiO₂ 之光學特性，所以性質自圖21及圖22所示之性質去耦合。換言之，可同時自單一比率量測確定所有三個參數：原生氧化物厚度、厚氧化物厚度及污染物層厚度。如前所述，所確定之厚度可反饋至方程式2之校準程序中。明顯地，在此情況下，若預期會變化的僅是污染物層，則任一或兩個氧化物厚度可固定至某先前確定值。另外，藉由假設相同量的污染物層累積在兩個樣本上來約束分析可能是合理的。An illustration of how the accumulation of contaminant layers may affect the reflectance ratio for different amounts of contaminants is provided in Figures 23A and 23B. The membrane structure is the contaminant layer of sample 1/10 SiO ₂ /Si and sample 2 contaminant layer / 1000 SiO ₂ /Si. Figure 23A shows for 10 in curves 2302, 2304, and 2306, respectively. 20 And 30 Comparison of R ₂ /R _{1 of the} thickness of three different contaminant layers. It can be noted that since the optical properties of the contaminant layer are actually different from the optical properties of SiO ₂ , the properties are decoupled from the properties shown in FIGS. 21 and 22 . In other words, all three parameters can be determined simultaneously from a single ratio measurement: native oxide thickness, thick oxide thickness, and contaminant layer thickness. As previously described, the determined thickness can be fed back into the calibration procedure of Equation 2. Obviously, in this case, if only the contaminant layer is expected to change, either or both oxide thicknesses may be fixed to a previously determined value. In addition, it may be reasonable to constrain the analysis by assuming that the same amount of contaminant layer accumulates on both samples.

通常，只要樣本的反射特性充分不同(因此，對於所有波長，比率不是正好為1)，此類型量測可用於分析樣本而不會影響不確定之校準標準。舉例而言，相對反射率量測可用於在與所觀察比率更一致之VUV區中獲得對SiO₂ 之經修改光學描述。Typically, this type of measurement can be used to analyze a sample without affecting the uncertainty of the calibration standard, as long as the reflection characteristics of the sample are sufficiently different (thus, for all wavelengths, the ratio is not exactly one). For example, relative reflectance measurements can be used to obtain a modified optical description of SiO ₂ in a VUV region that is more consistent with the observed ratio.

在以上所述之實例中，兩個樣本由同一材料形成(矽上之原生SiO₂ 及矽上之厚SiO₂ )。對於兩個樣本利用同一材料之優點可為：同一污染物可產生於兩個樣本之表面上。利用具有不同表面之樣本可引超產生之污染物膜的差異，使污染物層更難以特徵化。然而，將認識到，可在樣本具有不同材料的情況下使用本文所描述之技術。In the examples described above, the two samples were formed from the same material (primary SiO ₂ on the crucible and thick SiO ₂ on the crucible). The advantage of using the same material for two samples is that the same contaminant can be produced on the surface of the two samples. The use of samples with different surfaces can lead to differences in the resulting contaminant film, making the contaminant layer more difficult to characterize. However, it will be appreciated that the techniques described herein can be used where the samples have different materials.

另外，注意，以上所述之實例提供一種技術，其中確定樣本1(原生氧化物樣本)之特徵且接著利用彼資料作為校準標準。然而，或者可確定樣本2之特徵且利用彼資料作為校準標準。在一實施例中，對於校準樣本利用較厚的SiO₂ 樣本可為更有利的，因為任何剩餘誤差更可能在SiO₂ 干涉極值附近以假影形式顯示出來。通常，膜結構可為任何結構，對於此等結構，已知足夠資訊而能夠建構模型比率，且樣本之任一者可用於進一步校準。Additionally, it is noted that the examples described above provide a technique in which the characteristics of Sample 1 (a native oxide sample) are determined and then the data is used as a calibration standard. However, the characteristics of sample 2 can be determined and the data used as a calibration standard. In one embodiment, the calibration sample using a thicker SiO ₂ samples may be more advantageous, because any residual errors are more likely to SiO ₂ in the vicinity of the interference extremum displayed in the form of artifacts. Generally, the membrane structure can be any structure for which sufficient information is known to be able to construct the model ratio, and any of the samples can be used for further calibration.

如此項技術中已知，可以任何數目之多種方式建構校準樣本：樣本1及樣本2。在一實施例中，兩個樣本各自可形成於同一基板上。舉例而言，圖24說明反射計系統中校準程序之可能的機械實施例，其中不同厚度之兩個氧化物襯墊(諸如，以上實例中之樣本1及樣本2)作為襯墊1及襯墊2形成於半導體晶圓上或安裝於半導體晶圓夾盤上。然而，本文所描述之技術不限於所提供之概念之任何特定機械實施例。As is known in the art, calibration samples can be constructed in any number of ways: Sample 1 and Sample 2. In an embodiment, each of the two samples can be formed on the same substrate. For example, Figure 24 illustrates a possible mechanical embodiment of a calibration procedure in a reflectometer system in which two oxide liners of different thickness (such as Sample 1 and Sample 2 in the above examples) are used as liner 1 and liner 2 formed on a semiconductor wafer or mounted on a semiconductor wafer chuck. However, the techniques described herein are not limited to any particular mechanical embodiment of the concepts provided.

如上所述之技術因此提供兩個校準樣本，該等校準樣本用於自具有相對不同的反射特性之兩個樣本提供相對反射率比率R₂ /R₁ 。使用此技術，隨時間流逝可發生校準標準的變化，同時仍提供精確校準。可以多種方式實施此等技術。參考圖25及圖26描述例示性校準流程，然而，將認識到，可使用其他步驟及流程，同時仍利用本文所描述之技術。The technique described above thus provides two calibration samples for providing a relative reflectance ratio R ₂ /R ₁ from two samples having relatively different reflection characteristics. Using this technique, changes in calibration standards can occur over time while still providing accurate calibration. These techniques can be implemented in a variety of ways. An exemplary calibration process is described with reference to Figures 25 and 26, however, it will be appreciated that other steps and flows may be utilized while still utilizing the techniques described herein.

如圖25所示，提供一種例示性技術，其中假設第一校準樣本之原始反射率正確且接著形成第一校準樣本之反射率與第二校準樣本之反射率之間的比率，從而校準反射計。更明確地說，在步驟2502中，利用對校準樣本1之假設認識(預期校準樣本1在給定光譜區中會展示出實質的校準誤差特點)來計算樣本1之假設反射率。接著，在步驟2504中，記錄標準樣本1之強度。接著，在步驟2506中，利用校準樣本1之假設反射率計算源強度輪廓。在步驟2508中，記錄校準樣本2(預期在同一光譜區內會展示出實質上不同於校準樣本1之反射特性的樣本)之強度。接著，在步驟2510處計算校準樣本2之反射率。接著，在步驟2512中將校準樣本1之反射率與校準樣本2之反射率的比率表示為一比率。接著，如步驟2514所示，將用於校準樣本1及校準樣本2之假設模型建構成、表示成一反射率比率。在步驟2516中，可利用回歸演算法及優點函數來迭代地調整關於校準樣本1及校準樣本2之特性的假設且重新計算假設模型反射率，直至計算出的反射率比率與模型比率之反射率之間的差異最小化且因此獲得樣本1及樣本2之"實際"特性。接著，在步驟2518中，利用校準樣本1之"實際"反射率重新計算源強度輪廓。在步驟2520中，接著可記錄未知樣本之強度，且在步驟2522中，如所示地表示未知樣本之計算出的反射率。As shown in FIG. 25, an exemplary technique is provided in which it is assumed that the original reflectance of the first calibration sample is correct and then the ratio between the reflectance of the first calibration sample and the reflectance of the second calibration sample is formed, thereby calibrating the reflectometer . More specifically, in step 2502, the hypothetical reflectance of sample 1 is calculated using the hypothetical recognition of calibration sample 1 (expected calibration sample 1 will exhibit substantial calibration error characteristics in a given spectral region). Next, in step 2504, the intensity of the standard sample 1 is recorded. Next, in step 2506, the source intensity profile is calculated using the assumed reflectance of the calibration sample 1. In step 2508, the intensity of calibration sample 2 (expected to exhibit a sample substantially different from the reflectance characteristic of calibration sample 1 in the same spectral region) is recorded. Next, the reflectance of the calibration sample 2 is calculated at step 2510. Next, the ratio of the reflectance of the calibration sample 1 to the reflectance of the calibration sample 2 is expressed as a ratio in step 2512. Next, as shown in step 2514, the hypothetical model for calibrating sample 1 and calibration sample 2 is constructed and represented as a reflectance ratio. In step 2516, the regression algorithm and the merit function can be used to iteratively adjust the assumptions regarding the characteristics of the calibration sample 1 and the calibration sample 2 and recalculate the assumed model reflectance until the calculated reflectance ratio to the model ratio reflectance The difference between the two is minimized and thus the "actual" characteristics of Sample 1 and Sample 2 are obtained. Next, in step 2518, the source intensity profile is recalculated using the "actual" reflectivity of the calibration sample 1. In step 2520, the intensity of the unknown sample can then be recorded, and in step 2522, the calculated reflectance of the unknown sample is represented as shown.

圖26中展示另一例示性校準流程圖。如圖26所示，可使用簡化的過程，其中可利用來自兩個樣本之強度直接形成反射率比率(與圖25之技術相比，在圖25之技術中，自對該等樣本之一者的假設認識計算同一樣本的假設反射率)。如圖26中所示，在步驟2601中，記錄校準樣本1之強度。在步驟2603中，記錄校準樣本2(預期在同一光譜區內會展示出實質上不同於校準樣本1之反射特性的樣本)之強度。接著，如步驟2605所示，基於自樣本1及樣本2記錄之強度表示校準樣本1及校準樣本2之反射率的比率。接著，如步驟2614中所示，可將用於校準樣本1及校準樣本2之假設模型建構成、表示成一反射率比率。在步驟2616中，可利用回歸演算法及優點函數來迭代地調整關於校準樣本1及校準樣本2之特性的假設且重新計算假設模型反射率，直至計算出的反射率比率與模型比率之反射率之間的差異最小化且因此獲得樣本1及樣本2之"實際"特性。接著，在步驟2618中，利用校準樣本1之"實際"反射率重新計算源強度輪廓。在步驟2620中，接著可記錄未知樣本之強度，且在步驟2622中，如所示地表示未知樣本計算出的反射率。Another exemplary calibration flow diagram is shown in FIG. As shown in Figure 26, a simplified process can be used in which the reflectance ratio can be directly formed using the intensities from the two samples (compared to the technique of Figure 25, in the technique of Figure 25, from one of the samples) The hypothesis is known to calculate the assumed reflectivity of the same sample). As shown in Fig. 26, in step 2601, the intensity of the calibration sample 1 is recorded. In step 2603, the intensity of calibration sample 2 (expected to exhibit a sample substantially different from the reflectance characteristic of calibration sample 1 in the same spectral region) is recorded. Next, as shown in step 2605, the ratio of the reflectances of the calibration sample 1 and the calibration sample 2 is expressed based on the intensity recorded from the samples 1 and 2. Next, as shown in step 2614, the hypothetical model for calibration sample 1 and calibration sample 2 can be constructed and represented as a reflectance ratio. In step 2616, the regression algorithm and the merit function can be used to iteratively adjust the assumptions regarding the characteristics of the calibration sample 1 and the calibration sample 2 and recalculate the assumed model reflectance until the calculated reflectance ratio to the model ratio reflectance The difference between the two is minimized and thus the "actual" characteristics of Sample 1 and Sample 2 are obtained. Next, in step 2618, the source intensity profile is recalculated using the "actual" reflectivity of the calibration sample 1. In step 2620, the intensity of the unknown sample can then be recorded, and in step 2622, the reflectance calculated for the unknown sample is represented as shown.

應指出，在分析或以其他方式論述方程式3中的比率時，藉由首先計算來自標準薄膜模型(參看，例如H.G.Tompkins and W.A.McGahan,Spectroscopic Ellipsometry and Reflectometry：A User's Guide ,John Wiley and Sons,new York,(1999)，用於計算個別反射率之方法)之個別樣本之R₁ 及R₂ 來計算比率係便利的。然而，應顯而易見，可易於重新表述薄膜模型以將其直接應用於為在數學上及概念上等效的比率I₁ /I₂ 。It should be noted that when analyzing or otherwise discussing the ratios in Equation 3, by first calculating from a standard thin film model (see, for example, HGTompkins and WA McGahan, Spectroscopic Ellipsometry and Reflectometry: A User's Guide , John Wiley and Sons, new York, (1999), R ₁ and R ₂ of individual samples used to calculate individual reflectances are convenient to calculate ratios. However, it should be apparent that the thin film model can be easily re-presented to apply directly to the mathematically and conceptually equivalent ratio I ₁ /I ₂ .

圖27提供對圖23及圖26中所描述之概念之進一步說明。圖27展示用於自兩個校準樣本提取氧化物及污染物層厚度的反射率比率擬合，一校準樣本具有薄氧化物(樣本1)且一校準樣本具有較厚~1000的氧化物(樣本2)。每一樣本之表面亦具有在VUV反射計中利用期間累積起來的少量污染物層。自兩個校準樣本收集經反射強度且經反射強度用於形成經量測反射率比率。建構模型比率，且允許氧化物及污染物層厚度在回歸分析期間變化，該回歸分析最小化經計算比率與經量測比率之間的誤差。對於此分析，認為Si、SiO₂ 及污染物層之光學特性是已知且固定的(自對反射率比率之先前分析確定SiO₂ 及污染物光學特性，且圖23A及圖23B中所利用之光學特性稍微不同)。在經計算比率與經量測比率之間提供最佳擬合之最佳化厚度對於厚氧化物樣本為6.06的污染物及1052.0的SiO₂ 且對於薄氧化物樣本為9.49的污染物及18.62的SiO₂ 。此時，認為兩個樣本之絕對反射率已知，且最佳化參數可與每一層之光學特性及標準薄膜模型一起用來計算任一樣本之反射率。若藉由計算R₁ 及R₂ 在最佳化期間計算模型比率，則在擬合過程結束時可獲得最佳化樣本1及2之反射率而無需進一步計算。與具有相同SiO₂ 厚度但不具有污染物之膜的反射率相比，在圖28A及圖28B中對於樣本1展示且在圖28C及圖28D中對於樣本2展示由圖27的分析引起之薄SiO₂ 樣本及厚SiO₂ 樣本之反射率(曲線2802及2806具有污染物，且曲線2804及2808不具有污染物)。如所示，圖28B為圖28A之曲線之一部分的展開版本。類似地，圖28D為圖28C之曲線之一部分的展開版本。自該等圖顯而易見，隨著即使少量污染物累積，反射率可顯著變化，尤其在DUV波長以下之區中。若氧化物樣本之一者被用於在假設恆定反射率的情況下校準I₀ ，則在DUV以下的區中之誤差將為顯著的。隨著更多污染物產生於樣本上，此效應甚至更大。在圖27所說明分析結束時，樣本之經量測強度的任一者可與來自圖28之適當(具有污染物)反射率一起用來確定源強度輪廓。眾所熟知，薄的中間層存在於SiO₂ /Si系統之SiO₂ 膜與Si基板之間。此中間層可包括於膜模型中，且將改良校準程序之穩定性以及增強經校準反射率之精確性。存在許多用於模型化該界面之可能性。最簡單的係接近利用薄SiO層或非晶SiO₂ 與非晶Si光學特性之有效介質模型組合的中間層的效應。此系統比不具有界面之SiO₂ /Si系統更複雜，且藉由分析未污染的校準樣本之比率來預特徵化SiO₂ 及中間層厚度將為可行的。接著，校準程序將用於確定污染物層(隨著其累積)之特性，其中認為SiO₂ 及界面特性全部已知且其厚度及光學特性在比率分析期間是固定的。藉由自新樣本烘焙掉或清洗掉空浮分子污染物(AMC)，或在極端情況下中藉由化學蝕刻(其亦將移除一些SiO₂ 材料)，可獲得未受污染的樣本。除了中間層之外，超薄氧化物(其包括形成於矽上之原生氧化物)有可能具有不同於較厚熱生長氧化物之光學特性。反射率模型中亦可考慮此以在利用SiO₂ /Si校準樣本時進一步改良校準精確性。Figure 27 provides a further illustration of the concepts described in Figures 23 and 26. Figure 27 shows a reflectance ratio fit for extracting oxide and contaminant layer thickness from two calibration samples, one calibration sample with thin oxide (sample 1) and one calibration sample with thicker ~1000 Oxide (sample 2). The surface of each sample also has a small amount of contaminant layer accumulated during use in the VUV reflectometer. The reflected intensity is collected from the two calibration samples and the reflected intensity is used to form a measured reflectance ratio. The model ratio is constructed and the oxide and contaminant layer thicknesses are allowed to vary during the regression analysis, which minimizes the error between the calculated ratio and the measured ratio. For this analysis, the optical properties of the Si, SiO ₂ and contaminant layers were considered to be known and fixed (the SiO ₂ and contaminant optical properties were determined from previous analysis of the reflectance ratio and utilized in Figures 23A and 23B). The optical properties are slightly different). The optimum thickness for providing the best fit between the calculated ratio and the measured ratio is 6.06 for thick oxide samples. Contaminants and 1052.0 SiO ₂ and for the thin oxide sample is 9.49 Contaminants and 18.62 SiO ₂ . At this point, the absolute reflectance of the two samples is considered to be known, and the optimization parameters can be used with the optical properties of each layer and the standard film model to calculate the reflectance of either sample. If the model ratio is calculated during the optimization by calculating R ₁ and R ₂ , the reflectance of the optimized samples 1 and 2 can be obtained at the end of the fitting process without further calculation. Compared to the reflectance of a film having the same SiO ₂ thickness but no contaminants, the sample 1 is shown in FIGS. 28A and 28B and the sample 2 shown in FIG. 28C and FIG. 28D is thinned by the analysis of FIG. The reflectance of the SiO ₂ sample and the thick SiO ₂ sample (curves 2802 and 2806 have contaminants, and curves 2804 and 2808 have no contaminants). As shown, Figure 28B is an expanded version of a portion of the curve of Figure 28A. Similarly, Figure 28D is an expanded version of a portion of the curve of Figure 28C. As is apparent from these figures, as even a small amount of contaminants accumulate, the reflectance can vary significantly, especially in the region below the DUV wavelength. If one of the oxide samples is used to calibrate I ₀ with assuming a constant reflectance, the error in the region below the DUV will be significant. This effect is even greater as more contaminants are produced on the sample. At the end of the analysis illustrated in Figure 27, any of the measured intensities of the samples can be used with appropriate (with contaminant) reflectance from Figure 28 to determine the source intensity profile. It is well known that a thin intermediate layer exists between the SiO ₂ film of the SiO ₂ /Si system and the Si substrate. This intermediate layer can be included in the film model and will improve the stability of the calibration procedure as well as enhance the accuracy of the calibrated reflectance. There are many possibilities for modeling this interface. The simplest is close to the effect of an intermediate layer combined with a thin SiO layer or an effective dielectric model of amorphous SiO ₂ and amorphous Si optical properties. This system is more complex than an SiO ₂ /Si system without an interface, and it would be feasible to pre-characterize the SiO ₂ and interlayer thickness by analyzing the ratio of uncontaminated calibration samples. Next, the calibration procedure will be used to determine the characteristics of the contaminant layer (as it accumulates), where SiO ₂ and interfacial properties are all known and their thickness and optical properties are fixed during the ratio analysis. Uncontaminated samples can be obtained by baking or washing away empty floating molecular contaminants (AMC) from new samples, or in extreme cases by chemical etching (which will also remove some SiO ₂ material). In addition to the intermediate layer, ultrathin oxides, which include native oxides formed on the crucible, are likely to have optical properties different from thicker thermally grown oxides. This can also be considered in the reflectance model to further improve calibration accuracy when calibrating samples with SiO ₂ /Si.

用於分析反射率比率之便利的回歸程序為W.H.Press、S.A.Teukolsky、W.T.Vetterling及B.P.Flannery所著的Numerical Recipes in C：The Art of Scientific Computing，第二版 (Cambridge University出版社(Cambridge,MA：1992))中所描述之熟知Levenberg－Marquardt演算法，然而，將認識到此項技術中已知之任何數目種方法可用於最佳化或以其他方式提取膜參數。在一些情況下，回歸演算法及膜模型甚至可能為不必要的，因為有時有可能自反射率比率的變化更直接地推斷校準樣本中之一或多者的反射率變化。A convenient regression procedure for analyzing reflectance ratios is in Numerical Recipes in C: The Art of Scientific Computing by WHPress, SATeukolsky, WTVetterling, and BPF Lannery , Second Edition (Cambridge University Press (Cambridge, MA: 1992)). The well-known Levenberg-Marquardt algorithm is described, however, it will be appreciated that any number of methods known in the art can be used to optimize or otherwise extract membrane parameters. In some cases, regression algorithms and membrane models may even be unnecessary, as it is sometimes possible to more directly infer the change in reflectance of one or more of the calibration samples from changes in the reflectance ratio.

所描述方法無需限於兩個校準樣本，且可推廣為包括多個校準樣本。舉例而言，第三樣本(樣本3)可為厚(例如，3000A)的氟化鎂MgF₂ /Si樣本，且同時分析比率R2/R1及R3/R1以對樣本1(樣本1及樣本2可具有與圖27中實例類似的膜結構)之各種層提供進一步約束。在進行校準以確定I₀ 期間，將在時間標度內量測樣本1、2及3之強度，其中I₀ 大致恆定，對於經量測資料形成比率R2/R1及R3/R1，且回歸分析用於同時提取所有三個樣本之膜及污染物層的厚度。換言之，該回歸藉由最佳化經計算比率中所利用的參數來同時最小化經量測的R2/R1及R3/R1與經計算的R2/R1及R3/R1之間的誤差。在實現此概念之一過程中，分析可對多個樣本分析使用Levenberg－Marquardt程序之常見推廣，在該情況下，非線性卡方優點函數可被寫成： 其中下標i及j係指入射條件(通常為波長)，且N21及N31為對於每一比率所包括之資料點的總數目。多個比率通常將涵蓋相同的光譜範圍且由相同數目個經量測資料點組成，但是不嚴格要求此。通常，每一比率可涵蓋不同的光譜範圍且比率不必完全由相同數目個經量測資料點組成。在方程式4中，σ _i 及σ _j 為對經量測反射率比率之經估計的不確定性，其可取決於入射條件。因為樣本1之特性為兩個比率所共有，所以同時分析通常基本上藉由減小可導致經量測比率之可能的參數組的數目而在用於確定樣本1特性之擬合程序中提供額外約束。接著，利用樣本1之經最佳化參數來計算實際絕對反射率Rcal＝R1，接著利用該反射率來計算I0＝I1/Rcal。對樣本1之額外約束可輔助確定可同時存在於樣本1上之多種類型污染物的厚度，或輔助解決不均勻的污染物層。比率R3/R2亦可添加至分析。此概念可延伸至由標稱材料之任何組合組成的多個樣本。The described method need not be limited to two calibration samples and can be generalized to include multiple calibration samples. For example, the third sample (sample 3) can be a thick (eg, 3000 A) magnesium fluoride MgF ₂ /Si sample, and simultaneously analyze the ratios R2/R1 and R3/R1 to sample 1 (sample 1 and sample 2) The various layers, which may have a film structure similar to the example of Figure 27, provide further constraints. During calibration to determine I ₀ , the intensities of samples 1, 2, and 3 will be measured over a time scale, where I ₀ is approximately constant, and ratios R2/R1 and R3/R1 are formed for the measured data, and regression analysis is performed. Used to simultaneously extract the thickness of the film and contaminant layers of all three samples. In other words, the regression minimizes the error between the measured R2/R1 and R3/R1 and the calculated R2/R1 and R3/R1 by optimizing the parameters utilized in the calculated ratio. In implementing one of these concepts, the analysis can use a common generalization of the Levenberg-Marquardt program for multiple sample analyses, in which case the nonlinear chi-square merit function can be written as: Where subscripts i and j refer to incident conditions (usually wavelengths), and N21 and N31 are the total number of data points included for each ratio. Multiple ratios will typically cover the same spectral range and consist of the same number of measured data points, but this is not strictly required. Typically, each ratio can cover a different spectral range and the ratio does not have to consist entirely of the same number of measured data points. In Equation 4, σ _i and σ _j are estimated uncertainties over the measured reflectance ratio, which may depend on the incident conditions. Since the characteristics of sample 1 are common to both ratios, simultaneous analysis typically provides additional in the fitting procedure used to determine the characteristics of sample 1 by substantially reducing the number of possible parameter sets that can result in a measured ratio. constraint. Next, the actual absolute reflectance Rcal=R1 is calculated using the optimized parameters of the sample 1, and then the reflectance is used to calculate I0=I1/Rcal. Additional constraints on Sample 1 may assist in determining the thickness of multiple types of contaminants that may be present on Sample 1, or to assist in the resolution of uneven contaminant layers. The ratio R3/R2 can also be added to the analysis. This concept can be extended to multiple samples consisting of any combination of nominal materials.

圖29A至圖29L說明先前實例之樣本1、2及3上之污染物層累積的效應。圖29A至圖29L中之模擬對於SiO₂ 、Si及污染物層利用與圖27、圖28A及圖28B中相同的光學特性，且自可用文獻獲得MgF₂ 光學特性。圖29A及圖29B分別將樣本3與樣本1之比率(每一樣本上具有10、20及30的污染物)說明為曲線2902、2904及2906(圖29B為圖29A之一部分的展開版本)。圖29C及圖29D分別將樣本2與樣本1之比率(每一樣本上具有10、20及30的污染物)說明為曲線2908、2910及2912(圖29D為圖29C之一部分的展開版本)。圖29E及圖29F分別將樣本2與樣本1之比率(該等樣本僅展示樣本1上10、20及30的污染物累積之效應)說明為曲線2914、2916及2918(圖29F為圖29E之一部分的展開版本)。圖29G及圖29H分別將樣本2與樣本1之比率(該等樣本僅展示樣本2上10、20及30的污染物累積之效應)說明為曲線2920、2922及2924(圖29H為圖29G之一部分的展開版本)。圖29I及圖29J分別將樣本3與樣本1之比率(該等樣本僅展示樣本1上10、20及30的污染物累積之效應)說明為曲線2926、2928及2930(圖29J為圖29I之一部分的展開版本)。圖29K及圖29L分別將樣本3與樣本1之比率(該等樣本僅展示樣本3上10、20及30的污染物累積之效應)說明為曲線2932、2934及2936(圖29L為圖29K之一部分的展開版本)。圖29A至圖29L中之模擬展示，污染物累積影響不同比率之不同光譜區。樣本1上之污染物累積之效應傾向於在DUV以下的區中及DUV區中增加比率，而較厚膜上之累積的效應傾向於增加干涉振幅。具有不同的較厚膜(SiO₂ 及MgF₂ )有助於進一步約束可導致類似比率之可能的膜結構。來自對此等比率之分析的組合效應同時是對被確定的各種參數之去耦合。圖29A至圖29L說明一實例，但是如上所述，在多個樣本的情況下甚至更微小的去耦合是可能的，其(例如)允許對多種類型污染物膜的更精確之同時確定。29A to 29L illustrate the effects of accumulation of contaminant layers on samples 1, 2, and 3 of the previous examples. The simulation of FIG. 29A to 29L to the same optical characteristics as SiO _2, of Si layer and contaminants using FIG. 27, FIGS. 28A and 28B, and are available from the literature to obtain optical characteristics MgF _2. Figure 29A and Figure 29B show the ratio of sample 3 to sample 1 (10, 20 and 30 on each sample) The contaminants are illustrated as curves 2902, 2904, and 2906 (Fig. 29B is an expanded version of a portion of Fig. 29A). Figure 29C and Figure 29D compare the ratio of sample 2 to sample 1 (10, 20 and 30 on each sample) The contaminants are illustrated as curves 2908, 2910, and 2912 (Fig. 29D is an expanded version of a portion of Fig. 29C). 29E and 29F respectively compare the ratio of sample 2 to sample 1 (the samples only show 10, 20 and 30 on sample 1) The effect of the accumulation of contaminants is illustrated by curves 2914, 2916, and 2918 (Fig. 29F is an expanded version of a portion of Fig. 29E). Figure 29G and Figure 29H show the ratio of sample 2 to sample 1 respectively (the samples show only samples 10, 20 and 30) The effect of the accumulation of contaminants is illustrated as curves 2920, 2922, and 2924 (Fig. 29H is an expanded version of one of Fig. 29G). Figure 29I and Figure 29J compare the ratio of sample 3 to sample 1 (the samples only show samples 10, 20 and 30) The effect of the accumulation of contaminants is illustrated as curves 2926, 2928, and 2930 (Fig. 29J is an expanded version of a portion of Fig. 29I). Figure 29K and Figure 29L show the ratio of sample 3 to sample 1 respectively (the samples only show 10, 20 and 30 on sample 3) The effect of the accumulation of contaminants is illustrated as curves 2932, 2934, and 2936 (Fig. 29L is an expanded version of a portion of Fig. 29K). The simulations in Figures 29A-29L show that contaminant accumulation affects different spectral regions of different ratios. The effect of contaminant accumulation on sample 1 tends to increase the ratio in the region below DUV and in the DUV region, while the cumulative effect on thicker films tends to increase the interference amplitude. Having different thicker films (SiO ₂ and MgF ₂ ) helps to further constrain the possible film structure that can lead to similar ratios. The combined effect from the analysis of these ratios is at the same time the decoupling of the various parameters that are determined. Figures 29A-29L illustrate an example, but as noted above, even minor decoupling is possible with multiple samples, which, for example, allows for more precise simultaneous determination of multiple types of contaminant membranes.

論述一種方法，藉由該方法導出對於污染物層(諸如，圖23A及圖23B中所利用之污染物層)假設之光學特性。可執行此等步驟以獲得SiO₂ 及中間層之開始厚度以及污染物層之光學特性。經確定之光學特性可用於改良校準程序之品質(實際上藉由利用類似程序來確定對於圖23A及圖23B以及圖27中之模擬假設之污染物光學特性)。另外，一旦確定此等特性，校準樣本之比率便可用於在校準期間確定污染物層之厚度，其中認為所有其他預定特性(諸如SiO₂ 及界面厚度及光學特性以及污染物光學特性)是已知且固定的。A method is discussed by which the optical properties assumed for a contaminant layer, such as the contaminant layer utilized in Figures 23A and 23B, are derived. These steps can be performed to obtain the initial thickness of SiO ₂ and the intermediate layer as well as the optical properties of the contaminant layer. The determined optical characteristics can be used to improve the quality of the calibration procedure (actually by using a similar procedure to determine the contaminant optical properties for the simulation hypotheses in Figures 23A and 23B and Figure 27). Additionally, once these characteristics are determined, the ratio of calibration samples can be used to determine the thickness of the contaminant layer during calibration, where all other predetermined characteristics, such as SiO ₂ and interface thickness and optical properties, as well as contaminant optical properties, are considered known. And fixed.

利用反射率比率來預特徵化污染物光學特性，例示性分析可為：1自薄SiO₂ 及1k SiO₂ 樣本移除空浮分子污染物(AMC)。舉例而言，利用熱板、VUV預曝光、化學預清洗、蝕刻移除及預生長原生SiO₂ 層或此等技術之某組合。The reflectance ratio is used to pre-characterize the optical properties of the contaminant. An exemplary analysis can be: 1 removal of airborne molecular contaminants (AMC) from thin SiO ₂ and 1 k SiO ₂ samples. For example, hot plates, VUV pre-exposure, chemical pre-cleaning, etch removal, and pre-growth of native SiO ₂ layers or some combination of such techniques are utilized.

2記錄樣本之強度比率I₂ /I₁ (且因此記錄反射率比率R₂ /R₁ )。分析反射率比率以預定厚氧化物層及原生氧化物層之厚度。在對兩個樣本之分析中可包括SiO₂ /Si中間層。在分析期間，任何被視為已知的特性(諸如，Si及SiO₂ 光學特性)將是固定的。2 Record the intensity ratio I ₂ /I _{1 of the} sample (and thus record the reflectance ratio R ₂ /R ₁ ). The reflectance ratio is analyzed to predetermined thicknesses of the thick oxide layer and the native oxide layer. An SiO ₂ /Si intermediate layer may be included in the analysis of the two samples. During the analysis, any properties considered to be known (such as Si and SiO ₂ optical properties) will be fixed.

3允許AMC或VUV誘發的污染物在樣本上累積。當樣本儲存於環境中時，AMC將自然產生。當在VUV光學計量工具中重複量測樣本時，VUV污染物可隨時間流逝累積。3 Allow AMC or VUV induced contaminants to accumulate on the sample. AMC will naturally occur when the sample is stored in the environment. When the sample is repeatedly measured in a VUV optical metrology tool, VUV contaminants can accumulate over time.

4在污染物累積之後量測樣本。利用具有可調整光學特性之分散模型來分析新的反射率比率以確定污染物層之厚度及光學特性。利用先前確定(且現在固定)之厚及薄SiO₂ 以及中間層特性，可約束分析。另外，可在污染物生長的各階段收集比率資料以提供多個比率，每一比率具有不同的污染物厚度(多樣本分析)，但是另外具有共同的污染物光學特性。或者，若不能利用相同的污染物光學特性來擬合全部多個樣本，則可在假設不均勻污染物層、粗糙界面或表面等的情況下模型化額外複雜性。4 Measure the sample after the accumulation of contaminants. A new dispersion ratio is analyzed using a dispersion model with adjustable optical properties to determine the thickness and optical properties of the contaminant layer. The analysis can be constrained by the previously determined (and now fixed) thickness and thin SiO ₂ and intermediate layer characteristics. Additionally, ratio data can be collected at various stages of contaminant growth to provide multiple ratios, each having a different contaminant thickness (multi-sample analysis), but additionally having a common contaminant optical characteristic. Alternatively, if the same contaminant optical properties cannot be used to fit all of the multiple samples, additional complexity can be modeled assuming a non-uniform contaminant layer, a rough interface or surface, and the like.

5分析之結果為污染物層之厚度及污染物層之光學特性的表或分散。5 The result of the analysis is the surface or dispersion of the thickness of the contaminant layer and the optical properties of the contaminant layer.

6在隨後校準程序期間，分析反射率比率以確定樣本上一(或多種)類型之污染物的厚度，接著可利用該等厚度來導出該等樣本中之至少一者的反射率。在校準程序期間，通常將使污染物層之光學特性固定，從而減少未知參數的數目。6 During the subsequent calibration procedure, the reflectance ratio is analyzed to determine the thickness of the contaminant(s) of the type(s) on the sample, which thicknesses can then be utilized to derive the reflectivity of at least one of the samples. During the calibration procedure, the optical properties of the contaminant layer will typically be fixed, thereby reducing the number of unknown parameters.

應瞭解，雖然此係一種在比率量測中用於預特徵化已知數量的方法，但是其並非唯一的方式。詳言之，替代的計量學技術可用於確定界面厚度或獲得對標稱膜之更好的光學描述(例如，SiO₂ 、MgF₂ 、Si或甚至污染物光學特性)。在適用時，可自文獻獲得光學參數。在預特徵化期間確定之參數在校準程序期間通常將保持固定，其通常將僅確定預期會變化的彼等參數。初始樣本之特定膜結構無需限於SiO₂ /Si結構。可推廣該程序且在眾多樣本而不是僅兩個樣本上誘發污染物生長。It should be understood that although this is a method for pre-characterizing a known number in ratiometric measurements, it is not the only way. In particular, alternative metrology techniques can be used to determine interface thickness or to obtain a better optical description of the nominal film (eg, SiO ₂ , MgF ₂ , Si, or even contaminant optical properties). Optical parameters can be obtained from the literature when applicable. The parameters determined during the pre-characterization will typically remain fixed during the calibration procedure, which will typically only determine which parameters are expected to change. The specific film structure of the initial sample need not be limited to the SiO ₂ /Si structure. This procedure can be generalized and induce contaminant growth on numerous samples rather than just two samples.

亦可指出，關於分析反射率比率，在一些情況下，當分母反射率接近零時，比率可變得不定。實務上，此條件將為顯而易見的，因為比率將傾向於變得非常大。在此等情況下，發生此情況之光譜區可脫離該分析，或改為在彼等區中分析反比率。It may also be noted that with regard to analyzing the reflectance ratio, in some cases, the ratio may become indefinite as the denominator reflectance approaches zero. In practice, this condition will be obvious because the ratio will tend to become very large. In such cases, the spectral regions in which this occurs may deviate from the analysis or instead analyze the inverse ratios in their regions.

因為通常自比率分析確定所有校準樣本之絕對反射率，且對樣本之任一者的校準原則上將產生相同I₀ ，所以無需利用僅有的一樣本對於整個量測波長範圍校準I₀ 。舉例而言，樣本1可用於對於一光譜區確定I₀ ，而樣本2用於校準第二光譜區。Since the absolute reflectivity of all calibration samples is typically determined from the ratio analysis, and the calibration of either of the samples will in principle produce the same I ₀ , there is no need to calibrate I ₀ for the entire measurement wavelength range with the same. For example, sample 1 can be used to determine I ₀ for a spectral region and sample 2 is used to calibrate a second spectral region.

鑒於此描述，熟習此項技術者將明白本發明之另外修改及替代實施例。因此，此描述將僅被視作說明性的且係為了教示熟習此項技術者執行本發明之方式。將瞭解，本文所展示且描述之本發明的形式將被視作目前較佳實施例。在受益於本發明之此描述之後，熟習此項技術者將明白，等效元件可替換本文所說明並描述之元件且本發明之某些特點可獨立於其他特點之使用予以使用。In view of this description, additional modifications and alternative embodiments of the invention will be apparent to those skilled in the art. Accordingly, the description is to be regarded as illustrative only and illustrative of the embodiments of the invention. It will be appreciated that the form of the invention shown and described herein is to be considered as a presently preferred embodiment. Those skilled in the art will appreciate that equivalent elements can be substituted for the elements described and described herein and that certain features of the invention can be used independently of other features.

102．．．流程圖102. . . flow chart

202．．．流程圖202. . . flow chart

302．．．反射光譜302. . . Reflectance spectrum

304．．．反射光譜304. . . Reflectance spectrum

306．．．曲線306. . . curve

308．．．曲線308. . . curve

310．．．曲線310. . . curve

502．．．流程圖502. . . flow chart

602．．．光譜602. . . spectrum

604．．．光譜604. . . spectrum

702．．．反射光譜702. . . Reflectance spectrum

802．．．信號802. . . signal

902．．．CEF/參考反射率乘積導數信號902. . . CEF/reference reflectance product derivative signal

1002．．．曲線1002. . . curve

1004．．．曲線1004. . . curve

1102．．．反射光譜1102. . . Reflectance spectrum

1202．．．流程圖1202. . . flow chart

1302．．．靈敏度曲線1302. . . Sensitivity curve

1402．．．展開圖1402. . . Expanded view

1502．．．流程圖1502. . . flow chart

1602．．．靈敏度曲線1602. . . Sensitivity curve

1702．．．靈敏度曲線1702. . . Sensitivity curve

1802．．．靈敏度曲線1802. . . Sensitivity curve

1804．．．靈敏度曲線1804. . . Sensitivity curve

1902．．．靈敏度曲線1902. . . Sensitivity curve

2002．．．靈敏度曲線2002. . . Sensitivity curve

2102．．．曲線2102. . . curve

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2902．．．曲線2902. . . curve

2904．．．曲線2904. . . curve

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2920．．．曲線2920. . . curve

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2924．．．曲線2924. . . curve

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2936．．．曲線2936. . . curve

3201．．．源3201. . . source

3202．．．環境密封腔室3202. . . Environmentally sealed chamber

3203．．．源3203. . . source

3204．．．環境密封腔室3204. . . Environmentally sealed chamber

3206．．．樣本3206. . . sample

3210．．．樣本射束3210. . . Sample beam

3212．．．參考射束3212. . . Reference beam

3214．．．光譜儀3214. . . spectrometer

3216．．．光譜儀3216. . . spectrometer

3302．．．源3302. . . source

3304．．．光譜儀3304. . . spectrometer

3400．．．寬頻反射計系統3400. . . Broadband reflectometer system

BS．．．射束分離器BS. . . Beam splitter

FM－1~FM－4．．．內翻式面鏡FM-1~FM-4. . . Inverted mirror

M－1~M－9．．．面鏡M-1~M-9. . . Mask

S－1~S2．．．擋板S-1~S2. . . Baffle

W1~W6．．．視窗W1~W6. . . Windows

圖1說明用於反射計之先前技術校準及量測流程圖。Figure 1 illustrates a prior art calibration and measurement flow diagram for a reflectometer.

圖2說明用於反射計之先前技術詳細校準及量測流程圖。Figure 2 illustrates a prior art detailed calibration and measurement flow diagram for a reflectometer.

圖3說明來自超薄SiO₂ /Si樣本之反射光譜。Figure 3 illustrates the reflection spectrum from an ultra-thin SiO ₂ /Si sample.

圖4說明對於一系列假設厚度產生之20的SiO₂ /Si樣本的校準誤差光譜。Figure 4 illustrates 20 for a series of hypothetical thicknesses The calibration error spectrum of the SiO ₂ /Si sample.

圖5說明根據本發明之一實施例之例示性校準及量測流程圖。FIG. 5 illustrates an exemplary calibration and measurement flow diagram in accordance with an embodiment of the present invention.

圖6說明對於一系列假設厚度產生之10000的SiO₂ /Si樣本的校準誤差光譜。Figure 6 illustrates the 10,000 generated for a series of assumed thicknesses. The calibration error spectrum of the SiO ₂ /Si sample.

圖7說明由Acton Research公司製造之寬頻VUV面鏡(#1200)之反射光譜。Figure 7 illustrates the reflectance spectra of a broadband VUV mirror (#1200) manufactured by Acton Research.

圖8說明參考樣本反射光譜與自任意參考樣本之量測獲得之10000的SiO₂ /Si樣本之校準誤差函數的乘積。Figure 8 illustrates the reference sample reflectance spectrum and the measurement obtained from the measurement of any reference sample. The product of the calibration error function of the SiO ₂ /Si sample.

圖9說明對於10010假設厚度產生之10000的SiO₂ /Si樣本的校準誤差函數之導數。Figure 9 illustrates for 10010 Assume that the thickness is 10,000 The derivative of the calibration error function of the SiO ₂ /Si sample.

圖10說明利用10000的SiO₂ /Si標準樣本之校準誤差函數積分所計算的靈敏度曲線。Figure 10 illustrates the use of 10000 The sensitivity curve calculated by integrating the calibration error function of the SiO ₂ /Si standard sample.

圖11說明校準程序中所利用之參考樣本的反射率。Figure 11 illustrates the reflectivity of the reference samples utilized in the calibration procedure.

圖12說明根據本發明之一實施例之例示性詳細校準及量測流程圖。Figure 12 illustrates an exemplary detailed calibration and measurement flow diagram in accordance with an embodiment of the present invention.

圖12A說明可使用本發明之校準概念的例示性反射計系統。Figure 12A illustrates an exemplary reflectometry system in which the calibration concept of the present invention can be used.

圖13說明利用10000的SiO₂ /Si樣本之標準先前技術優點函數所計算的靈敏度曲線。Figure 13 illustrates the use of 10000 The sensitivity curve calculated by the standard prior art advantage function of the SiO ₂ /Si sample.

圖14說明在經量測之反射率資料上存在1%雜訊的情況下利用10000的SiO₂ /Si樣本之標準先前技術優點函數所計算的展開靈敏度曲線。Figure 14 illustrates the use of 10000 in the presence of 1% noise on the measured reflectance data. The expansion sensitivity curve calculated by the standard prior art advantage function of the SiO ₂ /Si sample.

圖15說明根據本發明之一實施例之例示性詳細量測流程圖。Figure 15 illustrates an exemplary detailed measurement flow diagram in accordance with an embodiment of the present invention.

圖16說明在經量測之反射率資料上存在1%雜訊的情況下利用10000的SiO₂ /Si樣本之MEF積分所計算的展開靈敏度曲線。Figure 16 illustrates the use of 10000 in the presence of 1% noise on the measured reflectance data. The expansion sensitivity curve calculated for the MEF integral of the SiO ₂ /Si sample.

圖17說明利用10000的SiO₂ /Si樣本之MEF積分所計算的靈敏度曲線。Figure 17 illustrates the use of 10000 The sensitivity curve calculated by the MEF integral of the SiO ₂ /Si sample.

圖18說明利用100的SiO₂ /Si樣本之MEF積分與標準先前技術優點函數所計算的靈敏度曲線的比較。Figure 18 illustrates the use of 100 The MEF integral of the SiO ₂ /Si sample is compared to the sensitivity curve calculated by the standard prior art advantage function.

圖19說明在經量測之反射率資料上存在1%雜訊的情況下利用100的SiO₂ /Si樣本之MEF積分所計算的展開靈敏度曲線。Figure 19 illustrates the use of 100 in the presence of 1% noise on the measured reflectance data. The expansion sensitivity curve calculated for the MEF integral of the SiO ₂ /Si sample.

圖20說明在經量測之反射率資料上存在1%雜訊的情況下利用100的SiO₂ /Si樣本之標準先前技術優點函數所計算的展開靈敏度曲線。Figure 20 illustrates the use of 100 in the presence of 1% noise on the measured reflectance data. The expansion sensitivity curve calculated by the standard prior art advantage function of the SiO ₂ /Si sample.

圖21A及圖21B說明兩個校準樣本之相對反射率比率的曲線，其中較薄氧化物在該等樣本之一者上變化。21A and 21B illustrate plots of relative reflectance ratios for two calibration samples, with thinner oxides varying on one of the samples.

圖22A及圖22B說明兩個校準樣本之相對反射率的曲線，其中較厚氧化物在該等樣本之一者上變化。22A and 22B illustrate plots of relative reflectance of two calibration samples in which a thicker oxide varies over one of the samples.

圖23A及圖23B說明具有不同厚度的污染物層之兩個校準樣本之相對反射率的曲線。23A and 23B illustrate plots of relative reflectance of two calibration samples of contaminant layers having different thicknesses.

圖24說明兩個校準樣本之例示性機械實施例。Figure 24 illustrates an exemplary mechanical embodiment of two calibration samples.

圖25說明使用兩個校準樣本之反射率比率來校準反射計量測的例示性技術之流程圖。Figure 25 illustrates a flow diagram of an exemplary technique for calibrating reflectance measurements using reflectance ratios of two calibration samples.

圖26說明使用兩個校準樣本之反射率比率來校準反射計量測的例示性技術之另一流程圖。Figure 26 illustrates another flow diagram of an exemplary technique for calibrating reflective metrology using reflectance ratios of two calibration samples.

圖27說明自兩個校準樣本擬合之反射率比率之結果的曲線，一校準樣本具有薄氧化物且一校準樣本具有較厚氧化物。Figure 27 illustrates a plot of the results of the reflectance ratios fitted from two calibration samples, one calibration sample having a thin oxide and one calibration sample having a thicker oxide.

圖28A至圖28D說明污染物層反射率對薄氧化物樣本及厚氧化物樣本之反射率的影響的曲線。28A-28D illustrate curves of the effect of contaminant layer reflectivity on the reflectance of thin oxide samples and thick oxide samples.

圖29A至圖29L說明具有污染物層累積之各種樣本之反射率比率的曲線。29A-29L illustrate curves of reflectance ratios for various samples with accumulation of contaminant layers.

(無元件符號說明)(no component symbol description)

Claims (117)

一種校準一獲得反射率資料之系統的方法，其包含：自一第一校準樣本獲得反射率資料，自一第二校準樣本獲得反射率資料，其中該第一校準樣本及該第二校準樣本中之至少一者的若干確切特性可與該等校準樣本之若干假設特性不同，且其中該第一校準樣本與該第二校準樣本之反射特性不同；及使用一基於自該第一校準樣本獲得之資料與自該第二校準樣本獲得之資料的比率，以便輔助校準該系統。 A method of calibrating a system for obtaining reflectance data, comprising: obtaining reflectance data from a first calibration sample, obtaining reflectance data from a second calibration sample, wherein the first calibration sample and the second calibration sample are Certain exact characteristics of at least one of the plurality may be different from a plurality of hypothetical characteristics of the calibration samples, and wherein the first calibration sample is different from the second calibration sample; and using a prediction based on the first calibration sample The ratio of the data to the data obtained from the second calibration sample to aid in calibrating the system. 如請求項1之方法，其中自該第一校準樣本收集第一組反射率資料，該第一校準樣本在一需要校準之第一波長範圍中具有一校準誤差函數，且自該第二校準樣本收集第二組反射率資料，該第二校準樣本與標準樣本相比在該第一波長範圍中具有較少光譜特點。 The method of claim 1, wherein the first set of reflectance data is collected from the first calibration sample, the first calibration sample having a calibration error function in a first wavelength range that requires calibration, and from the second calibration sample A second set of reflectance data is collected, the second calibration sample having less spectral characteristics in the first wavelength range than the standard sample. 如請求項2之方法，其中與該第二校準樣本上之一較薄氧化物相比，該第一校準樣本具有一較厚氧化物。 The method of claim 2, wherein the first calibration sample has a thicker oxide than the thinner oxide on the second calibration sample. 如請求項3之方法，其中該第一校準樣本包含一SiO₂ /Si結構且該第二校準樣本包含一SiO₂ /Si結構。The method of claim 3, wherein the first calibration sample comprises a SiO ₂ /Si structure and the second calibration sample comprises a SiO ₂ /Si structure. 如請求項4之方法，其中該第二校準樣本上之該較薄氧化物為一原生氧化物膜。 The method of claim 4, wherein the thinner oxide on the second calibration sample is a native oxide film. 如請求項1之方法，其中來自該第一校準樣本之該反射率資料已自來自該第二校準樣本之該反射率資料去耦合。 The method of claim 1, wherein the reflectance data from the first calibration sample has been decoupled from the reflectance data from the second calibration sample. 如請求項6之方法，其中與該第二校準樣本上之一較薄 氧化物相比，該第一校準樣本具有一較厚氧化物。 The method of claim 6, wherein the method is thinner than the second calibration sample The first calibration sample has a thicker oxide compared to the oxide. 如請求項6之方法，其中該第二校準樣本上之該較薄氧化物為一原生氧化物。 The method of claim 6, wherein the thinner oxide on the second calibration sample is a native oxide. 如請求項8之方法，其中該第一校準樣本包含一SiO₂ /Si結構且該第二校準樣本包含一SiO₂ /Si結構。The method of claim 8, wherein the first calibration sample comprises a SiO ₂ /Si structure and the second calibration sample comprises a SiO ₂ /Si structure. 如請求項1之方法，其中與該第二校準樣本上之一較薄氧化物相比，該第一校準樣本具有一較厚氧化物。 The method of claim 1, wherein the first calibration sample has a thicker oxide than a thinner oxide on the second calibration sample. 如請求項10之方法，其中該第一校準樣本包含一SiO₂ /Si結構且該第二校準樣本包含一SiO₂ /Si結構。The method of claim 10, wherein the first calibration sample comprises a SiO ₂ /Si structure and the second calibration sample comprises a SiO ₂ /Si structure. 如請求項10之方法，其中該第二校準樣本為一光譜上無特點的參考樣本。 The method of claim 10, wherein the second calibration sample is a spectrally uncharacterized reference sample. 如請求項10之方法，其中該第一校準樣本及該第二校準樣本之該等反射特性已自彼此去耦合，以致可基於該第一校準樣本及該第二校準樣本之所獲得的反射強度資料計算該第一校準樣本及該第二校準樣本中之至少一者的若干實際物理特性。 The method of claim 10, wherein the reflection characteristics of the first calibration sample and the second calibration sample have been decoupled from each other such that a reflection intensity obtainable based on the first calibration sample and the second calibration sample The data calculates a number of actual physical characteristics of at least one of the first calibration sample and the second calibration sample. 如請求項1之方法，其中該使用步驟進一步包含：組態一校準程序以使用來自該第一校準樣本之第一組反射率資料且至少部分地基於該第一組反射率資料而提供對該系統之一第一校準；及組態該校準程序以使用來自該第二校準樣本之第二組反射率資料，該第二組反射率資料具有比該第一組反射率資料少的特點。 The method of claim 1, wherein the using step further comprises: configuring a calibration procedure to provide a first set of reflectance data from the first calibration sample and based at least in part on the first set of reflectance data a first calibration of the system; and configuring the calibration procedure to use a second set of reflectance data from the second calibration sample, the second set of reflectance data having fewer features than the first set of reflectance data. 如請求項1之方法，其中自該第一校準樣本獲得之該資 料為強度資料，且自該第二校準樣本獲得之該資料為強度資料。 The method of claim 1, wherein the capital obtained from the first calibration sample The material is the intensity data, and the data obtained from the second calibration sample is the intensity data. 如請求項15之方法，其中自該第一校準樣本之強度資料及該第二校準樣本之強度資料獲得一反射率比率。 The method of claim 15, wherein a reflectance ratio is obtained from the intensity data of the first calibration sample and the intensity data of the second calibration sample. 如請求項16之方法，其中經由利用該反射率比率獲得一源強度輪廓且藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 16, wherein a source intensity profile is obtained by utilizing the reflectance ratio and the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 一種校準一反射計之方法，其包含：提供一第一校準樣本及一第二校準樣本，其中該第一校準樣本及該第二校準樣本之反射特性不同；自該第一校準樣本收集第一組資料；自該第二校準樣本收集第二組資料；及使用該第一組資料之至少一部分與該第二組資料之至少一部分的一比率來確定該第一校準樣本與該第二校準樣本中之至少一者的一特性，以使得可校準來自一未知樣本的反射率資料。 A method for calibrating a reflectometer, comprising: providing a first calibration sample and a second calibration sample, wherein the first calibration sample and the second calibration sample have different reflection characteristics; collecting the first from the first calibration sample Group data; collecting a second set of data from the second calibration sample; and determining a first calibration sample and the second calibration sample using a ratio of at least a portion of the first set of data to at least a portion of the second set of data A characteristic of at least one of the features such that reflectance data from an unknown sample can be calibrated. 如請求項18之方法，其中自該第一校準樣本獲得之該第一組資料包括強度資料且自該第二校準樣本獲得之該第二組資料包括強度資料。 The method of claim 18, wherein the first set of data obtained from the first calibration sample comprises intensity data and the second set of data obtained from the second calibration sample comprises intensity data. 如請求項19之方法，其中自該第一校準樣本之該強度資料及該第二校準樣本之該強度資料獲得一反射率比率。 The method of claim 19, wherein a ratio of reflectance is obtained from the intensity data of the first calibration sample and the intensity data of the second calibration sample. 如請求項20之方法，其中經由利用該反射率比率獲得一源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 20, wherein a source intensity profile is obtained by utilizing the reflectance ratio and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項20之方法，其中預期該第一校準樣本及該第二校準樣本中之至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 20, wherein at least one of the first calibration sample and the second calibration sample is expected to exhibit several variations from a number of hypothetical physical characteristics thereof. 如請求項22之方法，其中可為該第一校準樣本及該第二校準樣本中之至少一者獲得一實際反射率，預期該至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 22, wherein an actual reflectance is obtained for at least one of the first calibration sample and the second calibration sample, the at least one being expected to exhibit a number of variations from a plurality of hypothetical physical characteristics thereof. 如請求項23之方法，其中經由利用該實際反射率獲得一源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 23, wherein a source intensity profile is obtained by utilizing the actual reflectivity and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項18之方法，其中預期該第一校準樣本及該第二校準樣本中之至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 18, wherein at least one of the first calibration sample and the second calibration sample is expected to exhibit several variations from a number of hypothetical physical characteristics thereof. 如請求項25之方法，其中預期該第一校準樣本及該第二校準樣本兩者之該等假設物理特性會有若干變化。 The method of claim 25, wherein the assumed physical characteristics of both the first calibration sample and the second calibration sample are expected to vary. 如請求項25之方法，其中使用該第一校準樣本及該第二校準樣本的該至少一者的一假設反射率來計算一初始源強度輪廓，預期該至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 25, wherein an initial source intensity profile is calculated using a hypothetical reflectivity of the at least one of the first calibration sample and the second calibration sample, the at least one expected to exhibit a number of hypothetical physics Several changes in characteristics. 如請求項27之方法，其中使用該第一校準樣本及該第二校準樣本的該至少一者的一經計算實際反射率來計算一經重新計算之源強度輪廓，預期該至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 27, wherein a recalculated source intensity profile is calculated using a calculated actual reflectance of the at least one of the first calibration sample and the second calibration sample, the at least one being expected to exhibit Several variations of assumed physical characteristics. 如請求項18之方法，其中來自該第一校準樣本之該第一組資料已自來自該第二校準樣本之該第二組資料去耦 合。 The method of claim 18, wherein the first set of data from the first calibration sample has been decoupled from the second set of data from the second calibration sample Hehe. 如請求項18之方法，其中與該第二校準樣本上之一較薄氧化物相比，該第一校準樣本具有一較厚氧化物。 The method of claim 18, wherein the first calibration sample has a thicker oxide than a thinner oxide on the second calibration sample. 如請求項30之方法，其中該第一校準樣本包含一SiO₂ /Si結構且該第二校準樣本包含一SiO₂ /Si結構。The method of claim 30, wherein the first calibration sample comprises a SiO ₂ /Si structure and the second calibration sample comprises a SiO ₂ /Si structure. 如請求項31之方法，其中該第二校準樣本上之該較薄氧化物為一原生氧化物。 The method of claim 31, wherein the thinner oxide on the second calibration sample is a native oxide. 一種校準一反射計之方法，其中該反射計在包括深紫外(DUV)波長以下之至少一些波長的波長處操作，該方法包含：提供一第一校準樣本及一第二校準樣本，其中該第一校準樣本及該第二校準樣本之若干反射特性不同；自一第一校準樣本收集第一組資料，該第一組資料包括對於在DUV波長以下之波長收集的至少一些強度資料；自該第二校準樣本收集第二組資料，該第二組資料包括對於在DUV波長以下之波長收集的至少一些強度資料；及使用一基於該第一組資料與該第二組資料之比率來確定該第一校準樣本及該第二校準樣本中之至少一者的一反射率，以便輔助在包括至少一些DUV波長的波長處校準該反射計。 A method of calibrating a reflectometer, wherein the reflectometer operates at a wavelength comprising at least some wavelengths below a deep ultraviolet (DUV) wavelength, the method comprising: providing a first calibration sample and a second calibration sample, wherein the a plurality of reflection characteristics of a calibration sample and the second calibration sample are different; collecting a first set of data from a first calibration sample, the first set of data comprising at least some intensity data collected for wavelengths below a DUV wavelength; The second calibration sample collects a second set of data comprising at least some intensity data collected for wavelengths below the DUV wavelength; and using a ratio based on the first set of data to the second set of data to determine the first A reflectivity of at least one of the calibration sample and the second calibration sample to assist in calibrating the reflectometer at a wavelength comprising at least some of the DUV wavelengths. 如請求項33之方法，其中該第一校準樣本及該第二校準樣本之該等反射特性已自彼此去耦合，以致可基於該第 一校準樣本及該第二校準樣本之已獲得的強度資料來計算該第一校準樣本及該二校準樣本中之至少一者的若干實際物理特性。 The method of claim 33, wherein the reflection characteristics of the first calibration sample and the second calibration sample have been decoupled from each other such that the first A calibration sample and the obtained intensity data of the second calibration sample are used to calculate a plurality of actual physical characteristics of at least one of the first calibration sample and the second calibration sample. 如請求項33之方法，其中：該比率係基於自該第一校準樣本獲得之強度與自該第二校準樣本獲得之強度的一比率，經由利用該比率獲得一源強度輪廓，且藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 33, wherein: the ratio is based on a ratio of an intensity obtained from the first calibration sample to an intensity obtained from the second calibration sample, by using the ratio to obtain a source intensity profile, and by utilizing The source intensity profile is used to calibrate the reflectivity of an unknown sample. 如請求項33之方法，其中：使用該第一校準樣本之一假設反射率及該第一組資料來計算一初始源強度輪廓，使用該第二組資料及該初始源強度輪廓來獲得該第二校準樣本之一反射率，利用該第一校準樣本之假設反射率與該第二校準樣本之該已獲得之反射率的一比率來確定該第一校準樣本之一實際特性，且使用該第一校準樣本之一反射率來獲得一經重新計算之源強度輪廓，該反射率係基於該經確定之實際特性。 The method of claim 33, wherein: using one of the first calibration samples, assuming a reflectance and the first set of data to calculate an initial source intensity profile, using the second set of data and the initial source intensity profile to obtain the first a calibration rate of one of the calibration samples, using a ratio of the assumed reflectance of the first calibration sample to the obtained reflectance of the second calibration sample to determine an actual characteristic of the first calibration sample, and using the first A reflectance of one of the calibration samples is used to obtain a recalculated source intensity profile based on the determined actual characteristics. 如請求項36之方法，其中該第一校準樣本之該實際特性為一材料厚度。 The method of claim 36, wherein the actual characteristic of the first calibration sample is a material thickness. 如請求項33之方法，其中自該第一校準樣本之該強度資料及該第二校準樣本之該強度資料獲得一反射率比率。 The method of claim 33, wherein the intensity ratio from the intensity data of the first calibration sample and the intensity data of the second calibration sample is a reflectance ratio. 如請求項38之方法，其中經由利用該反射率比率獲得一 源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 38, wherein one is obtained by utilizing the reflectance ratio A source intensity profile and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項38之方法，其中預期該第一校準樣本及該第二校準樣本中之至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 38, wherein at least one of the first calibration sample and the second calibration sample is expected to exhibit several variations from a number of hypothetical physical characteristics thereof. 如請求項40之方法，其中可為該第一校準樣本及該第二校準樣本中之至少一者獲得一實際反射率，預期該至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 40, wherein an actual reflectivity is obtained for at least one of the first calibration sample and the second calibration sample, the at least one being expected to exhibit a number of variations from a plurality of hypothetical physical characteristics thereof. 如請求項41之方法，其中經由利用該實際反射率獲得一源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 41, wherein a source intensity profile is obtained by utilizing the actual reflectivity and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項33之方法，其中預期該第一校準樣本及該第二校準樣本中之至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 33, wherein at least one of the first calibration sample and the second calibration sample is expected to exhibit several variations from a number of hypothetical physical characteristics thereof. 如請求項33之方法，其中與該第二校準樣本上之一較薄氧化物相比，該第一校準樣本具有一較厚氧化物。 The method of claim 33, wherein the first calibration sample has a thicker oxide than a thinner oxide on the second calibration sample. 如請求項44之方法，其中該第一校準樣本包含一SiO₂ /Si結構且該第二校準樣本包含一SiO₂ /Si結構。The method of claim 44, wherein the first calibration sample comprises a SiO ₂ /Si structure and the second calibration sample comprises a SiO ₂ /Si structure. 如請求項45之方法，其中該第二校準樣本上之該較薄氧化物為一原生氧化物。 The method of claim 45, wherein the thinner oxide on the second calibration sample is a native oxide. 一種校準一反射計之方法，其包含：提供三個或三個以上的校準樣本，其中該等校準樣本之反射特性彼此不同；自該等校準樣本之每一者收集一組經量測資料；及 使用獨立於源強度I₀ 之該經量測資料的一組合來確定該等校準樣本中之至少一者的一特性以使得可校準來自一未知樣本之反射率資料。A method of calibrating a reflectometer, comprising: providing three or more calibration samples, wherein the calibration characteristics of the calibration samples are different from each other; collecting a set of measured data from each of the calibration samples; and used independent of the source intensity I ₀ of the measured data by determining a characteristic of a combination of these calibration samples of at least one of the calibration may be such that the reflectance of the data from an unknown sample. 如請求項47之方法，其中該等校準樣本中之一或多者具有一或多個污染物層，其中經由分析該經量測資料之該組合而確定該等污染物層之一或多個特性。 The method of claim 47, wherein one or more of the calibration samples have one or more contaminant layers, wherein one or more of the contaminant layers are determined by analyzing the combination of the measured data characteristic. 如請求項47之方法，其中自該等校準樣本收集之該資料包括強度資料。 The method of claim 47, wherein the data collected from the calibration samples comprises intensity data. 如請求項49之方法，其中自該等校準樣本之該強度資料獲得一或多個反射率比率。 The method of claim 49, wherein the intensity data from the calibration samples obtains one or more reflectance ratios. 如請求項50之方法，其中該等校準樣本中之一或多者具有一或多個污染物層，其中經由分析該等反射率比率中之一或多者而確定該等污染物層之一或多個特性。 The method of claim 50, wherein one or more of the calibration samples have one or more contaminant layers, wherein one of the contaminant layers is determined by analyzing one or more of the reflectance ratios Or multiple features. 如請求項50之方法，其中經由利用該等反射率比率獲得一源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 50, wherein a source intensity profile is obtained by utilizing the reflectance ratios and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項52之方法，其中藉由首先利用薄膜模型及一回歸分析來分析該等反射率比率以調整該等校準樣本中之一或多者的一或多個特性而獲得該源強度輪廓，且其中該分析之一結果用於導出該等校準樣本中之一或多者的一絕對反射率，其中該絕對反射率用於經由I₀ =I_cal /R_cal 獲得該源強度輪廓，其中藉由利用該經確定之源強度輪廓經由R=I_r /I₀ 來校準一未知樣本之一反射率。The method of claim 52, wherein the source intensity profile is obtained by first analyzing the reflectance ratios using a thin film model and a regression analysis to adjust one or more characteristics of one or more of the calibration samples, And wherein one of the results of the analysis is used to derive an absolute reflectance of one or more of the calibration samples, wherein the absolute reflectance is used to obtain the source intensity profile via I ₀ =I _cal /R _cal , wherein using the intensity profile of the source determined by the R = I _r / I ₀ to calibrate one of a sample of unknown reflectivity. 如請求項49之方法，其中預期該等校準樣本中之至少一 者會展示出自其若干假設物理特性的若干變化。 The method of claim 49, wherein at least one of the calibration samples is expected The person will demonstrate several changes from several of its hypothetical physical characteristics. 如請求項54之方法，其中可為該等校準樣本中之至少一者獲得一實際反射率，預期該至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 54, wherein an actual reflectivity is obtainable for at least one of the calibration samples, the at least one being expected to exhibit a number of changes from a number of hypothetical physical characteristics thereof. 如請求項55之方法，其中經由利用該實際反射率獲得一源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 55, wherein a source intensity profile is obtained by utilizing the actual reflectance and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項47之方法，其中預期該等校準樣本中之至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 47, wherein at least one of the calibration samples is expected to exhibit several variations from a number of hypothetical physical characteristics thereof. 如請求項57之方法，其中預期所有該等校準樣本之該等假設物理特性會有若干變化。 The method of claim 57, wherein there are several variations in the assumed physical properties of all of the calibration samples. 如請求項57之方法，其中使用若干校準樣本的該至少一者的一假設反射率來計算一初始源強度輪廓，預期該至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 57, wherein a hypothetical reflectivity of the at least one of the plurality of calibration samples is used to calculate an initial source intensity profile, the at least one of which is expected to exhibit several variations from a number of hypothetical physical properties thereof. 如請求項59之方法，其中使用該至少一校準樣本的一經計算之實際反射率來計算一經重新計算之源強度輪廓，預期該至少一校準樣本會展示出自其若干假設物理特性的若干變化。 The method of claim 59, wherein a calculated recalculated source intensity profile is calculated using a calculated actual reflectance of the at least one calibration sample, the at least one calibration sample being expected to exhibit a number of variations from its plurality of hypothetical physical characteristics. 如請求項47之方法，其中以一去耦合待確定之該等參數的效應之方式組合來自該等校準樣本之該等資料。 The method of claim 47, wherein the data from the calibration samples are combined in a manner that decouples the effects of the parameters to be determined. 如請求項47之方法，其中該等三個或三個以上的校準樣本包含一具有一較薄膜之第一校準樣本、一具有一第一較厚膜之第二校準樣本及一具有一第二較厚膜之第三校準樣本，該第一較厚膜及該第二較厚膜為不同的膜。 The method of claim 47, wherein the three or more calibration samples comprise a first calibration sample having a thinner film, a second calibration sample having a first thicker film, and a second calibration sample For the third calibration sample of the thicker film, the first thicker film and the second thicker film are different films. 如請求項62之方法，其中該第一校準樣本包含一薄SiO₂ 膜，該第二校準樣本包含一較厚SiO₂ 膜，該第三校準樣本則包含一較厚MgF₂ 膜。The method of claim 62, wherein the first calibration sample comprises a thin SiO ₂ film, the second calibration sample comprises a thicker SiO ₂ film, and the third calibration sample comprises a thicker MgF ₂ film. 如請求項63之方法，其中該第一校準樣本上之該薄SiO₂ 膜為一原生氧化物。The method of claim 63, wherein the thin SiO ₂ film on the first calibration sample is a native oxide. 如請求項64之方法，其中將一或多個污染物層明確地模型化成該等校準樣本中之一或多者的部分，其中經由利用經量測資料之該組合而確定該等污染物層之一或多個特性。 The method of claim 64, wherein the one or more contaminant layers are explicitly modeled into portions of one or more of the calibration samples, wherein the contaminant layers are determined via the use of the combination of the measured data One or more characteristics. 如請求項65之方法，其中將一SiO₂ /Si介面層明確地模型化成該等校準樣本中之一或多者的部分。The method of claim 65, wherein a SiO ₂ /Si interface layer is explicitly modeled as part of one or more of the calibration samples. 如請求項66之方法，其中該SiO₂ /Si介面層厚度經預特徵化且在該校準期間保持固定。The method of claim 66, wherein the SiO ₂ /Si interface layer thickness is pre-characterized and remains fixed during the calibration. 如請求項65之方法，其中將一MgF₂ /Si介面層明確地模型化成該等校準樣本之部分。The method of claim 65, wherein a MgF ₂ /Si interface layer is explicitly modeled as part of the calibration samples. 如請求項68之方法，其中該MgF₂ /Si介面層厚度經預特徵化且在該校準期間保持固定。The method of claim 68, wherein the MgF ₂ /Si interface layer thickness is pre-characterized and remains fixed during the calibration. 如請求項47之方法，其中該等校準樣本中之一或多者具有一或多個污染物層，其中經由分析該經量測資料之該組合而確定該等污染物層之一或多個特性。 The method of claim 47, wherein one or more of the calibration samples have one or more contaminant layers, wherein one or more of the contaminant layers are determined by analyzing the combination of the measured data characteristic. 如請求項47之方法，其中自該等校準樣本收集之該資料包括強度資料。 The method of claim 47, wherein the data collected from the calibration samples comprises intensity data. 如請求項71之方法，其中自該等校準樣本之該強度資料獲得一或多個反射率比率。 The method of claim 71, wherein the intensity data from the calibration samples obtains one or more reflectance ratios. 如請求項72之方法，其中該等校準樣本中之一或多者具有一或多個污染物層，其中經由分析該等反射率比率中之一或多者而確定該等污染物層之一或多個特性。 The method of claim 72, wherein one or more of the calibration samples have one or more contaminant layers, wherein one of the contaminant layers is determined by analyzing one or more of the reflectance ratios Or multiple features. 如請求項72之方法，其中經由利用該等反射率比率獲得一源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 72, wherein a source intensity profile is obtained by utilizing the reflectance ratios and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項74之方法，其中藉由首先利用薄膜模型及一回歸分析來分析該等反射率比率以調整該等校準樣本中之一或多者的一或多個特性而獲得該源強度輪廓，且其中該分析之一結果用於導出該等校準樣本中之一或多者的一絕對反射率，其中該絕對反射率用於經由I₀ =I_cal /R_cal 獲得該源強度輪廓，其中藉由利用該經確定之源強度輪廓經由R=I_r /I₀ 來校準一未知樣本之一反射率。The method of claim 74, wherein the source intensity profile is obtained by first analyzing the reflectance ratios using a thin film model and a regression analysis to adjust one or more characteristics of one or more of the calibration samples, And wherein one of the results of the analysis is used to derive an absolute reflectance of one or more of the calibration samples, wherein the absolute reflectance is used to obtain the source intensity profile via I ₀ =I _cal /R _cal , wherein using the intensity profile of the source determined by the R = I _r / I ₀ to calibrate one of a sample of unknown reflectivity. 如請求項72之方法，其中預期該等校準樣本中之至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 72, wherein at least one of the calibration samples is expected to exhibit several variations from a number of hypothetical physical characteristics thereof. 如請求項76之方法，其中可為該等校準樣本中之至少一者獲得一實際反射率，預期該至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 76, wherein an actual reflectivity is obtainable for at least one of the calibration samples, the at least one being expected to exhibit a number of variations from a number of hypothetical physical characteristics thereof. 如請求項77之方法，其中經由利用該實際反射率獲得一源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 77, wherein a source intensity profile is obtained by utilizing the actual reflectivity and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項47之方法，其中預期該等校準樣本中之至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 47, wherein at least one of the calibration samples is expected to exhibit several variations from a number of hypothetical physical characteristics thereof. 如請求項79之方法，其中預期所有該等校準樣本之該等 假設物理特性會有若干變化。 The method of claim 79, wherein all of the calibration samples are expected to be such Suppose there are several changes in physical properties. 如請求項79之方法，其中使用若干校準樣本之該至少一者的一假設反射率來計算一初始源強度輪廓，預期該至少一者會展示出自其若干假設物理特性的若干變化。 The method of claim 79, wherein a hypothetical reflectivity of the at least one of the plurality of calibration samples is used to calculate an initial source intensity profile, the at least one of which is expected to exhibit several variations from a number of hypothetical physical properties thereof. 如請求項81之方法，其中使用該至少一校準樣本的一經計算之實際反射率來計算一經重新計算之源強度輪廓，預期該至少一校準樣本會展示出自其若干假設物理特性的若干變化。 A method of claim 81, wherein a calculated recalculated source intensity profile is calculated using a calculated actual reflectance of the at least one calibration sample, the at least one calibration sample being expected to exhibit a number of variations from its plurality of hypothetical physical properties. 如請求項47之方法，其中以一去耦合待確定之該等參數之效應的方式組合來自該等校準樣本之該等資料。 The method of claim 47, wherein the data from the calibration samples is combined in a manner that decouples the effects of the parameters to be determined. 一種校準一反射計之方法，其中該反射計在包括在深紫外(DUV)波長以下之至少一些波長的波長處操作，該方法包含：提供複數個校準樣本，其中至少一些該等校準樣本之反射特性為不同的；自該等校準樣本收集資料組，其包括對於在DUV波長以下之波長收集的至少一些強度資料；及使用該等資料組的一獨立於一源強度I₀ 之組合來確定該等校準樣本中之至少一者的一反射率以輔助在包括在DUV波長以下之至少一些波長處校準該反射計。A method of calibrating a reflectometer, wherein the reflectometer operates at a wavelength comprising at least some wavelengths below a deep ultraviolet (DUV) wavelength, the method comprising: providing a plurality of calibration samples, wherein at least some of the calibration samples are reflected The characteristics are different; collecting data sets from the calibration samples, including at least some intensity data collected for wavelengths below the DUV wavelength; and using a combination of the data sets independently of a source intensity I ₀ to determine A reflectivity of at least one of the calibration samples to assist in calibrating the reflectometer at at least some of the wavelengths included below the DUV wavelength. 如請求項84之方法，其中該等校準樣本中之一或多者具有一或多個污染物層，其中經由分析若干資料組之該組合而確定該等污染物層之一或多個特性。 The method of claim 84, wherein one or more of the calibration samples have one or more contaminant layers, wherein one or more characteristics of the contaminant layers are determined by analyzing the combination of the plurality of data sets. 如請求項84之方法，其中該等校準樣本之若干反射特性 已自彼此去耦合以致可基於該等校準樣本之該等已獲得之強度資料來計算該等校準樣本中之至少一者的若干實際物理特性。 The method of claim 84, wherein the plurality of reflection characteristics of the calibration samples Decoupled from each other such that a number of actual physical characteristics of at least one of the calibration samples can be calculated based on the obtained intensity data of the calibration samples. 如請求項84之方法，其中：該等資料組之該組合包含自該等校準樣本獲得之若干強度的若干比率，經由利用該等比率獲得一源強度輪廓，及藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 84, wherein: the combination of the data sets includes a plurality of ratios of the plurality of intensities obtained from the calibration samples, obtaining a source intensity profile by utilizing the ratios, and utilizing the source intensity profiles Calibrate the reflectivity of an unknown sample. 如請求項84之方法，其中：使用該等校準樣本之一第一校準樣本的一假設反射率及對應之資料組來計算一初始源強度輪廓，藉由使用對應之資料組及該初始源強度輪廓來獲得其他校準樣本中之一或多者的一反射率，利用該第一校準樣本之假設反射率與該等其他校準樣本中之一或多者的該已獲得之反射率之一比率來確定該第一校準樣本之一實際特性，及使用該第一校準樣本之一反射率來獲得一經重新計算之源強度輪廓，該反射率係基於該經確定之實際特性。 The method of claim 84, wherein: using a hypothetical reflectivity of the first calibration sample of the one of the calibration samples and the corresponding data set to calculate an initial source intensity profile, by using the corresponding data set and the initial source intensity Contouring to obtain a reflectance of one or more of the other calibration samples, using a ratio of a hypothetical reflectance of the first calibration sample to a ratio of the obtained reflectance of one or more of the other calibration samples Determining an actual characteristic of the first calibration sample and using a reflectance of the first calibration sample to obtain a recalculated source intensity profile based on the determined actual characteristic. 如請求項88之方法，其中該第一校準樣本之該實際特性為一材料厚度。 The method of claim 88, wherein the actual characteristic of the first calibration sample is a material thickness. 如請求項84之方法，其中自該等校準樣本之該等強度資料獲得若干反射率比率。 The method of claim 84, wherein the plurality of reflectance ratios are obtained from the intensity data of the calibration samples. 如請求項90之方法，其中該等校準樣本中之一或多者具有一或多個污染物層，其中經由分析該反射率比率而確 定該等污染物層之一或多個特性。 The method of claim 90, wherein one or more of the calibration samples have one or more contaminant layers, wherein by analyzing the reflectance ratio Determining one or more characteristics of the contaminant layers. 如請求項90之方法，其中經由利用該等反射率比率獲得一源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 90, wherein a source intensity profile is obtained by utilizing the reflectance ratios and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項90之方法，其中預期該等校準樣本中之一或多者會展示出自其若干假設物理特性的若干變化。 The method of claim 90, wherein one or more of the calibration samples are expected to exhibit a number of changes from a number of hypothetical physical characteristics thereof. 如請求項93之方法，其中可為該或該等校準樣本獲得一實際反射率，預期該或該等校準樣本會展示出自其若干假設物理特性的若干變化。 The method of claim 93, wherein an actual reflectance is obtained for the or the calibration samples, and the or the calibration samples are expected to exhibit several variations from a number of hypothetical physical properties thereof. 如請求項94之方法，其中經由利用該實際反射率獲得一源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 94, wherein a source intensity profile is obtained by utilizing the actual reflectivity and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項84之方法，其中預期該等校準樣本中之一或多者會展示出自其若干假設物理特性的若干變化。 The method of claim 84, wherein one or more of the calibration samples are expected to exhibit several variations from a number of hypothetical physical characteristics thereof. 如請求項84之方法，其中提供三個或三個以上的校準樣本。 The method of claim 84, wherein three or more calibration samples are provided. 如請求項97之方法，其中該等三個或三個以上的校準樣本包含一具有一較薄膜之第一校準樣本、一具有一第一較厚膜之第二校準樣本及一具有一第二較厚膜之第三校準樣本，該第一較厚膜及該第二較厚膜為不同的膜。 The method of claim 97, wherein the three or more calibration samples comprise a first calibration sample having a thinner film, a second calibration sample having a first thicker film, and a second calibration sample For the third calibration sample of the thicker film, the first thicker film and the second thicker film are different films. 如請求項98之方法，其中該第一校準樣本包含一薄SiO₂ 膜，該第二校準樣本包含一較厚SiO₂ 膜，且該第三校準樣本包含一較厚MgF₂ 膜。The method of claim 98, wherein the first calibration sample comprises a thin SiO ₂ film, the second calibration sample comprises a thicker SiO ₂ film, and the third calibration sample comprises a thicker MgF ₂ film. 如請求項99之方法，其中該第一校準樣本上之該薄SiO₂ 膜為一原生氧化物。The method of claim 99, wherein the thin SiO ₂ film on the first calibration sample is a native oxide. 如請求項100之方法，其中將一或多個污染物層明確地模型化成該等校準樣本之三者或三者以上的部分，其中經由利用該等資料組之該組合而確定該等污染物層之一或多個特性。 The method of claim 100, wherein the one or more contaminant layers are explicitly modeled into three or more of the calibration samples, wherein the contaminants are determined by utilizing the combination of the data sets One or more characteristics of a layer. 如請求項101之方法，其中將一SiO₂ /Si介面層明確地模型化成該等校準樣本中之一或多者的部分。The method of claim 101, wherein a SiO ₂ /Si interface layer is explicitly modeled as part of one or more of the calibration samples. 如請求項102之方法，其中該SiO₂ /Si介面層厚度經預特徵化且在該校準期間保持固定。The method of claim 102, wherein the SiO ₂ /Si interface layer thickness is pre-characterized and remains fixed during the calibration. 如請求項101之方法，其中將一MgF₂ /Si介面層明確地模型化成該等校準樣本之部分。The method of claim 101, wherein a MgF ₂ /Si interface layer is explicitly modeled as part of the calibration samples. 如請求項104之方法，其中該MgF₂ /Si介面層厚度經預特徵化且在該校準期間保持固定。The method of claim 104, wherein the MgF ₂ /Si interface layer thickness is pre-characterized and remains fixed during the calibration. 如請求項84之方法，其中該等校準樣本中之一或多者具有一或多個污染物層，其中經由分析若干資料組之該組合而確定該等污染物層之一或多個特性。 The method of claim 84, wherein one or more of the calibration samples have one or more contaminant layers, wherein one or more characteristics of the contaminant layers are determined by analyzing the combination of the plurality of data sets. 如請求項84之方法，其中該等校準樣本之反射特性已自彼此去耦合以致可基於該等校準樣本之該等已獲得的強度資料來計算該等校準樣本中之至少一者的若干實際物理特性。 The method of claim 84, wherein the reflection characteristics of the calibration samples have been decoupled from each other such that a plurality of actual physics of at least one of the calibration samples can be calculated based on the obtained intensity data of the calibration samples characteristic. 如請求項84之方法，其中：該等資料組之該組合包含自該等校準樣本獲得之若干強度比率，經由利用該等比率獲得一源強度輪廓，及 藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 84, wherein: the combination of the data sets includes a plurality of intensity ratios obtained from the calibration samples, obtaining a source intensity profile by utilizing the ratios, and The reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項84之方法，其中：使用該等校準樣本之一第一校準樣本的一假設反射率及該對應之資料組來計算一初始源強度輪廓，藉由使用該對應之資料組及該初始源強度輪廓來獲得該等其他校準樣本中之一或多者的一反射率，利用該第一校準樣本之假設反射率與該等其他校準樣本中之一或多者的該已獲得之反射率之一比率來確定該第一校準樣本之一實際特性，及使用該第一校準樣本之一反射率獲得一經重新計算之源強度輪廓，該反射率係基於該經確定之實際特性。 The method of claim 84, wherein: using a hypothetical reflectivity of the first calibration sample of the one of the calibration samples and the corresponding data set to calculate an initial source intensity profile, by using the corresponding data set and the initial Source intensity profile to obtain a reflectance of one or more of the other calibration samples, utilizing the assumed reflectance of the first calibration sample and the obtained reflectance of one or more of the other calibration samples One ratio is used to determine an actual characteristic of the first calibration sample, and a recalculated source intensity profile is obtained using one of the first calibration samples, the reflectivity being based on the determined actual characteristic. 如請求項109之方法，其中該第一校準樣本之該實際特性為一材料厚度。 The method of claim 109, wherein the actual characteristic of the first calibration sample is a material thickness. 如請求項84之方法，其中自該等校準樣本之該等強度資料獲得若干反射率比率。 The method of claim 84, wherein the plurality of reflectance ratios are obtained from the intensity data of the calibration samples. 如請求項111之方法，其中該等校準樣本中之一或多者具有一或多個污染物層，其中經由分析該反射率比率而確定該等污染物層之一或多個特性。 The method of claim 111, wherein one or more of the calibration samples have one or more contaminant layers, wherein one or more characteristics of the contaminant layers are determined by analyzing the reflectance ratio. 如請求項111之方法，其中經由利用該等反射率比率獲得一源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 111, wherein a source intensity profile is obtained by utilizing the reflectance ratios and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項111之方法，其中預期該等校準樣本中之一或多者會展示出自其若干假設物理特性的若干變化。 The method of claim 111, wherein one or more of the calibration samples are expected to exhibit several variations from a number of hypothetical physical characteristics thereof. 如請求項114之方法，其中可為該或該等校準樣本獲得 一實際反射率，預期該或該等校準樣本會展示出自其若干假設物理特性的若干變化。 The method of claim 114, wherein the calibration sample is obtained for the or the calibration sample For an actual reflectance, it is expected that the or the calibration sample will exhibit several variations from its several hypothetical physical properties. 如請求項115之方法，其中經由利用該實際反射率獲得一源強度輪廓且其中藉由利用該源強度輪廓來校準一未知樣本之反射率。 The method of claim 115, wherein a source intensity profile is obtained by utilizing the actual reflectivity and wherein the reflectance of an unknown sample is calibrated by utilizing the source intensity profile. 如請求項84之方法，其中預期該等校準樣本中之一或多者會展示出自其若干假設物理特性的若干變化。The method of claim 84, wherein one or more of the calibration samples are expected to exhibit several variations from a number of hypothetical physical characteristics thereof.