JP4988303B2 - Prediction method of ultrasonic bonding strength - Google Patents
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- H—ELECTRICITY
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- H01L2224/00—Indexing scheme for arrangements for connecting or disconnecting semiconductor or solid-state bodies and methods related thereto as covered by H01L24/00
- H01L2224/01—Means for bonding being attached to, or being formed on, the surface to be connected, e.g. chip-to-package, die-attach, "first-level" interconnects; Manufacturing methods related thereto
- H01L2224/10—Bump connectors; Manufacturing methods related thereto
- H01L2224/15—Structure, shape, material or disposition of the bump connectors after the connecting process
- H01L2224/16—Structure, shape, material or disposition of the bump connectors after the connecting process of an individual bump connector
- H01L2224/161—Disposition
- H01L2224/16151—Disposition the bump connector connecting between a semiconductor or solid-state body and an item not being a semiconductor or solid-state body, e.g. chip-to-substrate, chip-to-passive
- H01L2224/16221—Disposition the bump connector connecting between a semiconductor or solid-state body and an item not being a semiconductor or solid-state body, e.g. chip-to-substrate, chip-to-passive the body and the item being stacked
- H01L2224/16225—Disposition the bump connector connecting between a semiconductor or solid-state body and an item not being a semiconductor or solid-state body, e.g. chip-to-substrate, chip-to-passive the body and the item being stacked the item being non-metallic, e.g. insulating substrate with or without metallisation
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
- H01L2224/00—Indexing scheme for arrangements for connecting or disconnecting semiconductor or solid-state bodies and methods related thereto as covered by H01L24/00
- H01L2224/80—Methods for connecting semiconductor or other solid state bodies using means for bonding being attached to, or being formed on, the surface to be connected
- H01L2224/81—Methods for connecting semiconductor or other solid state bodies using means for bonding being attached to, or being formed on, the surface to be connected using a bump connector
Description
本発明は、金属バンプを熱超音波接合する場合において、荷重と温度と超音波出力とを含む接合条件より、理想的な接合が行われた場合の剪断強度を予測する超音波接合強度の予測方法に関するものである。 The present invention predicts ultrasonic bonding strength for predicting shear strength when ideal bonding is performed based on bonding conditions including load, temperature, and ultrasonic output when metal bumps are bonded by thermal ultrasonic bonding. It is about the method.
半導体チップの上に錨形状の金ワイヤバンプを形成し、これに荷重，熱，及び超音波を加えてプリント配線基板に実装する超音波フリップ実装がある（特許文献１，２参照）。この実装においては、バンプの接合強度が歩留りや信頼性を左右するため、接合条件などにより予め接合強度を把握（推定）しておくことが重要となっている。 There is ultrasonic flip mounting in which a saddle-shaped gold wire bump is formed on a semiconductor chip, and a load, heat and ultrasonic waves are applied to the bump and mounted on a printed wiring board (see Patent Documents 1 and 2). In this mounting, since the bonding strength of the bumps affects the yield and reliability, it is important to grasp (estimate) the bonding strength in advance based on the bonding conditions.
従来、上述した接合における強度の推定は、主な接合条件である超音波の出力（振幅），荷重，温度，及び超音波発振（印加）時間を各々変えた実験サンプルを作製し、これら実験サンプルに対して剪断強度試験を行い、各条件と強度の関係を各々に求めて適切な条件を選ぶことで行われていた。また、各条件を多変量解析などにより相関関係を求め、多変量近似式によって各条件を変更した場合の接合強度の関係を実験式として表す試みも行われてきた。 Conventionally, the estimation of strength in the above-described bonding is performed by preparing experimental samples in which the ultrasonic bonding (amplitude), the load, the temperature, and the ultrasonic oscillation (application) time, which are the main bonding conditions, are changed. A shear strength test was performed on each of the above, and a relationship between each condition and strength was obtained for each, and appropriate conditions were selected. Attempts have also been made to obtain a correlation between each condition by multivariate analysis or the like, and to express the relationship of bonding strength as an empirical expression when each condition is changed by a multivariate approximate expression.
しかしながら、上述した従来の方法では、膨大な実験データの収集が必要となり、加えて、多変量近似式を構成する各常数は、剪断強度実験により得られた剪断強度データにより統計的に推定されるものであるから、工学理論に照らし合わせた理論強度を導き出すことができなかった。 However, in the conventional method described above, it is necessary to collect a large amount of experimental data, and in addition, each constant constituting the multivariate approximate expression is statistically estimated from the shear strength data obtained by the shear strength experiment. Therefore, the theoretical strength in light of engineering theory could not be derived.
また、超音波接合における実際の接合強度は、荒さや清浄度などの配線基板の表面処理状態、前処理としての洗浄工程、金属バンプ材質などの様々な要因により実強度が変化するため、各々の場合について実験データを取得する必要がある。従来では、これらを実現する現実的かつ実用的な強度の予測式が提案されていない。このため、現状では、超音波接合で実際に接合した接合部の剪断強度値が、要求特性を満たしている状態の判断は、経験的な実績との比較より行うようにしており、正確な状態が把握できていない。 In addition, the actual bonding strength in ultrasonic bonding varies depending on various factors such as the surface treatment state of the wiring board such as roughness and cleanliness, the cleaning process as the pretreatment, the metal bump material, etc. It is necessary to obtain experimental data about the case. Conventionally, a realistic and practical strength prediction formula for realizing these has not been proposed. For this reason, at present, the judgment of the state where the shear strength value of the joint part actually joined by ultrasonic joining satisfies the required characteristics is made based on comparison with empirical results, and the accurate state Is not grasped.
本発明は、以上のような問題点を解消するためになされたものであり、超音波接合における接合強度がより正確に予測できるようにすることを目的とする。 The present invention has been made to solve the above-described problems, and an object of the present invention is to make it possible to predict the bonding strength in ultrasonic bonding more accurately.
本発明に係る超音波接合強度の予測方法は、実装対象のチップに設けられたバンプに荷重、熱および超音波を印加してバンプをチップが実装される基板の接続端子に接続してチップを基板に実装したときのバンプと接続端子との接合強度を予測する超音波接合強度の予測方法であって、以下の式（１）を用い、常温におけるバンプの降伏応力σy及び予め得られている常数α1，α2，α3，・・・をもとに、熱をバンプに印加して常温より温度Ｔ上昇させたときのバンプの降伏応力である温度印加時降伏応力σyTを求める。次に、以下の式（２）を用い、温度印加時降伏応力σyT及び予め得られている常数β1，β2，β3，・・・をもとに、さらに振幅δの超音波をバンプに印加したときのバンプ降伏応力である熱、超音波印加時降伏応力σyUSを求める。次に、以下の式（３）を用い、熱、超音波印加時降伏応力σyUS，予め測定されている初期状態のバンプの高さｈ0，初期状態のバンプの等価的な径Ｄ0，及びバンプとこのバンプが接合される接続端子との間の摩擦係数μをもとに、さらに荷重Ｆを印加した超音波接合により変形した後のバンプの高さである接合バンプ高さｈを求める。次に、以下の式（４）を用い、高さｈ0，径Ｄ0，及び接合バンプ高さｈをもとに、このバンプと接続端子との接合面積Ｓを求める。次に、以下の式（５）を用い、接合面積Ｓ，常温におけるバンプの降伏応力σy，及び予め得られている常数φをもとに接合強度予測値ｆを求める。 The ultrasonic bonding strength prediction method according to the present invention applies a load, heat and ultrasonic waves to a bump provided on a chip to be mounted, and connects the bump to a connection terminal of a substrate on which the chip is mounted. An ultrasonic bonding strength prediction method for predicting the bonding strength between a bump and a connection terminal when mounted on a substrate, using the following formula (1), the yield stress σ y of the bump at room temperature and obtained in advance: Based on the constants α 1 , α 2 , α 3 ,..., The yield stress σ yT during temperature application, which is the yield stress of the bump when heat is applied to the bump and the temperature T is raised from room temperature, is obtained. . Next, using the following equation (2), an ultrasonic wave having an amplitude δ is further generated based on the yield stress σ yT at the time of temperature application and the constants β 1 , β 2 , β 3 ,. The heat, which is the bump yield stress when applied to the bump, and the yield stress σ yUS when applying ultrasonic waves are obtained. Next, by using the following equation (3), the yield stress σ yUS at the time of application of heat and ultrasonic waves , the height h 0 of the bump in the initial state measured in advance, the equivalent diameter D 0 of the bump in the initial state, Then, based on the friction coefficient μ between the bump and the connection terminal to which the bump is bonded, the bonding bump height h, which is the height of the bump after being deformed by ultrasonic bonding to which a load F is further applied, is obtained. . Next, using the following formula (4), on the basis of the height h 0, the diameter D 0, and bonding the bump height h, obtaining the junction area S between the connection terminal and the bumps. Next, using the following equation (5), the bonding area S, Ru determined yield stress sigma y of the bump at room temperature, and the previously obtained on the basis of constant φ are bonding strength predicted value f.
以上説明したように、本発明によれば、上記式（１），式（２），式（３），式（４），及び式（５）により超音波接合強度を求める（推定する）ようにしたので、超音波接合における接合強度がより正確に予測できるようになるという優れた効果が得られる。 As described above, according to the present invention, the ultrasonic bonding strength is obtained (estimated) by the above formulas (1), (2), (3), (4), and (5). Therefore, it is possible to obtain an excellent effect that the bonding strength in ultrasonic bonding can be predicted more accurately.
以下、本発明の実施の形態について図を参照して説明する。本発明では、超音波接合により接合されたバンプの接合（剪断）強度予測値ｆを、超音波接合に用いられるバンプの材料により決定される常数α1，α2，α3，・・・及び常数β1，β2，β3，・・・と、接合において加えられる荷重Ｆと、バンプとこのバンプが接合される接続端子との間の摩擦係数を示す常数μと、接合前の初期状態のバンプ高さｈ0と、接合前の初期状態のバンプの等価的な径Ｄ0と、バンプの材料の常温（２５℃）における降伏応力（実効降伏応力）σyと、常数φとを用い、以下の式（１），式（２），式（３），式（４），及び式（５）により求めるようにした。 Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the present invention, the predicted bonding strength (f) of bumps bonded by ultrasonic bonding is determined by constants α 1 , α 2 , α 3 ,... Determined by the material of the bumps used for ultrasonic bonding. Constant β 1 , β 2 , β 3 ,..., Load F applied in joining, constant μ indicating the coefficient of friction between the bump and the connection terminal to which the bump is joined, and the initial state before joining Bump height h 0 , equivalent bump diameter D 0 in the initial state before bonding, yield stress (effective yield stress) σ y of bump material at normal temperature (25 ° C.), and constant φ The following equations (1), (2), (3), (4), and (5) are used.
以下、本発明の実施の形態における超音波接合強度の予測方法を実施するための超音波接合強度予測装置について説明すると、図１の構成図に示すように、先ず、式（１）を用い、常温（２５℃）における降伏応力σy及び予め得られている常数α1，α2，α3，・・・をもとに、常温より温度Ｔを加えた場合のバンプ材料の降伏応力である温度印加時降伏応力σyTを求める温度条件設定部１０１を備える。 Hereinafter, the ultrasonic bonding strength prediction apparatus for carrying out the ultrasonic bonding strength prediction method in the embodiment of the present invention will be described. First, as shown in the configuration diagram of FIG. Yield stress of bump material when temperature T is applied from normal temperature based on yield stress σ y at normal temperature (25 ° C.) and constants α 1 , α 2 , α 3 ,... A temperature condition setting unit 101 for obtaining a yield stress σ yT at the time of temperature application is provided.
また、本装置は、式（２）を用い、温度印加時降伏応力σyT及び予め得られている常数β1，β2，β3，・・・をもとに、ヘッド振幅（μｍ）の超音波振動を与えた場合の超音波印加時降伏応力σyUSを求める超音波条件設定部１０２を備える。また、本装置は、式（３）を用い、超音波印加時降伏応力σyUS，予め測定されている初期状態のバンプ高さｈ0，初期状態のバンプ径Ｄ0，及びバンプとこのバンプが接合される接続端子との間の摩擦係数μをもとに、荷重Ｆを加えつつ超音波接合により変形した後の接合バンプ高さｈを求める変形バンプ高さ算出部１０３を備える。 In addition, this apparatus uses the equation (2) to calculate the head amplitude (μm) based on the yield stress σ yT during temperature application and the constants β 1 , β 2 , β 3 ,. An ultrasonic condition setting unit 102 is provided for determining the yield stress σ yUS when applying ultrasonic waves when ultrasonic vibration is applied. In addition, this apparatus uses the expression (3), the yield stress σ yUS when ultrasonic waves are applied, the bump height h 0 in the initial state measured in advance, the bump diameter D 0 in the initial state, and the bump and the bump. A deformation bump height calculation unit 103 is provided that calculates a bonding bump height h after being deformed by ultrasonic bonding while applying a load F based on a friction coefficient μ between the connection terminals to be bonded.
また、本装置は、式（４）を用い、初期状態のバンプ高さｈ0，予め測定されている初期状態のバンプ径Ｄ0，及び接合バンプ高さｈをもとに、接合した状態におけるバンプの接合面積Ｓを求める接合面積算出部１０４を備える。加えて、本装置は、式（５）を用い、接合面積Ｓ及び予め得られている降伏応力σy，常数φをもとに接合強度予測値ｆを求める接合強度予測部１０５を備える。なお、本装置により高さを測定する必要はなく、本装置と高さ測定装置とは一体である必要はない。 In addition, this apparatus uses the equation (4) and is in a bonded state based on the initial bump height h 0 , the initial bump diameter D 0 measured in advance, and the bonded bump height h. A bonding area calculation unit 104 for obtaining the bonding area S of the bumps is provided. In addition, the apparatus includes a joint strength prediction unit 105 that obtains a joint strength prediction value f based on the joint area S, the yield stress σ y obtained in advance, and the constant φ using Equation (5). Note that it is not necessary to measure the height with the present apparatus, and the present apparatus and the height measuring apparatus need not be integrated.
次に、上述した超音波接合強度予測装置による超音波接合強度の予測について、図２のフローチャートを用いて説明する。なお、常数α1，α2，α3，・・・及び常数β1，β2，β3，・・・や、バンプの各寸法及びバンプの実効降伏応力σyなどは、以降に説明するように、同種のバンプを使用した実験により、予め求めておく。 Next, prediction of ultrasonic bonding strength by the above-described ultrasonic bonding strength prediction apparatus will be described using the flowchart of FIG. The constants α 1 , α 2 , α 3 ,... And the constants β 1 , β 2 , β 3 ,..., The bump dimensions and the effective yield stress σ y of the bumps will be described later. As described above, it is obtained in advance by an experiment using bumps of the same type.
このように各常数が予め得られている状態で、先ず、ステップＳ２０１で、温度条件設定部１０１が、式（１）を用い、常温（２５℃）における降伏応力σy及び予め得られている常数α1，α2，α3，・・・をもとに、常温より温度Ｔを加えた場合の温度印加時降伏応力σyTを求める。 Thus, in the state where each constant is obtained in advance, first, in step S201, the temperature condition setting unit 101 uses the equation (1), and the yield stress σ y at room temperature (25 ° C.) and the obtained stress are obtained in advance. Based on the constants α 1 , α 2 , α 3 ,..., The temperature applied yield stress σ yT when the temperature T is applied from room temperature is obtained.
次に、ステップＳ２０２で、超音波条件設定部１０２が、式（２）を用い、温度条件設定部１０１により求められた温度印加時降伏応力σyT及び予め得られている常数β1，β2，β3，・・・をもとに、ヘッド振幅（μｍ）で与えられる状態量δの超音波振動を与えた場合の超音波印加時降伏応力σyUSを求める。 Next, in step S202, the ultrasonic condition setting unit 102 uses the equation (2) to calculate the temperature applied yield stress σ yT obtained by the temperature condition setting unit 101 and the constants β 1 and β 2 obtained in advance. , Β 3 ,..., Yield stress σ yUS at the time of applying an ultrasonic wave when an ultrasonic vibration having a state quantity δ given by the head amplitude (μm) is given.
次に、ステップＳ２０３で、変形バンプ高さ算出部１０３が、式（３）を用い、荷重Ｆと、超音波条件設定部１０２により求められた超音波印加時降伏応力σyUS，予め測定されている初期状態のバンプ高さｈ0，初期状態のバンプ径Ｄ0，及びバンプとこのバンプが接合される接続端子との間の摩擦係数μをもとに、超音波接合により変形した後の接合バンプ高さｈを求める。 Next, in step S203, the deformed bump height calculation unit 103 uses the equation (3) to measure the load F and the ultrasonic application yield stress σ yUS obtained by the ultrasonic condition setting unit 102 in advance. bump height h 0 of the initial state are, bump diameter D of the initial state 0, and on the basis of the friction coefficient μ between the connection terminal bumps and bump are bonded, joined after deformation by ultrasonic bonding Find the bump height h.
次に、ステップＳ２０４で、接合面積算出部１０４が、式（４）を用い、初期状態のバンプ高さｈ0，予め測定されている初期状態のバンプ径Ｄ0，及び変形バンプ高さ算出部１０３により求められた接合バンプ高さｈをもとに、接合した状態におけるバンプと接続端子との接合面積Ｓを求める。 Next, in step S204, the bonding area calculation unit 104 uses equation (4) to determine the initial bump height h 0 , the initial bump diameter D 0 measured in advance, and the modified bump height calculation unit. Based on the bonding bump height h determined by 103, the bonding area S between the bump and the connection terminal in the bonded state is determined.
最後に、ステップＳ２０５で、接合強度予測部１０５が、式（５）を用い、接合面積算出部１０４により求められた接合面積Ｓ及び予め得られている降伏応力σy，常数φをもとに接合強度予測値ｆを求める。 Finally, in step S205, the bonding strength prediction unit 105 uses the equation (5) to calculate the bonding area S obtained by the bonding area calculation unit 104, the yield stress σ y , and the constant φ obtained in advance. The joint strength prediction value f is obtained.
なお、上述した本実施の形態に係る超音波接合強度の予測方法は、上記各ステップの手順をプログラムとしてコンピュータにより処理させることで実施できる。例えば、演算処理部と、主記憶部と、外部記憶部と、入力部と、表示部と、プリンターとを備えたコンピュータを用いればよい。このコンピュータにおいて、例えば、磁気記録装置である外部記憶部に、上述した第１〜第５ステップを少なくとも備えたプログラムなどが記憶されている。 In addition, the prediction method of the ultrasonic joining intensity | strength which concerns on this Embodiment mentioned above can be implemented by making the computer process the procedure of said each step as a program. For example, a computer including an arithmetic processing unit, a main storage unit, an external storage unit, an input unit, a display unit, and a printer may be used. In this computer, for example, a program including at least the first to fifth steps described above is stored in an external storage unit which is a magnetic recording device.
このように外部記憶部に記憶されているプログラムが、演算処理部により主記憶部に展開して実行され、この実行の結果が表示部にリアルタイムに表示され、また、プリンターにより印刷出力される。また、処理結果は、外部記憶部に記憶される。また、演算処理に必要な常数などの情報（データ）は、操作者の操作により入力部より入力され、主記憶部に一時記憶され、また、外部記憶部に記憶される。これらの記憶された常数などのデータを用い、主記憶部に展開されたプログラムを実行することで、演算処理部は、接合強度予測値ｆを算出する。 The program stored in the external storage unit in this manner is expanded and executed in the main storage unit by the arithmetic processing unit, and the result of this execution is displayed in real time on the display unit and printed out by the printer. The processing result is stored in the external storage unit. In addition, information (data) such as constants necessary for the arithmetic processing is input from the input unit by the operation of the operator, temporarily stored in the main storage unit, and stored in the external storage unit. The arithmetic processing unit calculates a predicted joint strength value f by executing a program developed in the main storage unit using data such as the stored constants.
ここで、超音波接合について簡単に説明する。超音波接合は、例えば図３の構成図に例示する接合装置により行う。図３に示す接合装置を説明すると、本装置は、超音波ヘッド３０５と、回路基板３０３が載置されるホットプレート３０７を備えたステージ３１０と、振幅制御型の超音波発生部３０８と、加熱温度設定部３０９とを備える。また、超音波ヘッド３０５は、実装（接合）対象の半導体チップ３０１を吸着する吸着ノズル３５１と、加熱部３５２と、超音波振動伝達部３５３とを備える。また、超音波ヘッド３０５を介して半導体チップ３０１に対して荷重を印加する荷重印加部３０６を備える。なお、半導体チップ３０１は、電極に形成された金バンプ３０２を備え、回路基板３０３は、金バンプ３０２が接続（接合）される接続端子３０４を備えている。ここで、金バンプ３０２は、めっきによるバンプでもワイヤボンダによるバンプでもよい。また、接続端子３０４の表面には金めっきを施すことが必要である。 Here, the ultrasonic bonding will be briefly described. The ultrasonic bonding is performed by, for example, a bonding apparatus illustrated in the configuration diagram of FIG. The bonding apparatus shown in FIG. 3 will be described. This apparatus includes an ultrasonic head 305, a stage 310 including a hot plate 307 on which a circuit board 303 is placed, an amplitude-controlled ultrasonic generator 308, a heating A temperature setting unit 309. The ultrasonic head 305 includes an adsorption nozzle 351 that adsorbs the semiconductor chip 301 to be mounted (bonded), a heating unit 352, and an ultrasonic vibration transmission unit 353. Further, a load application unit 306 that applies a load to the semiconductor chip 301 via the ultrasonic head 305 is provided. The semiconductor chip 301 includes gold bumps 302 formed on the electrodes, and the circuit board 303 includes connection terminals 304 to which the gold bumps 302 are connected (bonded). Here, the gold bump 302 may be a bump by plating or a bump by wire bonder. Further, the surface of the connection terminal 304 needs to be plated with gold.
超音波ヘッド３０５において、半導体チップ３０１を保持する吸着ノズル３５１は、超音波発生部３０８から超音波振動伝達部３５３を経由して超音波振動する構造となっている。また、超音波ヘッド３０５に設けられている加熱部３５２は、超音波振動に悪影響を与えないような取り付け方法と質量とを備えた構造となっている。例えば、ペルチェ素子を超音波振動伝達部３５３と吸着ノズル３５１の中間に耐熱性接着剤で固定する方法を用いることができる。ここで、加熱方式は単純な常時加熱方式でもよく、また、パルスヒート方式でもよい。 In the ultrasonic head 305, the suction nozzle 351 that holds the semiconductor chip 301 has a structure that ultrasonically vibrates from the ultrasonic wave generation unit 308 via the ultrasonic vibration transmission unit 353. The heating unit 352 provided in the ultrasonic head 305 has a structure having an attachment method and a mass that do not adversely affect the ultrasonic vibration. For example, a method of fixing the Peltier element between the ultrasonic vibration transmission unit 353 and the suction nozzle 351 with a heat resistant adhesive can be used. Here, the heating method may be a simple constant heating method or a pulse heat method.
この接合装置の動作について簡単に説明すると、先ず、図示しない別途設けた入力装置から加熱温度設定部３０９に対し、回路基板３０３の熱膨張率と回路基板３０３の加熱温度ｔ2及び半導体チップ３０１の熱膨張率を入力する。続いて、回路基板３０３をホットプレート３０７の上に載置し、加熱温度設定部３０９からの設定のもとにホットプレート３０７を加熱し、回路基板３０３を加熱する。続いて、吸着ノズル３５１で半導体チップ３０１を吸着保持し、回路基板３０３の半導体チップ実装位置に位置合わせして載置する。 The operation of this bonding apparatus will be briefly described. First, the thermal expansion coefficient of the circuit board 303, the heating temperature t 2 of the circuit board 303, and the semiconductor chip 301 are supplied to the heating temperature setting unit 309 from a separately provided input device (not shown). Enter the coefficient of thermal expansion. Subsequently, the circuit board 303 is placed on the hot plate 307, the hot plate 307 is heated under the setting from the heating temperature setting unit 309, and the circuit board 303 is heated. Subsequently, the semiconductor chip 301 is sucked and held by the suction nozzle 351 and placed in alignment with the semiconductor chip mounting position of the circuit board 303.
次に、荷重印加部３０６により、超音波ヘッド３０５を介して半導体チップ３０１に所定の荷重を印加する。この後、加熱温度設定部３０９からの設定のもとに超音波ヘッド３０５に備えた加熱部３５２を所定温度に加熱し、超音波発生部３０８で超音波を発生させ、超音波振動伝達部３５３を介して吸着ノズル３５１に超音波を伝達し、吸着ノズル３５１に超音波振動を与えて吸着保持されている半導体チップ３０１を振動させる。例えば、半導体チップ３０１を、図３の紙面の左右方向（水平方向）に振動させる。このことにより、金バンプ３０２と接続端子３０４間に相対的な振動を加えて半導体チップ３０１を回路基板３０３に超音波接合させる。 Next, a predetermined load is applied to the semiconductor chip 301 via the ultrasonic head 305 by the load application unit 306. Thereafter, the heating unit 352 provided in the ultrasonic head 305 is heated to a predetermined temperature under the setting from the heating temperature setting unit 309, the ultrasonic wave is generated by the ultrasonic wave generation unit 308, and the ultrasonic vibration transmission unit 353. The ultrasonic wave is transmitted to the suction nozzle 351 via the ultrasonic wave, and the ultrasonic vibration is applied to the suction nozzle 351 to vibrate the semiconductor chip 301 held by suction. For example, the semiconductor chip 301 is vibrated in the left-right direction (horizontal direction) of the paper surface of FIG. As a result, relative vibration is applied between the gold bump 302 and the connection terminal 304 to ultrasonically bond the semiconductor chip 301 to the circuit board 303.
以下、前述したバンプ材料の温度印加時降伏応力σyT、超音波印加時降伏応力σyUS、変形した後の接合バンプ高さｈ、及びバンプの接合面積Ｓの算出と、これらによる接合強度予測値ｆの算出について、より詳細に説明する。なお、本実施の形態では、主に金バンプを例に説明するが、これに限るものではなく、他の金属からなるバンプについても同様である。 Hereinafter, the temperature applied at yield stress sigma yT bump material described above, ultrasonic wave application time yield stress sigma yus, deformed bonded bump height h after, and the calculation of the junction area S of the bump, these by bonding strength predicted value The calculation of f will be described in more detail. In the present embodiment, description will be given mainly using gold bumps as an example, but the present invention is not limited to this, and the same applies to bumps made of other metals.
［１．０］ 円柱の圧縮変形における基本理論式
前述した式（１）〜（５）による圧縮変形モデル（特に式（３））では、鍛造加工に必要な荷重を理論推定する際に用いられるスラブ法を用いている。この方法は、変形領域を板状微小要素（slab）に分割し、分割した要素に対して垂直に作用する応力を主応力として力の釣り合い条件と降伏条件を連立して解くものである。また、接続技術への応用としてバンプ又は粒子の変形を解析することを目的としているため、具体的には「円柱の圧縮変形」として、非特許文献１に詳細な記述のある「平面ひずみのすべり変形解析」より得られた式を使用する。本モデル式の概要は以下のとおりである。
[1.0] Basic theoretical formula for compressive deformation of a cylinder In the compressive deformation model (particularly, formula (3)) according to the above-described formulas (1) to (5), it is used when theoretically estimating a load necessary for forging. The slab method is used. This method divides a deformation region into plate-like microelements (slabs), and solves a force balance condition and a yield condition by using stress acting perpendicularly to the divided elements as a main stress. In addition, because the purpose is to analyze the deformation of bumps or particles as an application to the connection technology, specifically, “cylinder compression deformation” is described in detail in “Non-Patent Document 1”. The formula obtained from “deformation analysis” is used. The outline of this model formula is as follows.
例えば、図４（ａ）及び図４（ｂ）の斜視図に示すような構成とされた微小要素の場合、半径方向の力、円周方向からの力、上下面から圧縮圧力ｐを加えられた面における摩擦（摩擦係数μ）で釣り合っており、さらにミーゼス降伏条件を用いて連立して整理すると式（６）が得られる。 For example, in the case of a microelement configured as shown in the perspective views of FIGS. 4A and 4B, a radial force, a circumferential force, and a compression pressure p can be applied from the upper and lower surfaces. Equation (6) can be obtained by balancing with the friction (friction coefficient μ) on the surface and further organizing them using the Mises yield condition.
これを積分して境界条件（ｒがバンプ半径ａとなる場所でσr＝０）を用いて整理し、１軸引張方向の降伏応力σy とすれば、半径方向の位置に対する圧力ｐの分布式となる式（７）が得られる。 If this is integrated and arranged using boundary conditions (σ r = 0 where r is the bump radius a) and the yield stress σ y in the uniaxial tensile direction, then the distribution of pressure p relative to the radial position Equation (7) is obtained.
さらに、圧縮面全体の平均的な圧力Ｐは、半径方向に圧力分布を積分したものを面積で割ればよいので、以下の式（８）が得られる。この圧力Ｐは、変形状態における接続界面の平均圧力を意味するので、降伏圧力σyieldと表すことにする。 Furthermore, since the average pressure P of the entire compression surface may be obtained by dividing the pressure distribution integrated in the radial direction by the area, the following equation (8) is obtained. Since this pressure P means the average pressure at the connection interface in the deformed state, it is expressed as the yield pressure σ yield .
式（８）に示すように、圧縮変形における降伏圧力（荷重と面積）及び高さの関係を、摩擦係数と降伏応力という一般的に用いられている材料物性を使って表すことで汎用化できる。逆に言えば、材料物性として広く知られる１軸引張方向の降伏応力を、実際の使用状態の応力方向における降伏点に変換（換算）したものが、式（８）で表す降伏圧力であると言える。このような、応力方向を変換して基準となる応力を推定する解析手法は、自動車用など応力が加わる構造部品における解析（非特許文献２参照）などでは良く用いられているが、接合技術に適用して紹介される例は少ない。 As shown in Equation (8), the relationship between the yield pressure (load and area) and height in compressive deformation can be generalized by expressing the commonly used material physical properties of friction coefficient and yield stress. . In other words, the yield pressure expressed by the equation (8) is obtained by converting (converting) the yield stress in the uniaxial tensile direction, which is widely known as a material property, to the yield point in the stress direction in the actual use state. I can say that. Such an analysis method for converting a stress direction and estimating a reference stress is often used in an analysis of a structural component to which stress is applied such as for automobiles (see Non-Patent Document 2). There are few examples introduced by applying.
［２．０］円柱型バンプの変形挙動
フリップチップ接続（ＦＣＢ；Flip Chip Bonding）に良く用いられるめっきバンプは角柱型であるが、これを図５に示すような円柱形状のバンプ５０１とし、バンプ５０１の径を高さ及び断面積が等しい等価径Ｄとして定義すれば、式（８）は次の式（９）で示されるものとなる。なお、等価径とは、高さがｈである円柱と角柱とにおいて、圧縮方向に垂直な断面の面積が、角柱に等しい円柱の径を示すものである。角柱の横幅をＷ，奥行きをＬとし、円柱の直径をＤ0とすると「π（Ｄ0／２）2＝Ｌ・Ｗ→Ｄ0＝２（Ｌ・Ｗ／π）1/2」のようにして求めることができる。
[2.0] Deformation Behavior of Cylindrical Bump A plating bump often used for flip chip bonding (FCB) is a prismatic type. This is a cylindrical bump 501 as shown in FIG. If the diameter of 501 is defined as an equivalent diameter D having the same height and cross-sectional area, Expression (8) is represented by the following Expression (9). The equivalent diameter refers to the diameter of a cylinder having a cross-section area perpendicular to the compression direction in a cylinder and a prism having a height of h, the section being perpendicular to the compression direction. The width of the prism W, and the depth and L, and the diameter of the cylinder and D 0 "π (D 0/2) 2 = L · W → D 0 = 2 (L · W / π) 1/2 " of as Can be obtained.
次に、荷重を加えてバンプ変形が進行している過程において、体積Ｖは常に一定であるから、変形面積Ｓ，及びバンプ径Ｄとバンプ高さｈは、以下の式（１０）の関係式が得られる。ここで、Ｓ0は変形開始時の面積、Ｄ0は変形開始時の初期バンプ径、ｈ0は変形開始時の初期高さである。従って、接合面積が、この変形面積Ｓと等しいと仮定すれば、バンプ高さｈより接合面積を求めることができる。 Next, since the volume V is always constant in the process of applying the load and the deformation of the bump, the deformation area S, the bump diameter D, and the bump height h are expressed by the following equation (10). Is obtained. Here, S 0 is the area at the start of deformation, D 0 is the initial bump diameter at the start of deformation, and h 0 is the initial height at the start of deformation. Therefore, assuming that the bonding area is equal to the deformation area S, the bonding area can be obtained from the bump height h.
この式（１０）を式（９）に代入して整理すると、以下の式（１１）が得られる。 Substituting this equation (10) into equation (9) and rearranging results in the following equation (11).
従って、材料の１軸引張の降伏応力σyと摩擦係数μ及び変形前の寸法がわかれば、バンプ高さが変化（減少）していく際の降伏圧力σyieldを求めることができる。 Therefore, if the yield stress σ y of the uniaxial tension of the material, the friction coefficient μ, and the dimensions before deformation are known, the yield pressure σ yield when the bump height changes (decreases) can be obtained.
図６は、式（１１）の具体的計算例として、変形前に径６０μｍ、高さ６０μｍのめっきバンプが圧縮変形して高さが減少していく場合における降伏比を示したものである。これによれば、一般的な摩擦係数としてμ＝０．５前後と見込めば、バンプ高さが半分程度となる３０μｍまでは、変形に必要な降伏圧力が降伏応力の１．２から１．７倍程度へ僅かに上昇する程度だが、初期高さの１／３程度となる２０μｍまで変形させると変形抵抗が著しく増し、降伏応力の３倍程度の降伏圧力を必要とすることがわかる。すなわち、十分に変形が行える荷重で加圧しても、バンプ変形が進むにつれて変形抵抗が大きくなり、いずれは変形が止まるということが示されている。 FIG. 6 shows, as a specific calculation example of the expression (11), the yield ratio in the case where a plating bump having a diameter of 60 μm and a height of 60 μm is compressed and deformed before the deformation is reduced. According to this, assuming that μ = 0.5 as a general friction coefficient, the yield pressure required for deformation is 1.2 to 1.7 of the yield stress up to 30 μm where the bump height is about half. It can be seen that when it is deformed to 20 μm, which is about 1/3 of the initial height, the deformation resistance is remarkably increased, and a yield pressure of about 3 times the yield stress is required. That is, it is shown that even when pressure is applied with a load capable of sufficient deformation, the deformation resistance increases as the bump deformation progresses, and eventually the deformation stops.
次に、降伏圧力σyieldは、荷重Ｆと変形面積Ｓ（マクロ的な接触面積）との比であるから、以下に示す式（１２）と表せる。従って、式（１０）、式（１１）より以下の式（１３）が得られる。つまり、初期形状（初期バンプ径Ｄ0と初期高さｈ0）が与えられれば、バンプ変形に必要な荷重Ｆは、材料物性（降伏応力と摩擦係数）を用いてバンプ高さｈを変数として一義的に表すことができる。逆に、式（１３）の逆関数を用いれば、荷重Ｆから高さｈが求まり、これによって変形面積（マクロ的な接触面積）Ｓも計算（推定）できる。 Next, since the yield pressure σ yield is a ratio of the load F and the deformation area S (macro contact area), it can be expressed by the following equation (12). Therefore, the following equation (13) is obtained from the equations (10) and (11). In other words, given an initial shape (initial bump diameter D 0 and initial height h 0 ), the load F required for the deformation of the bump is determined by using the material height (yield stress and friction coefficient) and the bump height h as a variable. It can be expressed uniquely. Conversely, if the inverse function of equation (13) is used, the height h is obtained from the load F, and the deformation area (macro contact area) S can also be calculated (estimated).
ただし、過去に評価データのないバンプ材料に対して本モデル式を用いて荷重Ｆと高さｈの実験データを整理する場合には、降伏応力σyと摩擦係数μとの２つ常数が未知数となる。上記式より明らかなように、１組みのみの荷重と高さのデータから、一義的に摩擦係数μと降伏応力σyの２常数を特定することはできない。しかし、式（１３）よりわかるとおり、荷重Ｆを横軸、高さｈを縦軸として図示するとすれば、降伏応力σyは縦軸方向の位置を決め、摩擦係数μは曲線の曲率を決めている。従って、荷重範囲を広く変更した多くの水準の実験データを取得すれば、最小二乗法などによって摩擦係数μと降伏応力σyの各々について最適な値を導き出すことができる（以下の［６．０］項参照）。 However, when organizing experimental data of load F and height h for bump materials for which there is no evaluation data in the past, the two constants of yield stress σ y and friction coefficient μ are unknown. It becomes. As is clear from the above formula, it is not possible to uniquely specify the two constants of the friction coefficient μ and the yield stress σ y from only one set of load and height data. However, as can be seen from equation (13), if the load F is shown on the horizontal axis and the height h is shown on the vertical axis, the yield stress σ y determines the position in the vertical axis direction, and the friction coefficient μ determines the curvature of the curve. ing. Therefore, if many levels of experimental data obtained by changing the load range widely are acquired, optimum values can be derived for each of the friction coefficient μ and the yield stress σ y by the least square method or the like (refer to [6.0 below). ]).
なお、十分に荷重範囲の広いデータが得られない場合には、実測プロットの曲率を考慮しつつ摩擦係数をある値に仮定しておき、残された未知数である降伏応力は実測プロットの位置から近似計算に比較的合う値を推定すればよい。一般的に、大気中の摩擦係数は幅広い値ではなく、金同士は２．０以上とやや高めではあるものの、他の金属同士では概ね０．３〜０．８程度の範囲となっており（非特許文献３参照）、これから類推すれば、金と他金属又は酸化物間は他金属同士の場合もこの範囲にあると考えてよい。 If data with a sufficiently wide load range cannot be obtained, the friction coefficient is assumed to be a certain value while taking into account the curvature of the actual plot, and the remaining yield, yield stress, is calculated from the position of the actual plot. What is necessary is just to estimate the value comparatively suitable for approximate calculation. In general, the coefficient of friction in the atmosphere is not a wide value, and gold is slightly higher than 2.0, but other metals are generally in the range of about 0.3 to 0.8 ( Non-patent document 3), and by analogy from this, it may be considered that the distance between gold and another metal or oxide is within this range even when other metals are present.
実際の金めっきバンプ変形に関して、植田らが実験的に得た荷重とバンプ高さ変化量の相関関係に関する実験データ（非特許文献４参照）を本モデル式で解析すると、図７（プロットが実験値、曲線が本数式モデル）に示すとおり、摩擦係数０．４とした場合の降伏応力が２１２ＭＰａと、ほぼ妥当な結果となる。なお、２１２ＭＰａは、ビッカース硬度Ｈｖ６５に相当している（Ｈｖ≒３．０σyとする）（非特許文献５参照）。 When the experimental data (see Non-Patent Document 4) on the correlation between the load and the bump height variation obtained experimentally by Ueda et al. Is analyzed with this model formula for the actual gold plating bump deformation, Fig. 7 (plot shows the experiment) As the value and curve show in this mathematical model, the yield stress when the friction coefficient is 0.4 is 212 MPa, which is an almost appropriate result. Incidentally, 212MPa is equivalent to (and Hv ≒ 3.0σ y) is the Vickers hardness Hv65 (see Non-Patent Document 5).
従って、ここで用いたスラブ法を基本とする本モデルによって、実験値から降伏応力σyが概算推定でき、これを元に同等なバンプの変形挙動を数式化できることがわかる。 Therefore, it can be seen that with this model based on the slab method used here, the yield stress σ y can be roughly estimated from the experimental values, and based on this, the deformation behavior of the bump can be mathematically expressed.
なお、図７において、荷重１．０Ｎの条件では、計算上は降伏条件に達していないため変形が開始する荷重ではないが、実際のバンプでは表面凹凸範囲に相当する程度の僅かな変形は低荷重から開始することを示唆しているものと考えられる。 In FIG. 7, under the condition of the load of 1.0 N, the yield condition is not reached in the calculation, so the deformation does not start. However, in the actual bump, a slight deformation corresponding to the surface unevenness range is low. This is thought to suggest starting with a load.
また、図７では、Δｈ（バンプ高さ変化量）と荷重Ｆの関係を示したが、初期バンプ高さ２５μｍ、径７９μｍ、硬度６５Ｈｖ、摩擦係数０．４として、荷重とバンプ高さの関係を数値計算によって示すと、図８及び図９に示すとおりとなり、正確には非線形ではあるが、荷重範囲が狭ければ実験的にはバンプ高さｈは荷重の逆対数ｌｎ（１／Ｆ）にほぼ比例することが予測される。 FIG. 7 shows the relationship between Δh (bump height variation) and the load F, but the relationship between the load and the bump height with an initial bump height of 25 μm, a diameter of 79 μm, a hardness of 65 Hv, and a friction coefficient of 0.4. 8 and 9 are as shown in FIG. 8 and FIG. 9. Although the nonlinearity is exactly nonlinear, the bump height h is experimentally the inverse logarithm ln (1 / F) of the load if the load range is narrow. Is approximately proportional to
［３．０］ワイヤバンプの変形挙動
ワイヤボンディング法によるワイヤバンプは、トーチによってワイヤを溶断した後、ワイヤ端に再凝固時に形成された球状部分をキャピラリで圧縮変形させ、かつ球状部分につながるワイヤを引き千切りによって切断した形状が基本形状となる。この形状は、図１０の電子顕微鏡写真に示すとおり、主に３段構成であり、以下では先端（上端）から数えて１段目，２段目，３段目と呼ぶ。なお、１段目は、動物の尾に例えて「テール」、３段目は最下部であるため「台座」と呼ばれることもある。
[3.0] Deformation behavior of wire bumps Wire bumping by wire bonding is performed by fusing a wire with a torch and then compressing and deforming the spherical portion formed at the time of re-solidification at the end of the wire with a capillary and pulling the wire connected to the spherical portion. The shape cut by shredding is the basic shape. As shown in the electron micrograph of FIG. 10, this shape mainly has a three-stage configuration, and is hereinafter referred to as a first stage, a second stage, and a third stage, counting from the tip (upper end). The first tier is sometimes referred to as a “tail” by comparison with the tail of an animal, and the third tier is the lowermost portion, so it is sometimes called a “pedestal”.
この変形挙動を解析するには、円錐状（あるいは各種形状を複合）の近似モデルを考えなければならないが、以下では、便宜的に円柱形状が積み重なったものとして［１．０］項で示したモデル式を適用した場合について示す。 In order to analyze this deformation behavior, it is necessary to consider an approximate model with a conical shape (or a combination of various shapes), but in the following, it is shown in [1.0] as a stack of cylindrical shapes for convenience. The case where the model formula is applied is shown.
図１０に示すようなワイヤバンプを、接合装置などで圧縮変形させて接合する場合には、先端部分は実装段階初期でレベリングされて平坦となることから、図１１（ａ）に示す形状を図１１（ｂ）に示すような３段構成の円柱を初期形状と仮定する。また、変形においては、図１１（ｃ）に示すように、１段目が変形して高さが圧縮され、これに伴い１段目の変形に相当するだけ１段目の径が増加し、２段目の径と等しくなった段階で１段目の変形後の高さと２段目の高さの和として新たに２段目の寸法を設定する（図１１（ｄ））。このように順次変形していくことで、円柱が積み重なった形状における圧縮変形挙動を近似する。この変形を、以下では「逐次変形モデル」と呼ぶ。 When a wire bump as shown in FIG. 10 is compressed and deformed by a joining device or the like, the tip portion is leveled and flattened at the initial stage of the mounting stage, so the shape shown in FIG. A three-stage cylinder as shown in FIG. Further, in the deformation, as shown in FIG. 11C, the first stage is deformed and the height is compressed, and accordingly, the diameter of the first stage is increased by an amount corresponding to the deformation of the first stage, When the diameter becomes equal to the diameter of the second stage, the dimension of the second stage is newly set as the sum of the height after deformation of the first stage and the height of the second stage (FIG. 11 (d)). By sequentially deforming in this way, the compression deformation behavior in a shape in which cylinders are stacked is approximated. This deformation is hereinafter referred to as “sequential deformation model”.
このような逐次変形モデルを仮定することで、各段の変形は、めっきバンプと同様な変形として計算できる。実際に、図１１（ｂ）〜図１１（ｄ）に示すように変形状態が近似できるワイヤバンプに対し、接合装置を用いてヘッド温度を常温、２００℃、３５０℃の各温度帯で圧縮変形させ、圧縮変形させたバンプ高さを測定して本モデル式で整理すると図１２（ａ），図１２（ｂ）に示すとおりとなる。この場合の金バンプ物性は、各温度帯で、各々実効降伏応力１７０，１２１，７３ＭＰａ、摩擦係数０．８とすることで、実験値を理論予測することが可能となる。なお、本実験の荷重範囲では、２段目のみの計算（図１２（ｂ））で表すことができ、荷重の逆対数に対して直線に近い緩やかな曲率の曲線となる。 By assuming such a sequential deformation model, the deformation at each stage can be calculated as a deformation similar to the plating bump. Actually, a wire bump whose deformation state can be approximated as shown in FIGS. 11 (b) to 11 (d) is compressed and deformed in a temperature range of normal temperature, 200 ° C., and 350 ° C. using a bonding apparatus. When the compressed bump height is measured and arranged according to this model formula, the results are as shown in FIGS. 12 (a) and 12 (b). In this case, the physical properties of the gold bumps can be theoretically predicted by setting the effective yield stress to 170, 121, 73 MPa and the friction coefficient of 0.8 in each temperature zone. In addition, in the load range of this experiment, it can be represented by the calculation of only the second stage (FIG. 12B), and becomes a curve with a gentle curvature close to a straight line with respect to the inverse logarithm of the load.
また、ここで予測した実効降伏応力σyについて、常温を基準に比率ψで表し、温度を横軸にとって整理すると、図１３（ａ）に示すとおり、ほぼ直線に近い緩やかな曲線となる。なお、この減少傾向は図１３（ｂ）に示す非特許文献６に示される降伏応力の温度依存性（常温と３５０℃における降伏応力が、各々９９、８３ＭＰａ）よりも急激であることがわかる。通常、文献値等で用いられる物性が、アニール処理されて安定化したものを測定に使うのに対し、本実験で用いた材料は、延伸されたワイヤをさらにバンプ形成時に圧縮及び引き千切りで切断された加工歪みの多いものである。すなわち、元々常温では加工歪みの影響で、降伏応力が高い状態にあるものが、加熱を加えることによって本来の物性に近づくアニール効果が生じているものと考えられる。 Further, the effective yield stress σ y predicted here is expressed by a ratio ψ based on the normal temperature, and the temperature is arranged with respect to the horizontal axis, as shown in FIG. In addition, it turns out that this decreasing tendency is more rapid than the temperature dependence of the yield stress shown in Non-Patent Document 6 shown in FIG. 13B (the yield stress at room temperature and 350 ° C. is 99 and 83 MPa, respectively). Normally, the physical properties used in literature values are stabilized by annealing, but the materials used in this experiment are cut by cutting and shredding the stretched wire during bump formation. The processing distortion is large. That is, it is considered that an annealing effect that is close to the original physical properties is generated by applying heat to a material having a high yield stress due to processing strain at room temperature.
図１３（ａ）に示すように得られた実効降伏応力σyの温度依存性は、便宜的に超音波ヘッドの常温からの温度差をＴ、この温度のときの温度印加時降伏応力σyTは、以下の式（１４）に示す２次の近似式で表すことができる。 The temperature dependence of the effective yield stress σ y obtained as shown in FIG. 13 (a) is, for convenience, the temperature difference from the normal temperature of the ultrasonic head to T, and the yield stress σ yT during temperature application at this temperature. Can be expressed by a quadratic approximate expression shown in the following expression (14).
この温度依存性は、バンプ材料や加工履歴によって異なると考えられるため、一般的には、以下の式（１５）に示す多項近似式で表すことができるものと考えられる。この式（１５）が、前述した式（１）である。ここで、α1、α2、α3・・・は常数、σyは常温におけるバンプの実効降伏応力である。従って、同種のバンプを使用した実験により、予め常数α1、α2、α3・・・を求めておけば、実効降伏応力σyから温度印加時降伏応力σyTを推定する（求める）ことができる。 Since this temperature dependency is considered to vary depending on the bump material and processing history, it is generally considered that the temperature dependency can be expressed by a polynomial approximation represented by the following equation (15). This formula (15) is the above-described formula (1). Here, α 1 , α 2 , α 3 ... Are constants, and σ y is the effective yield stress of the bump at room temperature. Therefore, if the constants α 1 , α 2 , α 3 ... Are obtained in advance by experiments using the same type of bump, the yield stress σ yT during temperature application is estimated ( calculated ) from the effective yield stress σ y. Can do.
なお、上述の評価は、金ワイヤバンプをビルドアップ基板（ＦＣ−ＢＧＡ型専用評価基板）のパターン上で圧縮変形させたものであるが、ヘッド温度３５０℃のデータが他と異なり、荷重が増加しても変形が進まないことがわかる。これは、温度上昇によって基板材料が軟化し荷重印加時に銅箔が樹脂中に沈み込んでいるがため、本モデル式どおりに変形が進んでいないものと考えられる。このように、本モデル式によってバンプ変形寸法を予測することによって、この予測から外れた場合の他因子の影響性を評価することにも応用できる。 In the above evaluation, the gold wire bump was compression-deformed on the pattern of the build-up substrate (FC-BGA dedicated evaluation substrate), but the data at the head temperature of 350 ° C. was different from the others, and the load increased. However, it can be seen that the deformation does not progress. This is thought to be because the substrate material softens due to the temperature rise and the copper foil sinks into the resin when a load is applied, so that the deformation does not proceed according to this model formula. Thus, by predicting the bump deformation dimension by this model formula, the present invention can be applied to the evaluation of the influence of other factors in the case of deviation from this prediction.
［４．０］超音波接合におけるバンプ変形挙動
超音波接合では、ヘッドはチップ裏面から基板に向けて圧縮方向に荷重を加えつつチップ面に水平な超音波振動を加えるが、この超音波振動によって金バンプの変形抵抗が低下して変形し易くなる「Ｂｌａｈａ」効果と呼ばれる現象が生じる。これは、振動によって塑性変形時の金属結晶内の転位におけるポテンシャル障壁を下げる効果といわれている。ただし、チップに水平方向の振動を加えてもバンプ内部の応力方向は複雑であり、縦方向の圧縮応力成分も生じることを考慮すれば、実質的には接合装置が静的に加える荷重に加味して超音波振動による応力が加わっているため、上述した変形が進むと考えることができる。
[4.0] Bump deformation behavior in ultrasonic bonding In ultrasonic bonding, the head applies a horizontal ultrasonic vibration to the chip surface while applying a load in the compression direction from the back of the chip toward the substrate. A phenomenon called “Blaha” effect occurs in which the deformation resistance of the gold bump is lowered and the gold bump is easily deformed. This is said to be the effect of lowering the potential barrier at dislocations in the metal crystal during plastic deformation by vibration. However, even if horizontal vibration is applied to the chip, the stress direction inside the bumps is complex and the compressive stress component in the vertical direction is also generated. Since stress due to ultrasonic vibration is applied, it can be considered that the above-described deformation proceeds.
これを式（１３）で表現するためには、超音波振動による縦方向の圧縮応力を接合装置が加える圧縮応力に加えて荷重Ｆを見積もればよいが、超音波振動による圧縮応力を計算することは実質的に困難であるため、式（１３）の荷重Ｆは接合装置が加える荷重のみとし、実効降伏応力σyが見かけ上で低下すると考えれば、［１．０］，［３．０］項で示した近似計算を適用できる。 In order to express this by the expression (13), it is only necessary to estimate the load F by adding the longitudinal compressive stress caused by the ultrasonic vibration to the compressive stress applied by the bonding apparatus. Since the load F in the equation (13) is only the load applied by the joining device and the effective yield stress σ y is apparently reduced, [1.0], [3.0] The approximation calculation shown in the section can be applied.
そこで［３．０］項で示した実験と同様に，今度はヘッド温度２００℃（ステージ温度７６℃）で超音波をヘッド振幅で０，１，２，３μｍと変えて印加して圧縮変形させ、変形させたバンプ高さを測定して式（１３）の数式モデルで整理し、ヘッド振幅毎に降伏応力を推定する。なお、摩擦係数μは、［３．０］項で示した実験と同様に０．８と仮定している。 Therefore, in the same way as the experiment shown in the section [3.0], this time, at a head temperature of 200 ° C. (stage temperature of 76 ° C.), an ultrasonic wave is applied with a head amplitude changed to 0, 1, 2, 3 μm to compress and deform it. Then, the deformed bump height is measured and organized by the mathematical model of formula (13), and the yield stress is estimated for each head amplitude. The friction coefficient μ is assumed to be 0.8, similar to the experiment shown in [3.0].
状態量δを横軸にとりヘッド振幅毎の実効降伏応力を整理すると、図１４に示すとおりとなり、このときの超音波印加時降伏応力σyUSは、状態量δが増加するに従って減少し、図１３（ａ）と似たほぼ直線に近い緩やかな曲線となる。具体的には、振幅３μｍを荷重と共に印加すると、荷重のみを加えて圧縮変形させた場合の２倍の変形面積が得られることを示している。 When the effective yield stress for each head amplitude is arranged with the state quantity δ on the horizontal axis, it is as shown in FIG. 14, and the yield stress σ yUS at the time of ultrasonic application at this time decreases as the state quantity δ increases, and FIG. A gentle curve close to a substantially straight line similar to (a) is obtained. Specifically, it is shown that when an amplitude of 3 μm is applied together with a load, a deformation area twice as large as that obtained by compressing and deforming only the load can be obtained.
この振幅依存性は、以下の式（１６）に示す２次の近似式で表すことができる。 This amplitude dependency can be expressed by a quadratic approximate expression shown in the following expression (16).
従って、［３．０］項において温度上昇に伴って実効降伏応力が減少することを多項近似式で表したことと同様に一般的には、以下の式（１７）で表すことができると考えられる。ここで、β1、β2、β3・・・は常数、σyTは式（１５）で示したヘッド温度Ｔとした場合の超音波を加えていない場合の降伏応力を示す温度印加時降伏応力である。従って、同種のバンプを使用した実験により、予め常数β1、β2、β3・・・を求めておけば、式（１５）より推定した温度印加時降伏応力σyTから温度印加時降伏応力σyTを求める（推定する）ことができる。 Therefore, in general, it can be expressed by the following equation (17) as expressed by the polynomial approximation that the effective yield stress decreases as the temperature rises in the [3.0] term. It is done. Here, β 1 , β 2 , β 3 ... Are constants, and σ yT is the yield stress at the time of application of temperature indicating the yield stress when no ultrasonic wave is applied when the head temperature T shown in Equation (15) is applied. It is stress. Therefore, if the constants β 1 , β 2 , β 3 ... Are obtained in advance by experiments using the same type of bumps, the yield stress at temperature application is calculated from the yield stress σ yT at temperature application estimated from equation (15). σ yT can be obtained (estimated).
また、式（１７）のように表すことで、超音波出力（ヘッド振幅）とヘッド温度を同様に扱うことができる。例えば、図１３（ａ）で得た実効降伏応力の温度依存性は１０℃当たり概ね−２．８ＭＰａであり、図１４より、ヘッド振幅依存性は１μｍ当たり概ね−２０ＭＰａである。これは、例えば１３０℃，２μｍと、２００℃，１μｍのバンプ変形量は、同じであることを意味する。すなわち、バンプ変形量を基準にすれば、ヘッド振幅１μｍの増加は温度換算で約７０℃弱の温度上昇に相当する「超音波出力と温度の等価性」を定量的に表すことができる。なお、上述では、印加する超音波の指標となる状態量δとして、印加する超音波の振幅（ヘッド振幅）を用いるようにしたが、これに限るものではなく、状態量δとして、超音波ヘッドに印加する電力（出力Ｗ）を用いるようにしても同様である。 Further, by expressing as in Expression (17), it is possible to handle the ultrasonic output (head amplitude) and the head temperature in the same manner. For example, the temperature dependence of the effective yield stress obtained in FIG. 13A is about −2.8 MPa per 10 ° C., and the head amplitude dependence is about −20 MPa per 1 μm from FIG. This means that, for example, the bump deformation amounts at 130 ° C. and 2 μm and 200 ° C. and 1 μm are the same. In other words, on the basis of the amount of bump deformation, an increase in head amplitude of 1 μm can quantitatively represent “equivalence between ultrasonic output and temperature” corresponding to a temperature increase of about 70 ° C. in terms of temperature. In the above description, the amplitude (head amplitude) of the applied ultrasonic wave is used as the state quantity δ serving as an index of the applied ultrasonic wave. However, the present invention is not limited to this, and the ultrasonic head is used as the state quantity δ. The same applies to the case where the power (output W) applied to is used.
［５．０］接合剪断強度の予測法
接合条件を評価する際は、理想的な接合状態における強度と比較することで、設定した接合条件が適切か否かの判断を行うことが必要になる。
[5.0] Prediction method of joining shear strength When evaluating joining conditions, it is necessary to determine whether or not the set joining conditions are appropriate by comparing with the strength in an ideal joining state. .
界面活性化による常温接合又は超音波接合など、界面における凝着現象を利用した接合における理想的な接合条件下では、接合界面の破断応力は、金属バンプ自体の同破断応力に等しいかやや小さい値を示す。この原因の一つとして、先ず、超音波の印加などの界面活性化による常温接合では、凝着による強度自体がバルク強度よりも強くなるため、全面密着状態を強制破断させると界面近傍のバルク側で破断することが挙げられる。また、超音波接合の場合には、接合初期では界面の摺動と新生面形成によって接合が進み強度が増加するが、金属バンプ自体の強度に達した時点で界面の摺動が止まり、これより先は、金属バンプあるいは被接合体の弾塑性変形が優勢となり、強度増加の要因となる新生面形成が発生しないため、結果としてバルク強度とほぼ同等な値を示すものと考えられる。 Under ideal joining conditions for joints that use adhesion phenomena at the interface, such as room temperature bonding or ultrasonic bonding due to interface activation, the fracture stress at the joint interface is equal to or slightly smaller than the fracture stress of the metal bump itself. Indicates. As one of the causes, first, at room temperature bonding by activation of the interface such as application of ultrasonic waves, the strength itself due to adhesion becomes stronger than the bulk strength. It is mentioned that it breaks. In the case of ultrasonic bonding, bonding progresses and the strength increases due to the sliding of the interface and the formation of a new surface at the initial stage of bonding, but the sliding of the interface stops when the strength of the metal bump itself is reached. Is presumed to exhibit a value almost equal to the bulk strength because the formation of a new surface that causes an increase in strength does not occur because the elasto-plastic deformation of the metal bumps or the joined body becomes dominant.
従って、理想的な接合状態の剪断強度は、金属バンプの剪断方向の降伏応力τと接合面積Ｓによって計算することができる。すなわち、本発明における圧縮変形モデルを用いることで、降伏応力σyと接合面積Ｓを計算できるため、以下に示す手順により、接合条件として設定する荷重・温度・超音波出力から、理論強度である剪断強度ｆ（バンプの接合強度予測値ｆ）を推定することができる。 Therefore, the shear strength in the ideal bonded state can be calculated from the yield stress τ in the shear direction of the metal bump and the bonded area S. That is, since the yield stress σ y and the bonding area S can be calculated by using the compression deformation model in the present invention, the theoretical strength is obtained from the load / temperature / ultrasonic output set as the bonding condition by the following procedure. The shear strength f (prediction value f of bump bonding strength) can be estimated.
引張方向で定義される実効降伏応力σyと剪断方向の降伏応力τは、一般的な材料力学理論から以下の式（１８）の関係にあることが知られている（非特許文献７参照）。すなわち、剪断降伏は引張降伏の０．５０〜０．５８倍で生じる。 It is known that the effective yield stress σ y defined in the tensile direction and the yield stress τ in the shear direction have the relationship of the following formula (18) from general material mechanics theory (see Non-Patent Document 7). . That is, shear yield occurs at 0.50 to 0.58 times the tensile yield.
また、剪断方向の降伏応力τについても、式（１２）と同様に、剪断強度ｆと接合面積Ｓから式（１９）で表される。なお、降伏応力τは平均的な剪断応力として扱う。従って、剪断強度ｆは、以下の式（２０）で表される。なお、この場合の実効降伏応力σyは強度試験の環境温度（通常は常温；２５℃程度）における値を用いる。 Also, the yield stress τ in the shear direction is expressed by the equation (19) from the shear strength f and the bonding area S, as in the equation (12). Yield stress τ is treated as an average shear stress. Therefore, the shear strength f is expressed by the following formula (20). In this case, the effective yield stress σ y is a value at the environmental temperature of the strength test (normally normal temperature; about 25 ° C.).
ただし、式（１９）は、加工硬化の生じない場合に用いられるもので、圧縮変形では完全塑性と仮定したが、破断に至る応力を考えた場合には図１５で示すような加工硬化による応力増加を無視できない。従って、現実的には破断応力（最大強さ）と降伏応力との比として常数θを用い、式（１９）、（２０）を、各々以下の式（２１）、（２２）と書き改めることにする。この式（２２）の右辺の降伏応力（実効降伏応力）σy及び接合面積Ｓ以外を常数φとした式が、前述の式（５）である。 However, equation (19) is used when work hardening does not occur, and it is assumed that the plastic deformation is complete plasticity. However, when the stress to break is considered, the stress due to work hardening as shown in FIG. The increase cannot be ignored. Therefore, in reality, the constant θ is used as the ratio between the breaking stress (maximum strength) and the yield stress, and the expressions (19) and (20) are rewritten as the following expressions (21) and (22), respectively. To. The above equation (5) is an equation in which a constant φ other than the yield stress (effective yield stress) σ y and the bonding area S on the right side of the equation (22) is used.
なお、本来、常数θは、剪断方向の強度試験によって求めておくことが望ましいが、材料物性として一般的に用いられている引張方向の応力−ひずみ曲線から類推しても大きな違いは見られないとすれば、例えば、金ワイヤバンプの場合には、図１５に示す応力−歪み曲線より約１．４（破断応力は降伏応力の４０％増）となる。従って、この場合の式（２２）は、最大強度を推定する目的で使う場合には式（２３）となり、剪断方向の降伏応力τは、実効降伏応力σyの８０％程度と見込めばよいことになる。 In addition, it is desirable that the constant θ is originally determined by a strength test in the shear direction, but no significant difference can be seen by analogy with the stress-strain curve in the tensile direction generally used as material properties. For example, in the case of gold wire bumps, the stress-strain curve shown in FIG. 15 is about 1.4 (the breaking stress is 40% increase of the yield stress). Therefore, the equation (22) in this case becomes the equation (23) when used for the purpose of estimating the maximum strength, and the yield stress τ in the shear direction should be expected to be about 80% of the effective yield stress σ y. become.
実際に、［３．０］項の図１２（ａ），図１２（ｂ）で結果を示した実験において、ワイヤバンプの常温における実効降伏応力が１７０ＭＰａである結果を得ているが、これより強度を推定すると１４０ＭＰａ程度となり、超音波接合を行った場合に得られる単位面積当たりの剪断強度（バルク破断）１００〜１５０ＭＰａとほぼ一致する。なお、バンプ当たりの具体的な剪断強度についても、荷重・温度・超音波出力の各接合条件を変えた場合の接合面積Ｓを［１．０］〜［４．０］項に示した圧縮変形モデルから計算することで推定できる。 Actually, in the experiment whose results are shown in FIG. 12A and FIG. 12B in the section [3.0], the effective yield stress of the wire bump at room temperature is 170 MPa. Is about 140 MPa, which is almost the same as the shear strength (bulk fracture) of 100 to 150 MPa per unit area obtained when ultrasonic bonding is performed. As for the specific shear strength per bump, the compression area shown in [1.0] to [4.0] is the bonding area S when the bonding conditions of load, temperature, and ultrasonic output are changed. It can be estimated by calculating from the model.
［６．０］マイクロボールの変形挙動
マイクロボール（球形粒子）の変形挙動についても、変形過程においては円柱型に近似できる。円柱の場合には変形面積が増加し、高さが減少する相関を体積一定の関係から単純な式（１０）で表すことができた。しかし、初期形状が球の場合には、変形面積と高さの関係を与える式を仮定する必要がある。
[6.0] Deformation behavior of microballs The deformation behavior of microballs (spherical particles) can also be approximated to a cylindrical shape in the deformation process. In the case of a cylinder, the correlation in which the deformation area increases and the height decreases can be expressed by a simple equation (10) from the relationship of constant volume. However, when the initial shape is a sphere, it is necessary to assume an expression that gives the relationship between the deformation area and the height.
ここで、発明者は、１軸圧縮における球体の変形において、図１６（ａ），図１６（ｂ），図１６（ｃ）に示すとおり、変形部の外周円をバンプ中心からの半径ｒとして表した場合に、この径がバンプ全体の曲率半径にほぼ等しいものと考えた。つまり、バンプ表面は、常に同じ曲率半径ｒの中心を持つ（曲率半径自体はバンプ変形とともに増加する）ことを意味するから式（２４）に示すｈ、ｒ、ｄの相関式が得られる。 Here, in the deformation of the sphere in the uniaxial compression, the inventor sets the outer periphery circle of the deformed portion as the radius r from the bump center as shown in FIGS. 16 (a), 16 (b), and 16 (c). When expressed, this diameter was considered to be approximately equal to the radius of curvature of the entire bump. That is, the bump surface always has the center of the same radius of curvature r (the radius of curvature itself increases with the deformation of the bump), so the correlation equation of h, r, d shown in equation (24) is obtained.
また、変形前の体積Ｖ1と変形後の体積Ｖ2とは等しいから、式（２４）を用いて整理すると、以下の式（２５）が得られ、変形部半径ｄを初期ボール径Ｄ、変形後高さｈのみで表すことができる。すなわち、変形面積はｄより求めることができるから、高さｈより変形面積（接合面積）Ｓを求めることができる。 Further, since the volume V 1 before deformation and the volume V 2 after deformation are equal, when rearranged using the equation (24), the following equation (25) is obtained, and the deformed portion radius d is set to the initial ball diameter D, It can be expressed only by the height h after deformation. That is, since the deformation area can be obtained from d, the deformation area (joint area) S can be obtained from the height h.
また、変形過程の降伏圧力σyieldは、荷重Ｆと変形面積Ｓ（マクロ的な接触面積）との比（式（１２）参照）なので、式（９）を書き改めた式（２６）に式（２５）を代入して整理すると式（２７）が得られる。 Further, since the yield pressure σ yield in the deformation process is a ratio of the load F and the deformation area S (macro contact area) (see Expression (12)), Expression (26) is rewritten from Expression (9). Substituting (25) and rearranging gives equation (27).
このように、マイクロボールの場合も、材料物性（実効降伏応力と摩擦係数）を仮定すれば、変形に必要な荷重Ｆはボール高さｈを変数として、初期ボール径Ｄが与えられれば一義的に表すことができる。また、［２．０］項に示したとおり、逆関数として荷重Ｆからボール高さｈ、変形面積Ｓを計算できる。 Thus, even in the case of microballs, assuming material properties (effective yield stress and friction coefficient), the load F required for deformation is unambiguous if the initial ball diameter D is given with the ball height h as a variable. Can be expressed as Further, as shown in the section [2.0], the ball height h and the deformation area S can be calculated from the load F as an inverse function.
ところで、２個の未知数（常数）である摩擦係数μと実効降伏応力σyの特定について、［２．０］項及び［３．０］項で示した実験例では、変形範囲が狭くデータ数が少ないことより、実測プロットの曲率を考慮しつつ摩擦係数をある値に仮定しておき、残された未知数である実効降伏応力は実測プロットの位置から近似計算に合う値を推定した。しかし、変形範囲を広くとれるデータが取得できる場合には、以下に示すように、２段階の最小二乗法によって、より確度の高い常数の推定が可能となる。 By the way, in the experimental example shown in the items [2.0] and [3.0] for specifying the friction coefficient μ and the effective yield stress σ y which are two unknowns (constants), the deformation range is narrow and the number of data Therefore, the coefficient of friction was assumed to be a certain value in consideration of the curvature of the actual plot, and the effective yield stress, which is the remaining unknown, was estimated from the position of the actual plot to a value suitable for the approximate calculation. However, when data that can take a wide deformation range can be acquired, it is possible to estimate a constant with higher accuracy by a two-step least square method as shown below.
先ず、ある任意の実効降伏応力σy(i)を仮定し、次に、摩擦係数μを０．３〜０．８程度の範囲の中で順次変えて荷重Ｆ毎の高さの計算値ｈμを求め、実験における各荷重水準毎に高さの実測値ｈと計算値ｈμとの差を二乗したもの求め、この総和が最小となる摩擦係数μを特定する。次に、特定した摩擦係数μを用い、実効降伏応力σyを予想される範囲で順次変えて計算値ｈμを求め、同様な最小二乗法により実効降伏応力σy(i)を特定する。これにより、摩擦係数の最適値が若干変動する場合には、上記を繰り返して微調して最適な、摩擦係数μと実効降伏応力σyとの２つ常数を決定する。 First, an arbitrary effective yield stress σ y (i) is assumed, and then the calculated value h of the height for each load F is changed by sequentially changing the friction coefficient μ within a range of about 0.3 to 0.8. μ is obtained, the difference between the measured height h and the calculated value h μ is squared for each load level in the experiment, and the friction coefficient μ that minimizes the sum is specified. Next, using the identified friction coefficient μ, the effective yield stress σ y is sequentially changed within the expected range to obtain the calculated value h μ, and the effective yield stress σ y (i) is specified by the same least square method. As a result, when the optimum value of the friction coefficient varies slightly, the above two repetitions of the friction coefficient μ and the effective yield stress σ y are determined by fine adjustment by repeating the above.
この一例として、直径が２００μｍの金ボールを圧縮変形させて高さを測定し、荷重との相関を式（２７）によって表し、実測値と摩擦係数μ及び実効降伏応力σyとの関係を求めると、数回の微調の末、結果的には図１７に示すとおりとなる。この結果より、摩擦係数μは０．４５、実効降伏応力σyは１２０ＭＰａが、最小二乗法における最も適切な値として得られる。 As an example of this, a gold ball having a diameter of 200 μm is subjected to compression deformation, the height is measured, the correlation with the load is expressed by equation (27), and the relationship between the measured value, the friction coefficient μ, and the effective yield stress σ y is obtained. After a few fine adjustments, the result is as shown in FIG. From this result, a friction coefficient μ of 0.45 and an effective yield stress σ y of 120 MPa are obtained as the most appropriate values in the least square method.
このようにして得られた常数に基づき、荷重Ｆと高さｈの関係を表すと、図１８に示すとおりとなり、図中白丸のプロットで示す実験値と、図中実線で示す式（２７）による近似曲線（変形モデル曲線）とが、非常に良く一致する。 Based on the constants thus obtained, the relationship between the load F and the height h is represented as shown in FIG. 18, and the experimental value indicated by the white circle in the figure and the equation (27) indicated by the solid line in the figure. And the approximate curve (deformed model curve) by the above agree very well.
また、初期ボール径Ｄと変形後の高さｈ又は変形部径ｄとの比を、各々圧縮率Ｐ、扁平率Ｂとした以下に示す式（２８）、式（２９）として定義して無次元化し、荷重との関係について近似計算結果と実験値を比較すると、図１９に示すとおりとなる。図１９からわかるとおり、扁平率が１以上、すなわち変形部径が初期ボール径以上になるためには、材料物性や大きさに係わらず圧縮率を０．５５以下にすることが必要となる。つまり、接合部材にマイクロボールを使用した場合、導電路となる接合面積を使用するマイクロボール径以上にするためには、マイクロボールの径が初期の半分以下になるまで押しつぶせばよいことが分かる。 Further, the ratio between the initial ball diameter D and the height h after deformation or the deformed portion diameter d is defined as the following expression (28) and expression (29), where the compression ratio is P and the flatness ratio is B, respectively. FIG. 19 shows the result of dimensionalization and comparison of the approximate calculation result and the experimental value with respect to the relationship with the load. As can be seen from FIG. 19, in order for the flatness ratio to be 1 or more, that is, for the deformed portion diameter to be greater than or equal to the initial ball diameter, the compression ratio needs to be 0.55 or less regardless of the material properties and size. In other words, when a microball is used as the joining member, it can be understood that in order to make the joining area to be a conductive path larger than the diameter of the microball to be used, it is sufficient to squeeze until the diameter of the microball is less than half of the initial diameter .
なお、摩擦係数を前述のような最小二乗法を用いて求める場合には、変形範囲を広く採り、曲線の曲率に差が出やすいデータを得る必要があるが、図１９からわかるとおり圧縮率０．４付近で曲線の接線に大きな変化が生じるため、この点を中心とする圧縮率０．７５〜０．２５において少なくとも３点以上、望ましくは計５点以上のデータを取得することが必要であることがわかる。 Note that, when the friction coefficient is obtained by using the least square method as described above, it is necessary to take a wide deformation range and obtain data in which a difference in the curvature of the curve is likely to occur. Since a large change occurs in the tangent of the curve at around 4., it is necessary to acquire data of at least 3 points, preferably a total of 5 points or more at a compression ratio of 0.75 to 0.25 centered on this point. I know that there is.
なお、本モデルの基本式となる式（８）は公知の近似式であるが、マイクロボールの変形挙動を表すために用いた式（２４）は、発明者が独自に仮定したものであるため、実験値と比較してこの妥当性を検証する。この検証は、上記実験において高さとともに圧縮変形部径ｄ及び最外径２ｒを実測し、これと式（２５）及び式（２４）より得られる近似値を比較することにより行う。この結果、図２０に示す圧縮による変形部径近似値ｄについては、変形初期においては実測値とのズレが大きいが、変形の進行とともに近似値に近づき実際の接合に用いられるようなアスペクト比０．５〜０．２程度の範囲では、実験値により近い値を与えることがわかる。また、図２１に示す最外径２近似値ｒについては、実測した全領域で近似値とよい一致を示していることがわかる。 Note that the formula (8), which is the basic formula of this model, is a well-known approximate formula, but the formula (24) used to represent the deformation behavior of the microball is uniquely assumed by the inventor. This validity is verified by comparison with experimental values. This verification is performed by actually measuring the compression deformation portion diameter d and the outermost diameter 2r together with the height in the above experiment, and comparing this with approximate values obtained from the equations (25) and (24). As a result, the deformed portion diameter approximate value d by compression shown in FIG. 20 has a large deviation from the actually measured value in the initial stage of deformation, but the aspect ratio becomes 0 as it approaches the approximate value as the deformation progresses and is used for actual joining. It can be seen that a value closer to the experimental value is given in the range of about 0.5 to 0.2. In addition, it can be seen that the outermost diameter 2 approximate value r shown in FIG. 21 shows a good agreement with the approximate value in all measured regions.
なお、図２０における変形初期における実験値との差については、図２１がよい一致を示していることから、変形量が小さい場合には、弾性変形や局部変形の影響を受けており、実際の塑性変形面積が小さいことが示唆される。しかし、変形初期において高さに関する近似に多少の差異があったとしても、変形初期においては降伏圧力比の変化は少ない。つまり、高さに多少の誤差が生じても、変形抵抗に及ぼす影響が少ないため、図１７で示すような荷重と高さの関係として表せば、近似値と実験値は良く一致したものになるものと考えられる。従って、実際の接合における圧縮変形量を予測する上では、十分な計算精度であると言える。 As for the difference from the experimental value in the initial stage of deformation in FIG. 20, since FIG. 21 shows good agreement, when the amount of deformation is small, it is affected by elastic deformation and local deformation, It is suggested that the plastic deformation area is small. However, even if there is some difference in the approximation regarding the height in the early stage of deformation, the change in the yield pressure ratio is small in the early stage of deformation. In other words, even if a slight error occurs in the height, there is little effect on the deformation resistance. Therefore, if expressed as a relationship between the load and the height as shown in FIG. It is considered a thing. Therefore, it can be said that the calculation accuracy is sufficient for predicting the amount of compressive deformation in actual joining.
また、前述したように、バンプ当たりの具体的な剪断強度については、荷重・温度・超音波出力の各接合条件を変えた場合の接合面積Ｓを［１．０］〜［４．０］項に示した圧縮変形モデルから計算することで推定できるが、マイクロボールの場合についても同様である。例えば、図１７に示したように、直径２００μｍの金マイクロボールの圧縮変形挙動から界面において強固な凝着が行われていると仮定した理想的な接合剪断強度ｆは、接合時の荷重Ｆに対して図２２に示すとおりに推定することができる。なお、ここでは、常温における圧着のみによる常温接合を行った場合の式（２３）による最大強度の推定値として計算しており、常温の実効降伏応力σyは実験より得られた１２０ＭＰaを用いている。 In addition, as described above, regarding the specific shear strength per bump, the bonding area S when the bonding conditions of load, temperature, and ultrasonic output are changed is the items [1.0] to [4.0]. Although it can be estimated by calculating from the compression deformation model shown in (1), the same applies to the case of a microball. For example, as shown in FIG. 17, the ideal joint shear strength f assuming that strong adhesion is performed at the interface due to the compression deformation behavior of a gold microball having a diameter of 200 μm is equal to the load F at the time of joining. On the other hand, it can be estimated as shown in FIG. Here, calculation is performed as an estimated value of the maximum strength according to the equation (23) when normal temperature bonding is performed only by crimping at normal temperature, and the effective yield stress σ y at normal temperature is 120 MPa obtained from an experiment. Yes.
ところで、本発明における圧縮変形モデルを用いれば、従来では直接測定が困難であった微小金属球形粒子の硬さを、実効降伏応力として測定することに応用可能である。近年では、ＢＧＡ（Ball Grid Array）や、フリップチップ及びフレキシブル基板端子接続（ＦＯＢ；Flex On Board）などの電子部品の接続では、微細な導電粒子を介して電極間の電気的な接続を取る技術が開発されている。この技術でも、金属微粒子の降伏応力の把握が重要となる。 By the way, if the compression deformation model in the present invention is used, it can be applied to the measurement of the hardness of fine metal spherical particles, which has been difficult to directly measure conventionally, as an effective yield stress. In recent years, in the connection of electronic components such as BGA (Ball Grid Array), flip chip and flexible board terminal connection (FOB: Flex On Board), a technique for establishing electrical connection between electrodes via fine conductive particles Has been developed. Even with this technique, it is important to grasp the yield stress of metal fine particles.
従来の材料試験法は、引張試験によって降伏応力や破断強度が求められてきたが、微小球形粒子に対しては直接的に物性を測定することが困難であり、加工前の金属材料の物性値から加工後の物性を予測することが行われてきた。また、比較的粒子径の大きなものであれば、ビッカース法など測定法により、圧子を押し込みこの打痕跡の大きさで硬度を測定し、測定した硬度と降伏応力との換算式を元に、硬さを推定することができる。しかし、表面形状が曲面でしかも微小径の場合は、圧子で打痕を付ける大きさに限界がり、また微小圧子によるマイクロビッカース法を使ったとしても、押し込み深さが浅く表面の情報しか得られないという問題があった。 In conventional material testing methods, yield stress and rupture strength have been determined by tensile tests, but it is difficult to directly measure physical properties of microspherical particles, and physical properties of metal materials before processing It has been performed to predict physical properties after processing. If the particle size is relatively large, the indenter is pushed in by a measuring method such as the Vickers method, the hardness is measured by the size of the dents, and the hardness is calculated based on the conversion formula between the measured hardness and the yield stress. Can be estimated. However, if the surface shape is curved and has a small diameter, there is a limit to the size of the indentation with the indenter, and even if the micro Vickers method with a small indenter is used, only the surface information is obtained because the indentation depth is shallow. There was no problem.
接合分野においては、デバイスの小型化・狭ピッチ化に伴い接続材料微小化が進んでおり、使用材料物性の直接測定は重要な課題となっている。微小材料に対して直接的に試験が行える「圧縮試験法」自体は以前からも用いられてはいたが、変形荷重と高さ、降伏応力との相関が明らかになっておらず、これまでは、専らある一定の圧縮率にまで変形させるために必要な荷重をサイズ毎に比較する方法が採られていた。 In the bonding field, miniaturization of connecting materials is progressing with the miniaturization and narrowing of devices, and direct measurement of the physical properties of materials used is an important issue. The “compression test method” itself, which allows direct testing of minute materials, has been used for some time, but the correlation between deformation load, height, and yield stress has not been clarified. In other words, a method has been adopted in which the load necessary for deforming to a certain compression rate is compared for each size.
この圧縮試験法において、本発明に係る上述した実施の形態の式（３）による圧縮変形モデルを適用することで、実際の接合状態に近い試験方法で材料の降伏応力を推定することが可能であり、接合技術のみならず各種力学的シミュレーションなどの理論予測に役立てることができると考えられる。 In this compression test method, it is possible to estimate the yield stress of the material by a test method close to the actual bonded state by applying the compression deformation model according to the equation (3) of the above-described embodiment according to the present invention. Yes, it can be used not only for joining technology but also for theoretical predictions such as various mechanical simulations.
１０１…温度条件設定部、１０２…超音波条件設定部、１０３…変形バンプ高さ算出部、１０４…接合面積算出部、１０５…接合強度予測部、３０１…半導体チップ、３０２…金バンプ、３０３…回路基板、３０４…接続端子、３０５…超音波ヘッド、３０６…荷重印加部、３０７…ホットプレート、３０８…超音波発生部、３０９…加熱温度設定部、３１０…ステージ、３５１…吸着ノズル、３５２…加熱部、３５３…超音波振動伝達部。 DESCRIPTION OF SYMBOLS 101 ... Temperature condition setting part, 102 ... Ultrasonic condition setting part, 103 ... Deformation bump height calculation part, 104 ... Bonding area calculation part, 105 ... Bonding strength estimation part, 301 ... Semiconductor chip, 302 ... Gold bump, 303 ... Circuit board 304 ... Connection terminal 305 ... Ultrasonic head 306 ... Load application unit 307 ... Hot plate 308 ... Ultrasonic wave generation unit 309 ... Heating temperature setting unit 310 ... Stage 351 ... Suction nozzle 352 ... Heating unit, 353... Ultrasonic vibration transmission unit.
Claims (1)
以下の式（１）を用い、常温における前記バンプの降伏応力σy及び予め得られている常数α1，α2，α3，・・・をもとに、熱を前記バンプに印加して常温より温度Ｔ上昇させたときの前記バンプの降伏応力である温度印加時降伏応力σyTを求める第１ステップと、
以下の式（２）を用い、前記温度印加時降伏応力σyT及び予め得られている常数β1，β2，β3，・・・をもとに、さらに振幅δの超音波を前記バンプに印加したときの前記バンプ降伏応力である熱、超音波印加時降伏応力σyUSを求める第２ステップと、
以下の式（３）を用い、前記熱、前記超音波印加時降伏応力σyUS，予め測定されている初期状態の前記バンプの高さｈ0，初期状態の前記バンプの等価的な径Ｄ0，及び前記バンプとこのバンプが接合される前記接続端子との間の摩擦係数μをもとに、さらに荷重Ｆを印加した超音波接合により変形した後の前記バンプの高さである接合バンプ高さｈを求める第３ステップと、
以下の式（４）を用い、前記高さｈ0，前記径Ｄ0，及び前記接合バンプ高さｈをもとに、このバンプと前記接続端子との接合面積Ｓを求める第４ステップと、
以下の式（５）を用い、前記接合面積Ｓ，常温における前記バンプの降伏応力σy，及び予め得られている常数φをもとに接合強度予測値ｆを求める第５ステップと
を少なくとも備えることを特徴とする超音波接合強度の予測方法。
Using the following equation (1), heat is applied to the bump based on the yield stress σ y of the bump at room temperature and the constants α 1 , α 2 , α 3 ,. A first step for obtaining a yield stress σ yT at the time of temperature application, which is a yield stress of the bump when the temperature T is raised from room temperature;
Using the following formula (2), ultrasonic waves having an amplitude δ are further applied to the bumps based on the yield stress σ yT when temperature is applied and the constants β 1 , β 2 , β 3 ,. A second step of determining the yield stress σ yUS at the time of application of heat and ultrasonic wave, which is the bump yield stress when applied to
Using the following equation (3), the heat, the yield stress σ yUS when applying ultrasonic waves, the height h 0 of the bump in the initial state measured in advance, and the equivalent diameter D 0 of the bump in the initial state , And the bump height that is the height of the bump after being deformed by ultrasonic bonding to which a load F is applied based on the friction coefficient μ between the bump and the connection terminal to which the bump is bonded. A third step for determining the length h;
A fourth step of obtaining a bonding area S between the bump and the connection terminal based on the height h 0 , the diameter D 0 , and the bonding bump height h using the following formula (4):
And at least a fifth step of obtaining a bonding strength predicted value f based on the bonding area S, the yield stress σ y of the bump at normal temperature, and a constant φ obtained in advance using the following equation (5): A method for predicting ultrasonic bonding strength.
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