CN107677697A - A kind of chip thermal deformation measurement method based on SEM - Google Patents
A kind of chip thermal deformation measurement method based on SEM Download PDFInfo
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- CN107677697A CN107677697A CN201710852515.8A CN201710852515A CN107677697A CN 107677697 A CN107677697 A CN 107677697A CN 201710852515 A CN201710852515 A CN 201710852515A CN 107677697 A CN107677697 A CN 107677697A
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N25/00—Investigating or analyzing materials by the use of thermal means
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/16—Measuring arrangements characterised by the use of optical techniques for measuring the deformation in a solid, e.g. optical strain gauge
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- G—PHYSICS
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B15/00—Measuring arrangements characterised by the use of electromagnetic waves or particle radiation, e.g. by the use of microwaves, X-rays, gamma rays or electrons
- G01B15/06—Measuring arrangements characterised by the use of electromagnetic waves or particle radiation, e.g. by the use of microwaves, X-rays, gamma rays or electrons for measuring the deformation in a solid
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Abstract
The present invention discloses the chip thermal deformation measurement method based on SEM, belong to material property detection technique field, the present invention utilizes the high depth of field and the high-resolution characteristic of SEM, by integrated with In Situ Heating device, heat affecting taken into full account and measurement error that systematical distortion is brought and it has been corrected；Using the speckle image after distortion correction, calculated by digital picture related algorithm and try to achieve chip due to the heated in-plane deformation field to be deformed.On the basis of the above, the present invention realizes the chip whole audience thermal deformation measurement of micro/nano-scale and applied in Practical Project.
Description
Technical field
The invention belongs to material property detection technique field, and in particular to a kind of chip heat based on SEM
Deformation measurement method.
Background technology
With the continuous progress of semicon industry, MEMS (Micro Electro-Mechanical Systems,
MEMS tremendous expansion) has been obtained.The form of MEMS generally use chip assembly is packaged manufacture.Chip assembly generally by
A variety of different nano material compositions, the modulus of elasticity of material is different with thermal coefficient of expansion, in different loads, humidity and temperature
Under the conditions of, material junction, which is also easy to produce crackle, causes chip failure.Especially in encapsulation process, the thermal expansion system of layers of material
Number has differences, and after packaging, chip internal structure has larger thermal stress, residual stress.This is in whole chip internal meeting
Cause thermal deformation, influence work response and the service life of whole chip.Therefore, the thermal deformation to chip under micro/nano-scale is entered
The accurate measurement of row, to understand chip material mechanical property and deformation characteristic, instruct micro-nano device design and manufacture, analysis core
The inefficacy mechanism of piece is significant.
However, as chip manufacturing process level develops rapidly, test-material yardstick constantly subtracts from micron dimension to nanometer scale
It is small.Therefore, to carry out deformation measurement to it also more and more difficult.
Under micro/nano-scale, in the wider conventional contact measuring method of macro-scale application such as：Foil gauge, extensometer etc.
No longer it is applicable.In recent years, with the development of optical field, there are a variety of optical measurement mechanics methods.According to the difference of measuring principle,
It can be divided into two major classes：Interferometric method and non-interfering method.For interference technique, mainly including holographic interference【M,
Houdellier F,Hüe F&Snoeck E.Nanoscale holographic interferometry for strain
measurements in electronic devices.Nature,2008,453(7198):1086-1089】, moire method
【Wang Q H,Xie H M,Hu Z X,Zhang J,Sun J&Liu G.Residual thermo-creep
deformation of copper interconnects by phase-shifting SEM moirémethod.Applied
Mechanics and Materials,2011,83:185-190】Deng.But above-mentioned interference method needs relatively harsh experiment bar
Part, such as：Coherent source, shockproof optical table and less measurement range etc..Therefore, the application of interferometric method has certain office
It is sex-limited.
For non-interfering method, digital picture correlation (Digital Image Correlation, DIC)【Sutton M A,
Orteu J J,Schreier H W.Image correlation for shape,motion and deformation
measurements.Springer,New York,doi,2009,10:978-0】It is that one of which typically represents.This method
Two dimension or 3 D deformation information, the light with previous intervention method are obtained using the correlation of body surface speckle image before and after deformation
Survey method is compared, measurement process and sample prepare it is simple, and without coherent laser illumination and vibration isolation, to measuring environment requirement compared with
It is low.
Due to above-mentioned advantage, it is most active and of greatest concern that Digital Image Correlation Method has turned into current experiment mechanics field
One of optical measurement mechanics method, material and body structure surface deformation measurement, mechanics and physical parameter in macroscopic view characterize and checking
Theory of mechanics and the correctness of finite element analysis etc. obtain a large amount of fruitful successful applications.
In micro/nano-scale, Digital Image Correlation Method can (such as optics shows with the digital imaging apparatus of different spatial resolutions
Micro mirror, SEM, AFM etc.) combine, present very strong technological adaptability and application potential.Its
In, SEM (SEM) has resolution ratio, the high depth of field, the ease for use height of nanoscale rank and enlargement ratio can
The features such as by low power (10 ×) to high power (up to 50000 ×) regulation, be to obtain the preferable of digital speckle image in microscopic fields
Approach.But because SEM image-forming principle is different from ordinary optical imaging device, cause that there is multiple in image
Miscellaneous distortion；Varying temperature environment can also impact to the stability of SEM and bring extra thermal noise；It is above-mentioned because
Element can reduce the measurement accuracy of chip thermal deformation.
In summary, it is necessary to a kind of new method be developed to overcome drawbacks described above, so as to improve the survey of chip thermal deformation
Accuracy of measurement.
The content of the invention
For the disadvantages described above or Improvement requirement of prior art, the invention provides a kind of based on SEM
Chip thermal deformation measurement method, it comprises the following steps：
S1：Speckle pattern is prepared on chip sample surface to be measured.
S2：Warm table with function of temperature control is placed in the working chamber of SEM, the chip that will be prepared
Sample (referred to as later：Sample) it is fixed on warm table；Effective contact of thermocouple and sample is kept simultaneously and by thermoelectricity even number
According to being transferred on the computer outside working chamber；Finally, using the ceramic sheet other positions exposed to warm table covered with
It is thermally shielded, prevents that Scanning Electron microscope is impacted and damaged.
S3:Open SEM Low-vacuum mode, regulation SEM enlargement ratio, operating distance etc.
Parameter simultaneously shoots specimen surface picture rich in detail under acquisition normal temperature.Keep sample and systematic parameter constant, in equal time spacing
Inside it is continuously shot the drift distortion D that N pictures rich in detail are used for SEMd(t) modeling, passes through scanning electron microscopy
The sample stage of mirror translates to sample, and clearly image is used for SEM sky for shooting 2 respectively before and after translation
Between distort DfModeling.
S4:The heating function for opening warm table heats to the sample in SEM working chamber, leads to simultaneously
Cross the temperature of contact thermocouple measurement sample and carry out real-time display and record, according to temperature display, preset equal temperature
It is spaced and shoots the sample picture rich in detail sequence under different temperatures, time, temperature and the figure of every image is shot under corresponding record
As sequence number, the distortion model D established in step S3 is utilizeddAnd D (t)fAll images are corrected.
S5:Using the first width (under normal temperature) image of image sequence in step S4 as reference picture, digital picture phase is utilized
Close algorithm【Schreier H,Orteu J J,Sutton M A.Image correlation for shape,motion and
deformation measurements.Springer US,2009】Image after several distortion corrections in step S4 is entered
Row correlation calculations, chip is obtained due to heated and caused in-plane deformation.
Further, in step S3, drift is distorted using N pictures rich in detail are continuously shot in equal time spacing
Dd(t) it is as follows to model detailed process：
Using first image of continuous acquisition image as reference picture, and the total number of images amount shot is N, utilizes numeral
Image is related, Scale invariant operator feature point extraction algorithm carries out characteristic matching acquisition to follow-up N-1 images and reference picture
Match set Φ={ Φi, i=2 ..., N }, obtain image X-direction and Y-direction motion vector set U={ Ui, i=2,
... N }, V={ Vi, i=2 ... N } and image capture moment set T={ T corresponding to themi, i=1 ..., N }, T1Represent
Reference picture shooting time.
Then in drift distortion velocity field v corresponding to image X-direction and Y-directionx,vyIt can obtain by the following method：
Wherein, num (Φ) represents the point quantity of characteristic matching set.
Drift distortion velocity field v is obtained by above formulax,vy, the drift distortion to some moment t models as follows：
Dd(t)=[dx(t),dy(t)]；
dx(t)=vxt；
dy(t)=vyt；
Wherein, dxAnd d (t)y(t) drift value in moment t whole image in X-direction and Y-direction is represented.
Further, in step S3, by translate sample obtain two clearly image to SEM space
Distort DfModeling process is as follows：
Df(p)=[dfx(p)dfy(p)]；
Wherein, p be image on any point pixel coordinate, dfx(p)dfy(p) in pixel coordinate p X-direction and Y-direction
On space distortion.Due to dfx(p)、dfy(p) there is equivalence, herein only for dfx(p) derived in detail, dfx(p) footpath is used
Represent as follows to the form of cardinal interpolation function：
Wherein, a0,ap, W={ w1,...wMIt is coefficient to be resolved, φ represents radial direction kernel function, ciRepresent control point, M
For control point number,.a0,ap, w={ w1,...wMSolution process it is as follows：
Before sample is translated, if certain location of pixels put is p on image1, the distortion of its corresponding X-direction is：After sample is translated, the point is from p1Position is moved to p2Position, then it is now right
The X-direction answered distorts：
Because the distortion of SEM central area is minimum, therefore before and after sample is translated, by centre bit
Carry out correlation calculations are put, real X-direction shift value R can be obtainedx.Can be for p1Point and p2Point, because Existential Space distorts,
By correlation calculations, p can be obtained1Point and p2The X-direction shift value of point is Ux.Following relation is had according to distortion principle：
By carrying out correlation calculations to translating two front and rear figures, in whole image plane, there is K groups shaped like p2
And p1Corresponding points.It is expressed as：P1={ p1(1)...p1(K)},P2={ p2(1)...p2(K) }, further with matrix form table
Up to for:
Wherein, ap, W={ w1,...wMIt is except a0Outer coefficient matrix to be resolved, Δ Θ are known two groups of preset radials
The matrix that basic function φ subtracts each other, its size are that (K is the front and rear corresponding points number by correlation calculations of translation to K × M, and M is radially
The number of control points of basic function), it is represented by for position therein for the element of (k, m)：Δ Θ (k, m)=[φ (| | p2
(k)-cm||)φ(||p1(k)-cm||)].Δ P is known set P1={ p1(1)...p1(K)},P2={ p2(1)...p2
(K) } corresponding element subtracts each other the matrix of composition, is expressed as Δ P=[p2(1)-p1(1)...p2(K)-p1(K)]。
By carrying out least square solution to above formula, you can obtain coefficient a to be askedpWith w={ w1,...wMSolution.
Further, because the distortion of picture centre is approximately 0, therefore can be by picture centre coordinate pCSubstitution formulaCalculated, can obtain coefficient a0Solution.
Thus, can obtain for space distortion d in any point p X-direction on imagefx(p) analytical form：Due to dfx(p)、dfy(p) there is theoretical equivalence, therefore, in Y-direction
Distortion repeats above-mentioned flow, you can obtains dfy(p) analytical form.And then can be to SEM space distortion Df
(p)=[dfx(p)dfy(p)] it is modeled.
The invention provides a kind of chip thermal deformation measurement method based on SEM, by by scanning electron
Microscope is combined with digital image correlation technique, gives full play to both technical advantages；Pass through the collection with In Situ Heating device
Into having taken into full account heat affecting and measurement error that systematical distortion is brought and it be corrected；Utilize dissipating after distortion correction
Spot image, calculate and try to achieve the in-plane deformation field that chip is deformed due to heated, realize chip thermal deformation under micro/nano-scale
Measurement, so as to provide comprehensive measurement data to study the mechanical property of nano material and deformation characteristic.
In general, by the contemplated above technical scheme of the present invention compared with prior art, it can obtain down and show
Beneficial effect：
The present invention using SEM the characteristic such as the high depth of field and high-resolution, by with In Situ Heating device
It is integrated, take into full account heat affecting and measurement error that systematical distortion is brought and it has been corrected；After distortion correction
Speckle image, calculated by digital picture related algorithm and try to achieve chip due to the heated in-plane deformation field to be deformed.Upper
On the basis of stating, the present invention realizes the chip whole audience thermal deformation measurement of micro/nano-scale and applied in Practical Project.
Brief description of the drawings
Fig. 1 is the chip measuring system for thermal deformation schematic diagram provided in an embodiment of the present invention based on SEM.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is right below in conjunction with drawings and Examples
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in each embodiment of invention described below
Conflict can is not formed each other to be mutually combined.
Fig. 1 is the chip measuring system for thermal deformation schematic diagram provided in an embodiment of the present invention based on SEM,
As shown in figure 1, specifically include：SEM 1, computer 2, sample warm table control box 3, sample warm table 4, three axles
Sample stage 5, for heat-insulated ceramic sheet 6, contact thermocouple 7 and chip under test 8.
Wherein, the annexation of all parts and effect are as follows：Computer 2 connects sample warm table control box 3, for pair
Sample warm table control box 3 transmits temperature control instruction and transmits temperature data to preserving on computer 2；Sample warm table 4
It is arranged in the working chamber of SEM 1, chip under test 8 is arranged on sample warm table 4, sample computer heating control box 3
Sample warm table 4 is connected, for carrying out temperature control to sample warm table；Ceramic sheet 6 is arranged on sample warm table 4, with
Exposed locations on sample warm table 4 are covered so as to be thermally shielded, thermocouple 7 is connected with chip under test 8, directly to survey
Amount obtains the actual temperature of chip under test 8, and thermocouple 7 is also connected with sample warm table control box 3, for temperature data to be transmitted
Preserved to the real-time display of sample warm table control box 3 and being further transmitted on computer 2；Three axle sample stages 5 are arranged on scanning
In the working chamber of electron microscope, chip under test is arranged on three axle sample stages 5, and three axle sample stages 5 are used to move chip under test
8。
Chip thermal deformation measurement method provided by the present invention based on SEM is as follows：
First, before thermal deformation measurement is carried out, speckle is prepared on the surface of chip under test 8 using the method for electron-beam direct writing
Pattern.
Sample warm table 4 is placed in the working chamber of SEM 1, the chip under test 8 prepared is fixed on
On warm table, wherein, sample warm table 4 carries out temperature adjusting by sample warm table control box 3；Keep contact thermocouple simultaneously
7 with effective contact of chip under test 8 and the temperature data of contact thermocouple 7 to be transferred to out to the business computer outside working chamber
2；Finally, covered to be thermally shielded, prevented to scanning using the other positions exposed to sample warm table 4 of ceramic sheet 6
Electron microscope 1 is impacted and damaged.
Open the Low-vacuum mode of SEM 1, the enlargement ratio of regulation scanning SEM 1, work
Make the parameters such as distance and shoot to obtain the specimen surface picture rich in detail of chip under test 8 under normal temperature.Keep sample and systematic parameter constant,
N picture rich in detail I are continuously shot in equal time spacing1,...,IN, sample is translated by three axle sample stages 5,
Shoot 2 clearly images, Q respectively before and after translation1And Q2。
Utilize continuous acquisition image I1,...,INDrift distortion to SEM 1 is modeled, and makes I1Image
For reference picture, images and reference picture I are opened to follow-up N-1 using digital picture related algorithm1Matched, obtain set of matches
Close Φ={ Φi, i=2 ..., N }, and then obtain image X-direction and Y-direction motion vector set U={ Ui, i=2 ... N }, V
={ Vi, i=2 ... N } and image capture moment set T={ T corresponding to themi, i=1 ..., N }, T1Represent reference chart
As shooting time.Then in drift distortion velocity field v corresponding to image X-direction and Y-directionx,vyIt can obtain by the following method：
Wherein, num (Φ) represents the point quantity of characteristic matching set.
Drift distortion velocity field v is calculated by above formulax,vy, the drift distortion to any instant t models as follows：
Dd(t)=[dx(t),dy(t)]；
dx(t)=vxt；
dy(t)=vyt；
Wherein, dxAnd d (t)y(t) represent in moment t, drift value of the whole image in X-direction and Y-direction.
2 clearly image Q are obtained by translating sample1And Q2To the space distortion D of SEM 1fModeling process
It is as follows：
Df(p)=[dfx(p)dfy(p)]；
Wherein, p be image on any point pixel coordinate, dfx(p),dfy(p) it is in the X-direction and Y-direction of p points
Space distortion.Due to dfx(p),dfy(p) there is equivalence, herein only for dfx(p) derived in detail.dfx(p) can represent
For the form of radial base interpolation function：
Wherein, a0,ap, W={ w1,...wMIt is coefficient to be resolved, φ represents radial direction kernel function, ciRepresent control point, M
For control point number.
a0,ap, W={ w1,...wMSolution process it is as follows：
Before sample is translated, if image Q1The location of pixels of certain upper point is p1, the distortion of its corresponding X-direction is：After sample is translated, in image Q2On, the point is from p1Position is moved to p2Position
Put, then now corresponding X-direction distortion is：
Because the distortion of SEM central area is minimum, therefore before and after sample is translated, by image Q1
With image Q2Center carries out digital picture correlation computations【Schreier H,Orteu J J,Sutton M A.Image
correlation for shape,motion and deformation measurements.Springer US,2009】,
Real X-direction shift value R can be obtainedx.Can be for the point of image one p2,, can by correlation calculations because Existential Space distorts
Obtain p2Point is relative to p1The X-direction shift value of point is Ux.There is following relation by distortion principle：
By to translating front and rear image Q1With image Q2Correlation calculations are carried out, in whole image plane, there is K
Group is shaped like p2And p1Corresponding points.It is expressed as：
P1={ p1(1),...p1(K) }~P2={ p2(1),...p2(K)},
Further calculate, can be expressed as with matrix form:
Wherein, ap, W={ w1,...wMIt is except a0Outer coefficient matrix to be resolved, Δ Θ are known two groups of preset radials
The matrix that basic function φ subtracts each other, its size are that (K is the front and rear corresponding points number by correlation calculations of translation to K × M, and M is radially
The number of control points of basic function), it is represented by for position therein for the element of (k, m)：Δ Θ (k, m)=[φ (| | p2
(k)-cm||)φ(||p1(k)-cm||)].Δ P is known set P1={ p1(1)...p1(K)},P2={ p2(1)...p2
(K) } corresponding element subtracts each other the matrix of composition, is expressed as Δ P=[p2(1)-p1(1)...p2(K)-p1(K)]。
By carrying out least square solution to above formula, you can obtain coefficient a to be askedp, W={ w1,...wMSolution.
Further, because the distortion of picture centre is approximately 0, therefore can be by picture centre coordinate pCSubstitution formulaResolved, can obtain coefficient a0Solution.
Thus, can obtain for space distortion d in any point p X-direction on imagefx(p) analytical form：
Due to dfxAnd d (p)fy(p) there is equivalence, therefore above-mentioned flow is repeated for distortion in Y-direction, you can obtain
dfy(p) analytical form.
And then can be to SEM 1 space distortion Df(p)=[dfx(p)dfy(p)] be modeled, i.e., it is given
Any point p on image, you can the space distortion D of SEM 1 is obtained by above-mentioned flowf(p)=[dfx(p)dfy
(p)], dfx(p),dfy(p) it is the space distortion in the X-direction and Y-direction of p points.
The heating function for opening sample warm table 4 is carried out to the sample of chip under test 8 in the working chamber of SEM 1
Heating, while simultaneously real-time display is carried out by the measurement sample temperature of contact thermocouple 7, at the equal temperature interval moment
{τ1,...τsS measurement image sequence { Ψ under shooting different temperatures1,...Ψs, time series is under corresponding record
{t1,...ts}。
Utilize above-mentioned drift distortion modelIt is { t to shooting time1,...tsSurvey
Measure image sequence { Ψ1,...ΨsCarry out drift distortion correction, utilization space distortion model Df(p)=[dfx(p)dfy(p) it is] right
Measure image sequence { Ψ1,...ΨsCarry out the image sequence { Ψ after space distortion is correctedC1,...ΨCs}。
By ΨC1As reference picture, digital picture related algorithm is utilized【Schreier H,Orteu J J,Sutton M
A.Image correlation for shape,motion and deformation measurements.Springer
US,2009】To several distortion corrections after image { ΨC2,...ΨCsCorrelation calculations are carried out, chip is obtained due to heated
And caused in-plane deformation { ε2,...εs}。
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, all any modification, equivalent and improvement made within the spirit and principles of the invention etc., all should be included
Within protection scope of the present invention.
Claims (5)
- A kind of 1. chip thermal deformation measurement method based on SEM, it is characterised in that it comprises the following steps：S1：Speckle pattern is prepared on chip sample surface to be measured,S2：Warm table with function of temperature control is placed in the working chamber of SEM, the chip sample that will be prepared It is fixed on warm table,Thermocouple is connected with chip sample, so that the temperature of chip sample can be measured, moreover it is possible to by the temperature data of thermocouple measurement It is transferred on the computer outside working chamber,Warm table exposed locations are covered to be thermally shielded using ceramic sheet,S3:Open SEM Low-vacuum mode, regulation SEM enlargement ratio, operating distance, shooting Specimen surface image under normal temperature is obtained,Keep sample and systematic parameter constant, N chip sample images are continuously shot in equal time spacing, for scanning The drift distortion D of electron microscoped(t) modeling, chip sample is translated by the sample stage of SEM, Multiple images are shot respectively before and after translation is used for SEM space distortion DfModeling,S4:The heating function of warm table is opened, the chip sample in SEM working chamber is heated, is led to simultaneously Cross the temperature of thermocouple measurement sample and carry out real-time display and record,According to temperature display, default equal temperature interval simultaneously shoots the chip sample image sequence under different temperatures, corresponding note Time, temperature and the picture numbers of record every image of lower shooting, utilize the drift distortion D established in step S3d(t) and space is abnormal Become DfAll images are corrected,S5:Using the piece image of image sequence in step S4 as reference picture, using digital picture related algorithm to step Image after several distortion corrections in S4 carries out correlation calculations, calculates chip due to heated and caused in-plane deformation.
- A kind of 2. chip thermal deformation measurement method based on SEM as claimed in claim 1, it is characterised in that In step S3, images are opened to drift distortion D using N is continuously shot in equal time spacingd(t) detailed process is modeled such as Under：Using first image of continuous acquisition image as reference picture, the total number of images amount of shooting is N, utilizes digital picture phase Pass, Scale invariant operator feature point extraction algorithm carry out characteristic matching to follow-up (N-1) image and reference picture, are matched Set Φ={ Φi, i=2 ..., N }, obtain image X-direction and Y-direction motion vector set U={ Ui, i=2 ... N }, V= {Vi, i=2 ... N } and corresponding image capture moment set T={ Ti, i=1 ..., N }, T1Represent reference picture shooting Time,In drift distortion velocity field v corresponding to image X-direction and Y-directionx,vyObtained by equation below：<mrow> <msub> <mi>v</mi> <mi>x</mi> </msub> <mo>=</mo> <mo>&lsqb;</mo> <mfrac> <mrow> <munder> <mo>&Sigma;</mo> <msub> <mi>&Phi;</mi> <mn>2</mn> </msub> </munder> <msub> <mi>U</mi> <mn>2</mn> </msub> </mrow> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> <mo>)</mo> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>(</mo> <msub> <mi>&Phi;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mfrac> <mo>+</mo> <mn>...</mn> <mo>+</mo> <mfrac> <mrow> <munder> <mo>&Sigma;</mo> <msub> <mi>&Phi;</mi> <mi>N</mi> </msub> </munder> <msub> <mi>U</mi> <mi>N</mi> </msub> </mrow> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mi>N</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>(</mo> <msub> <mi>&Phi;</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> </mfrac> <mo>&rsqb;</mo> <mo>/</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow><mrow> <msub> <mi>v</mi> <mi>y</mi> </msub> <mo>=</mo> <mo>&lsqb;</mo> <mfrac> <mrow> <munder> <mo>&Sigma;</mo> <msub> <mi>&Phi;</mi> <mn>2</mn> </msub> </munder> <msub> <mi>V</mi> <mn>2</mn> </msub> </mrow> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> <mo>)</mo> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>(</mo> <msub> <mi>&Phi;</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mfrac> <mo>+</mo> <mn>...</mn> <mo>+</mo> <mfrac> <mrow> <munder> <mo>&Sigma;</mo> <msub> <mi>&Phi;</mi> <mi>N</mi> </msub> </munder> <msub> <mi>V</mi> <mi>N</mi> </msub> </mrow> <mrow> <mo>(</mo> <msub> <mi>T</mi> <mi>N</mi> </msub> <mo>-</mo> <msub> <mi>T</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mi>n</mi> <mi>u</mi> <mi>m</mi> <mo>(</mo> <msub> <mi>&Phi;</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> </mfrac> <mo>&rsqb;</mo> <mo>/</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>Wherein, num (Φ) represents the point quantity of characteristic matching set,Drift distortion velocity field v is obtained by above formulax,vy, the drift distortion to some moment t models as follows：Dd(t)=[dx(t),dy(t)]；dx(t)=vxt；dy(t)=vyt；Wherein, dxAnd d (t)y(t) drift value in moment t whole image in X-direction and Y-direction is represented.
- A kind of 3. chip thermal deformation measurement method based on SEM as claimed in claim 2, it is characterised in that In step S3, two chip sample images are obtained to SEM space distortion D by translating samplefModeling, specifically It is as follows：Df(p)=[dfx(p) dfy(p)]；Wherein, p be image on any point pixel coordinate, dfx(p),dfy(p) it is in pixel coordinate p X-direction and Y-direction Space distortion,dfx(p) represent as follows with the form of radial base interpolation function：<mrow> <msub> <mi>d</mi> <mrow> <mi>f</mi> <mi>x</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>p</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msubsup> <mi>a</mi> <mi>p</mi> <mi>T</mi> </msubsup> <mi>p</mi> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>w</mi> <mi>i</mi> </msub> <mi>&phi;</mi> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <mi>p</mi> <mo>-</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> </mrow>Wherein, a0,ap, w={ w1,...wMIt is coefficient to be resolved, φ represents radial direction kernel function, ciControl point is represented, M is control System point number,a0,ap, w={ w1,...wMSolution process it is as follows：Before chip sample is translated, if certain location of pixels put is p on image1, the distortion of its corresponding X-direction is：After sample is translated, the point is from p1Position is moved to p2Position, then now corresponding X-direction distortion is：Because the distortion of SEM central area is minimum, by carrying out correlation calculations to center, can obtain Real X-direction shift value Rx,For p1Point and p2Point, because Existential Space distorts, by correlation calculations, obtain p1Point and p2The X-direction shift value of point For Ux,Following relation is had according to distortion principle：<mrow> <msub> <mi>U</mi> <mi>x</mi> </msub> <mo>-</mo> <msub> <mi>R</mi> <mi>x</mi> </msub> <mo>=</mo> <msub> <mi>d</mi> <mrow> <mi>f</mi> <mi>x</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mi>f</mi> <mi>x</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>a</mi> <mi>p</mi> <mi>T</mi> </msubsup> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msub> <mi>w</mi> <mi>i</mi> </msub> <mo>&lsqb;</mo> <mi>&phi;</mi> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>p</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <mo>-</mo> <mi>&phi;</mi> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>c</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow>By carrying out correlation calculations to translating two front and rear figures, in whole image plane, there is K groups shaped like p2And p1 Corresponding points, be expressed as：P1={ p1(1)...p1(K)},P2={ p2(1)...p2}, (K) further it is expressed as with matrix form:<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>U</mi> <mrow> <mi>x</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>R</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>U</mi> <mrow> <mi>x</mi> <mi>K</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>R</mi> <mi>x</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>&Delta;</mi> <mi>&Theta;</mi> </mrow> </mtd> <mtd> <mrow> <msup> <mi>&Delta;P</mi> <mi>T</mi> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mi>W</mi> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mi>p</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>Wherein, ap, W={ w1,...wMIt is except a0Outer coefficient matrix to be resolved, Δ Θ are known two groups of preset radials base letters The matrix that number φ subtracts each other, its size are K × M, and K is the front and rear corresponding points number by correlation calculations of translation, and M is radial direction base letter Several numbers of control points,It is represented by for position therein for the element of (k, m)：Δ Θ (k, m)=[φ (| | p2(k)-cm||)φ(||p1 (k)-cm| |)], Δ P is known set P1={ p1(1)...p1(K)},P2={ p2(1)...p2(K) } corresponding element subtracts each other group Into matrix, be expressed as Δ P=[p2(1)-p1(1) ... p2(K)-p1(K)],By carrying out least square solution to above formula, coefficient a to be asked is obtainedpWith w={ w1,...wMSolution.
- A kind of 4. chip thermal deformation measurement method based on SEM as claimed in claim 3, it is characterised in that The distortion for setting picture centre is 0, by picture centre coordinate pCSubstitution formulaCarry out Calculate, obtain coefficient a0,Obtain for space distortion d in any point p X-direction on imagefx(p) analytical form：
- A kind of 5. chip thermal deformation measurement method based on SEM as claimed in claim 4, it is characterised in that Utilize dfx(p)、dfy(p) there is theoretical equivalence, repeat the flow that distorted in X-direction for distortion in Y-direction, obtain dfy(p) Analytical form,And then the space distortion D to SEMf(p)=[dfx(p) dfy(p)] it is modeled.
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