CN107677697B - A kind of chip thermal deformation measurement method based on scanning electron microscope - Google Patents
A kind of chip thermal deformation measurement method based on scanning electron microscope Download PDFInfo
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- 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 scanning electron microscope, belong to material property detection technique field, the present invention utilizes the high depth of field and high-resolution characteristic of scanning electron microscope, by integrated with In Situ Heating device, heat affecting and systematical distortion bring measurement error fully considered and it have been corrected；Using the speckle image after distortion correction, is calculated by digital picture related algorithm and acquire chip due to the heated in-plane deformation field being deformed.On the basis of the above, the present invention realizes the chip whole audience thermal deformation measurement of micro/nano-scale and is applied in practical projects.
Description
Technical field
The invention belongs to material property detection technique fields, and in particular to a kind of chip heat based on scanning electron microscope
Deformation measurement method.
Background technique
With being constantly progressive for semicon industry, MEMS (Micro Electro-Mechanical Systems,
MEMS tremendous expansion) has been obtained.The form that MEMS device generallys use chip assembly is packaged manufacture.Chip assembly usually by
A variety of different nano material compositions, elasticity modulus and the thermal expansion coefficient difference of material, in different loads, humidity and temperature
Under the conditions of, material junction, which is also easy to produce crackle, leads to chip failure.Especially in encapsulation process, the thermal expansion system of layers of material
Number has differences, and after packaging, there are biggish thermal stress, residual stress for chip internal structure.This is in entire chip interior meeting
Cause thermal deformation, influences work response and the service life of entire chip.Therefore, under micro/nano-scale to the thermal deformation of chip into
Row precise measurement to the mechanical property and deformation characteristic for understanding chip material, instructs the designing and manufacturing of micro-nano device, analyzes core
The inefficacy mechanism of piece is of great significance.
However, test-material yardstick constantly subtracts from micron dimension to nanometer scale as chip manufacturing process level rapidly develops
It is small.Therefore, to carry out deformation measurement to it also more and more difficult.
Under micro/nano-scale, wider conventional contact measurement method is applied such as in macro-scale: foil gauge, extensometer etc.
No longer it is applicable in.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: interferometry and non-interfering method.For interference technique, mainly include 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] etc..However above-mentioned interference method needs relatively harsh experiment item
Part, such as: coherent source, shockproof optical table and lesser measurement range etc..Therefore, the application of interferometry 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 one of typical representative.This method
Two dimension or 3 D deformation information are obtained using the correlation of deformation front and back body surface speckle image, the light with previous intervention method
Survey method is compared, measurement process and sample prepare it is simple, and without coherent laser illumination and vibration isolation, to measurement environmental requirement compared with
It is low.
Due to above-mentioned advantage, it is also of greatest concern that it is most active, which to have become current experiment mechanics field, for Digital Image Correlation Method
One of optical measurement mechanics method, in the material and body structure surface deformation measurement of macroscopic view, mechanics and physical parameter characterization and verifying
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 be aobvious with the digital imaging apparatus of different spatial resolutions
Micro mirror, scanning electron microscope, atomic force microscope etc.) it combines, present very strong technological adaptability and application potential.Its
In, scanning electron microscope (SEM) has resolution ratio, Gao Jingshen, ease for use height and the enlargement ratio of nanoscale rank can
The features such as being adjusted by low power (10 ×) to high power (up to 50000 ×) is to obtain the preferable of digital speckle image in microscopic fields
Approach.But since scanning electron microscope image-forming principle is different from ordinary optical imaging device, lead to that there is multiple in image
Miscellaneous distortion；Varying temperature environment can also impact the stability of scanning electron microscope and bring additional thermal noise；It is above-mentioned because
Element can reduce the measurement accuracy of chip thermal deformation.
In conclusion needing to develop the novel method of one kind to overcome drawbacks described above, to improve the survey of chip thermal deformation
Accuracy of measurement.
Summary of the invention
Aiming at the above defects or improvement requirements of the prior art, the present invention provides a kind of based on scanning electron microscope
Chip thermal deformation measurement method comprising following steps:
S1: speckle pattern is prepared on chip sample surface to be measured.
S2: the warm table with function of temperature control is placed in the working chamber of scanning electron microscope, the chip that will be prepared
Sample (later referred to as: sample) is fixed on warm table；Effectively the contacting and by thermoelectricity even number of thermocouple and sample is kept simultaneously
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: opening scanning electron microscope Low-vacuum mode, adjusts scanning electron microscope enlargement ratio, operating distance etc.
Parameter simultaneously shoots specimen surface clear image under acquisition room temperature.Keep sample and system parameter constant, in equal time interval
Inside it is continuously shot drift distortion D of the N clear images for scanning electron microscoped(t) modeling, passes through scanning electron microscopy
The sample stage of mirror translates sample, shot respectively before and after translation 2 clearly image it is empty for scanning electron microscope
Between distort DfModeling.
S4: the heating function for opening warm table heats the sample in scanning electron microscope working chamber, leads to simultaneously
It crosses the temperature of contact thermocouple measurement sample and carries out real-time display and record, according to temperature display, preset equal temperature
It is spaced and is shot the sample clear image sequence under different temperatures, the time, temperature and figure of every image are shot under corresponding record
As serial number, the distortion model D established in step S3 is utilizedd(t) and DfAll images are corrected.
S5: using the first width (under room 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] to the image after several distortion corrections in step S4 into
Row correlation calculations find out the in-plane deformation that chip is generated due to heated.
Further, it in step S3, is distorted using N clear images are continuously shot in equal time interval to drift
Dd(t) detailed process is as follows for modeling:
Using first image of continuous acquisition image as reference picture, and the total number of images amount shot is N, utilizes number
Image is related, Scale invariant operator feature point extraction algorithm carries out characteristic matching acquisition to subsequent 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 their corresponding image capture moment set T={ Ti, i=1 ..., N }, T1It indicates
Reference picture shooting time.
Then in the corresponding drift distortion velocity field v of image X-direction and Y-directionx,vyIt can obtain by the following method:
Wherein, num (Φ) indicates the point quantity of characteristic matching set.
Drift distortion velocity field v is obtained by above formulax,vy, it is as follows to the drift distortion modeling of some moment t:
Dd(t)=[dx(t),dy(t)]；
dx(t)=vxt；
dy(t)=vyt；
Wherein, dx(t) and dy(t) drift value in moment t whole image in the x direction and the y direction is indicated.
Further, in step S3, by translation sample obtain two clearly image to scanning electron microscope space
Distort DfModeling process is as follows:
Df(p)=[dfx(p)dfy(p)]；
Wherein, p is the pixel coordinate of any point on image, dfx(p)dfy(p) in the X-direction and Y-direction of pixel coordinate p
On space distortion.Due to dfx(p)、dfy(p) there is equivalence, herein only for dfx(p) it is derived in detail, dfx(p) diameter is used
It is expressed as follows to the form of cardinal interpolation function:
Wherein, a0,ap, W={ w1,...wMIt is coefficient to be resolved, φ indicates radial kernel function, ciIndicate control point, M
For control point number,.a0,ap, w={ w1,...wMSolution process it is as follows:
Before translating sample, if the location of pixels that certain is put on image is p1, correspond to the distortion of X-direction are as follows:After translating sample, the point is from p1Position is moved to p2Position, then it is right at this time
The X-direction distortion answered are as follows:
Since the distortion of scanning electron microscope central area is minimum, before and after translating sample, by centre bit
Carry out correlation calculations are set, can get true X-direction shift value Rx.It can be for p1Point and p2Point, due to there are space distortion,
By correlation calculations, p can get1Point and p2The X-direction shift value of point is Ux.According to distortion principle, there are following relationships:
Correlation calculations are carried out by two figures to translation front and back, in whole image plane, there is K groups shaped like p2
And p1Corresponding points.It indicates are as follows: P1={ p1(1)...p1(K)},P2={ p2(1)...p2(K) } matrix form table, is further used
It reaches are as follows:
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, size are that (K is the corresponding points number that translation front and back passes through correlation calculations to K × M, and M is radial
The number of control points of basic function), for position therein be (k, m) element may be expressed as: 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, coefficient a to be asked can be obtainedpWith w={ w1,...wMSolution.
It further, can be by picture centre coordinate p since the distortion of picture centre is approximately 0CSubstitution formulaIt is calculated, coefficient a can be obtained0Solution.
It is can be obtained as a result, for space distortion d in the X-direction of any point p on imagefx(p) analytical form:Due to dfx(p)、dfy(p) there is theoretical equivalence, therefore, in Y-direction
Distortion repeats above-mentioned process, can be obtained dfy(p) analytical form.It in turn, can space distortion D to scanning electron microscopef
(p)=[dfx(p)dfy(p)] it is modeled.
The chip thermal deformation measurement method based on scanning electron microscope that the present invention provides a kind of, by by scanning electron
Microscope is combined with digital image correlation technique, gives full play to the technical advantage of the two；Pass through the collection with In Situ Heating device
At having fully considered heat affecting and systematical distortion bring measurement error and be corrected to it；Utilize dissipating after distortion correction
Spot image calculates and acquires the in-plane deformation field that chip is deformed due to heated, realizes chip thermal deformation under micro/nano-scale
Measurement, to provide comprehensive measurement data to study the mechanical property of nano material and deformation characteristic.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, can obtain down and show
Beneficial effect:
The present invention using scanning electron microscope the high depth of field and the characteristics such as high-resolution, by with In Situ Heating device
It is integrated, it has fully considered heat affecting and systematical distortion bring measurement error and it has been corrected；After distortion correction
Speckle image is calculated by digital picture related algorithm and acquires chip due to the heated in-plane deformation field being deformed.Upper
On the basis of stating, the present invention realizes the chip whole audience thermal deformation measurement of micro/nano-scale and is applied in practical projects.
Detailed description of the invention
Fig. 1 is the chip measuring system for thermal deformation schematic diagram provided in an embodiment of the present invention based on scanning electron microscope.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
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 the various embodiments of the present invention described below
Not constituting a conflict with each other can be combined with each other.
Fig. 1 is the chip measuring system for thermal deformation schematic diagram provided in an embodiment of the present invention based on scanning electron microscope,
As shown in Figure 1, specifically including: scanning electron microscope 1, computer 2, sample warm table control box 3, sample warm table 4, three axis
Sample stage 5, for heat-insulated ceramic sheet 6, contact thermocouple 7 and chip under test 8.
Wherein, the connection relationship of all parts and act on it is as follows: computer 2 connect sample warm table control box 3, be used for pair
Sample warm table control box 3, which transmits temperature control instruction and temperature data is transmitted on computer 2, to be saved；Sample warm table 4
It is arranged in the working chamber of scanning electron microscope 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 cover being 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 transmitting temperature data
It controls 3 real-time display of box to sample warm table and is further transmitted on computer 2 and save；The setting of three axis sample stages 5 is scanning
In the working chamber of electron microscope, chip under test is arranged on three axis sample stages 5, and three axis sample stages 5 are for moving chip under test
8。
Chip thermal deformation measurement method provided by the present invention based on scanning electron microscope is as follows:
Firstly, preparing speckle on 8 surface of chip under test using the method for electron-beam direct writing before carrying out thermal deformation measurement
Pattern.
Sample warm table 4 is placed in the working chamber of scanning electron microscope 1, the chip under test 8 prepared is fixed on
On warm table, wherein sample warm table 4 carries out temperature regulation by sample warm table control box 3；It is kept in contact formula thermocouple simultaneously
7 effectively contact with chip under test 8 and the temperature data of contact thermocouple 7 are transferred to out to the business computer outside working chamber
2；Finally, being covered using the other positions exposed to sample warm table 4 of ceramic sheet 6 to be thermally shielded, prevent to scanning
Electron microscope 1 is impacted and is damaged.
The Low-vacuum mode of scanning electron microscope 1 is opened, enlargement ratio, the work of scanning scanning electron microscope 1 are adjusted
Make the parameters such as distance and shoot to obtain 8 specimen surface clear image of chip under test under room temperature.Keep sample and system parameter constant,
N clear image I are continuously shot in equal time interval1,...,IN, sample is translated by three axis sample stages 5,
Shoot 2 clearly images, Q respectively before and after translation1And Q2。
Utilize continuous acquisition image I1,...,INThe drift distortion of scanning electron microscope 1 is modeled, I is enabled1Image
For reference picture, images and reference picture I are opened to subsequent N-1 using digital picture related algorithm1It is matched, obtains 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 their corresponding image capture moment set T={ Ti, i=1 ..., N }, T1It indicates with reference to figure
As shooting time.Then in the corresponding drift distortion velocity field v of image X-direction and Y-directionx,vyIt can obtain by the following method:
Wherein, num (Φ) indicates the point quantity of characteristic matching set.
Drift distortion velocity field v is calculated by above formulax,vy, it is as follows to the drift distortion modeling of any moment t:
Dd(t)=[dx(t),dy(t)]；
dx(t)=vxt；
dy(t)=vyt；
Wherein, dx(t) and dy(t) it indicates in moment t, the drift value of whole image in the x direction and the y direction.
2 clearly image Q are obtained by translation sample1And Q2To 1 space distortion D of scanning electron microscopefModeling process
It is as follows:
Df(p)=[dfx(p)dfy(p)]；
Wherein, p is the pixel coordinate of any point on image, dfx(p),dfy(p) in the X-direction and Y-direction of p point
Space distortion.Due to dfx(p),dfy(p) there is equivalence, herein only for dfx(p) it is derived in detail.dfx(p) it can indicate
For the form of radial base interpolation function:
Wherein, a0,ap, W={ w1,...wMIt is coefficient to be resolved, φ indicates radial kernel function, ciIndicate control point, M
For control point number.
a0,ap, W={ w1,...wMSolution process it is as follows:
Before translating sample, if image Q1The location of pixels of certain upper point is p1, correspond to the distortion of X-direction are as follows:After translating sample, in image Q2On, the point is from p1Position is moved to p2Position
It sets, then corresponding X-direction distortion at this time are as follows:
Since the distortion of scanning electron microscope central area is minimum, before and after translating sample, by image Q1
With image Q2Center carries out digital picture relevant calculation [Schreier H, Orteu J J, Sutton M A.Image
Correlation for shape, motion and deformation measurements.Springer US, 2009],
It can get true X-direction shift value Rx.It can be for one point p of image2, due to there are space distortions can by correlation calculations
Obtain p2Point is relative to p1The X-direction shift value of point is Ux.There is following relationship by distortion principle:
Pass through the image Q to translation front and back1With image Q2Correlation calculations are carried out, in whole image plane, there is K
Group is shaped like p2And p1Corresponding points.It indicates are as follows:
P1={ p1(1),...p1(K) }~P2={ p2(1),...p2(K)},
It further calculates, can be expressed with matrix form are as follows:
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, size are that (K is the corresponding points number that translation front and back passes through correlation calculations to K × M, and M is radial
The number of control points of basic function), for position therein be (k, m) element may be expressed as: 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, coefficient a to be asked can be obtainedp, W={ w1,...wMSolution.
It further, can be by picture centre coordinate p since the distortion of picture centre is approximately 0CSubstitution formulaIt is resolved, coefficient a can be obtained0Solution.
It is can be obtained as a result, for space distortion d in the X-direction of any point p on imagefx(p) analytical form:
Due to dfx(p) and dfy(p) there is equivalence, therefore repeat above-mentioned process for distortion in Y-direction, can be obtained
dfy(p) analytical form.
It in turn, can space distortion D to scanning electron microscope 1f(p)=[dfx(p)dfy(p)] it is modeled, i.e., it is given
Any point p on image can obtain the space distortion D of scanning electron microscope 1 by above-mentioned processf(p)=[dfx(p)dfy
(p)], dfx(p),dfyIt (p) is the space distortion in the X-direction and Y-direction of p point.
The heating function for opening sample warm table 4 carries out 8 sample of chip under test in 1 working chamber of scanning electron microscope
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,...ΨsDrift distortion correction is carried out, utilize space distortion model Df(p)=[dfx(p)dfy(p)] 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 [Schreier H, Orteu J J, Sutton M is utilized
A.Image correlation for shape,motion and deformation measurements.Springer
US, 2009] image { Ψ after several distortion corrections coupleC2,...ΨCsCorrelation calculations are carried out, chip is found out due to heated
And in-plane deformation { the ε generated2,...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, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (4)
1. a kind of chip thermal deformation measurement method based on scanning electron microscope, which is characterized in that it includes the following steps:
S1: preparing speckle pattern on chip sample surface to be measured,
S2: the warm table with function of temperature control is placed in the working chamber of scanning electron microscope, the chip sample that will be prepared
It is fixed on warm table,
Thermocouple is connect with chip sample, to be capable of measuring the temperature of chip sample, 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: opening scanning electron microscope Low-vacuum mode, adjusts scanning electron microscope enlargement ratio, operating distance, shooting
Specimen surface image under room temperature is obtained,
It keeps sample and system parameter constant, N chip sample images is continuously shot in equal time interval, for scanning
The drift distortion D of electron microscoped(t) modeling translates chip sample by the sample stage of scanning electron microscope,
Multiple images are shot respectively before and after translation for scanning electron microscope space distortion DfModeling,
S4: opening the heating function of warm table, heats to the chip sample in scanning electron microscope working chamber, leads to simultaneously
It crosses the temperature of thermocouple measurement sample and carries out real-time display and record,
According to temperature display, presets equal temperature interval and shoot 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 the in-plane deformation that chip is generated due to heated,
Specifically, opening images to drift distortion D using N is continuously shot in equal time interval in step S3d(t) modeling tool
Body process is as follows:
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 subsequent (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 }, T1Indicate reference picture shooting
Time,
In the corresponding drift distortion velocity field v of image X-direction and Y-directionx,vyIt is obtained by following formula:
Wherein, num (Φ) indicates the point quantity of characteristic matching set,
Drift distortion velocity field v is obtained by above formulax,vy, it is as follows to the drift distortion modeling of some moment t:
Dd(t)=[dx(t),dy(t)]；
dx(t)=vxt；
dy(t)=vyt；
Wherein, dx(t) and dy(t) drift value in moment t whole image in the x direction and the y direction is indicated.
2. a kind of chip thermal deformation measurement method based on scanning electron microscope as described in claim 1, which is characterized in that
In step S3, two chip sample images are obtained to scanning electron microscope space distortion D by translation samplefModeling, specifically
It is as follows:
Df(p)=[dfx(p), dfy(p)]；
Wherein, p is the pixel coordinate of any point on image, dfx(p),dfy(p) in the X-direction and Y-direction of pixel coordinate p
Space distortion,
dfx(p) it is expressed as follows with the form of radial base interpolation function:
Wherein, a0,ap, w={ w1,...wMIt is coefficient to be resolved, φ indicates radial kernel function, ciIndicate control point, M is control
System point number,
a0,ap, w={ w1,...wMSolution process it is as follows:
Before translating chip sample, if the location of pixels that certain is put on image is p1, correspond to the distortion of X-direction are as follows:
After translating sample, the point is from p1Position is moved to p2Position, then corresponding X-direction distortion at this time are as follows:
Since the distortion of scanning electron microscope central area is minimum, by carrying out correlation calculations to center, can get
True X-direction shift value Rx,
For p1Point and p2Point obtains p by correlation calculations since there are space distortions1Point and p2The X-direction shift value of point
For Ux,
According to distortion principle, there are following relationships:
Correlation calculations are carried out by two figures to translation front and back, in whole image plane, there is K groups shaped like p2And p1
Corresponding points, indicate are as follows: P1={ p1(1)...p1(K)},P2={ p2(1)...p2(K) } it, is further expressed with matrix form are as follows:
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, size are K × M, and K is the corresponding points number that translation front and back passes through correlation calculations, and M is radial base letter
Several numbers of control points,
For position therein be (k, m) element may be expressed as: 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
At 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.
3. a kind of chip thermal deformation measurement method based on scanning electron microscope as claimed in claim 2, which is characterized in that
The distortion of picture centre is set as 0, by picture centre coordinate pCSubstitution formula
It is calculated, obtains coefficient a0,
It obtains for space distortion d in the X-direction of any point p on imagefx(p) analytical form:
4. a kind of chip thermal deformation measurement method based on scanning electron microscope as claimed in claim 3, which is characterized in that
Utilize dfx(p)、dfy(p) there is theoretical equivalence, repeat the process that distorts in X-direction for distortion in Y-direction, obtain dfy(p)
Analytical form,
And then to the space distortion D of scanning electron microscopef(p)=[dfx(p), dfy(p)] it is modeled.
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