Method for improving mechanical stress testing accuracy
Patent Information
- Application Number
- PCT/CN2025/082420
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2025-03-13
- Publication Date
- 2026-09-17
Smart Images
Figure CN2025082420_17092026_PF_FP_ABST
Abstract
Description
A method to improve the accuracy of mechanical stress testing Technical Field
[0001] This invention relates to the field of semiconductor testing, specifically a method for improving the accuracy of mechanical stress testing. Background Technology
[0002] As integrated circuit integration density increases, the mechanical stress accumulated during manufacturing and packaging significantly enhances its impact on device electrical performance. This stress alters the band structure of semiconductor devices, leading to changes in parameters such as carrier concentration, effective carrier mass, and mobility, ultimately causing variations in device parameters. During manufacturing, mechanical stress-induced parameter changes may prevent products from passing factory testing; during packaging, it can cause premature failures such as chip breakage, lead detachment, chip detachment, and sealant cracking. Therefore, stress detection is crucial for improving and optimizing integrated circuit manufacturing and packaging processes.
[0003] In engineering applications, the piezoresistive effect of silicon, along with conventional resistive stress sensors, MOS channel resistive stress sensors, and van der Burg resistive stress sensors, allows for the testing of multiple mechanical stress components at specific locations on a chip or silicon wafer. The error in stress testing is influenced by inherent errors in the measured quantities, such as the piezoresistive coefficient of the stress sensor, the rate of resistance change, and temperature differences. The full-scale error of the stress test can reach 80% or even approach 100%. The accuracy and precision of the stress test determine the magnitude of the stress test error. Summary of the Invention
[0004] The purpose of this invention is to provide a method for improving the accuracy of mechanical stress testing, comprising the following steps:
[0005] 1) Obtain the stress component calculation formula of the stress sensor to be tested;
[0006] 2) Combine the independent variables in the stress component calculation formula so that the sum of the stress sensitivity to these independent variables is 0, thereby constructing the optimal stress component calculation formula; the independent variables include piezoresistive coefficient, resistance change rate, and temperature difference.
[0007] 3) Select n stress test points on the silicon wafer to be tested for stress; n is a positive integer greater than or equal to 1;
[0008] 4) At stress test point i, the resistance of each resistor of the stress sensor to be tested is tested before and after stress is generated. The resistance change rate of each resistor of the stress sensor at stress test point i before and after stress is generated, as well as the temperature difference before and after stress is generated, are determined. The initial value of i is 1.
[0009] 5) Generate a new standard deviation of the piezoresistive coefficient S' < S; S is the original standard deviation of the piezoresistive coefficient; construct a piezoresistive coefficient distribution based on the new standard deviation of the piezoresistive coefficient and the original average value of the piezoresistive coefficient, and generate piezoresistive coefficient values within the piezoresistive coefficient distribution;
[0010] 6) Substitute the resistance change rate, temperature difference and the randomly generated piezoresistive coefficient value from step 4) into the optimal calculation formula for stress components to achieve mechanical stress testing of silicon wafers.
[0011] 7) Determine if i≥n holds true. If true, output the stress test results for each stress test point. Otherwise, set i = i+1 and return to step 4.
[0012] Furthermore, in step 1), the formula for calculating the stress components of the stress sensor to be tested is determined by the silicon wafer crystal orientation type and sensor structure used in the stress sensor to be tested.
[0013] Furthermore, the standard deviation of the original piezoresistive coefficient is determined by the process platform used to process the stress sensor to be tested.
[0014] Furthermore, the optimal formula for calculating stress components is a homogeneous function.
[0015] Furthermore, step 2), the step of combining the independent variables in the stress component calculation formula, includes:
[0016] 2.1) Combine all or some of the independent variables in the stress component calculation formula to obtain one or more combined variables; use the combined variables and the remaining independent variables that have not been combined as new independent variables, thereby updating the stress component calculation formula;
[0017] 2.2) Determine whether the updated stress calculation formula satisfies the definition of a homogeneous function and whether the summation of the stress sensitivity to the new independent variable is 0. If yes, output the optimal calculation formula for the stress components; otherwise, return to step 2.1) and recombine the independent variables.
[0018] Furthermore, in step 5), the piezoresistive coefficient value is generated randomly.
[0019] Furthermore, the new standard deviation of the piezoresistive coefficient Parameter b > 1.
[0020] Furthermore, the temperature difference refers to the temperature difference between the stress sensor before and after stress is generated; the temperature of the sensor before and after stress is generated is obtained by monitoring the temperature sensor.
[0021] Furthermore, when performing stress tests on the stress sensor to be tested, the temperature of the stress sensor is kept constant before and after the stress test, so that the temperature difference is 0.
[0022] Furthermore, in step 2), the rate of change of resistance is determined by measuring electrical parameters using PCM.
[0023] The technical effects of this invention are undeniable. This invention utilizes the homogeneous function characteristics of the stress calculation formula to calculate the sum of the sensitivities of stress components with respect to all independent variables in the formula. This sum satisfies Euler's theorem for homogeneous functions and represents the degree of the homogeneous function. By combining one or more constants that were originally coefficients and simultaneously treating them with the original independent variables as new independent variables, the sum of the stress sensitivities with respect to the new independent variables satisfies Euler's theorem and has a sum of 0, thus making the rate of change of stress zero, greatly improving the accuracy of stress testing. In the specific stress calculation process, the rate of change of resistance and temperature difference are measured by instruments. Based on the distribution (mean and standard deviation) of the offline test data of the piezoresistive coefficient, a set of piezoresistive coefficients is randomly generated by the stress calculation software, achieving the effect of simultaneous change with other independent variables, forcing the sum of stress sensitivities to zero. Attached Figure Description
[0024] Figure 1 is a flowchart of the method. Detailed Implementation
[0025] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.
[0026] Example 1:
[0027] A method for improving the accuracy of mechanical stress testing includes the following steps:
[0028] 1) Obtain the stress component calculation formula of the stress sensor to be tested; the stress component calculation formula takes the piezoresistive coefficient, resistance change rate and temperature difference as inputs and the stress component as output.
[0029] 2) Combine the independent variables in the stress component calculation formula so that the sum of the stress sensitivity to these independent variables is 0, thereby constructing the optimal stress component calculation formula; the independent variables include piezoresistive coefficient, resistance change rate, and temperature difference.
[0030] 3) Select n stress test points on the silicon wafer to be tested for stress; n is a positive integer greater than or equal to 1;
[0031] 4) At stress test point i, the resistance of each resistor of the stress sensor to be tested is tested before and after stress is generated, and the resistance change rate of each resistor of the stress sensor at stress test point i before and after stress is generated, as well as the temperature difference before and after stress is generated; the initial value of i is 1.
[0032] 5) Generate a new standard deviation of the piezoresistive coefficient S' < S; S is the original standard deviation of the piezoresistive coefficient; construct a piezoresistive coefficient distribution based on the new standard deviation of the piezoresistive coefficient and the mean of the original distribution of the piezoresistive coefficient, and generate piezoresistive coefficient values within the piezoresistive coefficient distribution;
[0033] 6) Substitute the resistance change rate, temperature difference and the randomly generated piezoresistive coefficient value from step 4) into the optimal calculation formula for stress components to achieve mechanical stress testing of silicon wafers.
[0034] 7) Determine if i≥n holds true. If true, output the stress test results for each stress test point. Otherwise, set i = i+1 and return to step 4.
[0035] In step 1), the formula for calculating the stress components of the stress sensor to be tested is determined by the type of silicon wafer and the sensor structure used in the stress sensor to be tested.
[0036] The standard deviation of the original piezoresistive coefficient is determined by the process platform used to fabricate the stress sensor to be tested.
[0037] The optimal formula for calculating stress components is a homogeneous function.
[0038] Step 2), the step of combining the independent variables in the stress component calculation formula includes:
[0039] 2.1) Combine all or some of the independent variables in the stress component calculation formula to obtain one or more combined variables; use the combined variables and the remaining independent variables that have not been combined as new independent variables, thereby updating the stress component calculation formula;
[0040] 2.2) Determine whether the updated stress calculation formula satisfies the definition of a homogeneous function and whether the summation of the stress sensitivity to the new independent variable is 0. If yes, output the optimal calculation formula for the stress components; otherwise, return to step 2.1) and recombine the independent variables.
[0041] In step 5), the piezoresistive coefficient value is generated randomly.
[0042] New standard deviation of piezoresistive coefficient Parameter b > 1.
[0043] Temperature difference refers to the temperature difference between the stress sensor before and after stress is generated; the temperature of the sensor before and after stress is generated is obtained by monitoring the temperature sensor.
[0044] When performing stress tests on the stress sensor to be tested, keep the temperature of the stress sensor constant before and after the stress test, so that the temperature difference is 0.
[0045] In step 2), the rate of change of resistance is determined by measuring electrical parameters using PCM.
[0046] Example 2:
[0047] A method for improving the accuracy of mechanical stress testing includes the following steps:
[0048] 1) Obtain the stress component calculation formula of the stress sensor to be tested;
[0049] 2) Combine the independent variables in the stress component calculation formula so that the sum of the stress sensitivity to these independent variables is 0, thereby constructing the optimal stress component calculation formula; the independent variables include piezoresistive coefficient, resistance change rate, and temperature difference.
[0050] 3) Select n stress test points on the silicon wafer to be tested for stress; n is a positive integer greater than or equal to 1;
[0051] 4) At stress test point i, the resistance of each resistor of the stress sensor to be tested is tested before and after stress is generated, and the resistance change rate of each resistor of the stress sensor at stress test point i before and after stress is generated, as well as the temperature difference before and after stress is generated; the initial value of i is 1.
[0052] 5) Generate a new standard deviation of the piezoresistive coefficient. b > 1; S is the original standard deviation of the piezoresistive coefficient; a piezoresistive coefficient distribution is constructed based on the new standard deviation of the piezoresistive coefficient and the mean of the original distribution of the piezoresistive coefficient, and piezoresistive coefficient values are generated within the piezoresistive coefficient distribution;
[0053] 6) Substitute the resistance change rate, temperature difference and the randomly generated piezoresistive coefficient value from step 4) into the optimal calculation formula for stress components to achieve mechanical stress testing of silicon wafers.
[0054] 7) Determine if i≥n holds true. If true, output the stress test results for each stress test point. Otherwise, set i = i+1 and return to step 4.
[0055] Example 3:
[0056] A method for improving the accuracy of mechanical stress testing, with the same technical content as in Embodiment 2, further wherein, in step 1), the formula for calculating the stress components of the stress sensor to be tested is determined by the type of silicon wafer and the sensor structure used in the stress sensor to be tested.
[0057] Example 4:
[0058] A method for improving the accuracy of mechanical stress testing, with the same technical content as any one of Examples 2-3, further wherein the standard deviation of the original piezoresistive coefficient is determined by the process platform for processing the stress sensor to be tested.
[0059] Example 5:
[0060] A method for improving the accuracy of mechanical stress testing, with the same technical content as any one of embodiments 2-4, further wherein the optimal calculation formula for stress components is a homogeneous function.
[0061] Example 6:
[0062] A method for improving the accuracy of mechanical stress testing, with technical content identical to any one of embodiments 2-5, further comprising, in step 2), the step of combining the independent variables in the stress component calculation formula, including:
[0063] 5.1) Combine all or some of the independent variables in the stress component calculation formula to obtain one or more combined variables; use the combined variables and the remaining independent variables that have not been combined as new independent variables, thereby updating the stress component calculation formula.
[0064] 5.2) Determine whether the updated stress calculation formula satisfies the definition of a homogeneous function and whether the summation of the stress sensitivity to the new independent variable is 0. If yes, output the optimal calculation formula for the stress components; otherwise, return to step 5.1) and recombine the independent variables.
[0065] Example 7:
[0066] A method for improving the accuracy of mechanical stress testing, with the same technical content as any one of embodiments 2-6, further wherein, in step 4), the piezoresistive coefficient value is generated in a random manner.
[0067] Example 8:
[0068] A method for improving the accuracy of mechanical stress testing, with the same technical content as any one of embodiments 2-7, further comprising a new standard deviation of the piezoresistive coefficient.
[0069] Example 9:
[0070] A method for improving the accuracy of mechanical stress testing, with the same technical content as any one of embodiments 2-7, further comprising a new standard deviation of the piezoresistive coefficient.
[0071] Example 10:
[0072] A method for improving the accuracy of mechanical stress testing, with the same technical content as any one of embodiments 2-7, further comprising a new standard deviation of the piezoresistive coefficient.
[0073] Example 11:
[0074] A method for improving the accuracy of mechanical stress testing, the technical content of which is the same as any one of embodiments 2-7, further wherein b is taken as 5-1000.
[0075] Example 12:
[0076] A method for improving the accuracy of mechanical stress testing, with the same technical content as any one of embodiments 2-11, further wherein the temperature difference refers to the temperature difference of the stress sensor before and after stress generation; the temperature of the sensor before and after stress generation is obtained by monitoring the temperature sensor.
[0077] Example 13:
[0078] A method for improving the accuracy of mechanical stress testing, with the same technical content as any one of embodiments 2-12, further wherein when performing stress testing on the stress sensor to be tested, the temperature of the stress sensor is kept constant during the two tests before and after stress testing, so that the temperature difference is 0.
[0079] Example 14:
[0080] A method for improving the accuracy of mechanical stress testing, with the same technical content as any one of embodiments 2-13, further wherein, in step 2), the resistance change rate is determined by PCM testing electrical parameters.
[0081] Example 15:
[0082] A method for improving the accuracy of mechanical stress testing, with the same technical content as any one of embodiments 2-14, further wherein the original method for determining the mean and standard deviation of the piezoresistive coefficient is as follows: the piezoresistive coefficient value can be obtained by combining the four-point bending method and the hydrostatic pressure method, and the distribution (mean and standard deviation) of the piezoresistive coefficient value can be obtained by multi-sample testing.
[0083] Example 16:
[0084] The stress component σ' of a stress sensor on a (111) type silicon wafer. 11 Taking calculation formulas (1)-(7) as an example, a method to improve the accuracy of mechanical stress testing is as follows:
[0085] 1) At the location of the stress to be measured on the silicon wafer, the resistance values of resistors R1, R3, R5, R7, etc. in the stress sensor at that location are measured before and after the stress is generated by the PCM test electrical parameters, and the rate of change is calculated and entered into the stress calculation system.
[0086] 2) The stress calculation system uses the distribution of piezoresistive coefficient data (mean and standard deviation) from offline tests, takes a fraction of the original standard deviation as the new standard deviation, and randomly generates piezoresistive coefficient values within this range, so as to achieve the effect of changing the piezoresistive coefficient, resistance change rate, and temperature difference in the stress component calculation formula.
[0087] The formula for calculating stress components is as follows:
[0088] In the formula, σ'11 ,σ' 22 ,σ' 33 ,σ' 13 ,σ' 23 ,σ' 12 For stress components, σ' 11 -σ' 22 The stress component after temperature compensation is given; ΔT is the temperature difference before and after the stress test; R1, R2, R3, and R4 are N-type resistors; R5, R6, R7, and R8 are P-type resistors; ΔR1, ΔR2, ΔR3, ΔR4, ΔR5, ΔR6, ΔR7, and ΔR8 are the resistance changes of resistors R1, R2, R3, R4, R5, R7, and R8 before and after stress generation. This refers to the piezoresistive coefficient; the superscripts n and p indicate N-type and P-type resistors, respectively. Temperature coefficient;
[0089] 3) According to Euler's theorem for homogeneous functions, the sensitivity of stress to changes in independent variables such as piezoresistive coefficient, rate of change of resistance, and temperature difference is 0, and the rate of change of the measured stress value is also 0, thus improving the accuracy of stress value measurement.
[0090] 4) After changing the location of the stress test, repeat steps 1), 2), and 3). Each time the test reaches step 2), the piezoresistive coefficient needs to be randomly generated again.
[0091] Example 17:
[0092] σ′ of a stress sensor on a (111) type silicon wafer 11 Taking the reduction of the number of independent variables in the stress component calculation formula as an example, here is a method to improve the accuracy of mechanical stress testing: The steps are as follows:
[0093] If the temperature of the stress sensor is kept constant during the two stress tests, the temperature difference in the stress component calculation formula will be 0, so this term can be cancelled, and the independent variables will only include the piezoresistive coefficient and the rate of change of resistance.
[0094] 1) At the location of the stress to be measured on the silicon wafer, the resistance values of resistors R1, R3, R5, R7, etc. in the stress sensor at that location are measured before and after the stress is generated by the PCM test electrical parameters, and the rate of change is calculated and entered into the stress calculation system.
[0095] 2) The stress calculation system takes a fraction of the original standard deviation as the new standard deviation based on the distribution (mean and standard deviation) of the piezoresistive coefficient data from the offline test, and randomly generates piezoresistive coefficient values within this range, thus achieving the effect of changing both the piezoresistive coefficient and the rate of change of resistance.
[0096] 3) According to Euler's theorem for homogeneous functions, the sensitivity of stress to changes in independent variables such as piezoresistive coefficient and resistance rate is 0, and the rate of change of the measured stress value is also 0, thus improving the accuracy of stress value measurement.
[0097] 4) After changing the location of the stress test, repeat steps 1), 2), and 3). Each time the test reaches step 2), the piezoresistive coefficient needs to be randomly generated again.
[0098] Example 18:
[0099] The stress component σ′ of a stress sensor on a (100) type silicon wafer. 11 Taking calculation formulas (8)-(12) as an example, the method to improve the accuracy of mechanical stress testing is as follows:
[0100] In the formula, R4 and R2 are resistors; ΔR4 and ΔR2 are the changes in resistance of R4 and R2 before and after stress is generated. It is the piezoresistive coefficient; This is the temperature coefficient.
[0101] 1) At the location of the stress to be measured on the silicon wafer, the rate of change of resistance of R1, R2, R3, R4, etc. in the stress sensor is measured by PCM test electrical parameters, and the data is entered into the stress calculation system.
[0102] 2) The stress calculation system takes a fraction of the original standard deviation as the new standard deviation according to the distribution (mean and standard deviation) of the offline test data of the piezoresistive coefficient and randomly generates the piezoresistive coefficient values in formula (8)-(12) within this range, so as to achieve the effect of changing the piezoresistive coefficient, resistance change rate and temperature difference in formula (8)-(12).
[0103] 3) According to Euler's theorem for homogeneous functions, the sensitivity of stress to changes in independent variables such as piezoresistive coefficient, rate of change of resistance, and temperature difference is 0, and the rate of change of the measured stress value is also 0, thus improving the accuracy of stress value measurement.
[0104] 4) After changing the location of the stress test, repeat steps 1), 2), and 3). Each time the test reaches step 2), the piezoresistive coefficient needs to be randomly generated again.
[0105] Example 19:
[0106] The stress component σ′ of a stress sensor on a (100) type silicon wafer. 11 Taking reducing the number of independent variables in the calculation formula as an example, here are the steps to improve the accuracy of mechanical stress testing:
[0107] If the temperature of the stress sensor is kept constant during the two stress tests before and after stress testing, the temperature difference in the formula will be 0, so this term can be cancelled, and the independent variables will become two.
[0108] 1) The rate of change of resistance of R1, R2, R3, R4, etc. in the stress sensor is measured by PCM test electrical parameters and the data is entered into the stress calculation system.
[0109] 2) The stress calculation system takes a fraction of the original standard deviation as the new standard deviation according to the distribution (mean and standard deviation) of the offline test data of the piezoresistive coefficient, and randomly generates the piezoresistive coefficient value within this range, so as to achieve the effect of changing both the piezoresistive coefficient and the rate of change of resistance.
[0110] 3) According to Euler's theorem for homogeneous functions, the sensitivity of stress to changes in independent variables such as piezoresistive coefficient and resistance rate is 0, and the rate of change of the measured stress value is also 0, thus improving the accuracy of stress value measurement.
[0111] 4) After changing the location of the stress test, repeat steps 1), 2), and 3). Each time the test reaches step 2), the piezoresistive coefficient needs to be randomly generated again.
[0112] In summary, this invention combines one or more constants that were originally coefficients in the stress calculation formula and treats them together with the original independent variables as new independent variables to determine whether the stress calculation formula satisfies the definition of a homogeneous function.
[0113] This invention finds a new combination of independent variables that satisfies the definition of a homogeneous function, such that the summation of the stress sensitivity to these independent variables changes from a non-zero integer to 0.
[0114] This invention, under a new combination of independent variables, randomly assigns values to one or more coefficients based on the mean and standard deviation of their measured values during each stress test. This transforms one or more constants into homogeneous function independent variables. The stress testing process ensures that one or more coefficients fluctuate simultaneously with the measured quantity, resulting in a zero rate of change for stress. In other words, the stress test value is unaffected by measurement errors in the coefficients and independent variables of the stress calculation formula.
[0115] Example 20:
[0116] The principle of a method to improve the accuracy of mechanical stress testing is as follows:
[0117] The accuracy of stress testing is affected by the inherent errors of the measured quantities, such as the piezoresistive coefficient, resistance change rate, and temperature difference, of the stress sensor. The σ' of an octagonal bipolar stress sensor with a (111) crystal orientation silicon wafer is... 11Taking the stress calculation formula (13) as an example, the measurement errors of resistance and temperature difference will seriously affect the accuracy of the stress value. Optimizing the stress testing method to improve the testing accuracy is a very important task.
[0118] The impact of a single independent variable error on the accuracy of stress values can be characterized by the stress sensitivity formula:
[0119] Where σ represents a stress component, and P represents the independent variable in the stress component calculation formula: resistance change rate, temperature difference, or piezoresistive coefficient.
[0120] During stress testing, a set of piezoresistive coefficients is usually assigned to the stress calculation program and kept constant. The change in resistance is measured. Without temperature compensation, it is also necessary to test the temperature difference before and after the resistance change. The stress value can be calculated by inputting the data into the program. Therefore, the piezoresistive coefficient is a coefficient and invariant in the function by default.
[0121] As can be seen from the stress calculation formula, when the piezoresistive coefficient remains constant and only the rate of change of resistance and temperature difference are taken as independent variables, the formula satisfies the characteristics of a homogeneous function. The sum of the sensitivity of stress to the rate of change of resistance and temperature difference satisfies Euler's theorem for homogeneous functions, and the sum is the power of the homogeneous function, which is an integer of 1, as shown in formula (15).
[0122] At this point, the accuracy of the stress test can be measured by the rate of change of stress. The above formula can be rewritten to obtain the formula for the accuracy of the stress test (16). The measurement errors of the rate of change of resistance and temperature difference cause errors in the stress test value, and this error can reach 80% or even close to 100%.
[0123] According to Euler's theorem for homogeneous functions, if the piezoresistive coefficient fluctuates simultaneously with the rate of change of resistance and temperature difference, the sensitivity of stress to changes in independent variables such as the piezoresistive coefficient, the rate of change of resistance, and temperature difference is zero, i.e., formula (17). The rate of change of the measured stress value is also zero, and the stress value is not affected by measurement errors of the piezoresistive coefficient, the rate of change of resistance, and temperature difference, thus greatly improving the accuracy of stress testing. 5000 sets of stress data were simulated using the Monte Carlo method, and the results show that compared to the case where the piezoresistive coefficient remains constant, the accuracy can be improved by at least four orders of magnitude, reaching 0.5 ppm, which is close to the theoretical value of zero.
[0124] This invention utilizes the homogeneous function characteristic of stress calculation formulas to propose a method for improving the accuracy of mechanical stress testing. This method is not limited to the field of mechanical stress testing; as long as the measured quantity in the relevant field is a homogeneous function of degree 0, this method can be used to reduce the error of the test value to zero, thereby improving the test accuracy.
Claims
1. A method for improving the accuracy of mechanical stress testing, characterized in that, Includes the following steps: 1) Obtain the stress component calculation formula of the stress sensor to be tested; 2) Combine the independent variables in the stress component calculation formula so that the sum of the stress sensitivity to these independent variables is 0, thereby constructing the optimal stress component calculation formula; the independent variables include piezoresistive coefficient, resistance change rate, and temperature difference; 3) Select n stress test points on the silicon wafer to be tested for stress; n is a positive integer greater than or equal to 1; 4) Perform stress testing on the stress sensor to be tested at stress test point i, and determine the resistance change rate of each resistor of the stress sensor at stress test point i before and after stress generation, as well as the temperature difference before and after stress generation; the initial value of i is 1. 5) Generate a new standard deviation of the piezoresistive coefficient S' < S; S is the original standard deviation of the piezoresistive coefficient; construct a piezoresistive coefficient distribution based on the new standard deviation of the piezoresistive coefficient, and generate piezoresistive coefficient values within the piezoresistive coefficient distribution; 6) Substitute the resistance change rate, temperature difference and the randomly generated piezoresistive coefficient value from step 4) into the optimal calculation formula for stress components to achieve mechanical stress testing of silicon wafers. 7) Determine if i≥n holds true. If true, output the stress test results for each stress test point. Otherwise, set i = i+1 and return to step 4.
2. The method for improving the accuracy of mechanical stress testing according to claim 1, characterized in that, In step 1), the formula for calculating the stress components of the stress sensor to be tested is determined by the silicon wafer crystal orientation type and sensor structure used in the stress sensor to be tested.
3. The method for improving the accuracy of mechanical stress testing according to claim 1, characterized in that, The standard deviation of the original piezoresistive coefficient is determined by the process platform used to fabricate the stress sensor to be tested.
4. The method for improving the accuracy of mechanical stress testing according to claim 1, characterized in that, The optimal formula for calculating stress components is a homogeneous function.
5. The method for improving the accuracy of mechanical stress testing according to claim 1, characterized in that, Step 2), the step of combining the independent variables in the stress component calculation formula includes: 2.1) Combine all or some of the independent variables in the stress component calculation formula to obtain one or more combined variables; use the combined variables and the remaining independent variables that have not been combined as new independent variables, thereby updating the stress component calculation formula; 2.2) Determine whether the updated stress calculation formula satisfies the definition of a homogeneous function and whether the summation of the stress sensitivity to the new independent variable is 0. If yes, output the optimal calculation formula for the stress components; otherwise, return to step 2.1) and recombine the independent variables.
6. The method for improving the accuracy of mechanical stress testing according to claim 1, characterized in that, In step 4), the piezoresistive coefficient value is generated randomly.
7. The method for improving the accuracy of mechanical stress testing according to claim 1, characterized in that, New standard deviation of piezoresistive coefficient Parameter b >
1.
8. The method for improving the accuracy of mechanical stress testing according to claim 1, characterized in that, Temperature difference refers to the temperature difference between the stress sensor before and after stress is generated; the temperature of the sensor before and after stress is generated is obtained by monitoring the temperature sensor.
9. The method for improving the accuracy of mechanical stress testing according to claim 1, characterized in that, When performing stress tests on the stress sensor to be tested, keep the temperature of the stress sensor constant before and after the stress test, so that the temperature difference is 0.
10. The method for improving the accuracy of mechanical stress testing according to claim 1, characterized in that, In step 2), the rate of change of resistance is determined by measuring electrical parameters using PCM.