Method of manufacturing a semiconductor device and process control system for a semiconductor manufacturing assembly

1. A method of manufacturing a semiconductor device, the method comprising:

defining a sampling plan in a process control system, the sampling plan containing position information about a first number N of sample points on a process wafer;

obtaining measurement values at the first number N of the sample points, the measurement values referring to a first physical property of the process wafer measured by a first metrology tool;

modelling the first number of the measurement values using a wafer model to generate a first set of coefficients according to a reference model, the wafer model being based on a model function describing the first physical property as a function of one or more position variables;

randomly selecting a second number M of the first number N of the sample points, wherein M<N;

modelling the second number M of the measurement values obtained at the second number M of sample points using the wafer model to generate a second set of coefficients according to a phase_1 model;

randomly replacing one of the second number M of sample points by one of N−M sample points to obtain a subsample;

modelling the measurement values of the subsample using the wafer model to generate a third set of coefficients according to a phase_2 model; and

using the subsample of sample points for performing further measurements.

2. The method according to claim 1 , further comprising calculating a first deviation between the reference model and the phase_1 model and calculating a second deviation between the reference model and the phase_2 model.

3. The method according to claim 1 , wherein randomly selecting the second number M of the first number N of the sample points and modelling the second number M of the measurement values using the wafer model to generate the second set of coefficients according to the phase_1 model is repeated until a predetermined number of random selections has been performed or a predetermined time has lapsed.

4. The method according to claim 2 , wherein randomly selecting the second number M of the first number N of the sample points and modelling the second number M of the measurement values using the wafer model to generate the second set of coefficients according to the phase_1 model is repeated until the first deviation is below a predetermined threshold value.

5. The method according to claim 2 , wherein randomly selecting the second number M of the first number N of the sample points and modelling the second number M of the measurement values using the wafer model to generate the second set of coefficients according to the phase_1 model is repeated until the first deviation does not further decrease.

6. The method according to claim 1 , wherein randomly replacing one of the second number M of the sample points by one of the N−M sample points to obtain the subsample and modelling the measurement values of the subsample using the wafer model to generate the third set of coefficients according to a phase_2 model is repeated until a predetermined number of random replacements has been performed or a predetermined time has been lapsed.

7. The method according to claim 2 , wherein randomly replacing one of the second number M of the sample points by one of the N−M sample points to obtain the subsample and modelling the measurement values of the subsample using the wafer model to generate the third set of coefficients according to a phase_2 model is repeated until the second deviation does not further decrease.

8. The method according to claim 1 , wherein M<0.9*N.

9. The method according to claim 8 , wherein M<0.5*N.

10. The method according to claim 1 , further comprising reducing the number of N measurement values before modelling the first number of measurement values or before randomly selecting the second number M of the first number N of the sample points.

11. The method according to claim 1 , wherein the measurement values are levelling data representing height maps of the process wafer in a chucked state.

12. The method according to claim 1 , wherein the measurement values refer to a critical dimension or an overlay.

13. The method according to claim 1 , wherein the wafer model comprises Legendre polynomials.

14. The method according to claim 1 , wherein the wafer model comprises Zernike polynomials.

15. The method according to claim 1 , wherein the wafer model comprises an interpolation model.

16. The method according to claim 1 , wherein the further measurements relate to a second physical property and the further measurements are performed using a second metrology tool.

17. The method according to claim 1 , wherein the further measurements relate to different process wafers.

18. A non-transitory computer-readable storage medium comprising a computer program with instructions which, when the program is executed by a computer, cause the computer to carry out the method of claim 1 .

19. A process control system for a semiconductor manufacturing assembly, the process control system being configured to

define a sampling plan in a process control system, the sampling plan containing position information about a first number N of sample points on a process wafer;

obtain measurement values at the first number N of the sample points, the measurement values referring to a first physical property of the process wafer measured by a first metrology tool;

model the first number of the measurement values using a wafer model to generate a first set of coefficients according to a reference model, the wafer model being based on a model function describing the first physical property as a function of one or more position variables;

randomly select a second number M of the first number N of the sample points, wherein M<N;

model the second number M of the measurement values obtained at the second number M of the sample points using the wafer model to generate a second set of coefficients according to a phase_1 model;

randomly replace one of the second number M of the sample points by one of N−M sample points to obtain a subsample;

model the measurement values of the subsample using the wafer model to generate a third set of coefficients according to a phase_2 model; and

provide the subsample of sample points as a reduced sampling plan for performing further measurements.