Methods and apparatuses for etch profile matching by surface kinetic model optimization

• US 10,386,828 B2
• Filed: 12/17/2015
• Issued: 08/20/2019
• Est. Priority Date: 12/17/2015
• Status: Active Grant

• Current Assignee: Lam Research Corporation
• Original Assignee: Lam Research Corporation
• Inventors: Tetiker, Mehmet Derya, Sriraman, Saravanapriyan, Bailey, III, Andrew D., Shoeb, Juline, Paterson, Alex, Gottscho, Richard A.
• Primary Examiner(s): Tran, Tan N
• Application Number:
  US14/972,969
• Publication Number:
  US 20170176983A1
• Time in Patent Office: 1,342 Days
• Field of Search: 700 98
• CPC Class Codes: G05B 17/02 electric
• CPC Class Codes: G05B 19/4188 characterised by CIM planning or realisation
• CPC Class Codes: G05B 2219/45031 Manufacturing semiconductor wafers
• CPC Class Codes: G05B 2219/45212 Etching, engraving, sculpturing, carving

Abstract

Disclosed are methods of optimizing a computerized model which relates etched feature profile on a semiconductor device to a set of independent input parameters via the use of a plurality of model parameters. The optimization methods may include modifying the model parameters so that an etch profile generated with the model is such that it reduces a metric indicative of the combined differences between experimental etch profiles resulting from experimental etch processes performed using different sets of values for sets of independent input parameters and computed etch profiles generated from the model and corresponding to the experimental etch profiles. Said metric may be calculated by projecting computed and corresponding experimental etch profiles onto a reduced-dimensional subspace used to calculate a difference between the profiles. Also disclosed herein are systems employing such optimized models, as well as methods of using such models to approximately determine the profile of an etched feature.

Claims

1. A method of optimizing a computerized model which relates an etched feature profile on a semiconductor device to a set of independent input parameters via the use of a plurality of model parameters, the method comprising:

(a) identifying a set of values for a selected set of the model parameters to be optimized;

(b) identifying multiple sets of values for a selected set of independent input parameters to optimize over, wherein the independent input parameters comprise an input parameter selected from the group consisting of temperature, plasma density, and etchant flux;

(c) for each set of values specified in (b), receiving an experimental etch profile resulting from an experimental etch process performed using the set of values specified in (b), wherein the experimental etch process comprised various experiments that etch semiconductor substrates and measure resulting experimentally produced feature profiles with one or more metrology tools;

(d) for each set of values specified in (b), generating a computed etch profile from the model using the set of values specified in (a) and (b), wherein the computed etch profile is provided for a grid having a grid spacing of between 1 angstrom and 10 micrometers, and wherein the computed etch profile is generated over a plurality of time steps; and

(e) modifying one or more values specified in (a) for the selected set of model parameters and repeating (d) with the modified one or more values so as to reduce a metric indicative of combined differences between the experimental etch profiles received in (c) and corresponding computed etch profiles generated in (d) over all the sets of values for the selected independent input parameters specified in (b) to thereby produce optimized model parameter values;

wherein calculating the metrics in (e) comprises;

projecting the computed and corresponding experimental etch profiles from a first space having multiple dimensions each representing one of a plurality of feature profile coordinates onto a reduced-dimensional subspace having fewer dimensions than the first space and reducing latent statistical correlations in etch profiles, wherein the reduced-dimensional subspace recasts the modifying operation in (e) to a computationally more efficient process; and

calculating a difference between the profiles as projected onto the subspace.

2. The method of claim 1, wherein:

the experimental etch profiles received in (c) each comprise a series of experimental values for a series of etch profile coordinates; and

the computed etch profiles generated in (d) each comprise a series of generated values for the series of etch profile coordinates.

3. The method of claim 2, wherein determining the reduced-dimensional subspace comprises a principle component analysis (PCA) of the experimental etch profiles as represented by values of the etch profile coordinates.

4. The method of claim 2, wherein the metric is the sum of the squares of the differences between the series of experimental values and the series of generated values for the series of etch profile coordinates of each experimental etch profile measured in (c) and corresponding computed etch profile generated in (d).

5. The method of claim 1, further comprising repeating (e).

6. The method of claim 5, further comprising further repeating (e) until a substantially local minimum in error with respect to the model parameters selected in (a) is obtained.

7. The method of claim 1, wherein the computerized model calculates local etch rates at a grid of points representing the feature profile as a function of time.

8. The method of claim 7, wherein the model parameters include thermal rate constants, reactant and product sticking coefficients, and reactant and product diffusion constants.

9. The method of claim 1, wherein the identifying in (b) of the multiple sets of values for the selected set of independent input parameters parameters comprises PCA.

10. The method of claim 9, wherein the PCA is performed with respect to concatenated vectors of independent input parameters and corresponding measured etch profiles.

11. A computer program product comprising a non-transient medium on which are provided computer readable instructions for executing an optimized computerized model which generates a computed etched feature profile from a set of values for a set of independent input parameters, the computerized model having been optimized by the method of claim 1.

12. A method of approximately determining the profile of a feature on a semiconductor substrate after the feature has been etched by an etch process, the method comprising:

specifying a set of values for a set of independent input parameters corresponding to the etch process; and

generating an etch profile using the optimized computerized model of claim 11 with the specified set of values for the independent input parameters.

13. A method of determining a set of values for a set of independent input parameters for an etch process which will approximately yield a desired etch profile of a feature on a semiconductor substrate after the feature is etched by said etch process, the method comprising:

(a) specifying a set of values for a set of independent input parameters corresponding to an etch process;

(b) generating a computed etch profile using the optimized computerized model of claim 11 with the specified set of values for the independent input parameters;

(c) computing a metric indicative of the difference between the desired etch profile and the computed etch profile; and

(d) modifying one or more values for the set of independent input parameters specified in (a) so as to reduce the difference between desired and computed etch profiles as ascertained by repeating (b)-(c).

14. The method of claim 13, further comprising:

(e) repeating (d) until a substantially local minimum in error with respect to the set of independent input parameters selected in (a) is obtained.

15. A system for processing semiconductor substrates, the system comprising:

an etcher apparatus for etching semiconductor substrates whose operation is adjusted by a set of independent input parameters; and

a controller for controlling the operation of the etcher apparatus, the controller comprising a processor and a memory;

wherein;

the memory stores an etched feature profile model optimized by the method of claim 1; and

the processor uses the etched feature profile model stored in the memory to compute an etched feature profile from a set of values for the set of independent input parameters.

16. The system of claim 15, wherein the controller adjusts the operation of the etcher apparatus by varying one or more values of the set of independent input parameters in response to the computed etched feature profile.

17. The system of claim 16, wherein the set of independent input parameters whose values are varied in response to the computed etched feature profile include one or more parameters selected from:

RF plasma frequency and RF plasma power level.

18. The system of claim 15, wherein the etcher apparatus comprises:

a processing chamber;

a substrate holder for holding a substrate within the processing chamber;

a plasma generator for generating a plasma within the processing chamber, the plasma generator comprising an RF power supply;

one or more valve-controlled process gas inlets for flowing one or more process gases into the processing chamber; and

one or more gas outlets fluidically connected to one or more vacuum pumps for evacuating gases from the processing chamber.

19. The system of claim 18, wherein the controller adjusts the frequency and/or the power level of the RF power supply to modify characteristics of the plasma in the processing chamber in response to the computed etched feature profile.

20. The system of claim 18, wherein the controller operates the one or more valve-controlled process gas inlets to adjust the flow rates of one or more process gases into the processing chamber in response to the computed etched feature profile.

21. The system of claim 18, wherein the controller adjusts a temperature and/or a pressure within the processing chamber in response to the computed etched feature profile.

22. The method of claim 1, further comprising:

(f) optimizing the computer model by applying one or more modified values produced in (e) to the computer model; and

(g) using the optimized computer model produced in (f) to develop a lithographic mask.

23. The method of claim 1, further comprising:

(f) optimizing the computer model by applying one or more modified values produced in (e) to the computer model; and

(g) etching a semiconductor substrate using a set of etch conditions determined using the optimized computer model produced in (f).

24. The method of claim 1, further comprising:

(f) using the model with the optimized model parameter values to enable development of a lithographic mask and/or enable etching a semiconductor substrate using a set of etch conditions.

25. A method of optimizing a computerized model which relates an etched feature profile to a set of independent input parameters via the use of model parameters, the method comprising:

(a) identifying a set of values for a selected set of the model parameters to be optimized;

(b) identifying multiple sets of values for a selected set of independent input parameters to optimize over, wherein the independent input parameters comprise an input parameter selected from the group consisting of temperature, plasma density, and etchant flux;

(c) for each set of values specified in (b), receiving an experimental etch profile resulting from an experimental etch process performed using the set of values specified in (b), wherein the experimental etch process comprised various experiments that etch semiconductor substrates and measure resulting experimentally produced feature profiles with one or more metrology tools;

(d) for each set of values specified in (b), generating a computed etch profile from the model using the set of values specified in (a) and (b) , wherein the computed etch profile is provided for a grid having a grid spacing of between 1 angstrom and 10 micrometers, and wherein the computed etch profile is generated over a plurality of time steps; and

(e) modifying one or more values specified in (a) for the selected set of model parameters and repeating (d) with the modified one or more values so as to reduce a metric indicative of combined differences between the experimental etch profiles measured in(c) and corresponding computed etch profiles generated in (d) over all the sets of values for the selected independent input parameters specified in (b) to thereby produce optimized model parameter values;

wherein calculating the metrics in (e) comprises;

differencing the computed and corresponding experimental etch profiles in a first space having multiple dimensions each representing one of a plurality of feature profile coordinates; and

projecting the differences onto a reduced-dimensional subspace having fewer dimensions than the first space and reducing latent statistical correlations in etch profiles, wherein the reduced-dimensional subspace recasts the modifying operation in (e) to a computationally more efficient process.

26. The method of claim 25, wherein:

the experimental etch profiles received in (c) each comprise a series of experimental values for a series of etch profile coordinates; and

the computed etch profiles generated in (d) each comprise a series of generated values for the series of etch profile coordinates.

27. The method of claim 26, wherein the reduced-dimensional subspace is determined from a PCA of the differences between the experimental and generated values of the corresponding etch profile coordinates.

28. A computer program product comprising a non-transient medium on which are provided computer readable instructions for executing an optimized computerized model which generates a computed etched feature profile from a set of values for a set of independent input parameters, the computerized model having been optimized by the method of claim 25.

29. A method of approximately determining the profile of a feature on a semiconductor substrate after the feature has been etched by an etch process, the method comprising:

specifying a set of values for a set of independent input parameters corresponding to the etch process; and

generating an etch profile using the optimized computerized model of claim 28 with the specified set of values for the independent input parameters.

30. A method of determining a set of values for a set of independent input parameters for an etch process which will approximately yield a desired etch profile of a feature on a semiconductor substrate after the feature is etched by said etch process, the method comprising:

(a) specifying a set of values for a set of independent input parameters corresponding to an etch process;

(b) generating a computed etch profile using the optimized computerized model of claim 28 with the specified set of values for the independent input parameters;

(c) computing a metric indicative of the difference between the desired etch profile and the computed etch profile; and

(d) modifying one or more values for the set of independent input parameters specified in (a) so as to reduce the difference between desired and computed etch profiles as ascertained by repeating (b)-(c).

31. The method of claim 30, further comprising:

(e) repeating (d) until a substantially local minimum in error with respect to the set of independent input parameters selected in (a) is obtained.

32. A system for processing semiconductor substrates, the system comprising:

an etcher apparatus for etching semiconductor substrates whose operation is adjusted by a set of independent input parameters; and

a controller for controlling the operation of the etcher apparatus, the controller comprising a processor and a memory;

wherein;

the memory stores an etched feature profile model optimized by the method of claim 25; and

the processor uses the etched feature profile model stored in the memory to compute an etched feature profile from a set of values for the set of independent input parameters.

33. The system of claim 32, wherein the controller adjusts the operation of the etcher apparatus by varying one or more values of the set of independent input parameters in response to the computed etched feature profile.