US 9,430,593 B2Granted

System and method to emulate finite element model based prediction of in-plane distortions due to semiconductor wafer chucking

AssigneeKLA-Tencor Corporation

InventorsPradeep Vukkadala, Sathish Veeraraghavan, Jaydeep Sinha, Haiguang Chen, Michael Kirk

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Abstract

Systems and methods for prediction of in-plane distortions (IPD) due to wafer shape in semiconductor wafer chucking process is disclosed. A process to emulate the non-linear finite element (FE) contact mechanics model based IPD prediction is utilized in accordance with one embodiment of the present disclosure. The emulated FE model based prediction process is substantially more efficient and provides accuracy comparable to the FE model based IPD prediction that utilizes full-scale 3-D wafer and chuck geometry information and requires computation intensive simulations. Furthermore, an enhanced HOS IPD/OPD prediction process based on a series of Zernike basis wafer shape images is also disclosed.

Claims36

Dependent claims

A computer implemented method for providing in-plane distortion (IPD) prediction, the method comprising:

(a) generating a plurality of sample wafer shapes, the plurality of sample wafer shapes generated by varying a set of coefficients B in a predefined shape equation;
(b) performing finite element (FE) model based IPD prediction for the plurality of sample wafer shapes, wherein IPD predictions with respect to x-axis (X-IPD) and IPD predictions with respect to y-axis (Y-IPD) are obtained for the plurality of sample wafer shapes;
(c) fitting equations to the FE model based X-IPD predictions and the FE model based Y-IPD predictions for the plurality of sample wafer shapes to obtain a set of coefficients A, wherein the set of coefficients A corresponds to the set of coefficients B of the shape equation used in step (a) to generate the plurality of sample wafer shapes;
(d) analyzing the set of coefficients B and the set of coefficients A to determine a mapping function ƒ suitable for calculating coefficients A based on coefficients B of the shape equation;
(e) calculating an interim shape for a given wafer utilizing the mapping function ƒ and a shape equation representing the initial shape of the given wafer;
and
(f) performing IPD prediction for the given wafer based on the interim shape calculated for the given wafer.

4 more elements

A system for providing in-plane distortion (IPD) prediction for a given wafer, the system comprising:

an optical system configured for obtaining a wafer shape of the given wafer;
and
an IPD prediction module in communication with the optical system, the IPD prediction module configured for:
(a) generating a plurality of sample wafer shapes, the plurality of sample wafer shapes generated by varying a set of coefficients B in a predefined shape equation;
(b) performing finite element (FE) model based IPD prediction for the plurality of sample wafer shapes, wherein IPD predictions with respect to x-axis (X-IPD) and IPD predictions with respect to y-axis (Y-IPD) are obtained for the plurality of sample wafer shapes;
(c) fitting equations to the FE model based X-IPD predictions and the FE model based Y-IPD predictions for the plurality of sample wafer shapes to obtain a set of coefficients A, wherein the set of coefficients A corresponds to the set of coefficients B of the shape equation used in step (a) to generate the plurality of sample wafer shapes;
(d) analyzing the set of coefficients B and the set of coefficients A to determine a mapping function ƒ suitable for calculating coefficients A based on coefficients B of the shape equation;
(e) calculating an interim shape for a given wafer utilizing the mapping function ƒ and a shape equation representing the initial shape of the given wafer;
and
(f) performing IPD prediction for the given wafer based on the interim shape calculated for the given wafer.

7 more elements

A computer implemented method for overlay error prediction, the method comprising:

(a) generating a plurality of sample wafer shapes, the plurality of sample wafer shapes generated by varying a set of coefficients B in a predefined shape equation;
(b) performing finite element (FE) model based in-plane distortion (IPD) prediction for the plurality of sample wafer shapes, wherein IPD predictions with respect to x-axis (X-IPD) and IPD predictions with respect to y-axis (Y-IPD) are obtained for the plurality of sample wafer shapes;
(c) fitting equations to the FE model based X-IPD predictions and the FE model based Y-IPD predictions for the plurality of sample wafer shapes to obtain a set of coefficients A, wherein the set of coefficients A corresponds to the set of coefficients B of the shape equation used in step (a) to generate the plurality of sample wafer shapes;
(d) analyzing the set of coefficients B and the set of coefficients A to determine a mapping function ƒ suitable for calculating coefficients A based on coefficients B of the shape equation;
(e) calculating a first interim shape for a given wafer utilizing the mapping function ƒ and a shape equation representing the initial shape of the given wafer;
(f) predicting the IPD for the given wafer based on the first interim shape calculated for the given wafer;
(g) obtaining a second shape of the given wafer after a wafer patterning process;
(h) calculating a second interim shape for the second shape of the given wafer utilizing the mapping function ƒ;
(i) predicting the IPD for the given wafer after the wafer patterning process based on the second interim shape;
(j) calculating differences between the IPD for the given wafer predicted before the wafer patterning process and the IPD for the given wafer predicted after the wafer patterning process;
and
(k) applying a linear scanner correction routine to the IPD differences to obtain the overlay error prediction.

9 more elements

Dependencies are inferred from the claim text.

Facts

Application: 13/735,737Filed 7 Jan 2013 · us provisional application
Priority: 11 Oct 2012
Published: US 2014/0107998 A117 Apr 2014
Granted: 30 Aug 2016
Term ends: Not estimatedThe source records don’t support an estimate.

Classification4 codes

G06F 30/23
Design optimisation, verification or simulation: using finite element methods [FEM] or finite difference methods [FDM]
H10P 72/0616
Apparatus for monitoring, sorting, marking, testing or measuring: monitoring of warpages, curvatures, damages, defects or the like
G06F
Computing and data processing
H10P
Generic processes or apparatus for the manufacture or treatment of devices covered