Optical parametric model optimization

• US 8,090,558 B1
• Filed: 06/03/2009
• Issued: 01/03/2012
• Est. Priority Date: 06/09/2008
• Status: Expired due to Fees

• Current Assignee: KLA-Tencor Corporation (KLA Corporation)
• Original Assignee: KLA-Tencor Corporation (KLA Corporation)
• Inventors: Dziura, Thaddeus G.
• Primary Examiner(s): Shah, Kamini S
• Assistant Examiner(s): PATEL, SHAMBHAVI K
• Application Number:
  US12/477,459
• Time in Patent Office: 944 Days
• Field of Search: 356/302, 356/303, 356/319, 356/451, 359/107, 359/108, 702/117, 702/159, 702/172, 703/2, 703/3, 703/4, 703/5, 703/13
• US Class Current: 703/2
• CPC Class Codes: G01B 11/0616 of coating
• CPC Class Codes: G01B 2210/56 Measuring geometric parameters of semiconductor structures, e.g. profile, critical dimensions or trench depth
• CPC Class Codes: G01N 2021/8438 Mutilayers
• CPC Class Codes: G01N 21/55 Specular reflectivity
• CPC Class Codes: G03F 7/70625 Dimensions, e.g. line width, critical dimension [CD], profile, sidewall angle or edge roughness

Abstract

A method is presented for selecting the order in which parameters are evaluated for inclusion in a model of a film stack, which is by ranking them according to measurement precision. Further, a method is presented for determining which parameters are to be floated, set, or discarded from the model, which is by determining whether average chi-square and chi-square uniformity decreases or increases when the parameter is added to the model. In this manner, a model for the film stack can be quickly assembles with a high degree of accuracy.

Claims

1. A computerized method of constructing a mathematical model of a film stack having parameters, the method comprising the steps of:

a. estimating a measurement precision value for each parameter,

b. normalizing each measurement precision value,

c. ordering the normalized precision values from lowest to highest,

d. collecting spectral data from the film stack at multiple locations,

e. constructing with a processor a model with a subset of the parameters having the lowest normalized precision values,

f. fitting the model to the spectral data,

g. computing with the processor average chi-square and chi-square nonuniformity three-sigma metrics for the model,

h. selecting a next parameter with a lowest normalized precision values,

i. adding the next parameter to the existing model to create a modified model,

j. fitting the modified model to the spectral data,

k. computing with the processor average chi-square and chi-square nonuniformity three-sigma metrics for the modified model,

l. comparing the average chi-square and chi-square nonuniformity for the modified model and the existing model,

m. when the average chi-square and chi-square nonuniformity are both reduced in the modified model, then retaining the next parameter in the modified model as a floated parameter, and designating the modified model as the existing model,

n. when the average chi-square is reduced and the chi-square nonuniformity increases in the modified model, then including the next parameter in the modified model as a constant that is set to a value that is an average of the parameters spectral data, and designating the modified model as the existing model,

o. when average chi-square is not reduced in the modified model, then discarding the modified model, and

p. iteratively repeating steps i-o with the processor until either all of the parameters have been investigated or a desired number of parameters have been added to the modified model.