Apparatus and method for generating profiles of constituents of chemical mixtures
First Claim
1. An apparatus having a computer for determining the most probable profile of concentrations of component chemical mixtures in a chemical mixture over a plurality of ordered samples of said chemical mixture, wherein there is a plurality of sets of relative concentrations for each of said samples comprising:
- a first storage location in said computer for storing said plurality of sets of relative concentrations;
means for assigning a probability, and for storing said probability in a second storage location in said computer, to each of said sets of relative concentrations for an initial sample of said samples;
means for assigning a transition probability, and for storing said transition probability in a third storage location in said computer, for a transition from each of said sets of one of said ordered samples to each of said sets of the next ordered sample;
a processor in said computer for accumulating said transition probabilities in said third storage location assigned to each of said sets including said transition probabilities of all transitions from a set in said initial sample in said second storage location; and
a processor on said computer for choosing, for each of said sets having more than one of said transitions, a transition resulting in the highest probability for said set and discarding all other transitions.
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Abstract
An apparatus, system and method are described for determining profiles of the absolute or relative concentrations of N constituent chemical components of a chemical mixture over a group of samples. For each sample a plurality of sets of concentrations is determined wherein each set has substantially the same error for corresponding to the absorption spectra measured for the composite sample. A plurality of samples of the chemical mixture are generated, for example, by removing parts of a surface sequentially. From amongst the plurality of sets of absolute or relative concentrations over the plurality of samples, a path of highest probability is determined from which profiles of each of the chemical components can be determined. The invention is applied to generating profiles of chemical constituents as material is received from a surface of a semiconductor chip to generate profiles as a function of depth into the sample.
20 Citations
37 Claims
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1. An apparatus having a computer for determining the most probable profile of concentrations of component chemical mixtures in a chemical mixture over a plurality of ordered samples of said chemical mixture, wherein there is a plurality of sets of relative concentrations for each of said samples comprising:
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a first storage location in said computer for storing said plurality of sets of relative concentrations; means for assigning a probability, and for storing said probability in a second storage location in said computer, to each of said sets of relative concentrations for an initial sample of said samples; means for assigning a transition probability, and for storing said transition probability in a third storage location in said computer, for a transition from each of said sets of one of said ordered samples to each of said sets of the next ordered sample; a processor in said computer for accumulating said transition probabilities in said third storage location assigned to each of said sets including said transition probabilities of all transitions from a set in said initial sample in said second storage location; and a processor on said computer for choosing, for each of said sets having more than one of said transitions, a transition resulting in the highest probability for said set and discarding all other transitions. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 33, 35)
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16. An apparatus for determining the most probable profile for concentrations Xj,k,l of N component chemical constituents, wherein j=1 to N, in a chemical mixture over a plurality of K ordered samples, wherein k=1 to K, wherein there are L sets of concentrations for each of said samples, wherein l=1 to L and L≧
- 1 for each of said samples using predetermined relative spectral intensities Aij of said N component chemical constituents at wavelength λ
i comprising;means for providing relative spectral intensities Ci,k,l of said chemical mixture at wavelengths λ
i ;means for determining said concentrations Xj,k,l from said relative spectral intensities Ci,k,l and said predetermined relative spectral intensities Ai ; an electromagnetic radiation source for providing an incident beam containing said λ
i, said incident beam having an intensity I0 (λ
i) at each of said λ
i ;a container through which said chemical mixture passes, said container being transparent to said λ
i ;a means for directing said incident beam at said container through which said incident beam passes as a transported beam; means for measuring each of said I0 (λ
i);means for measuring an intensity I(λ
i) of said transported beam at each of said λ
i ;means for comparing I0 (λ
i) and I(λ
i) for each of said λ
i to determine each of said Ci,k,l ;means for assigning a probability to each of said sets of relative concentrations for an initial one of said samples; means for assigning a transition probability for a transition from each of said sets of one of said ordered samples to each of said sets on the next ordered sample; means for accumulating said transition probability assigned to each of said sets including said transition probabilities of all transitions from a set in said initial sample; means for choosing, for each of said sets having more than one of said transitions, the transition resulting its the highest probability for said set and discarding all other transitions; means for generating a profile of at least one of said concentrations versus said samples.
- 1 for each of said samples using predetermined relative spectral intensities Aij of said N component chemical constituents at wavelength λ
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17. A method for use on a computer for determining the most probable profile for concentrations of component chemical constituents in a chemical combination over a plurality of ordered samples of said chemical combination wherein there is a plurality set of concentrations for each of said samples comprising:
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storing said plurality of sets of relative concentrations in a first storage location in said computer; assigning a probability and storing said probability in a second storage location in said computer to each of said sets of concentrations for an initial one of said samples; assigning a transition probability and storing said transition probability in a third storage location in said computer for a transition from each of said sets of one of said ordered samples to each of said sets of the next ordered sample; accumulating said transition probability stored in said third storage location, assigned to each of said sets including said transition probabilities for all transitions from a set in said initial sample stored in said second storage location; and choosing, for each of said sets having more than one of said transitions, the transition resulting in the highest probability for said set and discarding all other transitions. - View Dependent Claims (18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 36, 37)
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32. A method for determining the most probable profile for concentrations Xj,k,i of N component chemical constituents, wherein j=1 to N, in a chemical combination over a plurality of K ordered samples, wherein k=1 to K of said chemical combination wherein there are L sets of relative concentrations, where l=1 to L and l>
- 1 for each of said samples using predetermined relative spectral intensities Aij of said N component chemical constituents at wavelength λ
i wherein i=1 to M, M>
N comprising;providing relative spectral intensities Ci,k,l of said chemical combination at wavelengths λ
i,said relative concentrations Xj,k,l from said relative spectral intensities Ci,k,l and said relative spectral intensities Aij, providing an electromagnetic radiation source for generating an incident beam containing said λ
i, said beam having an intensity I0 at each of said λ
i ;passing said chemical combination through a container, said container transparent to said λ
i ;directing said incident beam at said container through which said beam passes as a transported beam; measuring each of said I0 (λ
i);means for measuring an intensity I(λ
i) of said transported beam at each of said λ
icomparing I0 (λ
i) an I(λ
i) for each of said λ
i to determine each of said Ci,k,lassigning a probability to each or said sets of concentrations for an initial one of said samples; assigning a transition probability for a transition from each of said sets of one of said ordered sample to each of said sets on the next ordered sample; accumulating said transition probability assigned to each of said sets including said transition probabilities of all transitions from a set in said initial sample; choosing, for each of said sets having more than one of said transition, the transition resulting in the highest probability for said set and discarding all other transitions; generating a profile of at least one of said relative concentrations versus said samples.
- 1 for each of said samples using predetermined relative spectral intensities Aij of said N component chemical constituents at wavelength λ
Specification