Method for predicting the formation of silicon nanocrystals in embedded oxide matrices
View Patent ↗A method for predicting the formation of silicon nanocrystals in an oxide matrix is disclosed. Initially, fundamental data for a set of microscopic processes that can occur during one or more material processing operations are obtained. Kinetic models are then built by utilizing the fundamental data for a set of reactions that can contribute substantially to the formation of silicon nanocrystals in a silicon oxide matrix. Finally, the kinetic models are applied to predict shape, size distribution, spatial arrangements of silicon nanocrystals.
1. A computer-implemented method, comprising:
generating, using a computing device, from fundamental data representative of processes that can occur in an oxide matrix during one or more material processing operations on the oxide matrix, a kinetic model representative of reactions that contribute substantially to formation of silicon nanocrystals in the oxide matrix; and
generating from the kinetic model, by the computing device, data representative of a profile for the formation of the silicon nanocrystals in the oxide matrix, including predicting the formation of the silicon nanocrystals using kinetic Monte Carlo simulations based at least in part on oxygen diffusion.
2. The method of claim 1 , further comprising generating, using the computing device, the fundamental data representative of processes that can occur in the oxide matrix during the one or more material processing operations on the oxide matrix, wherein said generating the fundamental data includes calculating changes in a total energy of silicon suboxide matrices by varying a Si:O ratio to determine a strain energy or a suboxide penalty energy for a chemical phase separation of silicon and silicon dioxide.
3. The method of claim 2 , wherein the strain energy represents an increase in energy arising from lattice distortions associated with bond stretching, bond angle bending, torsion strain, and non-bonding interactions.
4. The method of claim 2 , wherein the suboxide penalty energy represents an increase in Si—Si and Si—O bond energies due to incomplete O coordination.
5. The method of claim 1 , further comprising generating, using the computing device, the fundamental data representative of the processes that can occur in the oxide matrix during the one or more material processing operations on the oxide matrix, wherein said generating the fundamental data includes calculating formation energies of single Si atoms that exist in excess at various states in the oxide matrix to determine incorporation of single Si atoms in a Si—O bond network.
6. The method of claim 1 , further comprising generating, using the computing device, the fundamental data representative of the processes that can occur in the oxide matrix during the one or more material processing operations on the oxide matrix, wherein said generating the fundamental data includes calculating relative formation energies of single Si atoms in a crystalline silicon, an amorphous suboxide matrix, and a nanocrystal-matrix interface to determine a location at which excess Si atoms remain.
7. The method of claim 6 , wherein the relative formation energies of single Si atoms are substantially greater in an amorphous suboxide matrix than in a crystalline Si bulk or at a nanocrystal-matrix interface.
8. The method of claim 1 , wherein said generating the kinetic model includes simplifying an amorphous suboxide structure using a rigid diamond-lattice model, having silicon atoms at lattice sites and oxygen atoms at Si—Si bond centers.
9. The method of claim 1 , wherein said generating the kinetic model includes permitting oxygen atoms to diffuse through oxygen-empty sites.
10. The method of claim 9 , further comprising determining an extent of a diffusion of O atoms by calculating corresponding activation energies of Si neighbors of the O atoms.
11. The method of claim 1 , wherein said using kinetic Monte Carlo simulations includes evaluating an oxidation state of at least one Si atom by counting a number of neighboring oxygen atoms of the at least one Si atom.
12. The method of claim 1 , wherein said using kinetic Monte Carlo simulations includes controlling a magnitude of Si supersaturation by varying a number of O-empty sites.
13. The method of claim 1 , wherein the profile comprises at least one of shapes of the silicon nanocrystals in the oxide matrix, a size distribution of the silicon nanocrystals in the oxide matrix, or a spatial arrangement of the silicon nanocrystals in the oxide matrix.
14. The method of claim 1 , further comprising receiving, by the computing device, the fundamental data representative of the processes that can occur in the oxide matrix during the one or more material processing operations on the oxide matrix.
15. An article of manufacture including a non-transitory computer-readable medium having instructions stored thereon that, if executed by a computing device, cause the computing device to perform operations comprising:
generating, from fundamental data representative of processes that can occur in an oxide matrix during one or more material processing operations on the oxide matrix, a kinetic model representative of reactions that contribute substantially to formation of silicon nanocrystals in the oxide matrix; and
generating, from the kinetic model, data representative of a profile for the formation of the silicon nanocrystals in the oxide matrix, including predicting the formation of the silicon nanocrystals using kinetic Monte Carlo simulations based at least in part on oxygen diffusion.
16. The article of manufacture of claim 15 , further comprising generating the fundamental data representative of the processes that can occur in the oxide matrix during one or more material processing operations on the oxide matrix, wherein said generating the fundamental data includes calculating changes in a total energy of silicon suboxide matrices by varying a Si:O ratio to determine a strain energy or a suboxide penalty energy for a chemical phase separation of silicon and silicon dioxide.
17. The article of manufacture of claim 15 , further comprising generating the fundamental data representative of the processes that can occur in the oxide matrix during one or more material processing operations on the oxide matrix, wherein said generating the fundamental data includes calculating formation energies of single Si atoms that exist in excess at various states in an oxide matrix to determine incorporation of the single Si atoms in a Si—O bond network.
18. The article of manufacture of claim 15 , further comprising generating the fundamental data representative of the processes that can occur in the oxide matrix during one or more material processing operations on the oxide matrix, wherein said generating the fundamental data includes calculating relative formation energies of single Si atoms in a crystalline silicon, an amorphous suboxide matrix, and a nanocrystal-matrix interface to determine a location at which excess Si atoms remain.
19. The article of manufacture of claim 15 , wherein said generating the kinetic model includes simplifying an amorphous suboxide structure using a rigid diamond-lattice model, having silicon atoms at lattice sites and oxygen atoms at Si—Si bond centers.
20. The article of manufacture of claim 15 , wherein said generating the kinetic model includes permitting oxygen atoms to diffuse through oxygen-empty sites.
21. A system, comprising:
a processing unit; and
a tangible computer-readable medium coupled to the processing unit and having instructions stored thereon, the instructions comprising:
instructions to generate, from fundamental data representative of processes that can occur in an oxide matrix during one or more material processing operations on the oxide matrix, a kinetic model representative of reactions that contribute substantially to formation of silicon nanocrystals in the oxide matrix; and
instructions to generate, from the kinetic model, data representative of a profile for the formation of the silicon nanocrystals in the oxide matrix, including instructions to predict formation of the silicon nanocrystals using kinetic Monte Carlo simulations based at least in part on oxygen diffusion.
22. The system of claim 21 , wherein the instructions further comprise instructions to generate the fundamental data representative of the processes that can occur in the oxide matrix during the one or more material processing operations on the oxide matrix, wherein the instructions to generate the fundamental data include instructions to calculate changes in a total energy of silicon suboxide matrices by varying a Si:O ratio to determine a strain energy or a suboxide penalty energy for a chemical phase separation of silicon and silicon dioxide.
23. The system of claim 21 , wherein the instructions further comprise instructions to generate the fundamental data representative of the processes that can occur in the oxide matrix during the one or more material processing operations on the oxide matrix, wherein the instructions to generate the fundamental data include instructions to calculate formation energies of single Si atoms that exist in excess at various states in the oxide matrix to determine incorporation of the single Si atoms in a Si—O bond network.
24. The system of claim 21 , wherein the instructions further comprise instructions to generate the fundamental data representative of the processes that can occur in the oxide matrix during the one or more material processing operations on the oxide matrix, wherein the instructions to generate the fundamental data include instructions to calculate relative formation energies of single Si atoms in a crystalline silicon, an amorphous suboxide matrix, and a nanocrystal-matrix interface to determine a location at which excess Si atoms remain.
25. The system of claim 21 , wherein the instructions to generate the kinetic model include instructions to simplify an amorphous suboxide structure using a rigid diamond-lattice model, having silicon atoms at lattice sites and oxygen atoms at Si—Si bond centers.
26. The system of claim 21 , wherein the instructions to generate the kinetic model include instructions to permit oxygen atoms to diffuse through oxygen-empty sites.