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Lattice‐matching SiC substrates with GaN
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5.We have Å for GaN and 3.08 Å for 6H–SiC, from Ref. 6, giving Å.
6.Landolt–Börnstein Numerical Data and Functional Relationships in Science and Technology, New Series, Vol. 17a, Semiconductors: Physics of Group IV and III-V Compounds, edited by O. Madelung, M. Schulz, and H. Weiss (Springer-Verlag, Berlin, 1982).
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10.Sapphire is the most widely used substrate for GaN despite having a different crystal structure, =13.8%,and a proclivity toward producing buckled surfaces with pyramidal features similar to those observed for 6H–SiCC-terminated substrates.
11.J. A. Dean, Lange's Handbook of Chemistry, 14th ed. (McGraw-Hill, New York, 1992) lists the ionic radius of as 1.46 Å. The covalent radius of N is listed as 0.75 Å, in Periodic Table of the Elements (Papertech Marketing Group, Inc., 163 Buttermilk Ave., Unit 12, Concord, Ontario L48 3X8 Canada, 1994).
12.We reduced the covalent radii (Ref. 11) for Ga and N by 0.03 Å, in order to reproduce the measured lattice constant of GaN, 3.19 Å.
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14.W. A. Harrison, Electronic Structure and the Properties of Solids (W. H. Freeman, San Francisco, 1980) discusses how matrix elements of tight-binding Hamiltonians are constructed using chemical trends. The off-diagonal matrix elements of the Hamiltonian are obtained using , where d is the nearest-neighbor bond length, and we have A=0.51×(Harrison's interatomic matrix elements), found on p. 551. The diagonal elements are Herman and Skillman (Ref. 15) energies for s- and p-valence electron states, as tabulated in Ref. 17.
15.F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, Englewood Cliffs, 1963).
16.Similar superlattice Hamiltonians have been discussed in S. Y. Ren and J. D. Dow, Phys. Rev. B 39, 7796 (1989); J. Appl. Phys. 65, 1987 (1989).
17.S. Y. Ren and J. D. Dow (unpublished).
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