Lattice Vibration and Lattice Dilation Effects in the Temperature Dependence of the Silicon Energy Gap
Tahseen G. Abdullah
Department of Physics, College of Science, Salahaddin University- Erbil, Krg, Iraq
Corresponding author: email@example.com
A theoretical calculation using potential scaled orthogonalized plane wave (PSOPW) method was used and implemented to predict the effect of lattice vibration and lattice dilation in the temperature dependence of the fundamental energy gap for Si. Through the calculation of the maximum of valence band and minimum of conduction band at different temperatures, the effect of temperature on the energy gap for lattice vibration (electron-phonon interaction), lattice dilation (thermal expansion) and total effect were calculated separately using the computer Pascal code PSOPW. The calculation for the temperature dependence of the band gaps predict the contribution of lattice vibration dependence of the energy gap is more than that of lattice dilation and the rate of change of valence band with temperature is more than that of the conduction band.
Keywords: Energy Gap; Energy band; LV; LD; LDV
. I. Vurgaftman, J. R. Meyer and L. R. Ram-Mohan, J. Appl. Phys. 89, (2001) 5815.
. H. F. Wolf, Semiconductors, Wiley-Interscience, USA , 1971.
. S. M. Sze, Physics of Semiconductor Device” Wiley Interscience Publication, New York , 1981.
. D. Olguin, M. Cardona and A. Cantarero , Solid state Communications 122 (2002) 575.
. P. B. Allen and M. Cardona, Phys. Rev. B 27, (1983) 4760-4769.
. Y. F. Tsay, B. Gong, S. S. Mitra and J. F. Vetelino, Phys. Rev. B 6, (1972) 2330.
. F. Bassani and G. P. Parravicini , Electronic States and Optical Transitions in Solids, Pergamon Press, Oxford, 1975.
. W. A. Harrison, Elementary Electronic Structure , World Scientific Co. Pte. Ltd, London ,1999.
. M. L. Cohen and J. P. Chelikowsky, Electronic Structure and Optical Properties of Semiconductors, 2nd Edition, Springer Series in Solid State Sciences,1975.
. Sarkawt A. Sami, Modification of OPW Method and Using it to calculate Temperature Dependence of the Energy Gap for some III- V Semiconductors” Ph. D. Thesis, Dohuk university, Kurdistan Region, Iraq, 2004.
. Tahseen G. Abdullah, Temperature Dependence of Direct and Indirect Gaps of CuGe2P3 Semiconductor” Ph.D. Thesis, Salahaddin University-Erbil, Kurdistan Region, Iraq, 2008.
. T. O. Woodruff , On the Orthogonalized Plane Wave Method for Calculating Energy Eigenvalues in Periodic Potential”, Ph.D. Thesis, California Institute of Technology, Pasadena, California, USA, 1955.
. J. Camassel and D. Auvergne , Phys. Rev. B 12, (1975) 3258.
. D. Auvergne, J. Camassel, H. Mathieu and M. Cardona, Phys. Rev. B 9, (1974) 5168.
. J. P. Walter, R. L. Zucca, M. L. Cohen, and Y. R. Shen, Phys. Rev. lett. 24, (1970) 102.
. S.O. Pillai, Solid State Physics, 4th Ed., New Age International (P) Ltd., Publishers, New Delhi, India, 2001.
. M. S. Omar, Materials Research Bulletin. 42, (2007) 319-326.
. P. A. Seeger and L. L. Daemen, Appl. Phys. A 74, (2002) 1458-1461.
. W. Bludau, A. Onton and W. Heinke, J. Appl. Phys. 45, (1974) 1846.