Theoretical Study of Energy Gap for Silicon and Germanium Under High Pressure

Abstract

In this study the energy gap (E g) for both silicon and germanium under high pressure and different temperatures is evaluated using two approaches. One of them by evaluating the gradient of (E g) with pressure (dE g /dP), and with temperature (dE g /dT) under different pressures. The other, by using different equation of state (Birch-Murnaghan, Misra-Goyal, Vinet and modified Lennard-Jones) to evaluate the variation of lattice constant with pressure, and then evaluate the variation of (E g) with pressure. ‫ــــــــــــــــــــــــــــــــــــــــــــــــــــ‬ ‫ﺍﻟﻌﺎﻟﻲ‬ ‫ﺍﻟﻀﻐﻁ‬ ‫ﺘﺤﺕ‬ ‫ﺍﻟﺠﺭﻤﺎﻨﻴﻭﻡ‬ ‫ﻭ‬ ‫ﻟﻠﺴﻠﻴﻜﻭﻥ‬ ‫ﺍﻟﻁﺎﻗﺔ‬ ‫ﻟﻔﺠﻭﺓ‬ ‫ﻨﻅﺭﻴﺔ‬ ‫ﺩﺭﺍﺴﺔ‬ ‫ﺍﻟﻤﻠﺨﺹ‬ ‫ﻭﻋﻨـﺩ‬ ‫ﺍﻟﻌـﺎﻟﻲ‬ ‫ﺍﻟـﻀﻐﻁ‬ ‫ﺘﺤﺕ‬ ‫ﺍﻟﺠﺭﻤﺎﻨﻴﻭﻡ‬ ‫ﻭ‬ ‫ﺍﻟﺴﻠﻴﻜﻭﻥ‬ ‫ﻤﻥ‬ ٍ ‫ﻟﻜل‬ ‫ﺍﻟﻁﺎﻗﺔ‬ ‫ﻓﺠﻭﺓ‬ ‫ﺤﺴﺎﺏ‬ ‫ﺍﻟﺒﺤﺙ‬ ‫ﻫﺫﺍ‬ ‫ﻓﻲ‬ ‫ﺘﻡ‬ ‫ﻤﺩﺨﻠﻴﻥ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﻤﺨﺘﻠﻔﺔ‬ ‫ﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺎﺕ‬. ‫ﺃ‬ ‫ﺍﻨﺤﺩﺍ‬ ‫ﺒﺤﺴﺎﺏ‬ ‫ﺤﺩﻫﻤﺎ‬ ‫ﺭ‬ ‫ﺍﻟـﻀﻐﻁ‬ ‫ﻤﻊ‬ ‫ﺍﻟﻁﺎﻗﺔ‬ ‫ﻓﺠﻭﺓ‬ (dE g /dP) ، ‫وﻣﻊﻊ‬ ‫اﻟﺤﺮﺮارة‬ ‫درﺟﺔﺔ‬ (dE g /dT) ‫ﻤﺨﺘﻠﻔﺔ‬ ‫ﻀﻐﻭﻁ‬ ‫ﺘﺤﺕ‬. ‫ﻤﺨﺘﻠﻔﺔ‬ ‫ﺤﺎﻟﺔ‬ ‫ﻤﻌﺎﺩﻻﺕ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﻭﺍﻵﺨﺭ‬) ‫ﺒﺭﺥ‬-،‫ﻤﺭﻨﻜﻬـﺎﻥ‬ ‫ﻤﻴﺴﺭﺍ‬-‫ﻭﻟﻴﻨﺎﺭﺩ‬ ‫ﻓﻴﻨﺕ‬ ،‫ﻜﻭﻴﺎل‬-‫ﺍﻟﻤ‬ ‫ﺠﻭﻨﺱ‬ ‫ﻁ‬ ‫ﻭﺭﺓ‬ (‫ﺘﻐﻴﺭ‬ ‫ﺤﺴﺎﺏ‬ ‫ﺜﻡ‬ ‫ﻭﻤﻥ‬ ،‫ﺍﻟﻀﻐﻁ‬ ‫ﻤﻊ‬ ‫ﺍﻟﺸﺒﻴﻜﺔ‬ ‫ﺜﺎﺒﺕ‬ ‫ﺘﻐﻴﺭ‬ ‫ﻟﺤﺴﺎﺏ‬ ‫ﺍﻟﻀﻐ‬ ‫ﻤﻊ‬ ‫ﺍﻟﻁﺎﻗﺔ‬ ‫ﻓﺠﻭﺓ‬ ‫ﻁ‬ .