Question

o uVcaGver, thC Tauo S 4 LO1. 1.5 Show that the probability of an energy state being occupied AE above the Fermi level is the same as the probability of a state being empty AE below the Fermi level. 1 hoitoe f(EF+AE) = 1 - f(EF-AE)

Answer 1

According to the termi level 1hat tha telectron Oceupies ts formula, th pro babitity Sol state i e&nergy 1 E-E/KT +e fermi level ths above E us ket us Consider that EF luy E amount E EFt 4E E F Now, We lyet the lquation for probability inding above termi level us an electron tnergy AE (E-Ep)/KT 1 + e 1 FAE It e fCEtAE) KT 1+C Now, the phobability te tulectron not occupying the tnergy state us dyiven ly - f(E 1 - lte Ef/KT het s Consider at E us e tow he ley fermi levet AE Omount

1- fleF -DE) . 1- P(E') - I - F-AE KT 1t e AE/KT = 1 - E/KT 1-t e 1e4E/KT 1+e /Kt . -fCEF-AE) 1 I teE/KT From wauation and , ut s clear that probahility energy utafe deeing dccupi ed AE above ter mi devel AE e's oqual tho probabilify sfate heing dampty low the fermi devel CEF tAE CEF-AE tHence Proved