tailieunhanh - Electronic Materials Part 5

Tham khảo tài liệu 'electronic materials part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Density of Thermally Promoted of Carriers Number of electrons per f r . TT-TR volume in conduction J g band I Density of electron states per volume per dE Fraction of states occupied at a particular temperature E-Ef e kcT when E - EF kbT f E -1 1 e kbT 3 g E f I 2 e - E 2 g 2n 21 h2 I g f 1 n Since J x -e dx then n 2I 0 2 2nh2 3 . 1 f 2m Ì2 E f n rl - I e 2n H h2 J E Eg 3 u rr 2 EF Ec mekbT I e ĨÉ eltT 1 E 2 kT dE V J e- Eg Ỵe Nc n NC E. Fitzgerald-1999 11 Density of Thermally Promoted of Carriers A similar derivation can be done for holes except the density of states for holes is used Even though we know that n p we will derive a separate expression anyway since it will be useful in deriving other expressions g v E 3 1 f 2 111 - E 2 2n 2 I h - . 0 p J fh E gv E dE where fh 1 - f E -f 3 p mkT Ìf 2nh2 J E F - kb T e b Ef kb T p Nv e b E. Fitzgerald-1999 12 6 Thermal Promotion Because electron-hole pairs are generated the Fermi level is approximately in the middle of the band gap The law of mass action describes the electron and hole populations since the total number of electron states is fixed in the system _ c -Es 3 7 TiJm 1 n p gives Ef E kbTlnl I 2 4 t me J Since me and mh are close and in the ln term the Fermi level sits about in the center of the band gap 3 -E J kbT I 2 ị . 3 p or n ni 2l - b2-T- I Im m I4 e b t2nh2J y e v E. Fitzgerald-1999 13 Law of Mass Action for Carrier Promotion z -Ị rp 3 3 s _2 I kbT I kbT _ n. np 41 _ I -n mh I2 e b 12nh2 J v - Eg. El n NCNVe kbT Note that re-arranging the right equation leads to an expression similar to a chemical reaction where Eg is the barrier. NCNV is the density of the reactants and n and p are the products. N C NV e h - Eg .2 np ev n NcNv Nc N Thus a method of changing the electron or hole population without increasing the population of the other carrier will lead to a dominant carrier type in the material. Photon absorption and thermal excitation produce only pairs of carriers intrinsic .