2008半导体物理(精)

1、Concentrations.lf we assume the Boltzmann approximation to be valid ,the from Equation(3.11)we have n = Nc exp(Ec EF) / kT. We can solve for Ec - EF form this equation and odtain EC-EF=kT ln(叫) (3.63) Wh ere q is give n by Equati no (3.60).lf we con sider an n-type semic on ductor in which Nd n ,the

2、 n0 Nd ,so that N EC-EF 二 kTIn( -) (3.64) Nd The dista nce detwee n the bottom of the con duct ion band and the Fermi is alon garithmic fun ctio n of the donor concen trio n. As the donor concen trati on in crases, the Fermi level moves con duct ion band. Con versrly, if the Fermi level moves closer

3、 to the con duct ion band, the n the electr on concen trati on in the con duct ion band is in creas ing. We can note that if we have a compe nsated swmic on ductor, the n the Nd term in Equati on( 3.64) is simply rep;aced by Nd - Na, or the net effe ctive donor concentration. EXAMPLE 3.14 OBJECTIVE

4、Deermine the required donor impurity concentration to obtain a specified Fermi energy. Silicon at T = 300k contains an acceptor impurity concentration of Na =1016cm. of donor impurity atoms that must be added so that the From Equati on (3.64),we have Which can be rewritte n as （ E E ） 肌W 5丄异 The n 1

5、9 r 0.20 16 -3 =2.8 10 exp = 2.24 10 cm 0.0259 Or 16 16 3 Determine the concentration silic on is n type and the Fermi en ergy id Soluti on 0.20eV below the con duct ion-ba nd edge. Ec -EF =kTl n( N Nd Na) Nd -Na Nd =1.24 10 Na =2.24 10 cm Comme nt A compe nsated semic on ductor can be fabricated to

6、 provide aspecific Fenri en ergy level. Exercise Problem EX3.14 determ ine the positi on of the Fermi level with respect to the vale nce-ba nd en ergy in p-type GaAs at T = 300k . The doping concentrations are Na =5 1016cmJandNd =4 1015cm(Ans.EF - Ev = 0.130eV) We can develop a slightly differe nt e

7、xpressi on for the positi on of the Fermi level. We had form Equation (3.39) that n0 =niexp(EF -EFi)/kT. We can solve for EF - EFi as n0 EF -EFi 二 kTIn(-) (3.65) Equati on( 3.65) can be used specifically for an n-type semic on ductor, where n0 is give n by Equati on( 3.60), to find the differe nce b

8、etwee n the Fermi level and the in tri nsic Fermi level sa a function of the donor concentration. We can note that,if the net effectiv donor concen trati on is zero,that is, Nd - Na =0 , then n0 = n and EF EFi. A completely compe nsated semic on ductor has the chaaraceristics of an intrinsic materia

9、l in terms of carrier concentration and Fermi leve position. We can derive the same types of equations for a p-type semiconductor.From Equati on( 3.19), we have Fermi en ergy, p0 二 Nv exp-(EF - Ev)/ kT , so that p type Nv EF-Ev=kTl n( v) (3.66) P。 If we assume that Na L nj, then Equation (3.66)can b

10、e written as N EF-ERWI n( v) (3.67) Na The dista nce detwee n the Fermi leve and the top of the vale nce-ba nd en ergy for a p-type semic on ductor is a logarithmic of the acceptor con cetrati on: as the acceptor concen tratio n in creases,the Fermi level moves closer to the vale nce band. Equation(

11、3.67) still assumes that the Boltzmann approximation is valid. Again, if we have a compe nsated p-type semic on ductor, the n the Na term in Equati on( 3.67) is replaed by Na Nd ,or the net effective acceptor concen trati on. We can also derive an expressi on for the relati on ship detwee n the Fermi level