材料物理化学 第三篇习题

Chap 11、Semiconductors

11.1 (a) For a semiconductor, show that np product obtained from

Eq.(11.27) is proportional to exp(-βE g ) and thus is independent of the position of the chemical potential μ in the bandgap.

Eq.(11.27):

(b) The law of mass action in semiconductors for reaction creating

pairs of electrons and holes [e.g., Eq.(11.28)] has the form n(T)P(T)∝exp(-βE g ). Explain the significance of this law. (Hint: The law of mass action is described in Section 4.6)

Eq.(11.28): (c) Evaluate the np product at T=300K for Si with E g =1.11ev and

m eds ﹡=1.05m and m hds ﹡=0.58m.

11.2 Using Eq.(11.30) and m eds ﹡=1.05m and m hds ﹡=0.58m for Si,

calculate the change in the position of the chemical potential µ in the energy gap of intrinsic Si between T=0 and 300K.

Eq.(11.30): 11.3 Calculate the values of N c and N v as defined in Eq.(11.27) for Si

at T=300K. The appropriate of density-of-states effective masses for Si are m eds ﹡=1.05m and m hds ﹡=0.58m.

11.4 Consider a semiconductor with a bulk energy gap E g =1.5ev and

g

E v c i i e T N T N T p T n β-=)()()()()()(2/32)()2(2)()(μβμβπ----*===c c E c E B eds i e T N e T k T n T n m )()(2/32)()2(2)()(v v E v E B h ds i e T N e T k T p T p m ----*===μβμβπ **

+=eds hds

B g m m T k E T ln 432)(μ

with m e﹡=m h﹡=0.1m. Calculate the increase in the energy gap of

this semiconductor when it is incorporated into the following

structures:

(a) A quantum well (d=2) with L x=10nm.

(b) A quantum wire (d=1) with L x=L y=10nm

(c) A quantum dot (d=0) with L x=L y=L z=10nm

11.5 A Hall effect measurement is carried out on a rectangular bar

of a semiconductor with dimensions L x=0.04m (the direction

of current flow ) and L y=L z=0.002m. When a current I x=5mA

flows in the +x direction and a magnetic field B z=0.2T is

applied in the +z direction, the following voltages are

measured: V x=6V and V y=+0.3mV (i.e., increasing in the +y

direction). Determine the following properties of the

semiconductor bar from these data :

(a) The sign of the dominant charge carriers.

(b) The concentration of the dominant charge carriers.

(c) The electrical conductivity σ.

(d) The mobility µ of the dominant charge carriers.

11.6Using Eq.(11.59), estimate the increase △n in the electron

concentration in an n-type semiconductor due to the uniform

absorption of light with α=105m-1, I0=1W/m2, and hω=1e V, a

quantum efficiency η=1, and a minority-carrier lifetime ηp=10-3s.