EE133 Solid-State Electronics Fall, 2005

Homework Solutions Four

(Total: 100 Points)

3.11 (a) Show that the minimum conductivity of a semiconductor sample occurs when

npinn µµ /0 = . {Hint: begin with Eq. (3-43) and apply Eq. (3-24).} (15’)

(b) What is the expression for the minimum conductivity ? (5’) minσ

(c) Calculate for Si at 300K and compare with intrinsic conductivity. (5’) minσ

[Answer]

(5’)

(5’)

(5’)

(5’)

(3’)

(2’)

3.12 (a) A Si bar 0.1 cm long and 100 µm2 in corss-sectional area is doped with 1017 cm-3 phosphorus.

Find the current at 300 K with 10 V applied. Repeat for a Si bar 1 µm long. {Hint: Find the

mobility value in Figure 2-23.} (10’)

1

EE133 Solid-State Electronics Fall, 2005

(b) How long does it take an average electron to drift 1 µm in pure Si at an electric field of 100

V/cm? Repeat for 105 V/cm. (10’) [Answer]

phosphorus.

2

/Vscm900=nµ( and corresponding results are also correct!)

(8’)

(2’)

(8’)

(2’)

2

EE133 Solid-State Electronics Fall, 2005

3.21 Referring to Fig 3.25, consider a semiconductor bar with w=0.1 mm, t=10 µm and L= 5 mm. For B=10 kG in the direction shown and a current of 1mA, we have VAB=–2mV, VCD=100mV. Find the type, concentration and mobility of the majority carrier. (30’)

[Answer]

(5’)

(10’)

(5’)

(10’)

4.5 A sample is doped with donors such that n0=Gx for n0>>ni, where G is a constant. Find the built-in electric field E(x). (15’)

[Answer]

(5’)

(10’)

4.13 Boron is diffused into an intrinsic Si sample, giving the acceptor distribution shown in Figure P4-13. Sketch the equilibrium band diagram and show the direction of the resulting electric field, for Na(x)>>ni. Repeat for phosphorus, with Nd(x)>>ni. (10’)

[Answer]

(5’)

(5’)

3