ECE 250 Problem Set: Semiconductor Physics - Prof. Marc E. Herniter, Assignments of Electrical and Electronics Engineering

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V

bi

K

B

⋅ 300 ⋅K

q

ln

N

A

N

D

n i

(300 K ⋅ )

2

V

bi

=0.803 V

C

jo

:=2 pF⋅

C

J

C

jo

10 V⋅

V

bi

C

J

=0.545 pF

Homework 2 Problem 3

Define units and constants

eV 1.602 10

− 19 := ⋅ ⋅ coul⋅volt K B

− 6 ⋅

eV

K

Specify some constants for silicon

E

g_Si

:= 1.1 eV⋅ B Si

15 ⋅

cm

3 K

⋅

q 1.602 10

− 19 := ⋅ ⋅coul degC ≡K

pF 10

− 12 := ⋅F T :=273 K⋅ +50 degC⋅

n i

B

Si

T

⋅ exp

E

g_Si

2 K

B

⋅ ⋅T

n i

10 × cm

− 3

N

d

17 ⋅ cm

− 3 := ⋅ N a

15 cm

− 3 := ⋅

Define a function for the built-in barrier potential

V

bi

K

B

⋅T

q

ln

N

a

N

d

n i

2

:= ⋅ V

bi

=0.699 V

C

jo

:= 40 pF⋅ M := 0.5 C j

:=10 pF⋅

V

R

V

bi

C

jo

C

j

1

M

:= ⋅ V

R

=10.489 V

V

bi

K

B

⋅ 300 ⋅K

q

ln

N

A

N

D

n i

( 300 K⋅ )

2

:= ⋅ V

bi

= 0.803 V C

jco

:=2 pF⋅

m :=0.

Generate Logartihmically spaced points for Vr

k :=− 3 , −2.99.. 1

V

R

( )x 10

x := ⋅V

Define the reverse capacitance function at 300 K. Scale Cj to picofarads by dividing by 1 P

C

j

(V )

C

jco

V

V

bi

m

⋅ 1 ⋅pF

1 . 10

3 0.01 0.1 1 10

1

2

Reverse Bias Junction Capacitance

Reverse Voltage (Volts)

Junction Capacitance (pF)

C j

V R

( )k ( )

V R

( )k

eV 1.602 10

− 19 := ⋅ ⋅ coul⋅volt K B

− 6 ⋅

eV

K

Specify some constants for silicon

E

g

:= 1.1 eV⋅ B 5.23 10

15 ⋅

cm

3 K

⋅

q 1.602 10

− 19 := ⋅ ⋅coul

Problem 5:

N

d

17 cm

− 3 := ⋅ N a

16 cm

− 3 := ⋅

Define functions for the intrinsic carrier concentration

n i

( T) B T

⋅ exp

E

g

2 K

B

⋅ ⋅T

Define a function for the built-in barrier potential

V

bi

( T)

K

B

⋅T

q

ln

N

a

N

d

n i

(T )

2

Plot the function. Define the range of temperatures. (0 C to 125 C)

T :=273 K⋅ , 274K..398 K⋅