# Assignment 4

ELEC421/6221 Submission deadline October 29, 2014

Assignment 4

1. A uniformly doped silicon npn transistor is to be biased in the forward-active mode with the BC junction reverse biased by 3V. The metallurgical base width is 1.10 µm. The transistor dopings are

N E

 10 17

cm

 3 ,

N B

 10 16

cm

 3 , and

N C

 10 15

cm

 3 . (a) For T = 300K, calculate the BE voltage at which the minority carrier electron concentration at

x

= 0 is 10 percent of the majority carrier hole concentration. (b) At this bias, determine the minority carrier hole concentration at

x’

= 0. (c) Determine the neutral base width for this bias. 2. Consider a uniformly doped npn bipolar transistor at T = 300 K with the following parameters:

N E

 10 18

cm

 3

D E

E

0  8

cm

2 /

s

 10  8

s x E

 0 .

8 

m N B

 5  10 16

cm

 3

D B

B

0  15

cm

2 /

s

 5  10  8

s x B

 0 .

7 

m N C

 10 15

cm

 3

D C

 12

cm

2 

C

0

J r

0  10  7  3  10  8

s

/

s A

/

cm

2 For

V BE

 0 .

60

V

and

V CE

 5

V

, calculate (a) the currents

J nE

,

J pE

,

J nC

,

and J R

and (b) the current gain factors  , 

T

,  ,  ,

and

 .

3.

(a) The recombination current density,

J r

0 , in a npn silicon bipolar transistor at T = 300 K is

J r

0  5  10  8

A

/

cm

2 . The uniform dopings are

N E

 10 18

cm

 3 ,

N B

 5  10 16

cm

 3 , and

N C

 10 15

cm

 3 . Other parameters are

D E

 10

cm

2 /

s

,

D B

 25

cm

2 /

s

, 

E

0  10  8

s

,

and

B

0  10  7

s

. Determine the neutral base width so that the recombination factor   0 .

995 when

V BE

 0 .

55

V

. (b) If

J r

0 remains constant with temperature, what is the value of  when

V BE

 0 .

55

V

for the case when the temperature T = 400 K? Use the value of

x B

determined in part (a).