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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).