President University Erwin Sitompul SDP 11/1

Dr.-Ing. Erwin SitompulPresident University

Lecture 11Semiconductor Device Physics

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Chapter 12BJT Dynamic Response Modeling

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Cut-off(OFF)

Idealized switching circuit

Saturation(ON)

Load line

Qualitative Transient ResponseChapter 12 BJT Dynamic Response Modeling

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cutoff

active saturation

saturation active

1

5

2 3

4

1

2 3 4

5

Qualitative Transient ResponseChapter 12 BJT Dynamic Response Modeling

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B BB

B

,dQ Qidt

B B( , ) (0, ) 1 xp x t p tW

B BB

B

0dQ Qidt

B B B0

( , ) (0, )2

W qAWQ qA p x t dx p t

Small

Interpreted as average lifetime of an excess

minority carrier

Charge Control RelationshipsChapter 12 BJT Dynamic Response Modeling

A pnp BJT biased in the active mode has excess minority-carrier charge QB stored in the quasineutral base.

While

In steady state,

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2

tB2

WD

Interpreted as average time taken by minority carriers to diffuse across

the quasineutral base

BC B

( , )

x W

p x ti qADx

BC

t

Qi

(Active mode)

Base Transit Time tt Chapter 12 BJT Dynamic Response Modeling

B BB 2

B

(0, )( / 2 )

qAD Qp tW W D

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C Bdc

B t

II

B

Ct

Qi

BB

B

Qi

The lifetime of a minority carrier before it recombines in the base is much longer than the time it requires to

cross the quasineutral base region

Relationship between tB and ttChapter 12 BJT Dynamic Response Modeling

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2

tB

,2WD

B N nkTD Dq

2

t

n2

WkTq

From Figure 3.5, n 801 cm2/(Vs)

ExampleChapter 12 BJT Dynamic Response Modeling

Given an npn BJT with W = 0.1 μm and NB = 1017cm-3. Find t.

5 2

2

(10 cm) 2.414 ps2(25.86mV)(801cm /V s)

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B BBB

B

dQ QIdt

BB BB B( ) tQ t I Ae

BB BB B( ) (1 )tQ t I e

BB BB Br

t tC

CCCC r

L

( ) (1 ) for 0( )

for

tQ t I e t ti t V I t t

R

SB BB

S

,Vi IR

tr : rise time, period of active mode

Turn-On TransientChapter 12 BJT Dynamic Response Modeling

During the turn-on transient:

The general solution is:

Initial condition: QB(0)=0, since transistor is in cutoff:

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CC tr B

BB B

1ln 1 It

I

IBBB > ICCt

dc IBB > ICC

dc > ICC/IBB

dc > dc(saturation)

Turn-On TransientChapter 12 BJT Dynamic Response Modeling

In saturation mode:

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During the turn-off transient:

B BBB

B

dQ QIdt

B/B BB B( ) tQ t I Ae

B/B BB B( ) (1 ) tQ t I e

B

CC sd/

BB BC Bsd

t t

for 0(1 )( ) ( ) for

t

I t tI ei t Q t t t

SB BB

S

,Vi IR

tsd : storage delay time

Turn-Off TransientChapter 12 BJT Dynamic Response Modeling

The general solution is:

Initial condition: QB(0)=IBBB:

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CC tsd B

BB B

1ln It

I

Turn-Off TransientChapter 12 BJT Dynamic Response Modeling

The transient speed of a BJT depends on the amount of excess minority-carrier charge stored in the base and also the recombination lifetime B.

By reducing B, the carrier removal rate is increased, for example by adding recombination centers (Au atoms) in the base.

Tradeoff: dc= B/t will decrease.

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Collector current (actual form)

Collector current (mathematical model)

Practical ConsiderationsChapter 12 BJT Dynamic Response Modeling

The foregoing analysis was highly simplified to avoid excessive amount of mathematics.

More realistic iC transient response is shown below.Added delay time td (due to charging of junction capacitance)

and fall time tf.

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Homework 8

Deadline: 05.07.2012, at 08:00 am.

1.(Int.0)A pnp BJT has αF = 0.99, αR = 0.1, and IF0 = 10–16 A. If VBC = –0.68 V and IC = 0.1 mA, determine the mode of the device and the value of IB using the Ebers-Moll model.

Chapter 12 BJT Dynamic Response Modeling