ene 311 lecture 10. ohmic contact for metal-semiconductor contacts with low doping concentration,...

ENE 311 Lecture 10

Ohmic Contact

• - For metal semiconductor contacts with low doping c - oncentration, the thermionic emission current domin

ants the current transport. • Rc can be written as

(1)

* As seen from equation (1), in order to have a small value of Rc, a low barrier height should be used.

/

**be kT

c

kR e

eA T

Ohmic Contact

• - For metal semiconductor contacts with high doping concentration, the barrier width bec

omes very narrow and the tunneling current becomes dominant.

• The tunneling current can be found by

(2)

*

0

4exp e s b

D

m VJ J

N

Ohmic Contact• The specific contact res

istance for high dopingis

* *

0

4 41expe s e s b

C D D

m mJ

R N N

Upper inset shows the tunneling process. Lower inset shows thermionic emission over the low barrier.

Ohmic Contact

Ex. An ohmic contact has an area of 10-5 cm2 a nd a specific contact resistance of 10-6 -Ω cm

- 2. The ohmic contact is formed in an n type silicon. If ND =5 x 1019 cm-3 and b = 0.8 V,

and the electron effective mass is 0.26m0

, fi nd the voltage drop across the contact whe

n a forward current of1 A flows through it.

Ohmic ContactSoln The contact resistance for the ohmic cont

act is RC /Area = 10-6 / 10-5 = 0.1 Ω.

12

0

*

2

31 1214 -3/2 -1

2 34

20

220

0

1.cm

4

4 0.26 9.1 10 11.9 8.85 101.9 10 m V

1.05 10

exp

exp

VC

e s

b

D

b

V C D D

J

R V

mLet C

C

C VI I

N

CI A CI

V R N N

Ohmic Contact

Soln 1

220

19 6 14

14 19 16

8

0b

2

exp

5 10 10 1.9 10 0.810 exp

1.9 10 5 10 10

8.13 10 A

At I = 1A, we have ln 0.763 V

0.8 0.763 0.037 V

b

C D D

D

CA CI

R N N

N IV

C I

V

Transistor

• Transistor (Trans fer resistor ) is a multijunc tion semiconductor device.

• Generally, the transistor is used with other c ircuit elements for current gain, voltage gai

- n, or even signal power gain.

• There are many types of transistors, but all of them are biased on2 major kinds: bipola

r transistor and unipolar transistor.

Bipolar Junction Transistor (BJT)

• The BJT was invented by Bell laboratories in1947 . It is an active3- terminal device that c

an be used as an amplifier or switch.

• It is called bipolar since both majority and m inority carriers participate in the conduction

process.

• Its structure is basically that2 diodes are co nnected back to back in the form of - -p n p or

- -n p n.

Bipolar Junction Transistor (BJT)

Bipolar Junction Transistor (BJT)

• (a ) A - -p n p transistor wi th all leads grounded ( at thermal equilibrium)

.

• (b ) Doping profile of a t ransistor with abrupt i

mpurity distributions.

• (c - ) Electric field profile.

• (d ) Energy band diagr am at thermal equilibri

um.

Bipolar Junction Transistor (BJT)

Operational Mode

Emitter-base junction

Collector-base junction

Active (normal) Forward Reverse

Cutoff Reverse Reverse

Saturation Forward Forward

Inverse Reverse Forward

Bipolar Junction Transistor (BJT)

• When the transistor is biased in the active mode, holes are injected from the p+ emitter into the base and electrons are emitted from the n base into the emitter.

• For the collector-base reverse biased junction, a small reverse saturation current will flow across the junction.

Bipolar Junction Transistor (BJT)

• However, if the base wi dth is very narrow, the i

njected holes can diffus e through the base to r

- each the base collector depletion edge and the

n float up into the collector.

• This is why we called t hem “emitter” and “coll

ector” since they emit or inject the carriers an

d collect these injecte d carriers, respectively.

Bipolar Junction Transistor (BJT)• IEp is the injected hole

current. Most of these injected holes survive the recombination in the base, they will reach the collector giving ICp.

• There are three other base current: IBB, IEn, and ICn. IBB is the electrons that must be supplied by the base to replace electrons recombined with the injected holes. IBB = IEp – ICp .

Bipolar Junction Transistor (BJT)

• IEn is the injected electr on current (electrons in

jected from the base to the emitter.).

• ICn corresponds to ther mally generated electr

ons that are near the b- ase collector junction e dge and drift from the c

ollector to the base.

Bipolar Junction Transistor (BJT)

E Ep EnI I I

C Cp CnI I I

B E C En Ep Cp CnI I I I I I I

(4)

(5)

(6)

Bipolar Junction Transistor (BJT)

• The crucial parameter called - “common base current gain” α

0 is defined by

(7)

• Substituting (4) into (7) yields

(8)

0Cp

E

I

I

0Cp

TEp En

I

I I

Bipolar Junction Transistor (BJT)

• γ is the emitter efficiency written as

(9)

• αT is the base transport factor written as

(10)

Ep

E

I

I

CpT

Ep

I

I

Bipolar Junction Transistor (BJT)

• - For a well designed and fabricated transisto r, IEn is small compared to IEp and ICp is close t o IEp .

• Therefore, γ and α are close to1 and that m akes α0 is close to unity as well. Thus, the co

llector current can be expressed by

(11)

0C T Ep Cn E CnI I I I I

Bipolar Junction Transistor (BJT)

• Normally, ICn is know as ICB0 or the leakage c urrent between the collector and the base w

- ith the emitter base junction open.

• Thus, the collector current can be written as

(12)

0 0C E CBI I I

Bipolar Junction Transistor (BJT)

- In order to derive the current voltage expression

for an ideal transistor, we assume the following:

• The device has uniform doping in each region.

• The hole drift current in the base region and t he collector saturation current is negligible.

• - There is low level injection.

• - There are no generation combination current s in the depletion regions.

• There are no series resistances in the device.

Bipolar Junction Transistor (BJT)

Minority carrier distribution in various regions of a p-n-p transistor under the active mode of operation.

Bipolar Junction Transistor (BJT)• The distributions of the minority carriers can be found b

y

pn0 , nE0 , and nC0 - are the equilibrium minority carrier concentrati ons in the base, emitter, and collector, respectively. LE and LC are emitter and collector diffusion lengths, respectively.

/0( ) 1 (0) 1EBeV kT

n n n

x xp x p e p

W W

/0 0( ) 1 for -

E

EB E

x x

eV kT LE E E En x n n e e x x

0 0( ) for C

C

x x

LC C C Cn x n n e x x

Bipolar Junction Transistor (BJT)

• - Now the minority carrier distributions are kn own, the current components can be calcula

ted. The emitter current can be found by

(16)

0 /EBp n eV kTEp

eAD pI e

W /0 1EBeV kTE E

EnE

eAD nI e

L

/11 121EBeV kT

E Ep EnI I I a e a

0 0011 12,p n p nE E

E

D p eAD pD na eA a

W L W

Bipolar Junction Transistor (BJT)

• The collector current is expressed by

(17)

0 /EBp n eV kTCp

eAD pI e

W

0C CCn

C

eAD nI

L

/21 221EBeV kT

C Cp CnI I I a e a

0 0 021 12 22,p n p n C E

C

eAD p D p D na a a eA

W W L

Bipolar Junction Transistor (BJT)

• The ideal base current is IE – IC or

(18)

/11 21 12 221EBeV kT

BI a a e a a

Bipolar Junction Transistor (BJT)

Ex. An ideal Si p+- - n p transistor has impurity c oncentrations of 1019 , 1017 , and5 x 1015 cm-3

in the emitter, base, and collector regions, r espectively; the corresponding lifetimes are

10-8 , 10-7 , and 10-6 s. Assume that an effectiv e cross section area A is 0.05 mm2 and the e

- - mitter base junction is forward biased to 0.6 - V. Find the common base current gain of th

e transistor. Note: DE =1 cm2 /s, Dp = 10 cm2 /s, DC =2 cm2 /s, and W = 0.5 μm.

Bipolar Junction Transistor (BJT)

Soln

7 3

2922 -3

0 17

In the base region,

10 10 10 cm

9.65 109.31 10 cm

10

p p p

in

B

L D

np

N

Bipolar Junction Transistor (BJT)

8 4

292-3

0 19

19 4 20.6 / 0.0259 4

4

4

19 40.

4

In the emitter region,

1 10 10 cm

9.65 109.31 cm

10

1.6 10 5 10 10 9.31 101.7137 10 A

0.5 10

1.7137 10 A

1.6 10 5 10 1 9.31

10

E E E

iE

E

Ep

Cp Ep

En

L D

nn

N

I e

I I

I e

6 / 0.0259 8

0

1 8.5687 10 A

0.9995Cp

Ep En

I

I I

Bipolar Junction Transistor (BJT)

Bipolar Junction Transistor (BJT)

• The general expressions of currents for all o perational modes are

(19)

//11 12

//21 22

1 1

1 1

CBEB

CBEB

eV kTeV kTE

eV kTeV kTC

I a e a e

I a e a e

Current-Voltage Characteristics of Common-Base Configuration

• In this configurat ion, VEB and VCB a

re the input and output voltages

and IE and IC are the input and ou tput currents, re

spectively.

Current-Voltage Characteristics of Common-Emitter Configuration

• In many circuit applications, th

-e common emit ter configuratio

n is mostly used where VEB and IB

are the input pa rameters and VE

C and IC are the o utput paramete

rs.

Current-Voltage Characteristics of Common-Emitter Configuration

• The collector current for this configuration c an be found by substituting (6 ) into (12)

(20)

0 0C B C CBI I I I

0 0

0 01 1CB

C B

II I

Current-Voltage Characteristics of Common-Emitter Configuration

• We define β0 - as the common emitter current g

ain as

(21)

• Then, ICE0 can be written as

(22)

00

01C

B

I

I

00 0 0

0

11CB

CE CB

II I

• Therefore, (20 ) becomes

(23)

• Since α0 is generally close to unity, β

0 is muc

h larger than1 .• Therefore, a small change in the base curre

nt can give rise to a much larger change in t he collector current.

Current-Voltage Characteristics of Common-Emitter Configuration

0 0C B CEI I I

Frequency response

• (a ) Basic transistor equi valent circuit (low frequ

ency).

• (b ) Basic circuit with th e addition of depletion

and diffusion capacitan ces (higher frequency).

• (c ) Basic circuit with th e addition of resistance

and conductance (highfrequency).

Frequency response

• For a high frequency, w e expect to have these f

ollowing components:

• CEB = EB depletion capa citance, Cd = diffusion c

apacitance, CCB = CB de pletion capacitance, gm

= transconductance = iC/vEB , gEB = input conduc

tance = iB/vEB , gEC = iC /v = output conductance,

rB = base resistance, an d rC = collector resistan

ce.

Frequency response

• The current gain will decrease after the certai - n frequency is reached. The common base cu

rrent gain α can be expressed by

(24)

• where α0 -is the lowest frequency common ba

se current gain and fα - is the common base cut off frequency.

0

1 /j f f

Frequency response

(25)

where fβ - is the common emitter cutoff frequency given by (1-α

0) fα.

• Whereas fT is the cutoff frequency when β =1.

(26)

• fT is pretty close to but smaller than fα.

0

1 /j f f

0 0 01Tf f f

Frequency response• fT is pretty close to but smaller than fα

.