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