EMT 272 Semiconductor Fundamentals Semiconductor Physics: PN Junction
EMT 272 Semiconductor Fundamentals Semiconductor Physics: PN Junction
EMT 272 Semiconductor Fundamentals Semiconductor Physics: PN Junction
SEMICONDUCTOR PHYSICS
PN Junction
Outlines:
Depletion Capacitance
I V Characteristics
Junction Breakdown
Heterojunction
3. Depletion Capacitance
3. Depletion Capacitance
Basically, the junction depletion layer capacitance/area is defined as C j =
dQ/dV, where dQ incremental change in depletion layer/unit area for
an incremental change in the applied voltage dV.
The depletion capacitance/area is given by
W
dQ
W
dQ
Cj
dV
dQ
(18)
pn junction with
arbitrary impurity
profile under
reverse bias
Change in space
charge
distribution due
to change in
applied bias
Corresponding
change in
electric field
distribution
3.1 Capacitance-Voltage
Characteristics
Eq(18) for depletion capacitance/area is the same as for a parallelplate capacitor, where spacing between two plates represents the
depletion width. Its valid for any arbitrary impurity distribution.
For one-sided abrupt junction, depletion capacitance/area:
W
dQ
W
dQ
Cj
dV
dQ
2(Vbi V )
1
2
q s N B
Cj
(18)
(17)
(19)
EXAMPLE 1
For a silicon one-sided abrupt junction with NA = 2 x 1019 cm-3 and ND =
8 x 1015 cm-3, calculate the junction capacitance at zero bias and
reverse bias of 4V (T=300K)
3.2 Evaluation of
Impurity Distribution
dV
(20)
(20)
N (W )
qN (W ) dW
2 s
2
q s
2
d 1 / C j / dV
(21)
(21)
s
qa
Cj
W
12
V
V
bi
2
s
1/ 3
(22)
(22)
(a) p+-n junction with an arbitrary impurity distribution. (b) Change in space charge
distribution in the lightly doped side due to a change in applied bias. (c)
corresponding change in the electric-field distribution.
4. IV Characteristics
4. IV Characteristics
Refer next figure: Forward Bias: the applied voltage reduces the electrostatic potential
across the depletion region (middle figure a). Drift current is reduced in
comparison to the diffusion current - enhanced hole diffusion from pside to n-side and electron diffusion from n-side to p-side.
Note: minority carrier densities at the boundaries (-xp and xn) increase
substantially above their equilibrium values under forward bias and
decrease for reverse bias.
Depletion region
Energy band
diagram
Carrier
distribution
Forward bias
Reverse bias.
In ideal case, the expression for the built-in potential, Vbi may be
rewrite as
kT p po nno
kT nno
Vbi
ln
ln
2
q ni
q p po
(26)
Where nno and ppo equilibrium electron densities in the n and p sides
respectively
qVbi
nno n po exp
kT
and
p po
qVbi
p no exp
kT
(27)
q (Vbi V )
nn n p exp
kT
(28)
n p n po
qV
n po {exp
1}
kT
at x = -xp
(29)
p p p po
qV
p no {exp
1}
kT
at x = xn
(30)
and
qV
J J p ( x n ) J n ( x p ) J s exp
1
kT
(31)
Js
qD p p no
Lp
qDn n po
Ln
(31)
(32)
(32)
EXAMPLE 2
Calculate the saturation current density in a Si p-n junction diode. The
parameters of the diode are:
NA, = 5 x l016 cm3, ND, = l016 cm3, ni, = 9.65 x l09 cm3
Dn = 21 cm2/s, Dp =10 cm2/s, n= p = 5 x l0-7 s
4.2 Generation-Recombination
and High Injection Effects
For Si and GaAs p-n junction, the ideal equation (eq. 31) can only give
qualitative agreement because of generation or recombination of carrier in the
depletion region.
For reverse bias case with large values of ni, i.e Ge, the diffusion current
dominates at T = 300K, and the reverse current follows the ideal diode
equation, but if ni <<<, i.e Si and GaAs, the generation current in the
depletion region may dominate, and the total reverse current for p+ - n
junction (for NA >> ND and for VR > 3kT/q):
JR
D p ni2
qniW
q
p ND
g
(33)
(33)
0 vth N t ni
n
i
g
E Ei
2 cosh t
kT
(34)
(34)
For forward bias, concentration of both electrons and holes exceed their
equilibrium values. The carriers will attempt to return to their
equilibrium values by recombination. Therefore, the dominant
generation-recombination processes in the depletion region are the
capture processes.
The total forward current (for pno >> npo, and V > 3kT/q) is
D p ni2
qniW
qV
qV
JF q
exp
exp
p ND
2 r
kT
2kT
(35)
(35)
qV
J F exp
kT
- ideality factor. Ideal diffusion current dominant with = 1,
and for recombination current dominant, = 2.
- When both currents are comparable, has a value of between 1 and 2
(36)
(36)
This IR drop reduces the bias across the depletion region, the current
becomes
I s exp( qV / kT )
q(V IR )
kT
qIR
exp
kT
I I s exp
(37)
High temp:
diffusion current
dominates, n=1
Low temp:
recombination
current dominates,
n=2
I diff
I gen
ni L p g
N DW p
(40)
FORWARD BIAS:
The ratio of hole diffusion current to the recombination is given
by
I diff
2ni L p r
( E g qV )
qV
exp
exp
(38)
I recom N DW p
2kT
2kT
The ratio depends on both temperature and the s/c band gap.
Js
qD p p no
Lp
Eg
n exp
kT
2
i
(39)
5. Junction Breakdown
5. Junction Breakdown
5.2 Avalanche
Multiplication
6. Heterojunction
6. Heterojunction
Where
Vbi Vb1 Vb 2
2 N 2 (Vbi V )
Vb1
1 N1 2 N 2
and
Vb 2
1 N1 (Vbi V )
1 N1 2 N 2
Depletion width
x1
2 1 2 o N 2 (Vbi V )
qN1 ( 1 N1 2 N 2 )
x2
2 1 2 o N1 (Vbi V )
qN 2 ( 1 N1 2 N 2 )
Energy band
diagram for
isolated s/cond
Energy band
diagram for ideal
np heterojunction
EXAMPLE 3
Consider an ideal abrupt heterojunction with a built-in potential of 1.6
V. The impurity concentrations in semiconductor 1 and 2 are 1 x 10 16
donors/cm3 and 3 x 1019 acceptors/cm3, and the dielectric constants
are 12 and 13, respectively. Find the electrostatic potential and
depletion width in each material at thermal equilibrium.
At thermal equilibrium, V = 0