Download Ch19

Review of Basic Semiconductor Physics
Copyright © by John Wiley & Sons 2003
Semiconductor Physics - 1
Current Flow and Conductivity
• Charge in volume Ax = Q
= q n A  x = q n A vt
• Current density J = (Q/t)A-1
=qnv
• Metals - gold, platinum, silver, copper, etc.
• n = 1023 cm-3 ;
 = 107 mhos-cm
• Insulators - silicon dioxide, silicon nitride, aluminum oxide
• n < 103 cm-3 ;
< 10-10 mhos-cm
• Semiconductors - silicon, gallium arsenide, diamond, etc.
• 108 < n <1019 cm-3 ; 10-10 << 104 mhos-cm
Copyright © by John Wiley & Sons 2003
Semiconductor Physics - 2
Thermal Ionization
• Si atoms have
thermal vibrations
about equilibrium
point.
• Small percentage of
Si atoms have large
enough vibrational
energy to break
covalent bond and
liberate an electron.
Copyright © by John Wiley & Sons 2003
Semiconductor Physics - 3
Electrons and Holes
-
• T3 > T2 > T1
A
t=T 1
• Density of free electrons
= n : Density of free
holes = p
• p = n = ni(T) = intrinsic
carrier density.
•
ni2(T) = C exp(-qEg/(kT
= 1020 cm-6 at 300 K
B
-
))
generation of B
+
A
t=T
• T = temp in K
• k = 1.4x10-23 joules/ K
• Eg = energy gap = 1.1 eV
in silicon
•q=
1.6x10-19 coulombs
Copyright © by John Wiley & Sons 2003
recombination of B
-
apparent
movement
of "Hole"
A
t=T
Semiconductor Physics - 4
3
2
Doped Semiconductors
• Extrinsic (doped) semiconductors:p = po ≠ n = no ≠ ni
• Carrier density estimates:
• Law of mass action nopo = ni2(T)
• Charge neutrality Na + no = Nd + po
• P-type silicon with Na >> ni:
po ≈ Na , no ≈ ni2/ Na
Copyright © by John Wiley & Sons 2003
• N-type silicon with Nd >> ni:
no ≈ Nd , po ≈ ni2/ Nd
Semiconductor Physics - 5
Nonequilibrium and Recombination
• Thermal Equilibrium - Carrier generation = Carrier recombination
• n = no and p = po
• Nonequilibrium - n > no and p > po
• n = no + n and p = no + n ; n = excess carrier density
• Excess holes and excess electrons created in equal numbers by breaking of covalent
bonds
• Generation mechanisms -light (photoelectric effect), injection, impact ionization
• Recombination - removal of excess holes and electrons
• Mechanisms - free electron captured by empty covalent bond (hole) or trapped by
impurity or crystal imperfection
• Rate equation:
d(n)/dt
=
- n
• Solution n = n (0) e -t
Copyright © by John Wiley & Sons 2003
Semiconductor Physics - 6
Carrier Lifetimes
• = excess carrier lifetime
• Usually assumed to be constant. Changes in two important situations.
•  increases with temperature T
•  decreases at large excess carrier densities ;  = o/[1 + (n/nb)2 ]
• Control of carrier lifetime values.
• Switching time-on state loss tradeoff mandates good lifetime control.
• Control via use of impurities such as gold - lifetime killers.
• Control via electron irradiation - more uniform and better control.
Copyright © by John Wiley & Sons 2003
Semiconductor Physics - 7
Drift
Current Flow
Diffusion
p
n
J
p
Jn
+
-
x
x
• Jdrift = q µn n E + q p µp E
• µn = 1500 cm2/V-sec for silicon at
room temp. and Nd < 1015 cm-3
• µp = 500 cm2/V-sec for silicon at
room temp. and Na < 1015 cm-3
Copyright © by John Wiley & Sons 2003
• Jdiff = Jn + Jp = q Dndn/dx - q Dp dp/dx
• Dn/n = Dp/p = kT/q ; Einstein relation
• D = diffusion constant,  = carrier mobility
• Total current density J = Jdrift + Jdiff
Semiconductor Physics - 8
PN Junction
metallurgical junction
P
N
A
N
N
A
ND
NA
ND
NA
x
-
N
D
Step (abrupt) junction
Copyright © by John Wiley & Sons 2003
x
-
N
D
Linearly graded junction
Semiconductor Physics - 9
Formation of Space Charge Layer
metallurgical
junction
• Diffusing electrons and holes
leave the region near
metallurgical junction depleted
of free carriers (depletion
region).
x
ionized
acceptors
ionized
donors
+
P
+
N
Electric
field
opposing
diffusion
+
-
• Exposed ionized impurities
form space charge layer.
• Electric field due to space
charge opposes diffusion.
Diffusing
electrons
-
-
+
+
+
+
+
Diffusing
holes
+
space charge
layer width = W
Copyright © by John Wiley & Sons 2003
Semiconductor Physics - 10
Quantitative Description of Space Charge Region
• Assume step junction.
d2

= - 
dx 2
 = - qNa ; x < 0
 = qNd ; x > 0
E(x ) =
d
= - E(x )
dx
qNa(x +x p )
; - xp < x < 0

qNd (x - x n)
E(x ) =
; 0< x < x n

xn
c = -
E(x )dx

- xp
qNax p 2 + qNd x n2
c = 2
Copyright © by John Wiley & Sons 2003
Semiconductor Physics - 11
Contact (Built-in, Junction) Potential
• In thermal equilibrium Jn = q µn n
d
dn
+ q Dn
=0
dx
dx
n(xn)
(xn)
Dn dn


• Separate variables and integrate ;
d = µn  n
(xp)
n(xp)
kT NaNd
• (xn) - (xp) = c = q ln 2  ; c = contact potential
 ni 
• Example
•
•
•
Room temperature kT/q = 0.025 eV
Na = Nd = 1016 cm-3 ; ni2 = 1020 cm-6
Fc = 0.72 eV
Copyright © by John Wiley & Sons 2003
Semiconductor Physics - 12
Reverse-Biased Step Junction
• St art ing equat ions
• W( V) = x n( V) + x p ( V)
qNax p 2 + qNd x n2
• V + c = 2
• Charge neut ralit y qNax p = qNd x n
• Solv e equat ions simult aneously
• W( V) = Wo
• Wo =
1 + V/ c
2 c ( Na+ Nd )
qNaNd
2 c
• Emax =
Wo
1 + V/ c
Copyright © by John Wiley & Sons 2003
Semiconductor Physics - 13
Forward-Biased PN Junction
• Forward bias favors
diffusion over drift.
• Excess minority
carrier injection into
both p and n drift
regions.
• Minority carrier
diffusion lengths.
• Ln = [Dnn]0.5
• Lp = [Dpp]0.5
Copyright © by John Wiley & Sons 2003
Semiconductor Physics - 14
Ideal PN Junction I-V Characteristics
• Excess carriers in drift regions recombined and thus more must be constantly injected if
the distributions np(x) and pn(x) are to be maintained.
• Constant injection of electrons and holes results in a current density J given by
Qn
Qp
Lp 
 Ln
2

J =  +  = q ni 
+
n
p
N

N

 an
d p
J=
Js

qV

exp(
)

kT

-

1 

-

1 

Lp 
 Ln
2

; Js = q ni 
+
Nd p 
Nan
i
J
J

qV

exp(
)

kT

v
- Js
v
forward bias
Copyright © by John Wiley & Sons 2003
reverse
bias
combined
characteristic
v
Semiconductor Physics - 15
Reverse Saturation Current
V
• Carrier density gradient
immediately adjacent to
depletion region causes
reverse saturation current to
flow via diffusion.
+
+
+
+ +
P
N
• Js independent of reverse
voltage V because carrier
density gradient unaffected by
applied voltage.
Wo
W(V)
n po
p
no
n p(x)
• Js extremely temperature
sensitivity because of
dependence on ni2(T.)
+
p (x)
n
x
Electric field,
Copyright © by John Wiley & Sons 2003
J
s
Semiconductor Physics - 16
Impact Ionization
• E ≥ EBD ; free electron can
acquire sufficient from the field
between lattice collisions (tc ≈
10-12 sec) to break covalent bond.
Si
-
-
Si
• Energy = 0.5mv2 = q Eg ; v = q EBDtc
-
• Solving for EBD gives
EBD =
Si
2 Eg m
q tc2
Electric field E
-
• Numerical evaluation
• m = 10-27 grams, Eg = 1.1 eV, tc = 10-12 sec.
• EBD =
•
(2) (1.1) (1027)
= 3x105 V/cm
-19
-24
(1.6x10 ) (10 )
Experimental estimates are 2-3.5x105 V/cm
Copyright © by John Wiley & Sons 2003
Semiconductor Physics - 17