Section 12: Intro to Devices
Extensive reading materials on reserve, including
Robert F. Pierret, Semiconductor Device Fundamentals
EE143 – Ali Javey
Bond Model of Electrons and Holes
Si
Si
Si
Si
Si
Si
Si
Si
Si
 Silicon crystal in
a two-dimensional
representation.
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
Si
 When an electron breaks loose and becomes a conduction
electron, a hole is also created.
EE143 – Ali Javey
Semiconductors, Insulators, and Conductors
Ec
Top of
conduction band
Ec
E g= 9 eV
empty
E g = 1.1 eV
Ev
Ev
Si, Semiconductor
SiO , insulator
2
• Totally filled bands and totally empty bands
do not allow current flow. (Just as there is
no motion of liquid in a totally filled or
totally empty bottle.)
• Metal conduction band is half-filled.
• Semiconductors have lower EG’s than
insulators and can be doped
EE143 – Ali Javey
filled
Conductor
Ec
Intrinsic Carriers
electron
-
Bottom of
conduction band
Energy gap
=1.12 eV
hole
+
Top of
valence band
n (electron conc)
= p (hole conc)
= ni
EE143 – Ali Javey
Dopants in Silicon
Si
Si
Si
Si
Si
Si
Si
As
Si
Si
B
Si
Si
Si
Si
Si
Si
Si
 As, a Group V element, introduces conduction electrons and creates
N-type silicon, and is called a donor.
 B, a Group III element, introduces holes and creates P-type silicon,
and is called an acceptor.
EE143 – Ali Javey
Types of charges in semiconductors
Hole
Electron
Ionized
Donor
Ionized
Acceptor
Mobile Charge Carriers
they contribute to current flow
with electric field is applied.
Immobile Charges
they DO NOT
contribute to current flow
with electric field is applied.
However, they affect the
local electric field
EE143 – Ali Javey
Fermi Function–The Probability of an Energy
State Being Occupied by an Electron
f (E) 
1
1 e
Ef is called the Fermi energy or
the Fermi level.
( E  E f ) / kT
Boltzmann approximation:
f (E)  e
E
f (E)  e

 EE f
f (E)  1  e
Ef + 2kT
Ef
Ef + kT
Ef
Ef – kT
Ef – 2kT
f (E)  1  e


 E f  E kT
f(E)
0.5
 kT
E  E f  kT
 kT
Ef + 3kT
Ef – 3kT

 EE f
1
EE143 – Ali Javey


 E f  E kT
E  E f  kT
Electron and Hole Concentrations
n  N c e( E F  EC ) / kT
p  N v e( EV  E F ) / kT
Nc is called the effective
density of states.
Nv is called the effective
density of states of the
valence band.
Remember: the closer Ef moves up to E c , the larger n is;
the closer Ef moves down to Ev , the larger p is.
For Si, Nc = 2.8 1019 cm-3 and Nv = 1.041019 cm-3 .
EE143 – Ali Javey
Shifting the Fermi Level
EE143 – Ali Javey
Quantitative Relationships
n: electron concentration (cm-3)
p : hole concentration (cm-3)
ND: donor concentration (cm-3)
NA: acceptor concentration (cm-3)
Assume completely
ionized to form ND+
and NA-
1) Charge neutrality condition:
ND + p = NA + n
2) Law of Mass Action
n p = ni2
:
What happens
when one doping
species dominates?
EE143 – Ali Javey
General Effects of Doping on n and p
I. N d  N a  ni (i.e., N-type)
n  Nd  Na
p  ni n
2
If N d  N a ,
n  Nd
II. N a  N d  ni (i.e., P-type)
If N a  N d ,
p  Na
p  ni Nd
2
and
p  Na  Nd
n  ni
and
EE143 – Ali Javey
2
p
n  ni Na
2
Carrier Drift
• When an electric field is applied to a semiconductor, mobile
carriers will be accelerated by the electrostatic force. This
force superimposes on the random thermal motion of carriers:
2
3
1
electron
4
3
2
1
electron
4
5
5
E =0
E
E.g. Electrons drift in the direction opposite to the E-field
 Current flows
Average drift velocity = |
v|=mE
Carrier mobility
EE143 – Ali Javey
Carrier Mobility
• Mobile carriers are always in random thermal
motion. If no electric field is applied, the
average current in any direction is zero.
• Mobility is reduced by
1) collisions with the vibrating atoms
“phonon scattering”
Si
-
2) deflection by ionized impurity atoms “Coulombic
scattering”
BAs+
EE143 – Ali Javey
Total Mobility
1600
1
1400

Electrons
1
1000
m
2
-1
-1
Mobility (cm V s )
1200


1
 phonon

1
m phonon
1
 impurity

1
m impurity
800
600
400
Holes
200
0
1E14
1E15
1E16
1E17
1E18
1E19
-3
Na +Concenration
Nd (cm-3)
Total Impurity
(atoms cm )
EE143 – Ali Javey
1E20
Conductivity and Resistivity
Jp,drift = qpv = qpmpE
Jn,drift = –qnv = qnmnE
Jdrift = Jn,drift + Jp,drift =  E =(qnmn+qpmp)E
 conductivity of a semiconductor is  = qnmn + qpmp
Resistivity,  = 1/ 
EE143 – Ali Javey
DOPANT DENSITY cm-3
Relationship between Resistivity and Dopant Density
P-type
N-type
RESISTIVITY (cm)
 = 1/
EE143 – Ali Javey
I
V
+
_
W
Sheet Resistance
L
L
R
 Rs
Wt
W
t
Material with resistivity 
L
Rs is the resistance when W = L (in ohms/square)

Rs 
t
if  is independent of depth x
• Rs value for a given conductive layer (e.g. doped Si,
metals) in IC or MEMS technology is used
– for design and layout of resistors
– for estimating values of parasitic resistance in a device or
circuit
EE143 – Ali Javey
Diffusion Current
Particles diffuse from higher concentration to
lower concentration locations.
EE143 – Ali Javey
Diffusion Current
dn
J n ,diffusion  qDn
dx
dp
J p ,diffusion  qD p
dx
D is called the diffusion constant. Signs explained:
p
n
x
EE143 – Ali Javey
x
Generation/Recombination Processes
Recombination continues until excess carriers = 0.
Time constant of decay is called recombination lifetime
EE143 – Ali Javey
Continuity Equations
• Combining all the carrier actions:
n
t

n
t drift
 nt diff  nt thermalRG  nt others
• Now, by the definition of current, we know:
n
t drift

n
t diff
 (
1
q
J Nx
x

J Ny
y

J Nz
z
)  1q   J N
• Since a change in carrier concentration must occur from a net current
• Therefore, we can compactly write the continuity equation as:
n
t
 1q   J N  nt thermalR G  nt other
p
t
    JP 
1
q
p
t thermalR G
EE143 – Ali Javey

p
t other
PN Junctions
Donors
N-type
P-type
– V +
I
I
N
P
V
Reverse bias
Forward bias
diode
symbol
A PN junction is present in almost every semiconductor device.
EE143 – Ali Javey
Energy Band Diagram and Depletion Layer
N-region
P-region
Ef
(a)
Ec
(b)
Ec
Ef
Ev
Ev
Ec
Ef
Ev
(c)
Neutral
N-region
Depletion
layer
n  0 and p  0
in the depletion
layer
Neutral
P-region
Ec
Ef
Ev
(d)
EE143 – Ali Javey
kT N d N a
bi 
ln
2
q
ni
Qualitative Electrostatics
Band diagram
Built in-potential
From e=-dV/dx
EE143 – Ali Javey
a)
b)
Depletion-Layer Model
N
Nd
N eut ra l Re gion
N
P
Na
D eple tion L a yer
–xn
N e utral R egi on
P
On the P-side of the
depletion layer,  = –qNa
xp
0
d E   qN a
es
dx

qNd
xp
c)
–xn
x
–qN a

qN a
On the N-side,  = qNd
E
)
)
–xn
 bi
xp
0
qN a
p
E( x)   e s x  C  e s ( x  x)
1
x
V
EE143 – Ali Javey
x
E( x) 
qN d
es
( x  xn )
Effect of Bias on Electrostatics
EE143 – Ali Javey
Current Flow - Qualitative
EE143 – Ali Javey
PN Diode IV Characteristics
I  I 0 (e qV
kT
 1)
 Dp
Dn 

I 0  Aqni

L N

L
N
p
d
n
a


2
Ir  I0  A
EE143 – Ali Javey
qniWdep
τ dep
MOS Capacitors
MOS: Metal-Oxide-Semiconductor
Vg
Vg
gate
metal
gate
SiO 2
SiO 2
N+
N+
P-body
Si body
MOS transistor
MOS capacitor
EE143 – Ali Javey
MOS Band Diagram –
EE143 – Ali Javey
Flat-band Condition and Flat-band Voltage
E0
cSiO2 =0.95 eV
Ec
qyM
qys = cSi + (Ec –Ef )
3.1 eV cSi
3.1 eV
=4.05eV
Ec, Ef
Ec
Vfb
Ev
N+ -poly-Si
E0 : Vacuum level
E0 – Ef : Work function
E0 – Ec : Electron affinity
Si/SiO2 energy barrier
9 eV
P-body
4.8 eV
Ev
SiO2
EE143 – Ali Javey
Ef
Ev
Vfb  yM ys
Biasing Conditions
EE143 – Ali Javey
Biasing Conditions (2)
EE143 – Ali Javey
Depletion and the Depletion Width
• The charge within the depletion
region is:
qVox
q s
qV g
Wde p
depletion
region
Ec,E f
Ev
M
Ef
Ev
--
O
S
(b)
  qN A
Ec
• Poisson’s equation reduces to:
de

qN A


0  x  W
dx e Si
e Si
• Integrating twice gives:
qN A 2
S 
W
2e Si
• Or: W 
EE143 – Ali Javey
2e SiS
qN A
Surface Depletion
V g > Vfb
qVox
q s
gate
++ + + + +
V
-- -- -- -- -- -- --
SiO2
Wde p
depletion
region
Ec,E f
depletion layer
charge, Q de p
Ef
Ev
--
qV g
Ev
P-Si body
Qdep qN aWdep
Qs
Vox  
(a)



Cox
Cox
Cox
M
qN a 2e s s
Vg  V fb   s  Vox  V fb   s 
EE143 – Ali Javey
Cox
qN a 2e s s
Cox
O
S
(b)
Ec
Threshold Condition and Threshold Voltage
threshold of inversion
Ec
st
threshold : ns = Na
A
(Ec–Ef)surface= (Ef – Ev)bulk
 A=B, and C = D
Ei
C = q 
D
B
qVg = qVt
Ef
Ev
Ec,Ef
kT  N a 
 st  2 B  2 ln  
q  ni 
Ev
M
O
S
kT  N v  kT  N v  kT  N a 
 

q B 
 ( E f  Ev ) |bulk 
ln   
ln 
ln 
2
q  ni  q  N a  q  ni 
Eg
EE143 – Ali Javey
Threshold Voltage
Vg  V fb  Vs  Vox
qN a 2e s 2 B
Vt  V fb  2 B 
Cox
Summarizing both polarities:
st  2 B
qN sub 2e s |  st |
Vt  V fb   st 
Cox
+ : N-type device, – : P-type device
EE143 – Ali Javey
Strong Inversion–Beyond Threshold
• Past VT, the depletion
width no longer grows
Vg > Vt
Wdep
2e s st
 Wdmax 
gate qN a
SiO 2
qV g
- - - - - - - -

Ef
Ev
---
++++++++++
• All additional
voltage
- - V
results in Qinversion
Qinv
de p
P-Si substrate
layer charge
Ec
-
E c,Ef
Ev
Qinv  Cox (Vg  Vt )
(a)
M
O
(b)
EE143 – Ali Javey
S
Review : Basic MOS Capacitor Theory
s
2B
accumulation
Vf b
depletion
Vt
Vg
inversion
Wdep
Wdmax
Wdm ax = (2es 2 q a 
 s)1/2
accumulation
Vfb
depletion
Vt
EE143 – Ali Javey
Vg
inversion
Review : Basic MOS Capacitor Theory
Qdep = qNaWdep
accumulation
Vfb
depletion
(a)
0
–qNaWdep
inversion
Vg
Vt
total substrate charge, Qs
Qs  Qacc  Qdep  Qinv
–qNaWdmax
Qinv
Qs
accumulation Vfb depletion
inversion
Vg
Vt
(b)
accumulation
regime
depletion
regime
inversion
regime
slope = Cox
Vf b
0
Vg
Vt
Qa cc
Qinv
slope = Cox
slope =  Cox
(c)
accumulation
Vfb
depletion
Vt
Vg
inversion
EE143 – Ali Javey
Quasi-Static CV Characteristics
C ox
accumulation
Vfb
depletion
C
Vt
Vg
inversion
1
1
1


C Cox Cdep
1
1 2(Vg  V fb )


2
C
Cox
qN ae s
EE143 – Ali Javey
Qualitative MOSFET Operation
Depletion Layer
EE143 – Ali Javey
Channel Length Modulation
EE143 – Ali Javey
MOSFET I-V Characteristics – A 1st attempt
The Square Law Theory
• Current in the channel should be mainly drift-driven
d
J N  qm n ne  qm n n
dy
• The current is:
I D    J Ny dx  dz
 qZ
d
mn
dy
  Z m n QN
xc ( y )
  n( x, y)dx
0
d
dy
EE143 – Ali Javey
MOSFET I-V Characteristics – A 1st attempt
• But, current is constant through the channel:
VD
L
I
D
dy  I D L   Z  m n QN d
0
0
V
D
Z
I D   m n  Q N d
L
0
• We know the inversion layer charge:
Qinv  Cox (VG  VT )
• Accounting for the non-uniformity:
Qinv ( y)  Cox (VG  VT   )
2

Z
VD   0  VD  VDsat 

I D   m nCox VG  VT VD 
 
L
2   VG  VT 

EE143 – Ali Javey
MOSFET I-V Characteristics – A 1st attempt
• Past pinch-off, the drain current is constant
I D ,VD VDsa t  I D ,VD VDsa t  I Dsat
• So:
2

VDsat 
Z
I D   m nCox VG  VT VDsat 

L
2


• Now, in the pinched-off region:
Qinv ( y )  Cox (VG  VT  VDsat )  0
VDsat  VG  VT
Z
ID  
m nCox VG  VT 2
2L
EE143 – Ali Javey
N-channel MOSFET
Layout (Top View)
4 lithography steps
are required:
1. active area
2. gate electrode
3. contacts
4. metal interconnects
EE143 – Ali Javey
Simple NMOS Process Flow
1) Thermal oxidation
(~10 nm “pad oxide”)
2) Silicon-nitride (Si3N4)
deposition by CVD
(~40nm)
3) Active-area definition
(lithography & etch)
4) Boron ion implantation
(“channel stop” implant)
EE143 – Ali Javey
Simple NMOS Process Flow
5) Thermal oxidation to grow
oxide in “field regions”
6) Si3N4 & pad oxide
removal
7) Thermal oxidation
(“gate oxide”)
8) Poly-Si deposition by CVD
9) Poly-Si gate-electrode
patterning (litho. & etch)
10) P or As ion implantation
to form n+ source and drain
regions
Top view of masks
EE143 – Ali Javey
Simple NMOS Process Flow
Top view of masks
11) SiO2 CVD
12) Contact definition
(litho. & etch)
13) Al deposition
by sputtering
14) Al patterning
by litho. & etch
to form interconnects
EE143 – Ali Javey