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Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
Contributions from the Depletion Region
at reverse bias,
E
EFp
EFn
ideal reverse current
added reverse generation
current due to generation of
carriers from trap level in the
depletion region
ET
EV
EC
I0
Space-charge-region (SCR) currents
at small forward bias,
EFp
EFn
ET
ideal diffusion current
ideal diffusion current
recombination current
EC
EV
E
ISCR
ISCR
0 SCRI I I
ideal diffusion SCRI I I
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
Space-charge-region (SCR) currents
Inside the depletion region
( ) /( ) / 2 /Fn FpC VE E kTE E kT qV kT
C V ipn N N e e n e
The recombination rate is the largest where / 2 .qV kT
in p n e
/ 2( ) ( 1)qV kTi
dep
nNet recombination generation rate per unit volume e
/ 2
: / .
:
( 1) : 0 :
:
dep
qV kT
the generation recombination lifetime in the depletion layer
net generation
e equilibrium
net recombination
/ 2 / 2( 1) ( 1)N
P
x i depqV kT qV kTiSCR
xdep dep
qnWnI qA e dx A e
/ / 2
0, ( 1) ( 1)i depqV kT qV kT
ideal SCR
dep
qnWTotal diode current I I I I e A e
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
Total diode current can be written as,
/ / 2
0
/
0
( 1) ( 1)
( 1), 1 2 :
i depqV kT qV kT
dep
qV kT
qnWI I e A e
I e idealty factor
Junction leakage current is a very important
issue in DRAM technology and generate
noise in major devices. Manufacturing these
devices requires special care to make the
generation/recombination lifetime long with
super-clean and nearly crystal-defects free
processing to minimize the density of
recombination traps.
Under reverse bias,
0( )i dep
leakage
dep
qnWI I A
leakage dep rI W V
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
Stored excess minority carrier
charge in neutral region (Q)
negligible
( , )Px
Q qA n x t dx
Charge Storage
For forward biased one sided N+P junction,
2
2
( , )
1
n
n
n
n
n x t d n nD
t dx
dJ n
q dx
, since 0in neutral region .En n
dnJ qD
dx
By multiplying (-qA ) at both sides of the continuity equation and integrating,
( )
( )
1n
P n P P
J
nx J x x
n
dqA n dx A dJ qA n dx
dt
: Continuity equation
,( ) ( ) ( )n n P n P nP diffusion diffusionAJ AJ x AJ x AJ i
diffusion
n
dQ Qi
dt : Charge control equation
(continuity equation for excess electron)
include both ac and DC
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
( )n
dQ Qi t
dt
In steady state (DC),
0 diffusion diffusion
dQand i I I
dt for one-sided junction
n s
Q QI
s is called the charge-storage time.
• In a one-sided junction, is the recombination lifetime ( )
on the lighter-doping side.s ,n p
s n • For N+P one-sided junction,
In general, is an average of the recombination lifetime on the N side
and the P side.s
Similarly, for forward biased one sided P+N junction,
( )p
dQ Qi t
dt
For one sided N+P junction, ( ) :diffusioni i t total current
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
Small-Signal Model of the Diodea.c. small signal,V sin ,
acac
kTwhere v
qV v t
I i
The small-signal equivalent circuit of a PN diode.
V
SR
intrinsic part
I i
R
/ /
0 0( 1)qV kT qV kTI I e I e I
V-I0
V
I
Slope = 1/R
V0
0
/
0
/ /
0 0
1( ) ( 1)
/
qV kT
V V
qV kT qV kT
DC
dI dG I e
R dV dV
d q kTI e I e I
dV kT q
R is called diffusion
resistance
0( ) /d V V S S S DC
dQ dI kTC G I
dV dV q Small signal
diffusion
capacitance
Diffusion capacitance:
dominant in forward
bias
Junction capacitance:
dominant in reverse
bias
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
Transient and A-C Conditions
• Most solid state devices are used for switching or for processing a-c
signals.
• We investigate the important influence of excess carriers in transient
and a-c problems.
Time Variation of Stored Charge
• Any change in current a change of charge stored in the carrier
distributions.
• Since time is required in building up or depleting a charge distribution, the
stored charge must inevitably lag behind the current in a time-dependent
problem. This is inherently a capacitive effect.
• For a proper solution of a transient problem, we must use the time-
dependent continuity equations
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
For P+-N junction; two charge storage effects:
(1) The usual recombination term Qp/p in which the excess carrier distribution
is replaced every p seconds
(2) A charge buildup (or depletion) term dQp/dt, which allows for the fact that
the distribution of excess carriers can be increasing or decreasing in a time-
dependent problem
• Solving the equation with Laplace transform, with I (t > 0)=0 and
Qp(0)=Ip, we obtain
10 (0)
10
p p p
p
p p p
p
Q s sQ s Q
Q s sQ s I
, ,p p
P diffusion
p
Q t dQ ti total diode current i t
dt
Turn-off transient
i t
I
t=0
t
0( )p p p
p p
Q t dQ t Q ti t I for t at steady state
dt
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
( )
1( )
atf t e
fs a
L
• The stored charge dies out exponentially from its initial value Ip with a time
constant equal to the hole lifetime in the n material.
1
( ) p
p
p
p
t
p p
IQ s
s
Q t I e
P+ N
i(t)
v(t)
N
NxPx
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
becomes non-exponential as the transient proceeds.
• Even though the current is suddenly terminated, the voltage across the
junction persists until Qp disappears.
• At any time during the transient, the excess hole concentration at xN is
/' 1
qv t kT
np t p e
• The gradient of the hole distribution at xN = 0 (zero current implies zero
gradient).
• An approximate solution for v(t) can be obtained by assuming an
exponential distribution for at every instant during the decay
quasi-steady state approximation
'p
xNx
Transient Junction Voltage, v(t)?
'p
'p
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
( ) /
' , '( ) N px x Lp x t p t e
• For the stored charge at any instant
( ) /
' 'N p
N
x x L
p px
Q t qA p e dx qAL p t
/
'( ) 1pqv t kT
n
p
Q tp t p e
qAL
/
ln 1ptp
p n
IkTv t e
q qAL p
During turn-off, v(t) cannot be changed
instantaneously
Quasi-Steady State Approximation
( ) pt
p pQ t I e
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
hole distribution in the N-region as
a function of time during the transient
'( , )p x t
Reverse Recovery Transient• For t < 0 (positive bias steady I = If E/R)
• After the generator voltage is reversed (t > 0), the current must initially reverse to I = Ir -
E/R (temporarily).
The reason for this unusually large reverse current through the diode is that the stored
charge (and hence the junction voltage) cannot be changed instantaneously.
Nx
Switching voltage
Diode current
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
• As the current is reversed, the junction voltage remains at the small forward-bias it had before t = 0.
• While the current is negative through the junction, the slope of the distribution must be positive at xN.
• As long as pn is positive, the junction voltage v(t) is positive and small.
• When the stored charge is depleted and becomes negative, the junction exhibits a negative voltage.
• As time proceeds, the magnitude of the reverse current becomes smaller as
more of –E appears across the reverse-biased junction, until finally the only current is
the small reverse saturation current.
• The time tsd ( ) required for the stored charge (and therefore the junction voltage) to
become zero is called the storage delay time.
The critical parameter determining tsd ( ) is the carrier lifetime (p for the P+-N junction)
s
s
s
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
Part II: Application to Optoelectronic Devices
Solar Cells
Photonic Devices:
Solar Cells, Light Emitting Diode, Laser Diode, Photodiode
Solar Cell Basics
• Commonly made of silicon, solar cells, also known as photovoltaic cells, can convert sunlight
to electricity with 15 to 30 % energy efficiency.
• The structure of solar cell is identical to a PN junction diode but with finger-shaped or transparent
electrodes so that light can strike the semiconductor.
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
Depletion of fossil-fuel deposits and recent history
and projection of world energy consumption
assuming 3% annual growth. (From [3]. © 1992 IEEE.)
pn Junction Si solar cells at work. Honda„s two seated Dream car
is powered by photovoltaics. The Honda Dream was first to finish
3,010 km in four days in the 1996 World Solar Challenge.
SOURCE: Courtesy of Centre for Photovoltaic Engineering,
University of New South Wales, Sydney, Australia.
SOURCE: Courtesy of NASA, Dryden Flight Center
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
Solar cell inventors at Bell Labs (left to right) Gerald Pearson, Daryl Chapin
and Calvin Fuller are checking a Si solar cell sample for the amount of
voltage produced (1954).
SOURCE: Courtesy of Bell Labs, Lucent Technologies
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
The principle of operation of the solar cell (exaggerated features tohighlight principles)
Neutral
n-regionNeutral
p-region
W
Eo
Voc
Medium
Long
Depletion
region
DiffusionDrift
Finger
electrode
Back
electrode
n
p
Lh
Short
Le
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
• Photogenerated carriers within the volume Lh + W + Le give rise to a photocurrent Iph.
• The variation in the photogenerated EHP concentration with distance is also shown
where α is the absorption coefficient at the wavelength of interest.
Le
Lh W
Iph
x
EHPs
exp(x)
scI
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
(a) The solar cell connected to an external load R and the conventionfor the definitions of positive voltage and positive current. (b) Thesolar cell in short circuit. The current is the photocurrent, Iph. (c) The
solar cell driving an external load R. There is a voltage V and current Iin the circuit.
R
I
(a)
Light
Iph
V = 0
Isc
= Iph
(b)
Iph
I = Id
Iph
V
Id
R
(c)
V
Dry Battery +-
I
V
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
V
I (mA)
Dark
Light
Twice the light
0.60.40.2
20
20
0
Voc
Iph
Short circuit solar cell current in light
IKII phsc
Constant that depends on the particular device
Light intensity
Photocurrent generated by light
Solar cell I-V
1expph
kT
eVIII o
where Io is the reverse saturation current
and is the ideality factor: 1 - 2
short circuit
current (Isc)
open circuit
voltage
Typical I-V characteristics of a Si solar cell. The I-V curves for positive
current requires an external bias voltage. Photovoltaic operation is always
In the negative current region.
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
V
I (mA)
0.60.40.20
Voc
100
Isc = Iph
The load line for
R = 3
(I-V for the load)
I-V for a solar cell
under an illumination
of 700 W m-2
Operating point
Slope = 1/R
P
I
I
I
R
V
I
(a) (b)
0.50.30.1
V
200
(a) When a solar cell drives a load R. R has the same voltage as the solar cell but the current
through it is in the opposite direction to the convention that current flows from high to low
potential.
(b) The current I and voltage V in the circuit of (a) can be found from a load line construction. Point
P is the operating point .The load line is for R = 3 Ω.( ', ')I V
Load lineR
VI (The actual current I and voltage V in the circuit must satisfy both the
I - V characteristics of the solar cell and the load).
Fill factor
ocsc
FFVI
VI mm (The FF is a measure of the closeness of the solar cell I-V curve to the
rectangular shape (the ideal shape)).
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
• Electron-hole pair (EHP) generation by light illumination.
EHPs generated in SCR move toward to their respective majority-carrier regions,
due to electric field in SCR and form generation current called, - Isc.
• The power dissipated by the diode is negative (i.e., the product (V×I) is negative)
power generator (Solar power electrical power)
light illumination
EHP generation
(a) Light can produce a current in PN junction at V = 0.
(b) Solar cell IV product is negative, indicating power
generation.
/
0
,
( 1)qV kT
sc
Total diode current I
I I e I
ocV
Chapter 4. PN and Metal-Semiconductor JunctionsModern Semiconductor Devices for Integrated Circuits
Light Penetration Depth-Direct-Gap and Indirect-Gap Semiconductors
1.24( ) ( )
hcPhoton energy eV m
Photons with energy less than Eg are not absorbed
by the semiconductor. Photons with energy larger
than Eg are absorbed but some photons may travel
a considerable distance in the semiconductor
before being absorbed.
Light intensity( )x
x e :
1:
absorption coefficient
penetration depth
1The thickness of solar cell :
• The Si or Ge solar cell must be thick ( > 50 μm)
: due to low α
• The GaAs or InP solar cell is thin (~ 1 μm)
: due to high α
low
high
Related to the specific energy band structure
in order to capture nearly all the photons.