Lecture 8: Solar Cell, LED,
Metal/Semiconductor Junction and
Heterojunction
Requirement: understand and
explain in word.
* Some of the content from C. Hu : “Modern Semiconductor devices for Integrated Circuits”
5.7 Solar Cells
•Solar Cells is also known
as photovoltaic cells.
•Converts sunlight to
electricity with 10-30%
conversion efficiency.
•1 m2 solar cell generate
about 150 W peak or 25 W
continuous power.
•Low cost and high
efficiency are needed for
wide deployment.
Solar Cell Basics
I
Short Circuit
light
N
P
Dark IV
Eq.(4.9.4)
I
sc
0
-
V
Solar Cell
IV
Eq.(4.12.1)
Ec
Ev
0.7 V
–I
+
sc
(a)
I  I 0 (eqV kT 1)  I sc
Maximum
power-output
Direct-Gap and Indirect-Gap Semiconductors
•Electrons have both particle and wave properties.
•An electron has energy E and wave vector k.
direct-gap semiconductor
indirect-gap semiconductor
Direct-gap semiconductor: Absorption coefficient is larger .
Si is most prevalent for solar cell because of low cost.
Light Absorption
Light intensity(x) e-x
α(1/cm): absorption
coefficient
1/α : light penetration
depth
P hot onEnergy(eV) 
hc

1.24

( m)

A thinner layer of direct-gap semiconductor can absorb most of
solar radiation than indirect-gap semiconductor.
Si solar cell > 50 um in thickness to absorb most of the photons
because of low α
Short-Circuit Current and Open-Circuit Voltage
ea
ar
A
Jp (x + x)
Jp (x)
p
Volume = A·x
x
If light shines on the N-type
semiconductor and generates
holes (and electrons) at the
rate of G s-1cm-3 ,
d 2 p p G
 2 
2
dx
Lp Dp
x
If the sample is uniform (no PN junction),
d2p’/dx2 = 0  p’ = GLp2/Dp= Gtp
Solar Cell Short-Circuit Current, Isc
Assume very thin P+ layer and carrier generation in N region only.
G
p()  L
 t pG
Dp
2
p
Isc
P+
p(0)  0
N
0
p( x)  t pG(1  e
x
t pG
Lp
)
Dp
dp( x)
 x / Lp
J p  qDp
q
t pGe
dx
Lp
P'
0
 x / Lp
x
I sc  AJ p (0)  AqLpG
G is really not uniform. Lp needs be larger than the light
penetration depth to collect most of the generated carriers.
Open-Circuit Voltage
•Total current is ISC plus the PV diode (dark) current:
ni2 Dp qV / kT
I  Aq
(e
 1)  AqLpG
N d Lp
•Solve for the open-circuit voltage (Voc) by setting I=0
(assuming e
qVoc / kT
 1)
2
ni D p qVoc / kT
0
e
 LpG
N d Lp
kT
2
Voc 
ln(t p GNd / ni )
q
How to raise Voc ?
Output Power
A particular operating point on the
solar cell I-V curve maximizes the
output power (I V).
Output Pow
er  I sc Voc  FF
•Si solar cell with 15-20% efficiency
dominates the market now
•Theoretically, the highest efficiency (~24%) can be obtained with
1.9eV >Eg>1.2eV. Larger Eg lead to too low Isc (low light
absorption); smaller Eg leads to too low Voc.
•Tandem solar cells gets 35% efficiency using large and small Eg
materials tailored to the short and long wavelength solar light.
NRL’s new triple-junction solar cells could
achieve 50 percent efficiency
5.8 Light Emitting Diodes and Solid-State Lighting
Light emitting diodes (LEDs)
• LEDs are made of compound semiconductors such as InP
and GaN.
• Light is emitted when electron and hole undergo radiative
recombination.
Ec
Radiative
recombination
Ev
Non-radiative
recombination
through traps
Direct and Indirect Band Gap
Trap
Direct band gap
Example: GaAs
Indirect band gap
Example: Si
Direct recombination is efficient
as k conservation is satisfied.
Direct recombination is rare as k
conservation is not satisfied
4.13.1 LED Materials and Structure
1.24
1.24
LED wavelength (  m) 

photonenergy Eg (eV )
𝝀 = 𝒉𝒄/𝑬
LED Materials and Structure
compound semiconductors
EEgg(eV)
(eV )
Wavelength
(μm)
Color
Lattice
constant
(Å)
binary semiconductors:
- Ex: GaAs, efficient emitter
InAs
0.36
3.44
InN
0.65
1.91
InP
1.36
0.92
GaAs
1.42
0.87
6.05
infrared
red
Red
yellow
Yellow
blue
Green
violet
Blue
3.45
ternary semiconductor :
5.87
- Ex: GaAs1-xPx , tunable Eg (to
vary the color)
5.66
5.46
GaP
2.26
0.55
AlP
3.39
0.51
5.45
GaN
2.45
0.37
3.19
AlN
6.20
0.20
UV
Light-emitting diode materials
3.11
quaternary semiconductors:
- Ex: AlInGaP , tunable Eg and
lattice constant (for growing high
quality epitaxial films on
inexpensive substrates)
Common LEDs
Spectral
range
Material
System
Substrate
Infrared
InGaAsP
InP
Optical communication
Infrared
-Red
GaAsP
GaAs
Indicator lamps. Remote
control
AlInGaP
GaA or
GaP
Optical communication.
High-brightness traffic
signal lights
GreenBlue
InGaN
GaN or
sapphire
High brightness signal
lights.
Video billboards
Blue-UV
AlInGaN
GaN or
sapphire
Solid-state lighting
RedBlue
Organic
semiconductors
glass
RedYellow
Example Applications
Displays
AlInGaP Quantun
Well
5.9 Metal-Semiconductor Junction
Two kinds of metal-semiconductor contacts:
• Rectifying Schottky diodes: metal on lightly
doped silicon
•Low-resistance ohmic contacts: metal on
heavily doped silicon
fBn Increases with Increasing Metal Work Function
Vacuum level, E0
y M : Work Function
cSi = 4.05 eV
qyM
of metal
qfBn
Ec
c Si : Electron Affinity of Si
Ef
Theoretically,
Ev
fBn= yM – cSi
Schottky Barriers
Energy Band Diagram of Schottky Contact
Metal
Depletion
layer
Neutral region
qfBn
Ec
Ef
• Schottky barrier height, fB ,
N-Si
Ev
Ec
P-Si
qfBp
Ef
Ev
is a function of the metal
material.
• fB is the most important
parameter. The sum of qfBn
and qfBp is equal to Eg .
Schottky barrier heights for electrons and holes
Metal
f Bn (V)
f Bp (V)
Work
Function
y m (V)
Mg
0.4
3.7
Ti
0.5
Cr
0.61
0.61
0.5
4.3
4.5
W
0.67
Mo
0.68
Pd
0.77
0.42
4.6
4.6
Au
0.8
Pt
0.9
0.3
5.1
5.1
fBn + fBp  Eg
fBn increases with increasing metal work function
5.7
Fermi Level Pinning (Schottky barrier lowering)
Vacuum level, E0
cSi = 4.05 eV
qyM
qfBn
+ 
Ec
Ef
Ev
• A high density of
energy states in the
bandgap at the metalsemiconductor interface
pins Ef to a narrow
range and fBn is
typically 0.4 to 0.9 V
• Question: What is the
typical range of fBp?
Using C-V Data to Determine fB
qfbi  qf Bn  ( Ec  E f )
qfbi
qfBn
Ec
Ef
Ev
qfBn
q(fbi + V)
qV
Nc
 qf Bn  kT ln
Nd
Wdep 
C
Ec
Ef
Ev
2 s (fbi  V )
qNd
s
Wdep
A
Question:
How should we plot the CV
data to extract fbi?
Using CV Data to Determine fB
1/C2
1
2(fbi  V )

2
C
qNd  s A2
fbi
V
qfBn
Once fbi is known, fB can
be determined using
qfbi
Ec
Ef
E
v
Nc
qfbi  qfBn  ( Ec  E f )  qfBn  kT ln
Nd
Thermionic Emission Theory
vthx
-
V
Metal
N-type
Silicon
q(f B  V)
qfB
qV
Efm
Ec
Efn
Ev
x
 2mn kT 
n  N c e  q (f B V ) / kT  2
2

 h

vth  3kT / mn
J S M
3/ 2
e  q (f B V ) / kT
vthx   2kT / mn
4qmn k 2 2 qf B / kT qV / kT
1
  qnvthx 
T e
e
3
2
h
 J 0 e qV / kT , where J o  100e  qf B / kT A/cm2
Schottky Diodes
Forward
biased
V=0
I
Reverse
biased
Reverse bias
V
Forward bias
Applications of Schottly Diodes
I I
I  I 0 (e qV / kT  1)
Schottky
Schottky diode
I 0  AKT 2 e  qf B / kT
ffBB
PN junction
PN
junction
diode
V
V
• I0 of a Schottky diode is 103 to 108 times larger than a PN
junction diode, depending on fB . A larger I0 means a smaller
forward drop V.
• A Schottky diode is the preferred rectifier in low voltage,
high current applications.
5.10 Heterojunction
Heterojunction gives
us additional
parameters to
manipulate the ratio
of electron/hole
current
More will be discussed
in ECE684: HEMT
What is the energy band diagram at thermal equilibrium?
What is Vbi