Download ECE 7800: Renewable Energy Systems

ECE 7800: Renewable Energy
Systems
Topic 7: Photovoltaic Basics
Spring 2010
© Pritpal Singh, 2010
Learning Objectives
• Understand the basic physics of how
a solar cell works
• Understand materials selection
criteria
• Understand how to model the
terminal characteristics of solar
cells, modules and arrays under
different load and environmental
conditions
• Understand more advanced solar
cell designs
Basic Semiconductor Physics
A semiconductor is a material whose
conductivity may be adjusted by the
controlled addition of impurities. The
most widely used semiconductor in solar
cells is silicon which is a Gp. IV element
(in the Periodic Table). It can be made
p-type by doping with
Boron (Gp. III element)
and n-type by doping
with Phosphorus or
Arsenic (Gp. V elements).
Basic Semiconductor Physics (cont’d)
A semiconductor is characterized by a
filled valence band and empty conduction
band at absolute zero, with the bands
separated by a forbidden bandgap of size
Eg . Light may be considered to comprise
“particles of energy” (photons) whose
energy is given by:
Eph (eV) = 1.24/λ (μm)
A photon is absorbed by a semiconductor
by raising an electron from the valence
band up into the conduction band. Thus for
band-band optical absorption, Eph ≥ Eg.
Basic Semiconductor Physics (cont’d)
Carrier Transport in Semiconductors
Carriers move in semiconductors via
two principal mechanisms:
1) Carrier Drift (motivated by an
electric field)
2) Carrier Diffusion (motivated by a
carrier concentration gradient)
Drift and diffusion are balanced at
thermal equilibrium.
Current Density Equations
e- s:
dn( x )
J n  q n n( x ) E ( x )  qDn
dx
drift
diffusion
h+ s: J p  q p p( x ) E ( x )  qD p dp( x )
dx
Excess Carrier Concentrations
Introducing additional carriers over and
above number available at thermal
equilibrium is termed “carrier
generation” and/or “carrier injection”.
Additional carriers are called “excess
carriers” and may be created by light or
a forward biased p-n junction. Total
carrier concentration is given by
n = n0 + n
p = p0 + p
excess carrier
concentrations
Carrier Recombination
The energy lost when an erecombines with a h+ may be lost to
heat or as an emitted photon. The
former is termed “non-radiative”
recombination and the latter is termed
“radiative” recombination.
Three types of recombination:
1) Indirect (SRH)
non-radiative
2) Direct (band-to-band) radiative
3) Auger
non-radiative
The Continuity Equation
The continuity equation is a charge
conservation equation that takes account
of generation and recombination of
charge in addition to charge flow.
It is useful to find the temporal and
spatial distribution of excess carrier
concentrations, i.e. n(x,t), p(x,t).
Continuity Equation (cont’d)
The continuity equation for e-s is:
n( x, t ) 1 J n ( x, t )

 (Gn  Rn )
t
q dx
The continuity equation for h+s is:
p( x, t )
1 J p ( x, t )

 (G p  Rp )
t
q dx
The P-N Junction
The basic device that is used for most
solar cells is a p-n junction where a
p-type material and n-type material
are brought into intimate contact. In
the next few slides we will review the
physics of the p-n junction.
P-N Junction at Thermal
Equilibrium
p
n
h+ diffusion
p
n
e- diffusion
h+ drift
p
-
+
e- drift
n
P-N Junction at Thermal Equilibrium (cont’d)
Courtesy: Streetman and Banerjee, “Solid State Electronic Devices”
Contact Potential
The contact potential, Vbi, across a p-n junction at
thermal equilibrium is given by:
kT  N a N d 
Vbi  ln  2 
q  ni 
where NA = the doping density on the p-side of the
junction
ND = the doping density on the n-side of the
junction
ni = intrinsic carrier concentration in the
semiconductor
Qualitative Description of Current Flow in
a Biased P-N Junction
Thermal Equilibrium
Potential Barrier is just large enough
to create a balance between drift and
diffusion currents => no net current
flow.
Qualitative Description of Current Flow
in a Biased P-N Junction (cont’d)
Courtesy: Streetman and Banerjee,
“Solid State Electronic Devices”
Qualitative Description of Current Flow
in a Biased P-N Junction (cont’d)
Forward Bias
Under forward bias, the potential on the
p-side of the junction is raised relative
to the n-side. This lowers the energy
barrier to electron and hole diffusion
resulting in an increase in the forward
current. Drift current remains the same
as at thermal equilibrium.
Qualitative Description of Current Flow
in a Biased P-N Junction (cont’d)
Courtesy: Streetman and Banerjee,
“Solid State Electronic Devices”
Qualitative Description of Current Flow
in a Biased P-N Junction (cont’d)
Reverse Bias
In reverse bias , the potential on the
p-side is lowered relative to the n-side.
This results in a larger energy barrier
to e- and h+ diffusion resulting in
negligible forward current flow. The
drift current is the same as at thermal
equilibrium and is the main source of
current in the reverse-biased junction.
Qualitative Description of Current
Flow in a Biased P-N Junction (cont’d)
Courtesy: Streetman and Banerjee,
“Solid State Electronic Devices”
Qualitative Description of Current
Flow in a Biased P-N Junction (cont’d)
Forward Bias - current increases
exponentially with applied bias
across junction.
Reverse Bias - a constant, small
leakage current flows independent
of applied bias across junction
Qualitative Description of Current Flow
in a Biased P-N Junction (cont’d)
i
diffusion
-I0
drift
I0eqV/kT
V
Why Semiconductors ?
Why are solar cells made of semiconductors?
Because the bandgap of semiconductors
is in the visible part of the electromagnetic
spectrum.
0.1 eV < Eg < 3 eV
=>  lies between
m
and
m
Generic Solar Cell Structure
The generic structure of a solar cell is
shown below.
Transparent Contact
Absorber-Generator
Collector-Converter
Opaque Back Contact
The Photovoltaic Effect
Most solar cells work on the principle
of the photovoltaic effect which is
defined as:
“The generation of an electromotive
force when light shines on an
inhomogeneous medium”.
The inhomogeneous medium is
typically a p-n junction.
Photovoltaic Effect (cont’d)
p
n
E
iL
RL
Current-Voltage Characteristics
of an Illuminated P-N Junction
i
w/o light
-I0
V
-IL
w/light
Simple Equivalent Circuit of a Solar Cell
Based on the ideal i-v characteristics
of a solar cell, the following simple
equivalent circuit representation can
be derived:
I
ID
ISC
V
Load
Solar Cell Parameters
i
Vmp VOC
imp
iSC
FF =
V
(Vmp imp )
(VOC iSC )
Band Diagram of Solar Cell
Optical Absorption in Solar Cells
Light is absorbed in semiconductors by
taking an e- from the valence band and
putting it into the conduction band. The
decrease in intensity as a function of depth
into the semiconductor [I(x)] is given by:
I(x) = I(0) e -
x
where  is the optical absorption coefficient
(cm-1).
EC
Eph
EV
Maximum current in Solar Cells
The maximum current generated in a
solar cell depends on:
1. The optical absorption coefficient of
the solar cell material.
2. The thickness of the absorbing
region.
3. The bandgap of the semiconductor.
4. The quantum efficiency of the solar
cell.
Maximum Current in Solar Cells (cont’d)
Semiconductors can have direct or
indirect bandgaps. The optical
absorption coefficient is typically higher
for direct bandgap semiconductors.
E
E
k
Direct
k
Indirect
Maximum Current in Solar Cells (cont’d)
The maximum current output of a solar
cell (assuming 100% quantum
efficiency) is shown as a function of
bandgap and airmass number is shown
below:
Courtesy: Hu and White,
“Solar Cells”
=> smaller bandgap material gives higher
current output.
Solar Cell Efficiency
The voltage output of a solar cell
depends upon the bandgap of the
semiconductor. The larger the
semiconductor’s bandgap, the
higher the solar cell’s output
voltage. Typically,
VOC ~ 0.5-0.6 x Eg .
Thus, there is an optimal bandgap
(1.5 eV) where the solar cell
efficiency is maximized.
Solar Cell Efficiency vs. Semiconductor
Bandgap
Ref:
M. Green,
“Solar Cells”,
Prentice-Hall
1982
Solar Cell Short-Circuit Current
Consider a n-p homojunction solar cell
in the dark in forward bias.
E
H’
Light
n
0
p
xj
xj + W
H
Solar Cell Short-Circuit Current (cont’d)
In the quasi-neutral space charge regions
we can write the following continuity and
current equations for e- s and h+ s:
1 dJ n n p  n p 0

0
q dx
n
dn p
J n  qDn
dx
1 dJ p pn  pn 0

0
q dx
p
dp n
J p   qD p
dx
continuity eqn. for e-s
current eqn. for e-s
continuity eqn. for h+s
current eqn. for h+s
Solar Cell Short-Circuit Current (cont’d)
Boundary Conditions:
pn  pn 0 e
qV / kT
n p  n p 0e
qV / kT
(x=xj)
(x=xj+W)
dpn
S p ( pn  pn 0 )  D p
dx
Sn ( n p  n p 0 )   Dn
dn p
dx
(x=0)
Front surface
Recombination
(x=H)
Back surface
Recombination
Note: Sn , Sp are front and back surface recombination
velocities - J=qnv = q(np - np0)Sn.
Solar Cell Short-Circuit Current (cont’d)
Solution (w/o boundary conditions
applied):
pn  pn 0  C1 cosh( x / Lp )  C2 sinh( x / Lp )
n p  n p 0  C3 cosh( x / Ln )  C4 sinh( x / Ln )
Solar Cell Short-Circuit Current (cont’d)
Solution (after applying boundary
conditions):
J  J 0 (e
qV / kT
 1)
where
J0
D p ni 2
 q
Lp N D
Dn n i 2
q
Ln N A












S p Lp
Dp
S p Lp
Dp
xj 
cosh(
)  sinh(
)
Lp
Lp 
xj
xj 
sinh(
)  cosh(
)
Lp
Lp 
xj
Sn Ln
H'
H' 
cosh(
)  sinh(
)
Dn
Ln
Ln 
Sn Ln
H'
H' 
sinh(
)  cosh(
)
Dn
Ln
Ln 
(h+ drift
term)
(e- drift
term)
Solar Cell Short-Circuit Current (cont’d)
Now let us add light and see what
happens. The continuity equations
must be modified to include a
generation term for the EHP
generation rate. The generation
rate of EHPs is given by:
G ( x)  
dN ph
dx
 N ph ( 0) e x
Solar Cell Short-Circuit Current (cont’d)
The continuity and current equations in
the quasi-neutral regions now become:
1 dJ n n p  n p 0

 G ( x)  0 continuity eqn. for e-s
q dx
n
dn p
J n  qDn
current eqn. for e-s
dx
1 dJ p pn  pn 0

 G ( x)  0 continuity eqn. for h+s
q dx
p
dp n
J p   qD p
dx
current eqn. for h+s
Solar Cell Short-Circuit Current (cont’d)
Boundary conditions (for short-circuit
conditions, i.e. V=0)
pn = pn0
x=xj
np = np0
x=xj + W
Sp(pn-pn0) = Dp dpn
dx
x=0
Sn(np-np0) = -Dn dnp
dx
x=H
Solar Cell Short-Circuit Current (cont’d)
The solution with boundary conditions
applied is:
h+ diffusion current:
 qN ph ( ) ( ) Lp 
J p ( )  

2
2
  ( ) Lp  1 
 Sp Lp


xj
xj 
 (  ) x  Sp Lp
  ( ) Lp   e
cosh  sinh 


 ( )x j
D
D
L
L

 p
p
p
 p
 Lp e


Sp Lp
xj
xj
sinh  cosh


Dp
Lp
Lp


j
Solar Cell Short-Circuit Current (cont’d)
e- diffusion current:
 qN ph ( ) ( ) Ln   (  )( x  W )
j
J n ( )  
e

2
2

(

)
L

n 1 
Sn Ln
H'   (  ) H '
H'

 (  ) W 
(cosh

e
)

sinh


(

)
L
e
n


Dn
Ln
Ln
 ( ) Ln 

S
L
H
'
H
'
n n


sinh  cosh


Dn
Ln
Ln
Solar Cell Short-Circuit Current (cont’d)
In addition to the diffusion current terms,
there is a drift current contribution to the
short-circuit current given by:
J drift ( )  qN ph ( ) e
 (  ) x
j
(1 e
  (  )W
)
The total short-circuit current is given by:
J SC ( )  J n ( )  J p ( )  J drift ( )
Spectral Response of a Solar Cell
Internal spectral response, SRint is given by:
SRint
J SC ( )

qN ph ( )[1 R( )]
External spectral response, SRext is given by:
SRext
J SC ( )

qN ph ( )
Limits to Conversion Efficiency
• Bandgap Energy
The open-circuit voltage of a solar cell
is given by:
kT J SC
VOC 
ln
q
J0
where J 0  ni
Thus,
VOC
2
Cp
Cn
(

)  Be  E
Nd Na
g
kT  C p
Cn 
 

 Nd Na 
kT  B  Cp Cn  


ln 



q
q  J SC  N d N a  
Eg
Limits to Conversion Efficiency (cont’d)
• Bandgap Energy (cont’d)
Typically,
0.5
Eg
q
 VOC  0.6
Eg
q
Thus, for Si (Eg=1.1eV), VOC ~ 0.55V
for GaAs (Eg = 1.43 eV), VOC ~ 0.9V
Limits to Conversion Efficiency (cont’d)
• Temperature
The efficiency of a solar cell decreases
with temperature. ISC is relatively
insensitive to temp.; VOC is responsible
for the temp. dependence.
dVOC 1 dEg k  B Cp Cn 

 ln 
(

)
dT
q dT q  J SC N d N a 
1 dE g
1  Eg


 
 VOC 

q dT
T q
Limits to Conversion Efficiency (cont’d)
• Temperature (cont’d)
dEg
For Si:
 3x104 ev / K
dT
Eg
q
 VOC  0.5V
at room temp.
=> 0.4% change in VOC with 1 °C temp. rise
20% eff. @ 20 °C -> 16% eff. @ 70 °C
Limits to Conversion Efficiency (cont’d)
• Light Intensity
The efficiency of a solar cell increases
with increasing light intensity. JSC
increases by concentration, X and VOC
and FF increase logarithmically with X.
kT XJ SC
VOC  ln(
)
q
J0
with light concentrated X times.
Limits to Conversion Efficiency (cont’d)
• Light Intensity (cont’d)
If a Si solar cell has the following
characteristics:
VOC = 0.55V; JSC = 40 mA/cm2; FF=0.7
=> efficiency = 0.55V.40mA/cm2.0.7 = 15.4%
100mW/cm2
at 1 Sun
At 100 suns:
VOC = 0.67V; Jsc = 4A/cm2; FF=0.85
=> efficiency = 22.8 % at 100 Suns
Effect of Temperature and Light Intensity
Limits to Conversion Efficiency (cont’d)
• Series Resistance Losses
Series resistance losses in a solar cell
are associated with resistive losses in
the metal contact grid, in the leads,
contact resistance between the metal
and the semiconductor, and the bulk
resistance in the n+-layer. This results
in a reduced output voltage at a given
current level leading to a slope at VOC.
Limits to Conversion Efficiency (cont’d)
• Shunt Resistance Losses
These are associated with leakage
currents around the p-n junction and
pinholes within the p-n junction. Shunt
resistance losses appear as a slope at
JSC.
More Accurate Equivalent Circuit
A more accurate equivalent circuit of
a solar cell takes into account the
series and shunt resistances of the
diode.
Solar Cell I-V Characteristics
Based on the equivalent circuit of the
solar cell on the previous slide, the
terminal characteristics of the solar
cell can be expressed by the following
equation:
  q(V  IRs )    V  IRs 
I  I SC  I 0 exp 
 1 

kT
   R p 
 
Solar Cells, Modules and Arrays
An individual solar cell usually only
generates about 0.5V DC output voltage
but may generate >1A of current. Several
cells must therefore be strung together in
series to attain reasonable output
voltages. A solar module (or panel)
usually comprises approx. 30 seriesconnected cells – a standard that matches
the charging voltage for a lead acid
battery. The power output of a module
ranges from 10’s of Watts to >100W. A
solar array is made up of many
interconnected modules, typically ~ kW.
Solar Cells, Modules and Arrays
I-V Characteristics of a Solar Module
I-V Characteristics of a Solar Array
Physics of Shading
Consider one cell in a module shaded
while the other cells are in full sun.
Physics of Shading (cont’d)
Assuming that the current I is still
maintained in the other (n-1) cells in
the module, the voltage across the
module will drop to:
VSH = Vn-1 –I (Rp +Rs)
With all n cells in the sun, again
assuming the current is I, the voltage
across the n-1 cells is:
Vn-1 = (n-1/n) V
where V is the module voltage with
all cells in the sun.
Physics of Shading (cont’d)
Thus,
VSH
 n 1 

V  I ( RP  Rs )
 n 
The voltage drop at any current, ΔV
is given by:
 n 1 
V  V  VSH  V  
V  I ( R p  Rs )
 n 
V
V
  I ( R p  Rs )   IR p
n
n
Effects of Shading on Solar Module Output
Example 8.6
Effects of Shading on Solar Module Output
(cont’d)
It can be seen that the module power output
is reduced drastically by even single cell
shadowing.
While there was shadowing on only 2% of
the module area, the power output at MPP is
reduced by 70 %!
The shadowed cell acts as a load. To
prevent the rest of the array dumping power
into this cell (which can result in a fire) a
bypass diode is used to bypass current
around the cell.
Effect of Bypass Diodes
Heterojunction Solar Cells
To limit the effect of surface
recombination in a shallow n+-p
junction solar cell, a heterojunction
solar cell may be employed. An
example of such a structure using
GaAs/AlxGa1-xAs is shown below:
Heterojunction Solar Cells (cont’d)
The composition of the light absorbing
region may be graded or fixed. The
band diagrams for each case are shown
below:
Heterojunction Solar Cells (cont’d)
Interface recombination can be a
problem with heterojunction solar cells
because of work function difference
between materials resulting in a spike
at the heterojunction.
Multijunction Solar Cells
The optical spectrum may be more
effectively used by employing two
series-connected junctions rather than a
single p-n junction. Such devices are
called tandem or multijunction solar
cells.
In a two-cell stack, the top cell should
have a bandgap of 1.8 eV and the bottom
cell should have a bandgap of 1.0 eV to
ensure current matching between the
cells.
Multijunction Solar Cells (cont’d)
Solar Cell Materials
• Crystalline Silicon (Eg = 1.1eV)
- most widely used material for both
space and terrestrial applications
• Polycrystalline Silicon (Eg = 1.1eV)
- cast in ingots, polycrystalline silicon
solar cells are also widely used.
• Amorphous Silicon (Eg = 1.8 eV)
- thin film material; usually made in
multijunctions because of light-induced
defects: lower efficiency than c-Si or
mc-Si.
Solar Cell Materials (cont’d)
• Gallium Arsenide (Eg = 1.43 eV)
- higher efficiency than Si but more
expensive; seeing increasing use in
space applications.
• Cadmium Telluride (Eg = 1.5 eV)
- thin film material; can be made in large
areas; lower module efficiency than c-Si.
• Cu(In,Ga)Se2 (Eg = 1.1-1.4 eV)
- thin film material; module efficiency
similar to CdTe but lab efficiencies >19%
achieved.
Summary
In this topic we covered:
• the basic physics of how a solar cell
works
• materials selection criteria
• how to model the terminal
characteristics of solar cells,
modules and arrays under different
load and environmental conditions
• more advanced solar cell designs