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Solar Cells 2
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Solar Cells 2
We will look at some further issues for solar cells not
already discussed
- Design of the front contact
- Design of the emitter and base layers
- Effect of temperature
- Concentrating light
- Using multiple band gaps
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Front Contact design
• We have a good idea how to generate a large number of
carriers by optical absorption as well a high probability of
collection
• Also need to consider extraction of carriers through
contacts to external circuit
• Rear contact is easy and a complete coverage helps in
terms of reflecting carriers back for optical path length
enhancement
• Front contact is not so simple since we will block out
sunlight with any metal we put down
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Front Contact design
• The answer is to make a grid pattern but it needs to be
an optimized grid to minimize both series resistance
AND shadowing
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Extraction of carriers
•
Need to understand how
carriers are travelling to the
contacts and out of the solar
cell
“finger”
Rbase =
emitter
base
rear contact
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
ρl
A
Sheet resistivity
• Carriers in the emitter are moving across a sheet
• More appropriate to talk of sheet resistivity rather than a
bulk resistivity
• Defined simply by
ρ† = ρ bulk / t
• Units seem to be Ω but are actually Ω/□ (ohms/square)
• For a general case (non-uniform doping) we have
t
dx
ρ† = 1 / ∫
ρ bulk ( x)
0
• Very important to know voltage drop when carriers travel
laterally to the contacts for extraction
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Sheet resistivity
• Can easily measure the sheet resistivity using “four point
probe”
Note the relative positions of the
current probes (input) and the
voltage probes (output)
Find the sheet resistivity by
ρ‡ =
π V
ln 2 I
(Ω/□)
Typical values for silicon solar cells
lie between 30-100 Ω/□
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Grid spacing
• Find optimum spacing of fingers by considering power loss
in lateral flow to fingers
dPloss = I 2 ( y )dR
dR = ρ†dy / b
I ( y ) is the lateral current flow, it is
zero at the midpoint between fingers
and maximum under the
Fractional power loss given by
Pfrac
J mp ρ† S 2
Ploss
=
=
Pgen
12Vmp
This will be a homework question
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Grid aspect ratio
• Fingers and busbar also have resistance associated with
them
• It is a bulk resistance determined mostly by the crosssectional area
• Want tall fingers to minimize both shadowing of cell and
the resistance of the fingers
Unfortunately we are often limited
in the aspect ratio we can obtain
by processing issues
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
More resistances
• Busbar and finger resistive losses are given by
J mp S
J mp 1
1 2
1 2
prf = B ρ smf
prb = A Bρ smb
m
Vmp WF
m
Vmp WB
• Shadowing losses are
W
psf = F and
S
WB
psb =
B
Contact Resistance
J mp S
pcf = ρ c
Vmp WF
ρ smf , ρ smb
ρc
Sheet resistivities
Specific contact resistance
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Contact resistance
n-type
• Fermi levels must line up between metal and semiconductor
• Vacuum energy level must be continuous across junction
• Bands bend to accommodate these properties
• Barrier to flow is established with a built in voltage
Figures taken from “Semiconductor Devices” by Jaspat Singh
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Contact Resistance
The surface has a whole
bundle of defect levels
These act to clamp the
potential that can be
maintained at the junction
Built in voltage (barrier) is determined predominantly by the
semiconductor and only very weakly depends on the metal
Figures taken from “Semiconductor Devices” by Jaspat Singh
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Contact resistance
Actually get flow
both ways
Want to minimize
flow into the
semiconductor
Flow into metal is
Determined by
Vbi-V barrier
Make ϕb big
Current flow from metal to sc is given by
qφb
⎛ m * qk 2 ⎞ 2 −kT
⎟T e
where J S = ⎜⎜
2 3 ⎟
⎝ 2π h ⎠
J = J S (e
qV
kT
− 1)
Thermionic emission
Figures taken from “Semiconductor Devices” by Jaspat Singh
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Contact resistance
• Solution is to use an alloy process that will drive dopants
into the semiconductor below the contact
• This very high doping immediately below the contact
ensures high tunnelling between the semiconductor and
metal – lower contact resistance
• Can often alloy front and back in one step
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Emitter Layer
• For front contact want the sheet resistivity of emitter to be
low
• Sheet resistivity depends on bulk resistivity and emitter
thickness
ρ† =
ρ bulk
t
1
=
qµ n N D t
• Want highly doped thick emitter layer
• But junction needs to be close to the surface for efficient
collection of light generated carriers
• Compromise between collection and resistance losses of
front contact
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Dead Layer
• Want the emitter doping as high as possible to reduce sheet
resistivity
• Big problem when doping very heavily is reaching solubility
limit for dopant in semiconductor i.e. P in Si
• Can form precipitates of the dopant in the semiconductor
• Bad news since these are very efficient recombination
centres
• Form a so-called “dead layer” at the surface with a very high
concentration of light generated carriers that we cannot
hope to collect
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Base
• Base layer is normally uniformly doped when drawn from the
molten
• Higher doping in base has two effects
– Increase VOC
From the expression for J0 we know that increasing the doping in
both emitter and base will decrease J0 and open circuit voltage will
increase
– Decrease JSC
Many recombination mechanisms increase with doping density
including trap assisted, radiative and Auger recombination (energy
given to another carrier) so doping should be low to make JSC high
• Compromise between the two, based on the properties of
the substrate i.e. what type of recombination is present
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Efficiency
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Optimum Solar Cell
• Emitter heavily doped, base moderately doped
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Best efficiencies
• Bulk of commercial solar cells are made with silicon (either
single crystalline, multicrystalline, polycrystalline or
amorphous)
• Best efficiency of a silicon solar cell is 24.7% by University of
New South Wales, 1994 – upgraded to 25% recently after
review of solar spectrum
• Best efficiency of 25.7% for GaAs reported by NREL in 1990!
Why no follow up?
• Cost always comes in to consideration. Silicon is cheap and
has widely developed processes and also is mechanically
sturdy – GaAs is brittle, expensive and not compatible with
Silicon processing
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Efficiency
• Measure I-V using a solar
simulator
• Calibrate with a solar cell of
known parameters
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Effect of Temperature
• We have current flowing through an electronic device
with electrical resistance – power dissipation and hence
temperature change
• How does this affect a solar cell performance
• We will see the effect in both the light generated current
and the open circuit voltage
• Does heating hurt or help?
• Turns out we increase current and decrease voltage
• Which is the bigger effect?
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
JSC vs Temperature
• Band gap of semiconductor decreases with increasing
temperature according to
αT 2
α, β are material constants
EG (T ) = EG (0) −
T +β
• Means absorption edge is shifted to lower value as the
temperature of solar cell is increased
• JSC is increased since we can absorb more of the spectrum –
assuming everything else stays same
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
VOC vs Temperature
• Decrease in band gap also has the effect of increasing the
intrinsic carrier concentration and hence the equilibrium
minority carrier concentration
• This means more recombination and hence VOC goes down
dVOC
EG (0) − qVOC + γkT
=−
dT
qT
γ constant for semiconductor determining J0
• As an example for silicon VOC decreases ~ 0.4%/C
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Effect of Temperature
• Since VOC is decreasing, so is FF
• Temperature also increases series resistance further
reducing FF and power
• Overall, Temperature increase sees output power decrease
• Big problem for solar cells since some of the incident light
will heat it and the current flow produces heat
• Critical to have some way of dissipating heat
• Typically rely on convective heat dissipation i.e. a breeze
• Must be part of design to get good air flow under panels
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Cooling of Cells
Better
How to cool?
Nightmare
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Concentrating Light
• Concentrating light will reduce the area required for energy
conversion – cheaper
• Current will definitely go up but does voltage?
• Beyond concentrations of 10 the system must track the sun
– can only use direct component of sunlight
• Since light is concentrated the cell will heat more readily –
must be more mindful of cooling the cell
• Series resistance is a critical feature and determines the
concentration that will be used – must keep as low as
possible
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Concentration
• JSC increases linearly with concentration
• VOC increases logarithmically with concentration
• Fill factor, however may well be reduced for higher
concentrations
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Concentration
Recall, with series and shunt resistances I-V equation is
⎧ ⎡ V + IRS ⎤ (V + IRS ) ⎫
I = I L − I 0 ⎨exp ⎢
−
⎬
⎥
(
nkT
/
q
)
R
⎦
SH
⎭
⎩ ⎣
I is increasing linearly with concentration and so the IRS terms
are increasing linearly
Voltage is not increasing nearly as quickly
The effect of the series resistance is being increased as we
up the concentration
Fill factor is decreased by RS
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Concentration
Busbar
Active
Area
Heat Sink
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Concentration
• Assuming we can keep temperature fixed
• Increase in efficiency until the series resistance effect
‘kicks in’ and we see efficiency go down
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Concentration
• Other factor is the temperature – we know increasing
temperature reduces efficiency
Area
Concentration
TC ≈ Tambient + A.C.L.(1 − η ).RThermal
Light Intensity
Thermal resistance
Units: C/kW
Efficiency
• Cooling of the solar cell is therefore critical for concentrating
systems
– Passive: heat sinks, fins, even the design of the cell (make base and
emitter resistances low, top grid with very fine finger widths)
– Active: coolants are used to provide a heat exchange for the solar cell
to ‘dump’ heat
• Can also use heat for thermo-electric conversion (often
referred to as scavenging)
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Concentrators
Dish
Cmax =
1
sin 2 (θ max / 2)
Trough Cmax =
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
1
sin (θ max / 2 )
Concentrators
Fresnel lens
Compound parabolic concentrator
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Luminescent Concentrator
• Proposed to overcome limitations to concentration with
conventional systems
• Sheet of glass or plastic is doped with a luminescent
substance i.e. it emits light fairly efficiently
• Most of the emitted light can be internally reflected so escape
is low (we add mirrors to any ‘free’ sides
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Luminescent Concentrator
• Advantage is that emitted light is in much narrower
wavelength range (it has a colour)
• Problem has been luminescent efficiency of dyes, only
external quantum efficiencies of ~ 30% have been seen
– not enough for the big concentration we want
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Multiple Band Gaps
• Single band gap of semiconductor limits the segment of
incident spectrum that can be absorbed AND what can
be used effectively due to thermalization
• Use multiple band gaps
to increase amount of the
incident spectrum absorbed
AND minimize the amount
of power lost due to the
thermalization of carriers
• Can it be that easy?
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Multiple Gap Solar Cells
Tandems
Unconstrained
Constrained
Spectrum
Splitting
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Spectrum Splitting
• Basis for the DARPA Very High Efficiency Solar Cell
(VHESC) project
• Dichroic mirror splits incoming light to be sent to solar cell
where it is most efficiently coverted
• Much higher module efficiency than previous
• Expense (materials plus processing/manufacturing)
excludes it from large market
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Tandem Solar Cells
• Efficiency goes up with
more band gaps
In reality we are limited by lattice
constant constraints
Because of cost, almost exclusively used under concentration
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Tandem Solar Cells
• Possible to get to many junctions
• Reasonably easy to select optimum band gaps
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Tandem Solar Cells
• Practically the constrained tandem is choice as it has
minimum number of contacts
• Connection needs to be made via a tunnelling junction
between the solar cells in the stack
• Do this by heavy doping but is a source of series resistance
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Tandem Reality
• Complex structures requiring a lot of growth experience
• Each new layer brings its own problems, layers also
interact
3 junction tandem solar cells
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
High Efficiency
• Tandem solar cell efficiencies depend on concentration which
is in turn decided by series resistance etc..
• So efficiency is a bit of a slippery definition since concentration
will be different for different devices
• Current champion efficiency is 40.8% at 326 suns - National
Renewable Energy Lab
• Fraunhofer are claiming 41.1% at 454 suns
• Metamorphic growth is used along with an inverted growth
approach where the growth substrate is removed and not a
part of the final device
• The series resistance is obviously being improved since the
concentration is going up
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
High Efficiency
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner