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Solar Cells
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Solar Cells
We want to maximize the power generated by an illuminated
pn junction solar cell, this is done in three major ways:
1. Generate a large short circuit current
2. Generate a large open circuit voltage
3. Maximize the Fill Factor, this means minimizing parasitics as much
as possible
A lot of the time these requirements overlap
Some times they fight against each other
Must compromise
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Short circuit current
JSC depends on two things:
1. Generation of carriers by light absorption
– Absorb light in semiconductor to generate carriers
– Minimize reflection
– These two depend on the incident light, optical properties
of the solar cell, the band gap and thickness of
the solar cell
2. Collection of light generated carriers
– Depends on material and device parameters
– Depends on the surfaces
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Light Absorption
•
Absorption of photons where the energy of each photon is given by:
•
Energy of photon is primary determinant of what happens when it
hits the semiconductor
– If E < EG then (ideally) no absorption
– If E ≥ EG then absorption
•
•
Energy above the band gap
is lost as heat to the crystal
lattice (phonons)
Major fundamental losses
for a solar cell
excess holes
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Light Absorption
•
Band gap is the primary determinant of the amount of photons
available for generating carriers
– In general we have one band gap
– Lower band gap means more photons available but…..
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Reflections
Two causes of reflection on top surface
– Reflection from contact (we’ll come back to this)
– ‘Natural’ reflection from exposed semiconductor
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Anti-reflection
Use coatings that will ensure there is destructive interference
between the incoming and outgoing light waves
- need thickness that is ¼ of the target wavelength
- refractive index must be geometric mean of air and semiconductor
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Anti-reflection
• Can go to more anti-reflection coating
• Works to reduce reflection significantly
– has a target wavelength, we have a spectrum
– need material with optimum refractive index that also can be
incorporated with other processing
• Can go to more than one
anti-reflection coating
• Still are targeting a wavelength
- can we reduce reflections
for all incident wavelengths?
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Texturing
• What about texturing of surfaces (front and back)
• Use refraction of light to change angle of entry and
enhance optical path length
• Not as wavelength sensitive as AR coatings
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Texturing
• Very important for indirect material such as Si
• Generation still significant after 200 µm need to enhance
optical path length
• Texturing helps by making light have multiple passes
through Si
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Texturing
• Refracts or bends light that is transmitted into Silicon
• Reflected light is not lost but reflects to hit another angled
facet where more transmission/reflection takes place
• Two things achieved: more light is transmitted; light that is
transmitted goes through Silicon at an angle
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Texturing
• Turns out the optimum is to make them inverted pyramids
that are slightly offset with respect to each other
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Lambertian Reflector
• Can use a random (Lambertian) reflector at the rear of
the cell to also improve the light trapping ability
• Mostly useful for thin film solar cells – how do we get
such as surface for a bulk cell
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Collection Probability
• Light generated minority carriers recombine readily
• If light generated minority carrier can reach depletion region,
the electric field sweeps it across the junction to become a
majority carrier – “collection”
• Once a carrier is collected it is very unlikely to recombine
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Recombination
• Recombination rate is determined primarily by the minority
carrier concentration
– Majority carrier concentration stays very much constant, minority
carrier concentration varies greatly (orders of magnitude), the
recombination rate is, in general, determined by the product of the two
concentrations, n.p
• For direct band gap materials recombination is almost 100%
radiative
• For indirect materials typically have defect assisted
recombination
– Defects can be crystal lattice defects, doping related defects, grain
boundaries
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Recombination
• Defects act as mid-levels in a two transition process
– CB to defect level
– Defect level to VB
http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/point_defects.htm
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Recombination
• Grain boundaries (interfaces) and surfaces are two regions
with a high impact on the recombination rate
• Both represent significant disruption to the crystal lattice
• Energy levels within the forbidden gap are introduced
allowing greater recombination
• The effect is not localized to the interface or surface
– Carriers diffuse to the recombination centre so the entire region
surrounding the interface or close to the surface is affected
• Grain boundaries can be effectively eliminated by using
single crystalline material, can’t get around surfaces
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Surfaces
• Surfaces are the termination of a crystal lattice
• Since there is not the 3 dimensional symmetry like the
bulk case, surface energy states are very different
• Orbitals are not bonded to anything – “dangling” bonds
are present and very hungry
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Surfaces
• Surface has a recombination velocity associated with it,
we label it S
• We want to minimize S in a solar cell, this is referred to
as “passivation”
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Collection probability
• Collection probability is the probability that a light generated
carrier makes it to the depletion region edge
• Determined by diffusion length, type of recombination
present and where it is generated
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Collection Probability
• Collection probability is low when we are further than
one diffusion length away from the depletion region
• Can think of an “active” region
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Short circuit current
• JSC determined by generation rate AND the collection
probability
• Need to optimize thickness for good absorption but if
thickness >> diffusion length we don’t collect much
W
J L = q ∫ G ( x)CP ( x)dx
0
W
(
)
= q ∫ ∫ α (λ ) H 0 e −α ( λ ) x dλ .CP ( x)dx
0
• Junction should be as close to the surface as possible
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Current collection
• Long diffusion lengths are crucial for
our collection of light generated
carriers
• Diffusion length is strongly related to
the starting material
– FZ: Float zone, gives ‘best’ material but
also very expensive
– CZ: Single crystalline (Czochralski) very
good material, still costly
– Multicrystalline: not so good, still decent
though, cheap
– Polycrystalline: poor, cheap as dirt
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Quantum Efficiency
• How do we measure collection probability?
• Very difficult, better to measure the Quantum Efficiency
• Quantum Efficiency is simply the ratio of carriers collected,
i.e. the current, to the number of photons incident
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Spectral Response
• Similar to Quantum Efficiency but this time measure current
compared to the power
• We have
qλ
SR =
.QE
hc
• At higher energies we don’t have as many photons
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
JSC Summary
• Material thickness enough to absorb most of light but want to
be no more than a diffusion length to ensure collection
• Low reflection of light using anti-reflection coatings and/or
textured surface
• Junction depth optimized for absorption and collection in
emitter and base
• High diffusion length
• Good surface passivation, so carriers aren’t lost when trying
to extract
• Low metal coverage of front surface to minimize shadowing
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Open Circuit Voltage
• If collected carriers are not extracted from the solar cell
there is a charge separation that builds up
• This is essentially a forward bias on the cell, this then
lowers the barrier to diffusion – larger diffusion current
means higher recombination
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Band Gap vs VOC
• In general, a larger band gap means a larger VOC
• Larger band gap means there is a lower minority carrier
concentration and so lower recombination
• However, lower band gap gives greater short circuit current
which also increases VOC
VOC
nkT
=
q
⎛ JL ⎞
⎜⎜ ln
+ 1⎟⎟
⎝ J0
⎠
• VOC is more sensitive to reducing J0 so higher band gap wins
out
• But we want to maximize power not voltage
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
High Open Circuit Voltage
• For a given band gap we want to maximize the open circuit
voltage this means making J0 as low as possible
• In all previous considerations we have assumed the pn
junction is infinitely wide but we actually want a thin device –
the depletion region plus one diffusion length each side
• Dark current looks very different
• Notice the presence of the surface recombination velocity
• Recombination is determined by the minority carrier
concentration so……
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
High Open Circuit Voltage
…..why
don’t we just dope heavily
Why? This should drive down the minority carrier concentration
since in n type material we have
ni2
p≈
ND
Remember
L = Dτ
where
D=
kT
µ
q
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
High Open Circuit Voltage
• If cell is thin recombination is reduced and open circuit
voltage will increase BUT need the surface recombination to
be low, otherwise will go down
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Passivation
• We want to nullify any dangling bonds and the energy levels
in the forbidden gap so surfaces don’t siphon away the light
generated carriers
• Can use Hydrogen which will bond with any dangling bonds
• Can also ‘shift’ the surface
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Back surface field
• Have a very heavily doped layer at the rear
• Gives very low minority carrier concentration – minority
carriers are ‘reflected back
• Not really a field as such
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
VOC Summary
• Want the dark or recombination current to be as low as
possible. Carriers injected at the edge of depletion
region must see low recombination.
• Must have the following:
–
–
–
–
Long diffusion lengths
Low surface recombination (passivation)
Thin devices (minimize recombination)
High doping (not compatible with diffusion length)
• Must also be maximizing JSC – not all of the conditions
for both are compatible, nor even for maximizing one of
them, we need a compromise
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Fill Factor
• Strongly affected by parasitic losses like series resistance
and shunt resistance
• Also affected by VOC
• Can have drastic effect on actual efficiency even when JSC
and VOC are good
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Effect of VOC
• Higher VOC will generally give better FF
• Re-define VOC as normalized value vOC = VOC /(nkT / q )
• We can estimate very accurately the fill factor base on the
normalized open circuit voltage
vOC − ln(vOC + 0.72)
FF =
vOC + 1
for
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
vOC > 10
Efficiency vs Band Gap
• Best band gap depends on spectrum and concentration
“Pure” Blackbody Spectrum
Maximum Concentration
AM1.5G Spectrum
Unconcentrated
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Parasitic Resistances
• Series resistance, RS: comes about due to resistance of
materials, contact resistance and metal interconnect
resistivity
• Shunt resistance, RSH: leakage of current across the pn
junction i.e. doesn’t undergo diode action, this includes
transport around the edge of the junction as well as misfits
and defects providing alternate paths for carriers
• For good Fill Factor we want RS as low as possible and RSH
as high as possible
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Series Resistance
•
•
•
•
Material resistance of the base
Resistance of metal contacts and interconnects
Contact resistance between metal and semiconductor
Emitter resistance – sheet resistance
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Circuit Model
•
Include these parasitics for a
realistic model
⎧ ⎡ V + IRS ⎤ (V + IRS ) ⎫
I = I L − I 0 ⎨exp ⎢
−
⎬
⎥
(
nkT
/
q
)
R
⎦
SH
⎩ ⎣
⎭
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
RS and RSH and IV
• How do these parasitic resistances relate to the IV curve?
• If RS and/or RSH are not ideal then slopes in the IV curve will
change
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Effect of RS and RSH
• RS increase means voltage is being lost
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Effect of RS and RSH
• Shunt resistance not being infinite means that current is
being lost
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Effect of RS and RSH
• Affect FF the most but in extreme cases can also harm
JSC and VOC
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Characteristic Resistance
• Useful to measure RS and RSH against this characteristic
resistance defined by RCH = VOC/ISH
• If RS << RCH then little effect on FF
• If RSH >> RCH then little effect on FF
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Fill Factor
• In the presence of significant series resistance the Fill
Factor is now
FF = FF0 (1 − rs )
rs < 0.4
vOC > 10
• FF0 is the ideal fill factor (minus the parasitics)
• Normalized series resistance
RS
rs =
RCH
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Fill Factor
• In the presence of a low shunt resistance
⎧ (vOC + 0.7) FF0 ⎫
FF = FF0 ⎨1 −
⎬
vOC
rsh ⎭
⎩
rsh > 2.5
vOC > 10
RSH
rsh =
RCH
• In the presence of high RS and low RSH we have
⎧ (vOC + 0.7) FF0 (1 − rs ) ⎫
FF = FF0 (1 − rs )⎨1 −
⎬
vOC
rsh
⎩
⎭
Same conditions
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner