Effective Series Resistance document discusses how practical solar cells differ from ideal models and how series resistance affects performance. It describes: 1) How electron paths through surface regions and electrodes introduce an effective series resistance, Rs, lowering maximum output power. 2) Rs broadens the current-voltage curve, reducing short circuit current and cell efficiency. 3) Temperature also affects efficiency, with voltage increasing at lower temperatures as saturation current Io decreases exponentially with temperature.

1. Effective Series Resistance
• Practical devices can deviate substantially from the
ideal pn junction solar cell behavior.
• Consider an illuminated pn junction driving a load
resistance RL and assume that photo-generation takes
place in the depletion region.
– Photo-generated electron has to transverse a surface
semiconductor region to reach the nearest finger electrode
– All these electron paths in the n-layer surface region to
finger electrodes introduce an effective series resistance RS
into photovoltaic circuit as shown in Fig.9

2. Effective Series Resistance, cont
• If the finger electrodes are thin, then the
resistance of the electrodes themselves will
further increase RS
– This is also a series resistance due to the neutral p-
region but this is generally small compared with
the resistance of the electron paths to the finger
electrodes.

3. Neutral
n-region
Neutral
p-region
Finger
electrode
Back
electrode
Depletion
region
RL
Rs
Rp
Series and shunt resistances and various fates of photegenerated EHPs.
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig. 9

4. Equivalent circuit
• The photo-generation process is represented by a
constant current generator Iph ( light intensity)
• The flow of photo-generated carrier across the
junction gives rise to a photovoltaic voltage difference
V across the junction
– This voltage leads to the normal diode current
Id = Io [exp(eV/nkBT) – 1] = 0
• Iph and Id are in opposite directions
– So, in open circuit, the photovoltaic voltage is such that Iph
and Id have the same magnitude and cancel each other.

5. A
Iph Rp RLV
IIph
Id
Solar cell Load
B
Rs
The equivalent circuit of a solar cell
© 1999 S.O. Kasap,Optoelectronics (Prentice Hall)
Fig. 10

6. • Fig. 10 shows the equivalent circuit of a more
practical solar cell
– The series resistance RS give rise to a voltage drop and
therefore prevents the full photovoltaic voltage from
developing at the output between A and B.
• A fraction of the carriers flow through the crystal
surface or grain boundaries in polycrystalline devices
instead of external load RL
– These effects can be represented by an effective internal
shunt or parallel resistance Rp
– Typically Rp less important than Rs unless the device is
highly polycrystalline
Equivalent circuit

7. Series Resistance
• The series resistance Rs can significantly
deteriorate the solar cell performance as Fig.11
– Rs = 0 is the best solar cell case
• The available maximum output power decreases
with the series resistance
– Also reduces the cell efficiency
– When Rs is sufficiently large, it limits the short circuit
current
• Low shunt resistance Rp due to material defects
also reduces the efficiency
– Low Rp leads to a reduced Voc

8. I (mA)
V
0
0
0.2 0.4 0.6
5
10
Voc
Isc
Rs = 0
Rs = 20 
Rs = 50 
Iph
The series resistance broadens the I-V curve and reduces the maximum
available power and hence the overall efficiency of the solar cell. The example
is a Si solar cell with n 1.5 and Io  310-6 mA. Illumination is such that
the photocurrentIph = 10 mA.
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig. 11

9. Example
• Consider two identical solar cells with the properties
Io= 2510–6mA, n= 1.5, Rs=20 subjected to the
same illumination so that Iph =10mA.
• Explain the characteristics of two solar cells
connected in parallel.
• Find the maximum power that can be delivered by
one cell and two cells in series and also find the
corresponding voltage and current at the maximum
power point (assume Rp=)

10. Solution
• Consider one individual solar cell as shown in Fig.10.
The voltage Vd across the diode is V – RsI so that the
external current I is,
I = –Iph + Io [exp(eV/nkBT) – 1]
= –Iph + Ioexp[e(V – IRs)/nkBT] – Io (1)
• Eqn (1) gives the I-V characteristic of 1 cell and is
plotted in Fig.12.
• The output P=IV is also plotted in Fig.12
– The maximum power=2.2mW when I=8mA V=0.27V and
load = 34 

11. 0.60.40.20246
5
15
Voltage (V)Power (mW)
Current (mA)
20
10
1 cell
2 cells in parallel
Current vs. Voltage and Power vs. Current characteristics of one cell and two
cells in parallel. The two parallel devices have Rs/2 and 2Iph.
© 1999 S.O. Kasap,Optoelectronics (Prentice Hall)
Fig. 12

12. Solution, cont
• Fig 13 shows the equivalent circuit of the two solar
cells in parallel running a load RL.
• I and V now refer to the whole system of two devices
in parallel
• Each device is now delivering a current I/2. The diode
voltage for one cell is V – RsI/2 . Thus,
½I = –Iph+Ioexp[(eV – ½IRs)/nkBT] – Io
I = –2Iph+2Ioexp[(eV – ½IRs)/nkBT] – 2Io(2)

13. Solution, cont
• Comparing Eqs.(2) & (1), we see that the parallel combination
has halved the series resistance, doubled the photocurrent and
doubled the diode reverse saturation current Io.
• All these in line with intuitive expectation as the device are has
now been effectively doubled
• Fig.12 shows the I-V & I-P characteristics of the combined device
– The maximum power 4.4 mW, I16mA, V0.27V and load = 17 
– The parallel connection increases the available current and allows a
lower resistance load to be driven

14. A
Iph
V
Iph
Id
B
Rs
RL
I/2
Id
Iph
I
RsI/2
Two identical solar cells in parallel under the same illumination and
driving a load RL.
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig. 13

15. Solution, cont
• If we were to use the two solar cells in series, then
Voc= 1V, Isc=Iph=10mA and maximum power =
4.4mW at I=8mA, V= 0.55V & load= 34.
• These simple ideas however do not work when the
cells are not identical.
– The connections of such mismatched cells can lead to
much poorer performance than idealized predictions
based on parallel and series connections of matched
devices.

16. Temperature Effect
• The output voltage and the efficiency of a solar cell
increases with decreasing temperature; solar cells
operate best at lower temperature.
• Consider the open circuit voltage Voc of the device in
Fig. 8(b)
– As the total cell current is zero, Iph generated by light must
be balanced by Id generated by Voc
• If ni is the intrinsic concentration, Io  ni
2
– Which means Io decreases rapidly with decreasing
temperature

17. Temperature Effect, cont
• A greater voltage is developed to generate the
necessary Id that balances Iph
• The output voltage Voc when Voc »nkBT/e is given by
Voc = nkBT/e ln(Iph/Io)
• In Eq (1), Io is the reverse saturation current
– Io is strongly temperature dependent because it depends
on ni
2
• Since Iph=KI, we can write Eq (1) as
Voc = nkBT/e ln(KI/Io) or eVoc/nkBT = ln(KI/Io)

18. Temperature Effect, cont
• Assuming n=1, at two different temperature
T1 and T2but at the same illumination level
eVoc2/kBT2 – eVoc1/kBT1= ln(KI/Io2) – ln(KI/Io1)
= ln(Io1/Io2)  ln(ni1
2/ni2
2)
• Where the subscripts 1 and 2 refer to the
temperature T1 or T2 respectively

19. Temperature Effect, cont
• We can substitute ni
2 = NcNvexp(–Eg/kBT) and
neglect the temperature dependences of Nc
and Nv compared with the exponential part to
obtain,
eVoc2/kBT2 – eVoc1/kBT1= Eg/kB(1/T2–1/T1)
• Rearranging for Voc2 in terms of other
parameters we find,
Voc2 = Voc1(T2/T1) + Eg/e(1– T2/T1)

20. Temperature Effect, cont
• For example, a Si solar cell that has Voc1 = 0.55V at
20C (T1=293K) will have Voc2 at 60C (T2=333K)
given by
Voc2= (0.55V)(333/293)+(1.1V)(1 – 333/293) =
0.475 V
• If we assume to first order that the absorption
characteristics are unaltered (Eg, diffusion length etc
remaining roughly the same), so that Iph remains the
same, the efficiency decreases at least by this factor.

21. Solar cells efficiency
• The efficiency of a solar cell is one of its most important
characteristics
– Because it allows the device to be assessed economically in
comparison to other energy conversion devices
• The solar cell efficiency refers to the fraction of incident light
energy converted to electrical energy
• For a given spectrum, the conversion efficiency depends on
– the semiconductor material properties & the device structure.
– the effect of ambient conditions i.e. the temperature & high radiation
damage by energy particle (for space application)

22. Solar cells efficiency
• Solar cells efficiency is affected by
– Significant changes in the sun’s spectrum from one
location to another
– In location with a substantial diffuse component in the
spectrum, a device using a higher band-gap semiconductor
is more efficient
– Using solar concentrators to focus the light onto a solar cell
can substantially increase the overall efficiency.

23. Solar cells materials
• Most solar cells are silicon based
– Because Si fabrication is now a mature technology that
enables cost effective devices to be manufactured
• Typical Si based solar cell efficiencies
– about 18% for polycrystalline
– 22-24% for high efficiency single crystal device
• Fig. 14 illustrates how various factors typically reduce
the efficiency of a Si solar cell

24. 100% Incident radiation
 Insufficientphotonenergy
h < Eg

Excessivephotonenergy
Near surfaceEHPrecombination
h > Eg
 Collection efficiency of photons
 Voc  (0.6Eg)/(ekB)

 21%
FF0.85
Overall efficiency
Accounting for various losses of energy in a high efficiency Si
solar cell. Adapted from C. Hu and R. M. White, Solar Cells
(McGraw-Hill Inc, New York, 1983, Figure 3.17, p. 61).
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig. 14

25. Solar cells materials, cont
• Some 25% of solar energy is wasted because of
photon not having sufficient energy to generate
EHPs.
• At the end of the spectrum, high energy photons are
absorbed near the crystal surface & these EHPs
disappear by recombination
• The cell has to absorb as many of the useful photon
as possible
– The photon collection efficiency factor depends on the
particular device structure

26. Passivated Emitter Rear Locally-diffused
• Solar cells fabricated by a pn junction in the same
crystal are called homo-junctions
– Best homo-junction solar cell efficiencies are about
24% for single crystal PERL cells
• PERL or Passivated Emitter Rear Locally-diffused
have a texture surface as in Fig.15
– an array of “inverted pyramid” etched into the surface
to capture the incoming light
– Reflection inside the pyramid allow a second or third
chance for absorption
– After reflection, photon would be entering the
semiconductor at oblique angles or absorbed within Le
of the depletion layer.

27. Light
Oxide
n
p
Inverted pyramid textured surface substantially reduces reflection
losses and increases absorption probability in the device
Le
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig. 15

28. Hetero-junctions
• There are a number of III-V semiconductor alloys
– that can be prepared with different bandgaps but with the
same lattice constant.
• Fig.16 shows a thin AlGaAs layer on GaAs passivates
the surface defect in a homogenous GaAs cell
– AlGaAs has a wider bandgap than GaAs and would allow
most of solar photon to pass through
– AlGaAs window layer overcomes the surface recombination
limitation and improves the cell efficiency (~24%)

29. p-AlGaAs window (< 0.02 m)
p-GaAs
n-GaAs
Passivated GaAs surface
AlGaAs window layer on GaAs passivates the surface states
and thereby increases the low wavelength photogeneration
efficiency
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig. 16

30. • Hetero-junctions between different bandgap III-V
semiconductors that are lattice matched offer the potential of
developing high efficiency solar cells
• The simplest single hetero-junction example is shown in Fig.17
– It consists of a pn-junction using a wider bandgap n-AlGaAs with p-GaAs
– Energetic photons (h>2eV) are absorbed in AlGaAs
– Less energetic photons (1.4<h<2eV) are absorbed in the GaAs
• In more sophisticated cell, the bandgap of AlGaAs is graded
slowly from the surface by varying the composition of AlGaAs
layer

31. Fig. 17

32. Tandem or cascaded cells
• Tandem (cascaded) cells use two or more cells in
tandem or in cascade to increase the absorbed photon
from the incident light as Fig. 18.
– The first cell is made from a wider bandgap material and
only absorbs photons with h > Eg1.
– The second cell absorbs photons that pass the first cell and
have h > Eg2.
• The whole structure can be grown within a single
crystal by using lattice matched crystalline layers
leading to a monolithic tandem cell.

33. Tandem cells
• Light concentrators are used to further increase the
efficiency of tandem cell.
• A GaAs-GaSb tandem cell operating under a 100-sun
condition have exhibited an efficiency of about 34%
– 100 times of ordinary sunlight
• Tandem cells have been used in thin film a-Si:H
(amorphous hydrogenated amorphous Si) pin solar
cells to obtain efficiencies up to 12%
– Tandem cells have a-Si:H & a-Si:Ge:H cells are easily
fabricated in large areas.

34. np
Cell 1 (Eg1) Cell 2 (Eg2 < Eg1)
n p
Connecting region.
A tandem cell. Cell 1 has a wider bandgap and absorbs energetic
photons with h> Eg1. Cell 2 absorbs photons that pass cell 1 and
have h> Eg2.
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
Fig. 18