This document discusses key parameters of solar cells such as open circuit voltage (Voc), short circuit current (Isc), fill factor (FF), and efficiency. It describes how these parameters are affected by factors like series resistance (Rs), shunt resistance (Rsh), and quantum efficiency. Voc is the maximum voltage produced at zero current, while Isc is the maximum current at zero voltage. FF accounts for non-idealities and is used to calculate the maximum power point. Rs and Rsh are parasitic resistances that lower FF. Quantum efficiency measures the number of carriers collected per photon over absorption and reflects losses from reflection and recombination.

1. SOLAR CELL CHARACTERISTICS
• By 17MSE004
17MSE007
17MSE009
17MSE014
M.TECH ENERGY SYSTEMS
PANDIT DEENDAYAL PETROLEUM UNIVERSITY
18 August 2018SOLAR CELL PARAMETERS
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2. Basic Structure of a Solar Cell

3. KEY PARAMETERS
• Open Circuit Voltage Voc
• Short Circuit Current Isc
• Shunt Resistance
• Series Resistance
• Internal quantum efficiency
• External quantum efficiency

4. SOLAR CELL – A DIODE
A solar cell is a diode and hence an IV curve of a solar cell under dark
conditions will look similar to that of a diode.
When illuminated, the photons interact with the material to generate electron
hole pairs.

5. STANDARD TEST CONDITIONS
• Temperature = 25 ˚C
• Important device characteristics can be obtained from the I-V
measurements.

6. SOLAR SIMULATOR

7. OPEN CIRCUIT VOLTAGE VOC (V)
• In an ideal solar cell, Voc is independent of the illumination intensity.
• Maximum voltage generated across the terminals of a solar cell when they
are kept open i.e. I=0
• The open circuit voltage depends on the light generated current and the
reverse saturation current
• Material having larger band gap have higher Voc .The band gap of silicon
is 1.1 eV. Therefore maximum possible Voc is 1.1 ev .

8. SHORT CIRCUIT CURRENT ISC
• Short circuit current is the maximum current produced by a solar cell when its
terminal are short circuited.
• When a photon is absorbed in a solar cells it generates an electron-hole pair which
is separated by a junction and then transported to the external circuit.
• For maximum short circuit current, we have to assume that there is no
recombination in the material .
• A photon is required to possess energy higher than the band gap energy of the
material in order to be absorbed.
• A material with a large band gap will absorb less number of photons as compared to
the material with low band gap.
• Therefore short circuit current will increase with decrease in the band gap.

9. MAXIMUM POWER
• Draw a rectangle with the
origin, VOC and ISC as the 3
corners. The 4th corner will
give the maximum
theoretical power, PT.
• From the origin, draw a line
passing through the
maximum theoretical power,
PT. This is the load line
The point where the load
line crosses the I-V curve is
the maximum power point,
PMAX for the solar cell, for a
given load, with maximum
current and maximum
voltage.

10. CALCULATE THE EFFICIENCY &PEAK POWER OF A SI
SOLAR CELLS OPERATING AT 27˚CWITH A SHORT
CIRCUIT CURRENT OF 2.2 A& OPERATING UNDER
STANDARD ILLUMINATION OF 1000W/M².THE AREA OF
SOLAR CELLS IS ABOUT 100 CM²
Solution
= 0.616 v

11. Consider the FF of the solar cells to be 0.75 or 75 %
The efficiency is given by
= 0.616*2.2*0.75/ 1000*100*10^-4
= 0.10164
= 10.16%
The peak power in this case is given as
Pmax = voc * Isc *FF
= 1.01 W

12. PARASITIC RESISTANCE

13. CHARACTERISTIC RESISTANCE
• The characteristic resistance of a solar cell is the output resistance of the solar cell at its maximum power point.
• If the resistance of the load is equal to the characteristic resistance of the solar cell, then the maximum power is
transferred to the load and the solar cell operates at its maximum power point.
• The value of this resistance can be approximated by
• 𝑹 𝒄𝒉 =
𝑽𝒐𝒄
𝑰𝒔𝒉

14. PARASITIC RESISTANCES
• Series resistance Rs of a PV module represents resistances in cell solder bonds,
emitter and base regions, cell metallization, cell interconnect Bus bars and
resistances in junction box terminations.
• The shunt resistance, Rsh, represents any parallel high-conductivity paths (shunts)
across the solar cell p-n junction or on the cell edges . These are due to crystal
damage and impurities in and near the junction and give rise to the shunt current,
Ish.
• For a good Fill Factor we want Rs as low as possible and Rsh as high as possible.

15. SERIES RESISTANCE

16. • It is, therefore, evident that a small increase in Rs can be
detrimental to the performance of PV modules due to
the power loss. Dark current–voltage (I–V) measurements
can be used to quantitatively evaluate increases in Rs.
These measurements are also sensitive to changes in
module shunt resistance and other cell parameters.
• 𝑃′ 𝑀𝑃 = 𝑃 𝑀𝑃 1 − 𝑟𝑠
• Also, since the open circuit voltage and short circuit
current are not affected:
• 𝐹𝐹′
= 𝐹𝐹(1 − 𝑟𝑠)
• A straight-forward method of estimating the series
resistance from a solar cell is to find the slope of the IV
curve at the open-circuit voltage point
EFFECT OF SERIES RESISTANCE

17. SHUNT RESISTANCE

18. EFFECT OF SHUNT RESISTANCE
• Low shunt resistance causes power losses in solar cells by providing an alternate current
path for the light-generated current. Such a diversion reduces the amount of current
flowing through the solar cell junction and reduces the voltage from the solar cell.
• The effect of a shunt resistance is particularly severe at low light levels, since there will be
less light-generated current.at lower voltages where the effective resistance of the solar cell
is high, the impact of a resistance in parallel is large.
• 𝑃′ 𝑀𝑃 = 𝑃 𝑀𝑃 1 −
1
𝑟 𝑠ℎ
• Also, since the open circuit voltage and short circuit current are not affected:
• 𝐹𝐹′ = 𝐹𝐹(1 −
1
𝑟 𝑠ℎ
)

19. IMPACT OF SERIES AND SHUNT
RESISTANCES
• In the presence of both series and shunt resistances, the I-V curve of the solar cell
is given by;
• 𝐼 = 𝐼𝐿 − 𝐼 𝑜 exp
𝑞 𝑉+𝐼𝑅𝑠
𝑛𝑘𝑡
−
𝑉+𝐼𝑅𝑠
𝑅𝑠ℎ
• The overall fill factor FF is
• 𝐹𝐹′ = 𝐹𝐹(1 − 𝑟𝑠)(1 −
1
𝑟 𝑠ℎ
)

20. TWO DIODE MODEL
• From Fig it is clear that the shunt current, Ish, detracts from the current output and the potential
drop across Rs reduces the voltage output of the solar cell. The influence of Rs and Rsh on the I–V
characteristics can be determined by using
• Eq.
• 𝐼 = 𝐼𝐿 − 𝐼 𝑜 exp
𝑞 𝑉+𝐼𝑅𝑠
𝑛𝑘𝑡
−
𝑉+𝐼𝑅𝑠
𝑅𝑠ℎ
• In this study, all simulated I–V characteristics were generated using PV simulation software, PVSIM
This software uses the two-diode model and calculates I–V characteristics based on typical solar
cell parameters. The simulations were done using 1000 W/m2 irradiance and 25 C cell
temperature.

21. MEASURING PARASITIC
RESISTANCES
• A straight-forward method of estimating the series resistance from a solar cell is to
find the slope of the IV curve at the open-circuit voltage point
• A straight-forward method of estimating the shunt resistance from a solar cell is to
find the slope of the IV curve at the short circuit current point
• This, however, does not represent the true values and only gives a rough indication
of respective resistance values.

22. MEASURING PARASITIC
RESISTANCES PRACTICALLY
• Rs can be determined by measuring I–V curves at different light intensities from a line
drawn through points corresponding to a fixed current below the respective Isc on each
curve. Rs is then obtained from the slope of this curve, with Rs = DV/DI. This result
generally gives good results and is independent of Io, n and Rsh
• The system used is a non-intrusive technique that measures the individual cell shunt
resistances of cells in encapsulated modules
• In this system, a variable power supply is used to bring the illuminated module to zero bias.
At this condition, a small AC signal is applied to the module, the only conduction path
being through the shunt resistances of the individual cells. The cells are then sequentially
shaded each time ensuring the DC supply remains equal to the Voc of the module. The
magnitude of the AC signal when the cells are sequentially shaded is directly proportional
to the conductance of the module in the dark i.e., the shunt current.

23. QUANTUM EFFICIENCY
OF SOLAR CELL

24. WHAT IS QUANTUM EFFICIENCY?
•
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑟𝑖𝑒𝑟𝑠 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑒𝑑 𝑏𝑦 𝑠𝑜𝑙𝑎𝑟 𝑐𝑒𝑙𝑙
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛𝑠 𝑜𝑓 𝑎 𝑔𝑖𝑣𝑒𝑛 𝑒𝑛𝑒𝑟𝑔𝑦 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑜𝑛 𝑠𝑜𝑙𝑎𝑟 𝑐𝑒𝑙𝑙
• Function of Wavelength(λ) or Energy(E).
• All photons of certain wavelength are absorbed → efficiency is
unity of that wavelength.
• For energy below wavelength → zero.
18 August 2018SOLAR CELL PARAMETERS
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25. QUANTUM EFFICIENCY
External Quantum
Efficiency(EQE)
• EQE =
𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝑠𝑒𝑐
𝑃ℎ𝑜𝑡𝑜𝑛𝑠 𝑠𝑒𝑐
=
𝐶𝑢𝑟𝑟𝑒𝑛𝑡/𝑐ℎ𝑎𝑟𝑔𝑒 𝑜𝑓 𝑜𝑛𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛
𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑤𝑒𝑟 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛𝑠/𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑓 𝑜𝑛𝑒 𝑝ℎ𝑜𝑡𝑜𝑛
• Effect of optical losses
→ Transmission
→ Reflection
Internal Quantum
Efficiency(IQE)
• IQE =
𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝑠𝑒𝑐
𝐴𝑏𝑠𝑜𝑟𝑏𝑒𝑑 𝑃ℎ𝑜𝑡𝑜𝑛𝑠 𝑠𝑒𝑐
=
𝐸𝑄𝐸
1−𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
• Effect of collection probability.
→ charge recombination
18 August 2018SOLAR CELL PARAMETERS
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26. QUANTUM EFFICIENCY
External Quantum
Efficiency(EQE)
• By surface texturing this can be
improved.
• For organic solar cells efficiency is high.
Internal Quantum
Efficiency(IQE)
• after optical losses, absorbed photons
which can generate collectable carriers.
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27. 18 August 2018SOLAR CELL PARAMETERS
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• Ideally square
shape.
• Reduced due to
 recombination
effects
 Collection
probability

28. In blue portion
→ front surface recombination affects the efficiency.
→ due to surface passivation absorption of light is high.
 In green portion
→ absorption in bulk of solar cell.
→ low diffusion length will affect the collection probability
 Can be viewed as the collection probability due to generation profile
of single wavelength, integrated over device thickness and
normalized to incident number of photons.
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29. QUANTUM EFFICIENCY
•
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑜𝑢𝑡𝑝𝑢𝑡 𝑐𝑢𝑟𝑟𝑒𝑛𝑡(𝑁𝑒)
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛𝑠 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑙𝑖𝑔ℎ𝑡 𝑡ℎ𝑎𝑡 ℎ𝑖𝑡𝑠 𝑡ℎ𝑒 𝑑𝑖𝑜𝑑𝑒(𝑁𝑝)
• QE =
𝑁 𝑒
𝑁 𝑝
• First step is to measuring a laser with both photo diode and a power meter to
obtain 𝑁 𝑒 and 𝑁 𝑝
• Two methods
1) Using Power Meter
2) Using Radiation Pressure
18 August 2018SOLAR CELL PARAMETERS
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30. USING POWER METER
• Aligned through the
Faraday isolator
• HWP change the amounts
of light being transmitted
and reflected by the PBS.
• Using HWP power of the
reflected light coming from
the PBS can be adjusted.
• aligned onto a photo diode
or power meter to be
measured.
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31. 18 August 2018SOLAR CELL PARAMETERS
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• First step required was to measure the photo diode's output
without being exposed to any laser light → Vdark
• Then the laser light being reflected by both polarizing beam splitters is aligned
onto the photo diode
• With the help of HWP and PBS → power is minimized.
• At this minimized power voltage is measured.→ Vmeasured
• The power meter is inserted directly in front of the photo diode to measure
the power of the laser at the same point.
• Then HWP and PBS adjust to increase the power and readings are taken.
• Then efficiency is calculated at each power level.
• Until the saturation voltage of photo diode is reached.

32. 18 August 2018SOLAR CELL PARAMETERS
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I =
V Measured−V Dark
𝑅
Ne=
𝐼
𝑞
Np=
𝑃
ℎ∗𝑣
P = power
v = frequency
h = plank’s constant.

33. USING RADIATION PRESSURE
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• Aligned through the Faraday isolator
• HWP change the amounts of light being transmitted and reflected
by the PBS.
• Using HWP power of the reflected light coming from the PBS can be
adjusted.
• Several focusing lenses were also placed to control the size of the
laser beam.
• Another component of interest is the 90 % beam splitter used to
direct the beam toward the interferometer.
• This splitter allows 10 % of incident light to be transmitted.
• 10 % for symmetric port
• 90 % towards the vacuum chamber in order to reduced the noise.

35. 18 August 2018SOLAR CELL PARAMETERS
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I =
V Measured−V Dark
𝑅
Ne=
𝐼
𝑞
F =
N p∗2∗h∗ν
𝑐
F = m∗ω2∗X
dX=
λ
2∗π∗V0
* dV PD
V0= Vmax- Vmin
P = power
v = frequency
h = plank’s constant
Michelson interferometer

36. SPECTRAL RESPONSIVITY(Rλ)
• How much current comes out per incoming photon of given energy and
wavelength.
• Unit of Rλ =
𝑎𝑚𝑝𝑒𝑟𝑒𝑠
𝑤𝑎𝑡𝑡
• With the help of spectral responsivity we can find quantum efficiency of solar cell.
• For that,
η =
Rλ
λ
×
ℎ𝑐
𝑒
≈
Rλ
λ
× (1240 W*nm/A)
18 August 2018SOLAR CELL PARAMETERS
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37. • PROBLEM : A photodiode is made with p-type Si doped with boron atoms/m and n-
type Si phosphorus with As atoms/m . The width of the p- side is 1 m. For Si, . The
carrier concentration of Si at 300 K is given by . The index of refraction of Si is 3.5 and
absorption coefficient is m . Calculate the quantum efficiency of the photodiode at 300
• SOLUTION:
18 August 2018SOLAR CELL PARAMETERS
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VB =
𝑘∗𝑇∗𝑁𝑑∗𝑁𝑎
q∗ni2 = 0.369 v
W =
2∗𝜖0
∗𝑘
𝑞
∗
𝑁 𝑎
+𝑁𝑑
𝑁 𝑎
∗𝑁𝑑
∗ 𝑉𝐵 = 0.27 µm
xp =
𝑁 𝑑
𝑁 𝑑
+𝑁𝑎
* W = 0.03 µm
xn= 0.97 µm
R=
𝑛−1 2
𝑛+1 2 = 0.31
So 0.31 times power is reflected a0nd 0.69 times power
is transmitted.
optical power which can reaches to depletion region is
0.69*Po∗ 𝑒−𝑎𝑥
= 0.69*Po∗ 𝑒−0.97
= 0.26Po
The power which is converted to electron-hole pair
0.26Po∗ (1 − 𝑒−0.03
) = 0.008Po
which implies that the efficiency of the device is less
than 1%.

38. THANK YOU
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