Electromagnetic Properties of

Materials
Lecture 7
Part 2
1
Contents

1- Diffusion length
2- Absorption depth
3- Solar cell efficiency
4- Solar cell types
5- Solar cell connection & Implementation

2
 Review
A = 1 − exp(− b ( ) * d )
We want to absorb all photons that can generate electron-
hole pairs in the absorber (N-type, depletion region, and P-
type). Thus, we need a very thick absorber. But, if the solar
cell is very thick, the chance of recombination is very high
as well as the high cost. The optimal thickness of the solar
cell is a trade-off (‫ )مفاضله‬between the having high
absorption and generating more free electrons without
recombination. Generated power is proportional to the
carrier concentration (free electrons).

A higher light absorption can be achieved with a

thinner PV cell by using light trapping techniques:
Lambertian light scattering or using an interlayer
with refractive index with a value between 𝒏𝟎 (air)
and 𝒏𝟐 (silicon).

What about
recombination? 3
Diffusion Length ( ‫)طول االنتشار‬
The diffusion length (micrometer) of a carrier type in a material can be defined as the
average distance that an excited carrier will travel before recombining. The diffusion
length can be defined as follows:

𝐿𝐷 = 𝐷𝜏 A B C
N-type N-type N-type
where D is the diffusion coefficient (cm2/sec ) Depletion Depletion Depletion
and 𝝉 is the lifetime of the excited carrier (𝝁𝒔).
The diffusion coefficient can be written as: P-type P-type P-type

 k BT 𝐿𝐷
D=
q
D T  eff 
where μ is the charge carrier mobility, 𝑲𝑩
is the Boltzmann constant, T is the
temperature, and q is the charge of an
electron. It should be noted that the mobility
of the electron isn’t equal the mobility of
hole. Thus, diffusion length of electron 4
differs the diffusion length of hole.
Diffusion Length ( ‫)طول االنتشار‬
When the minority carrier diffusion length is smaller than the thickness of the absorber
(P type or N type), there is a high chance that many of the electrons generated deep in the
absorber (P type or N type) for recombination. Thus, these electrons will not reach the
depletion region and not collected in the N type layer. As a result, it makes no sense to
have a thick absorber layer when a large amount of photogenerated carriers cannot be
collected due to the recombination. It should be noted that the higher the cell thickness,
the higher the light absorbed. But, a large amount of photogenerated carriers cannot be
collected due to the recombination.

The thickness of the absorber layer (P type or N type) has to be

smaller than the minority carrier diffusion length
The electron diffusion length is generally in the range of 100 to 300
𝝁𝒎. That’s why a practical crystalline-silicon solar has the P type
layer with a thickness 100 or 200 𝝁𝒎. Due to the hole mobility is
less than electron mobility, the hole diffusion length L is about 1.3
𝝁𝒎. Thus, the N type layer thickness is 1 𝝁𝒎.
As a result, the N- layer is the upper and its thickness is less than 5
that of the P-layer.
 Absorption Depth
Absorption Depth: it describes how deeply light penetrate into a semiconductor before being
absorbed. is given by the inverse of the absorption coefficient (1/𝜶𝒃 ).
From this figure, a higher absorption coefficient means lower absorption depth and thus the light is
absorbed near to the surface of silicon (short distance).
While a smaller absorption coefficient means a higher absorption depth and thus the light is
absorbed near to the bottom (long distance).
Once the photon is absorbed, an electron –hole pair is generated.
Sun light

6
Higher absorption coefficient Lower absorption depth
 Solar cell efficiency
Vmp I mp
Po Po J sc  Voc  FF FF ( Fill Factor) =
= = = Voc I sc
Pin Po + Plosses Po + Plosses 
For higher efficiency: (a) Higher Voc
(b) Higher Jsc, and © Less losses

290* 294 FF is the ratio of maximum power

FF = = 0.75
363*313.6 generated to the product of open circuit
voltage and short circuit current. 7
Typical values are between 0.7 and 0.8.
 Solar cell efficiency
J sc  Voc  FF kT  J SC N D eff  
= Voc  ln  
Po + Plosses  
q  qni d  
2

𝑱𝑺𝑪 is the short circuit current density (I/A), 𝑵𝑫 is the donor concentration, and 𝒏𝒊 is the
intrinsic carrier concentration. With reduction the layer thickness and increasing the
minority life time, the open circuit voltage will be higher.

J sc = qG ( Ln + L p )
Where G: the
generation rate, 𝑳𝒏 and
𝑳𝒑 are the electron and
hole diffusion lengths. I S .C = J S .C A 

This figure shows that the efficiency is a function in the solar cell 8
thickness. It is clear that the optimum thickness around 50 – 100 𝝁𝒎.
Solar Cell Types
PV cells can be made from several processes or technologies. They all do the same job :
produce electricity from sunlight.
Cell material Efficiency Area required to generate
1 kW peak power
Monocrystalline silicon 15 –18% 7–9 m2
Polycrystalline silicon 13 –16% 8–11 m2
Thin-film copper indium 7.5 – 9.5% 11–13 m2
diselenide (CIS)
Cadmium telluride 6–9% 14–18 m2
Amorphous silicon 5–8% 16–20 m2

9
Solar cell connection

1 String

Module

2 String
VO.C 36.3
Vcell = = = 0.6 V
N Cell 60
A single solar cell is impractical for most applications because it can produce only
about 0.5 V to 0.6 V. Thus, multiple solar cells are connected in series, it is called
module or panel, to produce high voltage. These modules or panels are
connected in series to produce higher voltage, it is called string. For increased
current capacity, many strings are connected in parallel. 10
Implementation

Charge controller (solar controller): A PV battery Batteries is used for solar

charge controller serves generally to protect the battery energy storage.
against overcharging and deep discharge. It is absolutely
necessary for the efficient operating conditions of the
battery and of the complete PV system. 11
References
No. Reference List
1 “Analysis of Effects of Sun`s Position in the Sky on Solar Radiation and Solar Panel Output Power” IEEE,
2013. DOI: 10.1109/AFRCON.2013.6757768
https://www.sciencedirect.com/science/article/pii/B9780081022849000073
2 Handbook of Organic Materials for Electronic and Photonic Devices (Second Edition) 2019
7 - Hybrid perovskites for device applications
3 SOLAR ELECTRIC POWER - DESIGN GUIDE
https://www.sciencedirect.com/science/article/pii/B9780125249751500112
4 Materials Science of Thin Films (Second Edition) Deposition and Structure 2002, Pages 417-494
Chapter 8 - Epitaxy
Gan Huang1, Kai Wang2 and Christos N. Markides “Efficiency limits of concentrating spectral-splitting hybrid
5 photovoltaic-thermal (PV-T) solar collectors and systems” 2021
Third Generation Photovoltaics
6
Ch 8- “Durable Polymeric Films for Increasing the Performance of Concentrators” T. J. Hebrink, 2011
S. Regmi and S. Adhikary, “Solar energy potential in Kathmandu Valley, Nepal,” Journal of Hydrology and
7
Meteorology, vol. 8, no. 1, pp. 77–82, 2012
Arun Kumar Shrestha,Arati Thapa,and Hima Gautam“Solar Radiation, Air Temperature, Relative Humidity,
8 and Dew Point Study: Damak, Jhapa, Nepal” International Journal of Photoenergy
2019. https://doi.org/10.1155/2019/8369231

12
References
“Physical operation of back-surface-field silicon solar cells”
https://ieeexplore.ieee.org/abstract/document/1478927
9 “Temperature Dependent Photovoltaic (PV) Efficiency and Its Effect on PV Production in the World A Review”
https://www.sciencedirect.com/science/article/pii/S1876610213000829
https://www.youtube.com/watch?v=3SI90fe1MwU&list=PLb7OD10zQUdWgOe1GVsQpGeijgSUfiOfJ&index=6
10
Comprehensive Semiconductor Science and Technology
11
https://www.sciencedirect.com/science/article/pii/B9780444531537001103
A Comprehensive Guide to Solar Energy Systems (Ch 8 Photovoltaics: The Basics)
12
https://www.sciencedirect.com/science/article/pii/B9780128114797000087
https://www.pveducation.org/pvcdrom/characterisation/bulk-lifetime
13
Chapter IA-2 - Semiconductor Materials and Modelling
14
https://www.sciencedirect.com/science/article/pii/B9780123869647000020
15 https://www.youtube.com/watch?v=dERGxS2pYyw
https://www.pveducation.org/pvcdrom/design-of-silicon-cells/surface-recombination

Efficiency Improvement of HIT Solar Cells on p-Type Si Wafers

16 https://www.youtube.com/watch?v=QOZZ2Qy1NAI
https://www.youtube.com/watch?v=MoksY1w8-f0
13
https://www.youtube.com/@pv1xsolarenergyengineering390/videos
14