Electronic Engineering Materials and IC Fabrication [PHT201] Study Material

Lecture 05: Solar Cells

IntroductionThe material here is entirely based on Kasap.

Earlier we discussed light producing devices based on optical properties of semiconductors. These

are LEDs and semiconductor lasers. These devices are pn-junctions with physical structures suited

to their purpose of consuming electrical power and producing radiation of predetermined char-

acteristics like wavelength, linewidth and power. We also saw that device functionality can be

signi�cantly improved by use of semiconductor heteostructures. We now look at another type of

devices, which in a sense do the opposite: absorb radiation and produce electrical power. These

are solar cells.

Radiation and its AbsorptionSolar cells are of great importance because the radiation used to produce power is not man-made,

like the electric power supplied to LEDs and lasers. It comes naturally from the sun and it is

available in abundance in many parts of the world. Thus, solar cells have a grand role to play in

answering the so-called energy question.

I Sun’s radiation

Sun is directly, or indirectly the great source of all available

energy, except perhaps, nuclear energy. Its surface glows

at ∼ 6000 K and can be assumed to radiate like a black-

body at that temperature. Therefore, the energy density,

which reaches the surface of earth is primarily determined

by Planck's blackbody spectrum formula. However, there

is some modi�cation of blackbody radiation due to absorp-

tion in space and in Earth's atmosphere by factors like ozone, water vapour and oxygen. For

instance, the intensity cut-o� on the low wavelength side is determined by UV absorption by

ozone layers and some of the dips (as seen in AM1.5 in the �gure) are due to water and oxygen.

The �gure above shows this [See Fig 6.1 Kasap, 2011]. AMx for x 6= 0 is the radiation intensity

received at surface of Earth on a plane with plane-normal inclined at Sec−1x to the vertical

direction. Thus, AM1 is received vertically at surface of the Earth. AM0 is received at the top

of the atmosphere in the vertical direction.

I Photovoltaic effectGeneration of electrical potential di�erence on exposure to light is known as photovoltaic effect.

An electronic device which achieves generation of power by harnessing this potential di�erence

is called a photovoltaic device. Semiconductor and other (like biological) photovoltaic devices

are known as solar cells.

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Principle and StructureI Principle of Operation

A solar cell is a pn-junction. It absorbs photons in Sun's radiation if they have appropriate

energies. Photon absorption produces electron-hole pairs. The EHP separate due to built-in

�eld around the junction and produce a photocurrent. This current which can be supplied to

an external load. Thus, optical (photonic) energy is converted to electrical energy. The solar

cell acts like a dc power supply, or a battery.

I Structure and details of operationMost of the solar cells in use are made from crystalline silicon (c-Si). Many other materials

including amorphous silicon (a-Si) are also in use. These we discuss later. For the moment we

assume that we are dealing with c-Si solar cell.

Figure on the right shows a schematic of one such cell. The pn-junction has a thin n side (∼) and relatively thicker (∼) p side.

Radiation is incident on the cell from the n side, which is covered

with an anti-reflection coating to enhance the photon energy

received. The electrode on the n side, called finger electrode,

is designed to allow maximum possible radiation to enter the

semiconductor. The p side is covered with the second electrode. Lower wavelength, higher

energy photons are absorbed near the surface and in the n region, medium wavelength photons

in the depletion region around the junction and long wavelength ones in the p region. This is

because the absorption coe�cient is large for higher energy photons and becomes smaller with

decreasing energy. Photons with energies smaller than Eg are not absorbed by the device.

Figure shows the absorption coe�cient of c-Si superposed

on the solar spctrum as recived on the surface of the Earth.

There is no absorption above ∼ 1100 nm, which corre-

sponds to Eg ∼ 1.1 eV. It is clear that a considerable

region of wavelengths carrying ∼ 25% of incident energy

is not absorbed. Also, in the remaining wavelength re-

gion, absorption is not total. Both these factors a�ect cell

conversion e�ciency.

Photons are absorbed in the cell as described above. Ab-

sorption generates EHP in the regions of photon absorp-

tion. Out of all these EHP, only those for which elec-

trons and hole can be �nally separated contribute to cell

function. Which EHP are these? To answer this we have

understand the fundamental role played by the built-in

electric field in the depletion region (width W) around

the junction. This �eld points from n side to p side and

exists only in the region where di�usion carries electrons

from n region (holes from p region) into the p region (respectively, the n region) till any further

net di�usion is stopped by the �eld. There is no �eld in the neutral parts of the n and the pregions.

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This means the following: (i) EHP created within the built-in �eld region are de�nitely sep-

arated by the �eld - electrons drift in the �eld to the n side, and holes to p side. (ii) EHP

created at points such that the minority carrier can di�use before recombination to the edge

of the boundary of the region of built-in �eld are also carried to the other edge. On an average

the minority carriers can be taken to di�use a distance called the minority carrier diffusion

length in the device. This is Lh for the n side and Le for the p side. In general, in c-Si Le > Lh.

This is all the more so because of the higher doping of the n side making a recombination of

the minority hole with electron easier. This is the reason for the structural feature that n side

is much thinner than the p side. From this discussion it is clear (see �gure above) that the

EHP produced in a region of width Lh + W + Le are separated by the built-in �eld.

The separated electrons go into the n region and the holes go into the p region. This transport

of charge carriers makes the p side positive and the n side negative. Moreover the transport of

these carriers under action of the built-in �eld constitutes a current known as the photocurrent,

Iph. It is obvious that the direction of photocurrent is opposite to the conventional diode

current. In the absence of any external load, that is in open circuit condition, there is an equal

opposite diode current, Id, with electrons (hole) owing to p (respectively, n) side as happensin a pn junction diode. In this condition there is a voltage drop Voc across the diode. On the

other hand in the zero-load (short-circuit) condition, there is no voltage across the diode as

well as no diode current and only the photocurrent ows through the outer circuit.

Circuit DescriptionWe can now consider the circuit picture of all these processes.

I Ideal solar cell circuit picture

The �gure on the right shows the conven-

tion (circuit (a)) for V and I. The voltageV is potential of p side relative to n side.

The current is positive in the direction pto n through the pn junction. Since there

is no drop (V = 0) when external load is

zero (circuit (b)) there is no diode current,

that is Id = 0. Thus,

V = 0, Id,sc = 0, I = Isc = −Iph, (Short Circuit)

In open circuit condition diode current must equal photocurrent as they ow in opposite di-

rection and there is no net current in the external load R = ∞. Thus,

V = Voc, I = 0 and Id,oc = Iph, (Open Circuit)

In the working case there is a �nite non-zero load R in the external circuit (circuit (c)). For

this condition we have,

V = −IR, I = Id − Iph, (Working condition, Load R)

Note that cell current I < 0 when the cell supplies power. In all the above cases we also have,

Iph = KL (Photovoltaic e�ect)

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where, K is a constant for a given cell, L is the luminous intensity of light incident on the cell,

and

Id = Io

[Exp

(eVf kT

)− 1], (Diode recti�er equation)

where, Io is the reverse saturation current for the pn junction and f is a factor dependent on

material and detailed geometry of the cell. (For an ideal pn junction f = 1.)

I CharacteristicsSince we have a pn junction we naturally talk of the V − I characteristics of the cell. Also,

as this cell is working as a supply of electrical power (rather than as a simple rectifying pnjunction connected to an external supply) the current which dominates (Iph) is a reverse

current, owing opposite to the conventional diode current. This means that the interesting

characteristics are in the fourth quadrant of the V − I plane.

The �gure shows these characteristics. The `Dark' charac-

teristic is the normal type of forward characteristic. The

other two are for light intensities L and 2L, showing that

the current is proportional to the intensity. The curves

are for a cell with an open circuit voltage Voc just under

0.5 V and a photon current (−Isc) just over 20 mA at light

intensity 2L. Note another important di�erence between

characteristics for the solar cell and for a normal diode:

While there is a unique characteristic for the diode, in case of a solar cell there is a di�erent

characteristic for each value of light intensity incident on the cell. This is to be expected be-

cause in the case of a solar cell light intensity provides a new independent parameter. For a

diode there is no such third parameter: V completely determines I and vice-versa. Also, since

the cell voltage V and cell current I are related by V = −IR, each point on a characteristic

corresponds to a unique load R = −V/I (which is positive as I < 0).

The �gure shows operating point for a cell

with external load R, and the straight lineI = −V/R. The operating point is cho-

sen in order to maximize power delivery

to the load by the cell. The power deliv-

ered is |V′ I′|, the area of the rectangle ofsides V′ on voltage axis and −I′ on cur-

rent axis. The ratio of this area to the

area of rectangle with sides Voc and Isc is called the fill factor, FF. The �ll factor is a measure

of how close the characteristic is to rectangle of dimensions Voc × Isc. Thus, FF is the ratio

of maximum possible power delivered to the load by a cell to the power delivered by an ideal

solar cell with rectangular characteristic of dimensions Voc × Isc.

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I Practical solar cell circuit pictureThe above circuit picture needs some modi�cations for a real solar cell. Surface e�ects, material

properties, features like �nger electrode etc make these modi�cations necessary.

After the electrons in the net current reach the

surface of the n side, they have to �nd the �n-

ger electrodes, which requires movement along the

surface and gives rise to a series resistance,Rs. in

the circuit. Similarly, some of the electrons in the

current may not go through the external resistance

but return to the p side along the device surfaces

normal to the junction. This gives rise to an equiv-

alent parallel resistance Rp (see Fig. 6.9, Kasap).

Generally the e�ect of Rs on degradation of device

performance is much more than that of Rp. The

�gure shows the equivalent circuit of such a real cell. The main e�ect is a pronounced depar-

ture of the characteristic from rectangular shape. This in turn leads to reduction in maximum

power output (see Fig. 6.11, Kasap).

EfficiencyThe e�ciency of a solar cell is generally de�ned as the percent fraction of total energy received

from the sun which is converted to electrical energy elivered to the external load. There are several

factors which determine and a�ect the e�ciency.

I Factors affecting / ways to increase efficiency

1. The �rst determining factor is the fraction of incident radiation that is actually absorbed

by the device. This is largely determined by the quality of anti-re ection coating, surface

characteristics and geometry and the material of the cell. For example as the �gure on

p.2 shows for c-Si, the coe�cient of absorption is not 1 and varies signi�cantly, becoming

zero at wavelengths corresponding to photons of energies smaller than Eg. For a c-Si solar

cell about 26% of solar energy is lost due to size of energy gap. This gives a factor of 0.74in e�ciency.

2. Another important e�ciency limiting factor (∼ 0.59 for c-Si cell) is photon absorption

at the surface followed by defect induce EHP recombination. This a�ects very short

wavelength, high energy photons.

3. Collection of generated EHP is not total and gives a factor of ∼ 0.95 for the c-Si cell.

4. Fill factor FF is never 1 (∼ 0.85 for c-Si cell) as the characteristics of a real device depart

from rectangular shape.

These limitations give a conversion e�ciency of about 21% for the c-Si cell. Apart from these

increase in operating temperature can decrease the e�ciency. For silicon cell this decrease is

about 0.49% per oC. The quality of anti-re ection coating also a�ects the amount of radiation

actually entering the device.

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E�ciency can be

increased by tex-

turing the surface

by dents shaped

like inverted pyra-

mids to make some

of the re ected ra-

diation to again

fall on the sur-

face of the de-

ice. Absorption of

lower than Eg en-

ergy photons can

be achieved by cells in tandem with the second cell made of lower Eg material. An exam-

ple is a GaIn (Eg = 1.95 eV) − GaAs (Eg = 1.42 eV) − Ge (Eg = 0.66 eV) cell on a Gesubstrate with e�ciency of ∼ 32%. The table lists info on a solar cells of di�erent type. The

PERL c-Si cell is one in which front surface is passivated with high quality oxide and rear

surface is locally di�used near metal contacts to minimize surface EHP recombination. (For

details, see this paper and this website.) It is also known now that a-Si cells can be fabri-

cated using thin-�lm technology. These require less material and a-Si has better absorption

characteristics for solar radiation. Such cells also have a favourable mass per unit power �gure

important for space applications where weight is an important consideration.

Jul 2013

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