Solar Cells

• Silicon solar cells ( Mono & polycrystalline)

• Thin Film solar cells

• Photoelectrochemical cells

• Dye sensitized solar cells

Solar cell structure ( Crystalline silicone solar cell)

The basic steps in the operation of a solar cell are:

•the generation of carriers; electron –hole pairs

•the collection of the light-generated carries to produce a current;

•the generation of a potential difference across the solar cell; and

•the dissipation of power in the load and in parasitic resistances

Photodiode Operation

holes

electrons

When light is incident , electron –hole pairs are generated .The electrons move towards the n-side and holes move towards the p side-setting up a current .

An illuminated p-n junction

IF

Photodiode operation

• Electron-hole pairs are generated when radiation hits the junction region

• Electrons move towards the n-region and holes towards the p-region

• The excess carriers near the junction produce a current IP which adds to the thermally generated current I0

• I0 is the current flowing (reverse) when there is no illumination and is called the dark current

• On illumination, the reverse current becomes IP+ I0

• IP is related to power P of the incident radiation

hc

e

hcn

ne

P

I

enI

hcnhfnP

P

iPP

iPP

PP

P= power of the radiation

nP=no. of photons incident per second on the diode

niP = no. of electron-hole pairs created per second

ζ = the quantum yield

IP is proportional to the power of radiation at a particular wavelength

VR VF

IR

IF

I-V characteristics of a photodiode

Photocurrent

Dark currentPhotocurrent is directly proportional to the illumination

Power is being produced

P= -IVPhotocurrent varies directly with illumination levels

Equivalent Circuit • A solar cell is represented by the circuit below• The effect of light is represented by the constant-current generator

across a normal diode D• RL is the load resistance• The diode current and voltage are related by

• When the diode is open circuited ( disconnect RL), illumination makes

I = IP

Current generator

RL

0

00

1ln

ln)ln(

I

I

e

kTV

kT

eVIII

• Then, the voltage ( called the Open Circuit Voltage VOC ) is

• VOC increases with the illumination

0

1lnI

I

e

kTV POC

VOC

With the load resistance RL connected , we have

I = IP - I L where IL = V / RL

And

Which is less then VOC .

For RL = 0 ( short circuited ) , the diode behaves as a current generator with IL = IP and V=0. This is the maximum current that a solar cell can produce and is called the short circuit current

0

1lnI

II

e

kTV LP

The I-V characteristic of an ideal solar cell are given by the Shockley solar cell equation

Fig. below shows a plot of above equation

)1(0 kT

eV

P eIII

)1(0 kT

eV

P eIII

For ideal case the short circuit current Isc = IP

ISC

VOC

Pmax

Power produced by a cell

• The power P = IV

• The cell produces the maximum power Pmax at a voltage Vm (<Voc) and a current Im (<Isc) : Their product is maximum

• Fill factor (FF) : The fill factor of a solar cell is defined by

• Efficiency η: The efficiency of a solar is defined as

scocsc

mm

I

P

VI

VIFF max

FFP

VI

P

VI

in

ocsc

in

mmPP

in max

Where Pin is the input power ( solar radiation)

Fill factor

• The FF for an ideal solar cell is given by the following empirical equation

kT

Vv

whereV

vvFF

ococ

oc

ococ

1

)72.0ln(0

Practical Solar Cells• The equivalent circuit for a practical solar cell is shown

below

D2

RP

RS

A two diode model is used. The second diode has an ideality factor of 2 . There is a resistance RP ( called the shunt resistance ) in parallel and another resistance Rs( called the series resistance ) in series . Then the I-V characteristics are given by

P

sssP R

IRV

kT

IRVI

kT

IRVIII

12

exp1exp 0201

D1

The effect of series resistance on the FF is given by

FF = FF0 (1- r s ) where rs = Rs I sc / Voc

The antireflection coatingA thin dielectric layer coated on the top surface of the solar cell reduces the reflection of light

22

22

)1(

)1(

kn

knR

The reflection coefficient for silicon for light incident from air is given by

Where n and k are the refractive index and extinction coefficient of the semiconductor respectively.

The extinction coefficient is related to the absorption coefficient α as

nk

4

The reflection coefficient of an anti reflection coating sandwiched between two media - E.g. air of refractive index n0 and a semiconductor with refractive index nsc is given by

dnnn

nnr

nn

nnr

whererrrr

rrrrR

ararsc

arscsc

ar

ar

scsc

scsc

2;;

cos21

2cos2

0

00

022

0

022

0

nar = refractive index of the coating , n0= refractive index of air, nsc= refractive index of the semiconductor, d= thickness of the coating.

The transmission coefficient T = 1-R ( neglecting absorption).

R becomes negligible when

andnnn

dararar 4

5,

4

3,

4

scar nnn 0

An AR coating of thickness d= λ/4nar is a called a quarter wave coating since the wavelength of light in the coating is ¼ of the incoming wave.

Effect of AR coating on the reflection coefficient for Silicon

Efficiency of solar cells and the semiconductor

band gap

The band gap of the semiconductor material is the most important parameter in determining the conversion efficiency of a solar cell since only the photons with energy hν> Eg can create an electron-hole pair.

The maximum theoretical efficiency is given by

g

df

AP

E

P

IEe

in

g

in

incg

)()(

1

max

This gives a maximum efficiency of 48% at Eg ~1.1 eV which is close to that of silicon.- ideal case with FF=1. The actual maximum theoretical efficiency turns out to be ~ 30%.

Solar cells made from materials with band gaps between 1.0 and 1.6 eV have almost sane maximum theoretical efficiencies.

f(λ) is the incident photon flux (no. of photons per unit area per second per wavelength)

Factors affecting the annual performance of PV modules*

• Cumulative solar irradiance

• Operating temperature

• Dependence of maximum power point voltage (Vm) on irradiance level

• Soiling

• Variation in solar spectrum

• Optical losses at a high angle of incidence

*Photovoltaics Handbook; Markvart & castaner

SemiConductors

Silicon and Germanium

• Solid state electronics arises from the unique properties of silicon and germanium, each of which has four valence electrons and which form crystal lattices in which substituted atoms (dopants) can dramatically change the electrical properties.

Silicon

• In solid state electronics, either pure silicon or germanium may be used as the intrinsic semiconductor which forms the starting point for fabrication. Each has four valence electrons, but germanium will at a given temperature have more free electrons and a higher conductivity. Silicon is by far the more widely used semiconductor for electronics, partly because it can be used at much higher temperatures than germanium.

Silicon Lattice

• Silicon atoms form covalent bonds and can crystallize into a regular lattice. The illustration below is a simplified sketch; the actual crystal structure of silicon is a diamond lattice. This crystal is called an intrinsic semiconductor and can conduct a small amount of current

• The main point here is that a silicon atom has four electrons which it can share in covalent bonds with its neighbors.

Valence Electrons

• The electrons in the outermost shell of an atom are called valence electrons; they dictate the nature of the chemical reactions of the atom and largely determine the electrical nature of solid matter.

The band theory

• The electrical properties of matter are pictured in the band theory of solids in terms of how much energy it takes to free a valence electron.

Band theory of solids

• A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands.

• Crucial to the conduction process is whether or not there are electrons in the conduction band. In insulators the electrons in the valence band are separated by a large gap from the conduction band, in conductors like metals the valence band overlaps the conduction band, and in semiconductors there is a small enough gap between the valence and conduction bands that thermal or other excitations can bridge the gap. With such a small gap, the presence of a small percentage of a doping material can increase conductivity dramatically.

• An important parameter in the band theory is the Fermi level, the top of the available electron energy levels at low temperatures. The position of the Fermi level with the relation to the conduction band is a crucial factor in determining electrical properties.

Energy Bands for Solids

Energy bands comments

Insulator energy bands

• Most solid substances are insulators, and in terms of the band theory of solids this implies that there is a large forbidden gap between the energies of the valence electrons and the energy at which the electrons can move freely through the material (the conduction band).

Glass

• Glass is an insulating material which may be transparent to visible light for reasons closely correlated with its nature as an electrical insulator. The visible light photons do not have enough quantum energy to bridge the band gap and get the electrons up to an available energy level in the conduction band. The visible properties of glass can also give some insight into the effects of "doping" on the properties of solids. A very small percentage of impurity atoms in the glass can give it color by providing specific available energy levels which absorb certain colors of visible light. The ruby mineral (corundum) is aluminum oxide with a small amount (about 0.05%) of chromium which gives it its characteristic pink or red color by absorbing green and blue light.

Semi conducting

• While the doping of insulators can dramatically change their optical properties, it is not enough to overcome the large band gap to make them good conductors of electricity. However, the doping of semiconductors has a much more dramatic effect on their electrical conductivity and is the basis for solid state electronics.

Semiconductor Energy Bands

• For intrinsic semiconductors like silicon and germanium, the Fermi level is essentially halfway between the valence and conduction bands. Although no conduction occurs at 0 K, at higher temperatures a finite number of electrons can reach the conduction band and provide some current. In doped semiconductors, extra energy levels are added.

Conductor energy bands

• In terms of the band theory of solids, metals are unique as good conductors of electricity. This can be seen to be a result of their valence electrons being essentially free. In the band theory, this is depicted as an overlap of the valence band and the conduction band so that at least a fraction of the valence electrons can move through the material.

Silicon energy bands

• At finite temperatures, the number of electrons which reach the conduction band and contribute to current can be modeled by the Fermi function. That current is small compared to that in doped semiconductors under the same conditions.

Germanium energy bands

The Doping of Semiconductors

• The addition of a small percentage of foreign atoms in the regular crystal lattice of silicon or germanium produces dramatic changes in their electrical properties, producing n-type and p-type semiconductors.

• Impurity atom with 5 valence electrons produce n-type semiconductors by contributing extra electrons.

Impurity atoms with 3 valence electrons produce p-type semiconductors by

producing a "hole" or electron deficiency.

*antimoni, stibiumSb, atomic number 51metal

n- and p- Type Semiconductors

N-type semi conductors

• The addition of pentavalent impurities such as antimony, arsenic or phosphorous contributes free electrons, greatly increasing the conductivity of the intrinsic semiconductor.

http://hyperphysics.phy-astr.gsu.edu/Hbase/solids/dsem.html

P-Type Semiconductor

• The addition of trivalent impurities such as boron, aluminum or gallium to an intrinsic semiconductor creates deficiencies of valence electrons,called "holes".

http://hyperphysics.phy-astr.gsu.edu/Hbase/solids/dsem.html

Bands for Doped Semiconductors

• The application of band theory to n-type and p-type semiconductors shows that extra levels have been added by the impurities. In n-type material there are electron energy levels near the top of the band gap so that they can be easily excited into the conduction band. In p-type material, extra holes in the band gap allow excitation of valence band electrons, leaving mobile holes in the valence band.

P-N Junction

• One of the crucial keys to solid state electronics is the nature of the P-N junction. When p-type and n-type materials are placed in contact with each other, the junction behaves very differently than either type of material alone.

• Specifically, current will flow readily in one direction (forward biased) but not in the other (reverse biased), creating the basic diode. This non-reversing behavior arises from the nature of the charge transport process in the two types of materials.

• Near the junction, electrons diffuse across to combine with holes, creating a "depletion region".

Depletion Region

• When a p-n junction is formed, some of the free electrons in the n-region diffuse across the junction and combine with holes to form negative ions. In so doing they leave behind positive ions at the donor impurity sites.

• Filling a hole makes a negative ion and leaves behind a positive ion on the n-side. A space charge builds up, creating a depletion region.

Bias effect on electrons in depletion zone

• Equilibrium of junction• Coulomb force from ions

prevents further migration across the p-n junction. The electrons which had migrated across from the N to the P region in the forming of the depletion layer have now reached equilibrium. Other electrons from the N region cannot migrate because hey are repelled by the negative ions in the P region and attracted by the positive ions in the N region.

Reverse bias

• An applied voltage with the indicated polarity further impedes the flow of electrons across the junction. For conduction in the device, electrons from the N region must move to the junction and combine with holes in the P region. A reverse voltage drives the electrons away from the junction, preventing conduction.

Forward bias

• An applied voltage in the forward direction as indicated assists electrons in overcoming the coulomb barrier of the space charge in depletion region. Electrons will flow with very small resistance in the forward direction.

Reverse Biased P-N Junction

• The application of a reverse voltage to the p-n junction will cause a transient current to flow as both electrons and holes are pulled away from the junction.

Reverse bias

• When the potential formed by the widened depletion layer equals the applied voltage, the current will cease except for the small thermal current.

Reverse bias

The P-N Junction Diode

• The nature of the p-n junction is that it will conduct current in the forward direction but not in the reverse direction. It is therefore a basic tool for rectification in the building of DC power supplies.

Forward bias

Forward Biased P-N Junction

• Forward biasing the p-n junction drives holes to the junction from the p-type material and electrons to the junction from the n-type material. At the junction the electrons and holes combine so that a continuous current can be maintained.

Fermi Level

• "Fermi level" is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. This concept comes from Fermi-Dirac statistics. Electrons are fermions and by the Pauli exclusion principle cannot exist in identical energy states. So at absolute zero they pack into the lowest available energy states and build up a "Fermi sea" of electron energy states.

• The Fermi level is the surface of that sea at absolute zero where no electrons will have enough energy to rise above the surface. The concept of the Fermi energy is a crucially important concept for the understanding of the electrical and thermal properties of solids. Both ordinary electrical and thermal processes involve energies of a small fraction of an electron volt. But the Fermi energies of metals are on the order of electron volts.

• This implies that the vast majority of the electrons cannot receive energy from those processes because there are no available energy states for them to go to within a fraction of an electron volt of their present energy. Limited to a tiny depth of energy, these interactions are limited to "ripples on the Fermi sea".

• At higher temperatures a certain fraction, characterized by the Fermi function, will exist above the Fermi level. The Fermi level plays an important role in the band theory of solids. In doped semiconductors, p-type and n-type, the Fermi level is shifted by the impurities, illustrated by their band gaps. The Fermi level is referred to as the electron chemical potential in other contexts.

• In metals, the Fermi energy gives us information about the velocities of the electrons which participate in ordinary electrical conduction. The amount of energy which can be given to an electron in such conduction processes is on the order of micro-electron volts (see copper wire example), so only those electrons very close to the Fermi energy can participate. The Fermi velocity of these conduction electrons can be calculated from the Fermi energy.

           

This speed is a part of the microscopic Ohm's Law for electrical conduction. For a metal, the density of conduction electrons can be implied from the Fermi energy.

• The Fermi energy also plays an important role in understanding the mystery of why electrons do not contribute significantly to the specific heat of solids at ordinary temperatures, while they are dominant contributors to thermal conductivity and electrical conductivity. Since only a tiny fraction of the electrons in a metal are within the thermal energy kT of the Fermi energy, they are "frozen out" of the heat capacity by the Pauli principle. At very low temperatures, the electron specific heat becomes significant.

Band theory of solids

Metals : Topmost occupied band is half –filled (a) . In case of bivalent materials the topmost occupied (full) band overlaps the next empty band. (b)

Semiconductor: Topmost occupied band is completely full and the next band is completely empty The band gap is small. Insulator at 0K. E.g. silicon ,Eg ~1.1 eV

Insulators: Topmost occupied band is completely full and next band ic completely empty. Energy gap is large . E.g. diamond Eg ~8 eV

Review of semiconductor physics

Fermi level and impurity levels (Applet)

ni=intrinsic carrier densityNc, Nv = Density of statesNd,Na = doping concentrationEg = Band gapEF =Fermi energy

Intrinsic n=p

n p= ni2 (all cases)

Transport properties

• Mobility μ: Drift velocity per unit electric field

Intrinsic semiconductors: the conductivity σ is given by

For n-type (n>>p = Nd) , then

For p-type (p>>n =Na), then

pn pene

ndnn eNne

papp eNpe