semi conducting & magnetic materials hetero structures pv

8/2/2019 Semi Conducting & Magnetic Materials Hetero Structures PV

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Semi-conducting & Magnetic Materials

Semiconductor Heterojunctions

Egap,1Egap,2

C Bands

V Bands

EC

EV

Stradd

lingGap

EV

EC

C Bands

V Bands

Egap,1

Egap,2

Offse

tGap

Brok

enGap

Egap,2

Egap,1

C Bands

ECE

V

V Bands

Electronic Properties of a semiconductor heterojunction determined by:

Energy Gaps Electron Affinities

Doping Types & levels.

(a) (c)(b)

CB & VB edges of one lies

within the energy gap of the other.Eg1>Eg2.

Electron affinity of the small gap

material slightly larger than the

wider gap material.

Eg1-Eg2>2- 1>0

E.g.: AlAs-GaAs

Eg1~Eg2.

Electron affinities different, and the

difference is less than either band

gap.

2> 1>0

Both Band Edges of one SC lies

above both Band Edges of the other.

Portion of band Gap over lap at the

interface.E.g.: InSb-InP

Extreme difference in Electronaffinity .

Band gaps do not overlap.

VBE of one lies above the CBE of

Other.

One SC has narrow band gap.

E.g.: InAs-GaSb


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Semiconductor HeterojunctionsImportant consideration is the Energy of the Band Edges.

Some simple rules:

Linearity: The intrinsic energy gap and band edge positions do not change on joining 2

semiconductors. On joining, the band edge discontinuity can be determined.Mathematically the linearity principle is:

Ev=Ev(A)-Ev(B) Valence Band Offset

EC=EC(A)-EC(B) Conduction Band Offset

Transitivity: If you know the discontinuity between any two semiconductors and a thirdone, the discontinuity between the first two can be inferred.

Ev(A:B) + Ev(B:C) + Ev(C:A) = 0

Common Anion Rule: When the anion is common, the change in CBE is greater thanthe change in VBE across the semiconductor heterojunction.

EV < EC

Common Cation Rule: When the cation is common, the VBE scales with the anionelectronegativities.

E.g., VBE of Phosphides will be below Arsenides which will be below Antimonides.

EV(CA1)


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Semiconductor Heterojunctions Electron Transport

NA(GaAs)~ND(AlAs)

1.42 eV4.07 eVP-GaAs

2.16 eV3.56 eVn-AlAs

EnergyGap

ElectronAffinity

Compound

Data used in drawing the figureSketch a Band edge diagram

Mark a vertical line on a page to indicate the junction& a horizontal line to indicate flat-band vacuum level.

Mark the band edge positions on the vertical lineusing electron affinity & energy band gap values for

the 2 semiconductors.

These are doping independent & fix the band edges. Draw a horizontal dashed line indicating the Fermilevel at equilibrium tricky & important

determines how band bending is distributed.

Far from the junction, mark the band edges relative tothe Fermi level depending on doping.

Connect the band edges far from the junction to theband edges in Step 2. Requirements for this are:1) Slopes of the connecting segments must match where

they intercept the points in Step 2

satisfy electron continuity.

2) Energy gaps must be constant on each side of the

junction.

3) Depletion widths are fixed by the doping levels.

D is the potential energy difference associated with

band bending.

DA + D

B = EF or the contact potential which is the

difference in Fermi energies of the semiconductors

before contact.


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Diffusion & Drift of Carriers

Real particles move to lower their chemical potential. Charged particles in an electrical field move according to their electrostatic potential. Large particles in a gravitational field move to the center of mass. Particles placed in a concentration gradient move from high concentration to low concentration (diffuse).

Once the chemical potential of a particle is known, its motion can be easily described.

When 2 systems interact exchange matter or energy equalization of chemical potential equilibrium.

Fermi level gives a measure of the chemical potential of the lowest energy free electron

or the highest energy free hole.

Carrier motion in a chemical potential gradientThermodynamics deals with driving force for particle movement

the potential energy of a particle at a given position.


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The force, F, on a particle is through the corresponding gradient in the chemical potential, :

Diffusion & Drift of Carriers

dF C

dx

= (1)

Where C is a constant. Let us consider a specific particle the electron.

The force on a electron due to the chemical potential gradient produces a current density, J:

n

d

J q n dx

=

(2)

n is the electron mobility & is the chemical potential of the electron.

Let us consider the electron chemical potential gradient due to electric fields & concentration gradients.

The general chemical potential gradient in the system is given by:

Bk Td dn dV

dx qn dx dx

=

(3)


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Diffusion & Drift of CarriersThe general chemical potential gradient in the system is given by:

Bk Td dn dV

dx qn dx dx

= (3)

Change in concentration, n,

in the absence of an electric field

Voltage (potential) gradient at constant

concentration of electrons electric field.

} }

n n n n

B

B

k Td dn dn J q n q n E k T q nE

dx qn dx dx

= = + = +

Substituting into (2):

(4)

Using Einstein relation between diffusivity & mobility:

n Bk T

Dq

= (5)


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Diffusion & Drift of CarriersThe standard form for the current density:

n

dn J qD q nE

dx

= + (6)

Current due to concentration.

} }

Diffusion Current

Current due to the electric field.

Drift Current

Both related to the chemical potential gradient


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pn junction

N-type there is higher concentration of electrons energies close to CBE (high chemical potential)P-type there is empty states near the VBE & having low chemical potential for electrons.

On contact, electrons are free to flow - Electrons drift and diffuse across a junction between unlike materials.

Large concentration gradient across the junction electrons diffuse from n-type to p-type,

leaving positively-charged donor dopants atoms behind.

The residual electric potential resulting from carrier diffusion presents a barrier to further electron motion

in one direction fundamental of diode behavior.


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Energy Bands in Crystalscontd.pn junction

V.B.

V.B.

C.B.

C.B.

Difference in Fermi Energies before contact establishes a band bending edge and

a contact potential Vbi after contact.


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Energy Bands in Crystalscontd. pn junction

Band diagrams for (a) n-type whose surface is negatively charged

(b) p-type whose surface is positively charged.

Assume that the surface of an n-type SC has somehow been negatively charged willrepel the free electrons near the surface leaving +vely charged holes behind. Any

electron that drifts towards the surface feels this repelling force. Far fewer free

electrons at surface compared to the interior depletion region is a potential barrier

for electrons.


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Semiconductor HeterojunctionsThe Junction Contact Potential

Diffusion of charged species build up of electrostatic potential opposes further diffusion of electrons.

Initial difference in chemical potential of the electrons on the 2 sides of the junction decreases

goes to zero diffusion stops. Result is:Accumulation of positive charge on the n-side & negative charge on the p-side

gives rise to electric field at the junction whose magnitude is given when J=0

n n n nB

B

k Td dn dn J q n q n E k T q nE

dx qn dx dx

= = + = +

n

dn J qD q nE

dx= +

Solving for E: ln /Bn p

k T E n n

qn

=

(7)

We know that for the effect of the electric field, E=-dV/dx


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Semiconductor HeterojunctionsIntegrating across all x in the electric field:

ln /B

bi n p

k TV n n

q

=

(8)

Vbi is the built-in voltage or the contact potential across the junction,

nn & np are the electron concentrations on the n & p sides of the junction respectively.

For a shallow dopant at high temperature, nn~ND where ND is the donor concentration on the n-side.

Likewise, np

=ni

2/pp

or

/ E k T gap BC V

pA

N Nn e

N=

/ln ln ln

E k T gap B gapn D A D

p C V B C V

En N N N N e

n N N k T N N

= = +

(9)


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Putting (9) in the expression for Vbi (8):

ln A Dbi gap B

C V

N NqV E k T N N

= +

(10)

Vbi is zero if both sides are undoped and increases with NA and ND.


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Heterojunctions as Diodes

Forward Bias:

A forward applied bias will reduce the potential between

the layers, narrow the depletion region & lower the barrier

for carrier injection (by diffusion) across the junction.

The band-gap discontinuities have opposite sign

-one is step upward, other is step downward,-electrons emitted into the GaAs will have a much lower barrier

to overcome than holes injected from GaAs into the AlAs.

Most of the forward diffusion current will be carried by electrons.

Reverse Bias:

Current is from thermally generated carriers reach depletion

region swept into the AlAs.

Larger energy gap of AlAs relatively few minority carriers & drift

from AlAs to GaAs.

P-type N-type


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Semiconductor HeterojunctionsBipolar Junction TransistorBegan the microelectronics revolution.

Consists of 2 diodes joined back to back by a thin semiconductor layer (the base).

p-n-p or n-p-n depending whether the common base is n-type or p-type.

Consider a n-p-n bipolar junction transistor (BJT):

The 1st n-p junction is Emitter-Base.The 2nd p-n junction is Base-Collector.

On turning it on, the emitter junction is forward biased.

Electrons are injected into the Base & holes into the Emitter.

The holes in the base recombine & have no function.

The electrons emitted into the base can recombine or travel.

If base is thin, most of the electrons pass through it- reach the reverse biased collector junction &

accelerated into the collector.

As long as the time required for the injected electrons to diffuse

through the base is < minority carrier lifetime, the

transistor will permit more current to flow E C than E B

icollector

ibase

, c n

b t

iGaini

= = n is electron lifetime in base region

tis transit time in base region

If base is wider than mfp between collisions, carrier must diffuse

across the base. Minority Carrier Devices.

High gain by high n & low t ie high carrier mobility.

This requires high quality materials, low doping & no defects.GaAs has higher electron mobility than Si high n-p-n speeds.


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Semiconductor HeterojunctionsField Effect Transistor

Different from BJT.

Current flow by majority carriers.

Continuous current path of one conductivity type.

E.g., 2 heavily doped n-type regions in a lightly doped

p-type substrate.

Short p-type region between the n-type regions.

The heavily doped n-type regions are called:

(a) Source (from where the electron flow)

(b) Drain (into which the electrons drain).

(c) Gate controls the current.

Device is normally off.

Conduction is enhanced by applying a negative gate bias

relative to the source creates a n-type channel.

Source-drain voltage adds to it.

Increasing bias voltage provides a wider channel

lowers resistance.

Speed of FET - depends on time it takes for electrons or

holes to transit the channel.

Smaller channels shrinking devices faster PC!

MISFET or MOSFET


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PhotovoltaicsConcept of converting light to electricity possible by the discovery of

The Photoelectric Effect in 1839 by Edmond Becquerel

First commercial solar cell crystalline Si in 1954 of 4%.Over the next 50 years, has gone to 25% close to the theoretical of 31%.

Typical commercially available PV cell is at of 17%.

Photovoltaic Devices - conversion of radiant Solar Energy into Electrical Energy.

Amount of Electrical Energy consumed annually ~ 1,000 GWTerrestrial installed capacity ~ 1GW i.e. 0.1% - growing 40% per year.

Each PV module can produce 1 kW.

Total Solar energy falling on the Earths surface annually is huge 10,000 times the annual consumption.

Objective of a PV cell capture as much of solar energy & convert into Electrical Energy.


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Photovoltaics

Single Crystal

Si

38.0%

Poly-Crystalline

Si46.0%

Amorphous Si

4.0%

Other

CrystallineProducts

6.0%

CIGS

0.3%Si ribbon

3.0%

CdTe

2.7%

Cost is the over-riding factor GOAL is $1/Watt


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PhotovoltaicsSolar radiation wide spectrum of wavelengths.

Atmospheric gases will absorb certain wavelengths.Shift in the spectral distribution will effect the efficiency of absorption

of solar radiation.Additionally, all semiconductors will display cut-off wavelength

dictated by its energy band gap.

Need to specify the atmospheric absorption when quoting efficiency as:

Depth of atmosphere that solar radiation has passed through will affect:Spectral distribution & Total amount of energy.

Atmospheric absorption measurement is Air Mass (AM) which is:Zero for solar radiation outside the atmosphere AM 0 &

One for radiation reaching the ground when sun has reached its zenithAM 1

For space application (e.g. satellites), AM 0 1353 W/m2 &

for terrestrial application AM 1.5 925 W/m2 - solar angle of 45


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Photovoltaics

Si is not the ideal PV semiconducting material Indirect Band-Gap.

Optical absorption is not efficient since we have Phonon scattering & emissionWith Photons.

Therefore thickness of Si required to absorb 90% of sunlight(photons above the band-gap) is ~ 125 m, while for a

Direct Band-Gap Semiconductor, GaAs, it is 0.9 m.

So, why Si? it is the 2nd most abundant element cost is the issue.And? Since PV cell is a Semiconductor Device & Si technology is mature

manufacturing integration is well established again cost!

In 2008, PV is estimated to be a $17B industry & growing 30-40% annually.

Most importantly, clean energy with Free input source Sunlight.


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Photovoltaics

Thermodynamic calculations show that solar energy conversion efficiencycan be maximum 85%, while single band-gap thermodynamic efficiency

is ~ 44% assuming blackbody radiation;

PV cell limits are ~ 31% due to a number of factors:Refractive index, shape of solar cell, realistic solar spectrum, concentration

and recombination effects.

The main reason Single junction PV cell limits are around 31% is that theydo not absorb a significant fraction (~ 20%) of the photons in the solar

Spectrum below the band-gap the photons are simply lost.

Significance ofEg for PV application.

Semiconductor is assumed to be opague for Photon energies > Eg& transparent forPhoton energies < Eg


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PhotovoltaicsFor space application (e.g. satellites), AM 0 1353 W/m2 & forterrestrial application AM 1.5 925 W/m2 - solar angle of 45

Simple PV cells are homojunction diodes convert light to electricity.

Electron- Hole pairs are created by absorption of light &they are separated by the built-in voltage of the junction.

They are similar to and opposite in functionality of Light-Emitting Diodes.


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Photovoltaics

Absorption of light can occur on both sides of the junction creating minority carriers that can diffuse towards the junction.

-If there is no recombination, a photocurrent can be generated.-The junction is shallow & absorption will occur on one side

-where there is greater depth of absorbing material.- In the dark, no current is created.

-When light impinges on the PV device, current flows through the wire from the-p-type side to the n-type side as in conventional current.


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Photovoltaics

Heterojunction p-ndevicesTwo semiconductors different Band-Gaps.

Wider Eg - less absorption. Why?


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Photovoltaics

Heterojunction p-ndevices

Two semiconductors different Band-Gaps.

Wider Eg - less absorption.Why?

Narrower Eg absorption layerAbsorption characteristics of

this layer determines the

maximum absorption possible.


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Photovoltaics

Heterojunctionp-ndevices

Two semiconductors different Band-Gaps.

Wider Eg - less absorption. Why?


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Photovoltaics

Ideal J-V characteristics for a PV cell with Js = 30 mA/cm2.

Shaded area = Maximum extracted power.

LsJeJJ

TkqV B

= 1

/JS is saturation current reverse bias

zero illumination.q is charge on carrier

V is applied voltage

kB is Boltzmanns constant

T is temperature of cellJL is photogenerated current.


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Photovoltaics

Ideal J-V characteristics for a PV cell with Js = 30 mA/cm2.

Shaded area = Maximum extracted power.

Ls JeJJ

TkqV

B

= 1

/

In the ideal cell, JL is the short-circuit current shown as JSC.Power extracted (JV) lies in shaded area ie, (+V J) quadrant.

Load determines operating point.

Maximum Power at the operating point is given by the largest JV area.


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Photovoltaics

Ideal J-V characteristics for a PVcell with Js = 30 mA/cm

2. Shadedarea = Max extracted power.

LsJeJJ

TkqVB

= 1

/

Maximum Power, Pm = Im. Vm

=

+=

q

EI

q

Tk

Tk

qV

q

TkVIP m

L

B

B

mB

OCLm

1ln

Em is max energy that can be extracted / photon depends on bandparameter of absorber layer this determines VOC and Vm.


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Photovoltaics

LsJeJJ

TkqVB

= 1

/

Maximum Power, Pm = Im. Vm

=

+=

q

EI

q

Tk

Tk

qV

q

TkVIP m

L

B

B

mB

OCLm1ln

2 Fundamental parameters that will limit the Efficiency of the PV cell:

Fraction of Solar photons absorbed by the PV cell.

Electrical energy created by the photon.


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Photovoltaics

Fraction of Solar photonsabsorbed by the PV cell.

Calculate by integrating over the solar spectrum for the appropriate AM number

- include the cut-off wavelength of semiconductor absorber layer.

=

0 )(

)(

dEEEn

dEEE

n

abs

g


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PhotovoltaicsFraction of Solar photons absorbed by the PV cell.

Calculate by integrating over the solar spectrum for the appropriate AM number

- include the cut-off wavelength of semiconductor absorber layer.

=

0 )(

)(

dEEEn

dEEE

n

abs

g

Photons with Energy < Band-Gap

will not be absorbed & will not

contribute to the Photocurrent.

Maximum energy that can be extracted with a CdTesolar cell with a band-gap of 1.45 eV.


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Photovoltaics

Implies that not all of the photon energy

will be converted into electrical energy

even if one photon absorbed constitutes

one minority carrier crossing the junction.

Electrical energy per carrier is given by

Em, so the maximum power of thedevice = absorption rate of photons x

mean electrical energy created per photon.

This is shown by the inner shaded area.

Electrical energy created by the photon.Units?

Ideal value of Em will track the band-gap. Narrower Eg materials larger

proportion of photons absorbed, but less electrical energy per photon.


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Photovoltaics

Ideal efficiency against band-gap energy for

single-junction cell for AM 1.5 radiation.

Efficiency versus Eg

Optimum Efficiency for semi-

conductors in the near-infrared

region, around 1.5 eV.

Compromise between

(1) Absorption of solar radiation &

(2) Transfer of optimum amount ofenergy/photon to electrical energy.

Max Efficiency (~30%) for

Si, InP, GaAs & CdTe.

Reality much less:

Optical reflections, poor junctions,

carrier recombination.


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Photovoltaics

Ideal efficiency against band-gap energy for

single-junction cell for AM 1.5 radiation.

Materials issues:

Single crystal vs polycrystalline films

Multiple junctions better costly.

Absorber coefficient

Contact resistance

Raw materials costs

Toxicity of process gases?

Stability of materials & junctions.

We shall discuss only terrestrial

applications.


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Photovoltaics


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Photovoltaics


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Energy Bands in Crystalscontd.

Table 1. Chemical Composition of Commercial LEDs.

Color Wavelength (nm) Composition

Blue 470 In0.06Ga0.94N

Green 556 GaPYellow 578 GaP0.85As0.15Orange 635 GaP0.65As0.35Red 660 GaP

0.40

As0.60or Al0.25Ga0.75As

Infrared >700 GaAs


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Photovoltaics Si PV

>80% of PV is Single Crystal or polycrystal Si drawback is that it isan Indirect Band-Gap Semiconductor lower absorption.Si absorption coefficient ~ 2 x 103/cm, for CdTe it is 1 x 105/cm

~ 17%Need thicker material to absorb Photon Energy > EgPolycrystal Si random grains of size 1 cm loss of photogeneratedcharge at the g.b - ~ 15%


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Photovoltaics

Si PV CdTe PV


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Photovoltaics

III-V Multi-junction PV

S i d ti & M ti M t i l


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Photovoltaics

Eg1 > Eg2 > Eg3

Ge substrate, Eg3 = 0.67 eV

Anti-reflection Coating, eg, ZnO:Al

GaAs, Eg2 = 1.42 eV red to infraredGaInP2, Eg1 = 1.9-2 eV visible light

Metal contact

Triple junction PV cell

Ge substrate, Narrow band-gap absorber to capture theradiation that passes throughthe GaInP2/GaAs cell.



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Photovoltaics

III-V Multi-junction PV CuInxGa1-xSe2 PV



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Photovoltaics



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Photovoltaics

Semi conducting & Magnetic Materials


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Photovoltaics



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Photovoltaics

Eg1 > Eg2 > Eg3 > Eg4

Eg1= 2.583 eV

Eg4 = 1.84 eV

Anti-reflection Coating, eg, ZnO:Al



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Photovoltaics

Band-Gap Engineering InxAl1-xN

y = 0.0532x + 0.7

0.0

0.5

1.0

1.5

2.02.5

3.0

3.5

4.0

4.5

5.0

5.56.0

6.5

0 20 40 60 80 100

% Al

Energy

Band-Gap(eV)

15% Al



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Photovoltaics

Band-Gap Engineering GaAsxP1-x

y = 0.0084x + 1.42

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100

%P

EnergyBa

nd-Gap(eV)

9.524% P



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Photovoltaics

Band-Gap Engineering GaxIn1-xP

y = 0.0092x + 1.34

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100

%Ga

EnergyBan

d-Gap(eV)

17.4% Ga



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Photovoltaics



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Photovoltaics



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Photovoltaics



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Photovoltaics



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Photovoltaics

Triple Junction GaAs Solar cell



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Misfit Dislocations



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g gMisfit Dislocations



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g gEnergy Bands in Crystalscontd.

semi conducting & magnetic materials hetero structures pv

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