wave – particle duality 24... · 2020. 9. 9. · wave – particle duality • light behaves as...

$: Wave – Particle Duality 24... · 2020. 9. 9. · Wave – Particle Duality • Light behaves as both a wave and a particle – Wave Properties • Refraction • Diffraction •$
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EELE408 Photovoltaics

Montana State University1

Overview

Wave – Particle Duality

• Light behaves as both a wave and a particle– Wave Properties

• Refraction• Diffraction• Interference

– Particle Properties• Emission and Absorption of Light• Blackbody Radiation• Photoelectric effect

hE

cc: speed of light

: frequency: wavelength

E: Energyh: Planck’s Constant


seVsJhsmc

1534

8

10136.410636.6/103

Photon Flux & Energy Density

AreasecondPhotons ofNumber FluxPhoton

For the same intensity of light shorter wavelengths require fewer photons, since the energy content of each individual photon is greater

JhcmWH 2:Photonper Energy FluxPhoton :DensityEnergy

3

Blackbody Radiation

• Ideal absorber and emitters of electromagnetic radiation– The hotter the body the more radiation emitted

– The hotter the body the higher the energy of the spectrum peak

• Classical physics unable to explain blackbody radiation– 1900-Max Planck: Quantization of Energy Radiation

– 1905-Albert Einstein: Photoelectric Effect


Planck’s Formula

33

3

1exp

8m

sJd

kThc

hE

Integrate over all energies to get the intensity emitted into a hemisphere

0

4

4TdEcH

H: intensity of radiation (W/m2)Stefan-Boltzmann Constant = 5.67x10-8 (W/(m2K4)


Solar Light Distribution


80

60

40

20

0

x1012

2.52.01.51.00.5

2500

2000

1500

1000

500

0

Blackbody Radiation at 6000 K (yellow)Air Mass 0: Outside Earth's Atmosphere (orange)Air Mass 1.5: Sun 48.2 degrees from horizon (blue)

Asorption of energy by water vapor and carbon dioxide

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Air Mass• The path length that light takes through the atmosphere

normalized to the shortest possible path length

xh

cos1

1cos

AMh

hhx

Montana State University7Montana State University7

Polar Plot of Sun Position for Bozeman

Summer

Spring/Fall

Winter


Peak Elevation Angle (Bozeman)

Summer

Fall/Spring

Winter

Latitude + Declination

Latitude - Declination

Latitude45.6845.2345

55.2145.2345

45

Solar Radiation on a Tilted Surface

Sincident

Shorizontal

Smodule

noonsolar at 90latitude

anglen declinatio panel of angletilt

angleelevation

sinsin

sinsin

horizontalmodule

incidentmodule

incidenthorizontal

SS

SSSS

Peak Sun Hours

1kW/m2

EqualAreas

Sola

r Rad

iati

on

Time of Day

Peak Sun Hours

Area under curves = Solar InsolationSi Si Si Si Si Si Si

Si Si Si Si Si Si Si




Poor conductor: No free electrons to carry currentNeed to engineer electrical properties (conduction)


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Si Si As Si Si Si Si

Si Si Si Si Si As Si

Si As Si Si Si Si Si


Each N-type dopant brings an extra electron to the latticeMontana State University

13


Si B Si Si B Si Si


Si Si Si B Si Si Si


Each P-type dopant is short an electron, creating a hole in the latticeMontana State University

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Orbital Shells and Energy Levels

n =1n =2

n =3

Zero energy Ionization Level

1st Excitation Level

Energy

Potential Well at the nucleus of the atom

Splitting of Energy Levels in a Crystalline Lattice

Energy

Interatomic Distanced

DiscreteEnergy States

Continuum ofEnergy States

Band gaps

Allowed

Allowed

Forbidden

Forbidden

Forbidden

Allowed and forbidden energy levels at atomic spacing

Si Si

Valence Band

Conduction Band

SurfaceOf

Crystal

SurfaceOf

Crystal

VacuumEnergy

Bands from inner orbits

Position

Energy

EnergyGap

ConductionBand

ValenceBand

Band Diagram

It is easier to think of a positive hole moving in the valence band


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Position

Energy

EnergyGap

ConductionBand

ValenceBand

N-Type DopingDoping the silicon lattice with atoms with 5 valence electrons (V) create sites in the band diagram that require little energy to break the bond to the dopant atom and become free to move in the lattice or in other words move into the conduction band.

As As As As As As As As As As As As As


N type Material

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

Majority Charge Carriers are Negative electrons

Few holes

Position

Energy

EnergyGap

ConductionBand

ValenceBand

P-Type DopingDoping the silicon lattice with atoms with 3 valence electrons (III) create sites in the band diagram that require little energy to trap an electron into the dopant atom. Holes are created in the valence band that are free to move.

B B B B B B B B B B B B B


P type Material

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Majority Charge Carriers are Positive holes

Few electrons

Position

Energy

EnergyGap

ConductionBand

ValenceBand

Eph=EG

When the photon energy is equal to the gap energy, the photon is again absorbed but no thermal energy is generated.


23Montana State University

Generation is wavelength dependent


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Band to Band Recombination

• Dominate effect in lasers and LED’s• In Si PV devices relatively unimportant since Si is

an indirect material

EnergyConductionBand

ValenceBand


Diffusion Current

• Rate of diffusion depends on the speed of the particles which is temperature dependent

• Redistributes carrier concentration such as induced by photogeneration without an external force applied to device

dxdpqDJ

dxdnqDJ

hh

ee

hh

ee

qkTD

qkTD

Current is proportional to gradient and diffusion constant

Diffusion is proportional to temperature and mobility


Drift Current

pqnqEJpEqJ

nEqqnvJEJ

he

hh

ede

1


DDe NnpnNqN-type

P-type AAh NpnpNq

Drift and Diffusion Currents

• Mobility and Diffusion are related to each other by the Einstein Equation:

pqDEpqJ

nqDEnqJ

ppp

nnn

pp

nn

qkTD

qkTD


pn Junction in Thermal Equilibrium

++++

-

-

-

++++

++++

++++

++++

++++

++++

++++

++++

++++

++++

++++

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

p:NA n:ND

E

V

dp dn

+qND

-qNA

Built-in voltage


pn Junction in Thermal Equilibrium

++++

-

-

-

++++

++++

++++

++++

++++

++++

++++

++++

++++

++++

++++

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

p:NA n:ND

30

Depletion RegionElectric field in the depletion region due to the ionized dopant atoms

Montana State University

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pn Junction with Illumination 1

++++

-

-

-

++++

++++

++++

++++

++++

++++

++++

++++

++++

++++

++++

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

p:NA n:ND

31

Depletion RegionThe absorption of light create photogeneratedcarriers (electron hole pairs)



++++

-

-

-

++++

++++

++++

++++

++++

++++

++++

++++

++++

++++

++++

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

p:NA n:ND

32

Depletion Region Photogeneratedcarriers create an electric field opposing the existing field

Photogenerated carriers are separated by the electric field in the depletion region



++++

-

-

-

++++

++++

++++

++++

++++

++++

++++

++++

++++

++++

++++

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

p:NA n:ND

33

Depletion Region The bias increases until the drift current balances the photogeneratedcurrent

The new charge distribution reduces the electric field and creates a forward bias

Open Circuit Voltage


Forward Bias

Montana State University 34

qVEFn

EFp

EC

EC

EV

EV

h

Fn

Optically Forward Biased

Collection Probability Chart

Colle

ctio

n Pr

obab

ility

Distance into the device

1

Unity collection probability for carriers generated in the depletion region

Solar cell with good surface passivation

Solar cell with poor surface passivation

Solar cell with low diffusion length

With high surface recombination the collection probability at the surface is low

Front Surface

Rear Surface

Depletion Region


Quantum Efficiency

• The ratio of the number of carriers collected by the solar cell to the number of photons of a given energy incident on the solar cell

• If all the photons at a certain wavelength are absorbed and the resulting minority carriers are collected then the QE at that wavelength is unity

• The QE for photons below the band gap energy is zero


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Quantum Efficiency Chart

Ideal Quantum Efficiency

Qua

ntum

Eff

icie

ncy

1.0

gEhc

No light is absorbed below the band gap so the Quantum Efficiency is Zero for wavelengths longer then those at the band gap energy

A reduction of the overall QE is caused by reflection and low diffusion lengths

Blue response is reduced due to front surface recombination

Red response is reduced due to back surface recombination, reduced absorption at long wavelengths and low diffusion lengths

Wavelength


Spectral Response

• Ratio of current generated by the solar cell to the power incident on the solar cell

• Limited at long wavelengths by the inability of the semiconductor to absorb photons with energies below the band gap (Same as QE)

• Any energy above the band gap energy is not utilized by the solar cell and instead goes to heating the solar cell

• This is a measured quantity and used to calculate the Quantum Efficiency

QEhcqSR


Spectral Response

Spec

tral

Res

pons

e

1.0

gEhc

Wavelength

Ideal Spectral Response

No light is absorbed below the band gap so the Spectral Response is Zero below the band gap energy

QEhcqSR


Short Circuit Current PointCurrent

Voltage

The short circuit current is the current through the cell when the voltage across the cell is zero (the solar cell is short circuited)

scI


Short Circuit Current Dependence:

• Area of Solar Cell– To remove the dependence on solar cell area, it is common to

use the Short Circuit Current Density (Jsc in mA/cm2)• Intensity of Light

– Isc is directly dependent on the number of photons entering the cell

• Spectrum of Light– For most measurements the spectrum is standardized to AM1.5

• Optical Properties of the Cell– Reflection and absorption

• Collection Probability– Chiefly depends on surface passivation and minority carrier

lifetime


Open Circuit Voltage PointCurrent

Voltage

The open circuit voltage is the maximum voltage available from the solar cell. It occurs at the zero current point

scI

ocV


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• Corresponds to the amount of forward bias on the cell due to the bias generated by the illumination of the cell

• Solve for the Voltage when the net current is set to zero

1ln

1exp0

0

0

II

qnkTV

InkTqVI

Loc

Loc


Volt (V) 0 0.1 0.3 0.5 0.54 0.57

Current (A) 1.3 1.3 1.3 1.2 0.75 0

Power (W) 0 0.13 0.39 0.6 0.4 0

Voltage (V)

IV Plot

Current Power

Short Circuit Current


Maximum Power

Operating Point

44

ocsc

mpmp

VIVI

FF

Vmp

Imp


Sheet Resistivity

layer theof Thicknesstlayer theofy Resistivit

yResistivitSheet

/

s

s SquareOhmst

wL

twtL

ALR Number of “Squares”

A

L

w

t


4-point Probe

s s s

I IV

t

IV

IV

t

tsIVt

stIVs

s 53.42ln

2ln

2

The typical sheet resistivity for the emitter in silicon solar cells is 30-100 /


Efficiency

• Most commonly used parameter to compare the performance of one solar cell to another

• Defined as the ratio of energy output by the solar cell to input energy from the sun

• Efficiency depends on:– Spectrum

– Intensity– Temperature

in

scoc

in PFFIV

PPmax


Circuit Diagram

IRsh

RLoad

SolarInput

Front Contact

Rear Contact

RecombinationOhmic Flow

CurrentSource

V

I

ExternalLoad


Rs

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Effect of Series Resistance

-10

-8

-6

-4

-2

0

0.30.20.10.0-0.1-0.2

I0 = 5x10-6 mAIL = 10 mARs = 0,1,2,10, 20,50 Ohm

Rs = 0

Rs =50


0.38 V

7.6 mA

50106.738.0

3R

RIVIRV

Effect of Shunt Resistance

-10

-8

-6

-4

-2

0

x10-3

0.40.30.20.10.0

Io=5x10-6 mAIL= 10mARsh = 10000,1000,100,10,1 Ohm

Rs = 10000Rs = 1000

Rs = 100

Rs = 10

Rs = 1


0.27 V

2.7 mA

100107.228.0

3R

RIVIRV

Multi-Junction III-V Cells

• Stacked p-n junctions on top of each other• Each junction has a different band gap energy so

each will respond to a different part of the solar spectrum

• Very high efficiencies, but more expensive• Each junction absorbs what it can and lets the

remaining light pass onto the next junction• Widely used for space applications because they are

very expensive• Overall record for electrical efficiency is 35.2%


Highest Efficiency Device

Solar Cell Panels

Voltage

Curr

ent

Voltage

Curr

ent

Voltage

Curr

ent

53

Series connections increase the voltage output

Parallel connections increase the current output

Blocks increase both current and voltage output

Series connected solar cells with by-pass diode (mismatched) at short circuit


2 1

By-pass diodes

Some current from the ‘good’ cell forward biases the ‘good’ cell

The bypass diode of the ‘good’ cell is reverse biased and has no effect

The bypass diode of the ‘poor’ cell forwarded biased from the ‘good’ cell and conducts current

The ‘poor’ cell is reversed biased, but only about ~0.5 V

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Operation of Blocking Diode


Battery Voltage

Illuminated

Dark

Battery Discharge Current

Current

Voltage

Battery Discharge Current Path

Automated Electronics


Two sweeps 0-70% of Voc then 70%-100% of Voc in smaller increments

IV Dark (linear)


IV Dark (semilog)


Semilog IV plot reveals more information about the diode. Different regions of the IV curve are dominated by different loss mechanisms

Double Diode Equations


shunt

sssL R

JRVkT

JRVqJkT

JRVqJJJ 12

exp1exp 0201

shunt

sss

RJRV

kTJRVqJ

kTJRVqJJ 1

2exp1exp 0201

Dark

Light

Small fluctuations in the light intensity overwhelm the effects of the second diode. More common to use the double diode equation in the dark

• Direct Powering of Load

• No Energy Storage

Simple DC

DC

60

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Small DC

• Home and Recreational Use

DC

Single Battery

Single PanelDC Load

Charge Regulator

61

Utility Grid Connected

• No On-Site Energy Storage

~/=

Inverter

AC

AC Load

Electric Grid

62

Multiple Panels

Photovoltaic System Design Block Diagram

Photovoltaic Generator

AC Load

DC Load

Back-up Generator

Grid

Battery

Power Conditioning

Not all the subsystems will be necessary

Electric Use, Made & Meter Total

64

10000

8000

6000

4000

2000

0Ele

ctric

y U

sed

& M

adeT

otal

(kW

-h)

5/1/2011 9/1/2011Date

1500

1000

500

0

-500

Meter (kW

-h)

Final Lab Report (Wafer Number)• Background

– Fabrication Sequence– Device Cross Section

• Measurements– N+ Final Sheet Resistivity– P+ Final Sheet Resistivity– Front Al Sheet Resistivity– Back Al Sheet Resistivity– Front Al Thickness

• Wafer Testing– Pre-anneal– Post-anneal

• Device Testing– IV curves (4)

• Resistance Estimation• Fill Factor• Efficiency Estimations

– PV Curves• Max power point

– Dark I-V curves (SDA)• Linear• Semilog

• Analysis– 4 solar cell data table– Series resistance calculations– Annealing impact– Class Data Table– 4 devices Variances– Comparison of Class Data

• Summary– Results

• Maximum Voltage• Maximum Current Density• Maximum Fill Factor• Efficiency

– Course recommendations

wave – particle duality 24... · 2020. 9. 9. · wave – particle duality • light behaves as...

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