wave – particle duality 24... · 2019-06-10 · wave – particle duality • light behaves as...
TRANSCRIPT
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EELE408 Photovoltaics
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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
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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
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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
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Planck’s Formula
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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)
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Solar Light Distribution
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80
60
40
20
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x1012
2.52.01.51.00.5
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2000
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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
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Polar Plot of Sun Position for Bozeman
Summer
Spring/Fall
Winter
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Peak Elevation Angle (Bozeman)
Summer
Fall/Spring
Winter
Latitude + Declination
Latitude - Declination
Latitude45.6845.2345
55.2145.2345
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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
Si Si Si Si Si Si Si
Si 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 Si Si Si Si Si
Si Si As Si Si Si Si
Si Si Si Si Si As Si
Si As Si Si Si Si Si
Si Si Si Si Si Si Si
Each N-type dopant brings an extra electron to the latticeMontana State University
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Si Si Si Si Si Si Si
Si B Si Si B Si Si
Si Si Si Si Si Si Si
Si Si Si B Si Si Si
Si Si Si Si 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
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N type Material
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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
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P type Material
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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.
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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
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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
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Drift Current
pqnqEJpEqJ
nEqqnvJEJ
he
hh
ede
1
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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
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pn Junction in Thermal Equilibrium
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p:NA n:ND
E
V
dp dn
+qND
-qNA
Built-in voltage
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pn Junction in Thermal Equilibrium
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p:NA n:ND
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Depletion RegionElectric field in the depletion region due to the ionized dopant atoms
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pn Junction with Illumination 1
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p:NA n:ND
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Depletion RegionThe absorption of light create photogeneratedcarriers (electron hole pairs)
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pn Junction with Illumination 2
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p:NA n:ND
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Depletion Region Photogeneratedcarriers create an electric field opposing the existing field
Photogenerated carriers are separated by the electric field in the depletion region
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pn Junction with Illumination 3
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p:NA n:ND
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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
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Forward Bias
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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
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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
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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
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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
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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
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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
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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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Open Circuit Voltage
• 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
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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
Open Circuit Voltage
Maximum Power
Operating Point
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ocsc
mpmp
VIVI
FF
Vmp
Imp
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Sheet Resistivity
layer theof Thicknesstlayer theofy Resistivit
yResistivitSheet
/
s
s SquareOhmst
wL
twtL
ALR Number of “Squares”
A
L
w
t
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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 /
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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
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Circuit Diagram
IRsh
RLoad
SolarInput
Front Contact
Rear Contact
RecombinationOhmic Flow
CurrentSource
V
I
ExternalLoad
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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
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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
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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%
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Highest Efficiency Device
Solar Cell Panels
Voltage
Curr
ent
Voltage
Curr
ent
Voltage
Curr
ent
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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
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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
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Battery Voltage
Illuminated
Dark
Battery Discharge Current
Current
Voltage
Battery Discharge Current Path
Automated Electronics
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Two sweeps 0-70% of Voc then 70%-100% of Voc in smaller increments
IV Dark (linear)
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IV Dark (semilog)
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Semilog IV plot reveals more information about the diode. Different regions of the IV curve are dominated by different loss mechanisms
Double Diode Equations
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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
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Small DC
• Home and Recreational Use
DC
Single Battery
Single PanelDC Load
Charge Regulator
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Utility Grid Connected
• No On-Site Energy Storage
~/=
Inverter
AC
AC Load
Electric Grid
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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
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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