Lecture Conference Ourzazate ennaoui

Solar Photovoltaic Technology from atoms to arrays

Ahmed EnnaouiHelmholtz-Zentrum Berlin für Materialien und EnergieScience Advisory Board Member of IRESEN - Morocco

E-mail: [email protected]

https://www.helmholtz-berlin.de

The International Renewable and Sustainable Energy Conference(IRSEC'13) March 7-9 2013, Ouarzazate, Morocco

http://www.iresen.org/index.phpLecture 4 on Friday 09h30 ‐ 10h15

Introduction: PV from atom to array

Array

s

Absorbed photon creates 1 electron-hole pair. The electric field separates the electron-hole pair. The electrons are collected in the external load. Generation-Recombination.

Enery levels

Atom

Module

Solar cell

Prof. Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie

Photo absorption and photo generation Direct and indirect band gap. External and Internal Quantum Efficiency (EQE and IQE). Absorption coefficient, absorption length, excess minority carrier. Recombination: Non Radiative, Radiative, Auger. Shockley-Read Hall Recombination. Continuity equation and Transport process. Basic J-V equation. Equivalent Circuit model. Silicon Technology versus. Thin Film technology. Basic building block for PV: cells in series, cells in parallel. Change in short circuit current and open-circuit with solar radiation. Change in short circuit current and open-circuit with the temperature Performance measurement standard conditions

What we have to learn

Task of Photovoltacis: Photo absorption and photo generation

Light = wave , and particle with energy E = hAlbert Einstein

1879 - 1955

Max Planck1858 - 1947

)(

1239)(

hch E

nmeVE

)rkexp()rk,()rk,( iunn

Function with the periodicity of the crystal

lattice Plane wave

)rkexp()rk,()rk,( iunn

Function with the periodicity of the crystal

lattice Plane wave

Use of Bloch functions

Band structure of Si E(k)

1000 nm 1.239 eV 1.4 eV

Solving Schrödinger equation

ErVm

)(2

2

0

2

Particle in a box: wave functions and energies

n ; the quantum number (n= 1, 2, 3,....)L ; the length one dimensional) molecular box m ; the mass of the particle (electron) h ; Planck's constant

Device fabrication1. Surface etch, Texturing2. Doping: p-n junction formation3. Edge etch: removes the junction at the edge4. Oxide Etch: removes oxides formed during diffusion5. Antireflection coating: Silicon nitride layer reduces reflection

Cells

Purifying the silicon:

STEP 1: Metallurgical Grade Silicon (MG-Silicon is produced from SiO2 melted and taken through a complex series of reactions in a furnace at T = 1500 to 2000°C.

STEP 2: Trichlorosilane (TCS) is created by heating powdered MG-Si at around 300°C in the reactor, Impurities such as Fe, Al and B are removed.

Si + 3HCl SiHCl3 + H2

STEP 3: TCS is distilled to obtain hyper-pure TCS (<1ppba) and then vaporized, diluted with high-purity hydrogen, and introduced into a deposition reactor to form polysilicon: SiHCl3 + H2→Si + 3HCl Electronic grade (EG-Si), 1 ppb Impurities

STEP 1

STEPE 2 and 3

Electronic Grade Chunks

Source: Wacker Chemie AG, Energieverbrauch: etwa 250kWh/kg im TCS-Process, Herstellungspreis von etwa 40-60 €/kg Reinstsilizium

Ingot sliced to create wafers

Making single crystal silicon

Czochralski (CZ) process

crucible

Seed crystal slowly grows

Microelectronic

1G: Crystalline Si PV technology

P-N Junction

Si14

Ge32

Ga31

As33

Cd48

Te52

P15

In49

Al13

Sb51

Cu29

Se34

In

49

31

IIB IIIB

IVB

VB VIB

IB

C 6

B 5

Zn

30

Sn50

S16 O

8

N 7

Periodic Table

Doping Technology of Silicon: pn junction of Silicon

Silicon (IV) Diamond Structure

Boron doping Phosphorus doping

Martin Green, UNSW’s cell concepts PIP 2009; 17:183–189 / http://www.unsw.edu.au/

External Load +-

Emitter Base Rear Contact

Front Contact

Antireflection coating

Absorption of photon creates an electron hole pair. If they are within a diffusion length of the depletion region the electric field separates them.

The electron after passing through the load recombines with the hole completing the circuit

n pFront contact

Task of Photovoltacis: Photo absorption and photo generation

1. Light absorption: Generation of free excess2. Charge separation: a) Photocurrent, I [A] (Ampere) b) Photovoltage, V [V] (Volt)

3. Recombintion (defect recombination centers)

V[A] x I[V] = Power [Watt]

Light flux

Valence band

Conduction band

ZnO

, 250

0 Å

CdS

700

Å

Mo

0.5-

1 µm

Glass, Metal Foil, Plastics

Glass

Cd 2SnO 4

SnO 2

0.2-0.5 µm

CdS

600-2000

Å

CdTe

2-8 µm

CIG

S 1-

2.5

µm

C-Paste

with

Cu,

CdTe based device

Quelle: Noufi, NREL, Colorado, USA,

*CIGS based device

CdTe and CIGS Thin Film Solar cells (2G)

GlassMoly rear contact

CIGS

Buffer

ZnO Front contact

Technology: monolithic" interconnect from three scribes P1 to P3

P1

Step 1: Deposition of Cu, In,Ga (Se)(sputtering, codeposition, Electrodeposition)Step 2: Rapid Thermal Processing (RTP)

Pulsed Picosecond Laser

Front ZnO of one cell is connected to back Mo contatc of the next.

dead-zone width can be up to 500 μm for mechanical scribing.

Se Cu

Ga In

Cu(In,Ga)Se2

P3P2 P1

P1 periodic scribes to defines the width of the cells. P2 scribe removes the CIGS down to the Moly back contact. P3 scribe can also remove the whole layer stack down to the Moly

Si

Module

Vmodule= Vcell x Ncell 24 V for battery charging

Quelle: HZB / M. Lux-Steiner

Radiative recombination

EV

ECA

uger

reco

mbi

natio

nEx

cess

ene

rgy

give

n to

ano

ther

car

rier i

n th

e sa

me

band

EC

EV

Electron thermalizes to band edge

Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie

Recombination (r) is the opposite of generation, leading to voltage and current loss. Non-radiative recombination phonons, lattice vibrations. Radiative recombination photons (dominating in a direct bandgap materials ) Auger recombination charge carrier may give its energy to the other carrier.

E(eV

) Non-radiative recombination

EC

EV

Phonon

Recombination processes are characterized by the minority carrier lifetime . Equilibrium: charge distributions np = ni

2

Out of equilibrium: The system tries to restore itself towards equilibrium through R-G Steady-state rates: deviation from equilibrium

npnBgrRBnnB.pg

.pn Br 2

i2i00

/scm102B(Si) 315

Generation vs. recombination processes

Summary: Generation & Recombination


Shockley-Read Hall recombination

Direct recombination

direct band

Auger recombination(dominant effect at high carrier concentration)

EV

EC

Ekin

Ekin= -qELsc

Generation

Impact ionization is a generation mechanism. When the electron hits an atom, it may break a covalent bond to generate an electron-hole pair.

The process continues with the newly generated electrons, leading to avalanche generation of electrons and holes.

: average time it takes an excess minority carrier to recombine

(1 ns to 1 ms) in Si

: depends on the density of metallic impurities and the density

of crystalline defects.t/teff

2DAugern,DTn .NcBNNcΔn

AugerDirectSRH

111n

τττRRRR AugerDirectSRH

1

eff

2

DAugern,DTn .NcBNNcτ

Loss to thermal vibrations


Sun

Task of Photovoltacis

• 100 W light bulb is turning on for one hour • Energy consumed is 100 W·h = 0.1 kW.h.

Production vs. consommation100 W light bulb

Controller, (charge regulator) regulates the voltage and current coming from the solar panels Determines whether this power is needed for home use or whether it will charge a deep-cycle solar battery to be drawn upon later on.

All other current must pass through a DC to AC inverter, transforming it into electricity usable by general household appliances.

DC-current from the controller can be used to run electronic devices that don't require an AC-current.

all surplus electricity not being drawn by your home can be sent to your utility company's power grid.

PhotovoltaicP > C

Traditional System

PhotovoltaicP < C

Copyrighted Material, from internetTask of Photovoltacis

Efficiencies beyond the Shockley-Queisser limit

(1) Lattice thermalization loss (> 50%)(2) Transparency to h < Band gap(3) Recombination Loss(4) Current flow(5) Contact voltage loss

Not all the energy of absorbed photon can be captured for productive use (Th. Maxi efficiency ~32% ).

R.R. King; Spectrolab Inc., AVS 54th International Symposium, Seattle 2007

Reflection loss

Recombination loss

Resistive loss Top contactloss

Back contact„Loss“

Good surface passivation. Antireflection coatings. Low metal coverage of the top surface. Light trapping or thick material (but not thicker than diffusion length). High diffusion length in the material. Junction depth optimized for absorption in emitter and base. Low reflection by texturing

Route to high efficiency solar cells

Traditional cell design PERLPERCIBCPESCMINP

(1) (2) (3)

(1) PERL developed at UNSW (EFF. 25%) Passivated Emitter and Rear Locally diffused 1

(2) Localized Emitter Cell Using Semiconducting Fingers. (EFF. 18.6%, CZ n-type) (3) Laser-grooved, buried front contact (LGBC; EFF. 21.1%)

1 Martin Green, PIP 2009; 17:183–189, University of New South Wales, Australia

Copyrighted Material, from internet


We need to use most of the solar spectrum: Tandem solar cells

Power [Watt/cm2] = Voltage [Volt ] x Current density [A/cm2]

Materials with small Band gapBut low voltageExcess energy lost to heat

Generating a large current (JSC)Materials with large band gapBut low currentSub-band gap light is lost

Generating a large voltage (VOC)

Solar cell versus

Solar spectrum

= (in flow – out flow) + Rain - Evaporation

rain

In flow

Out flow

Evaporation

Rate of increase of water level

in lake r -g .Jq

1 nnn

dt

dn

nnnn

nnn

qDEqnμJ

r -g .Jq

1

t

n


A little bit of Math: Continuity equation and Transport process

t

n0

Voc

0 La= 1/LpW

Rec

F,ne

F,ph

WLnLa= 1/

Rec

F,ph

F,ne

Generated closer to the junction Generated within a diffusion length of the junction Key issues: Minority carrier diffusion Surface recombination Collection near front surface and also rear

conditions Bondary GτL

xBexp

L

xAexpΔn(x) n

nn

t

n0

Differential equation is simple only when G = constant. n

2n

2

2

D

x)G(λ(

L

Δn

dx

Δnd

p2

p2

2

D

x)G(λ(

L

Δp

dx

Δpd


Basic: Continuity equation and Transport process

Basic Diode J-V equation

NL

nD

NL

nDqJ

Dp

2ip

An

2in

0

+ JD

)( 1Tk

qVexp p

L

Dqn

L

DqJ

Bn,0

p

pp,0

n

n

0J

L

Jcurrent, Dark

Tn.k

qV

0 J1expJJ

D

B

- JL

W)LqG(L pn

LJnt Photocurre

Applying boundary conditions (ideal diode case) Differentiating to find the currentEquating the currents on the n-type and p-type sides

J0 : saturation currentkB : Boltzmann`s constant, 1.381 10-23 J/Kelvinn : ideality factorni: carrier concentrationNA,ND. Doping concentration

dx

pdqDJ n

pp

dx

ndqDJ p

nn


One diode model / Equivalent Circuit

RLoad

J

VD

JD Ideal diode (dark current , ID) (Shockley diode equation)

1exp0 nkT

qVJJ D

D

SD RJVV . add a serie resistance RS

jsh . RshCurrent loss

R

J.RVJ-

Sh

SL

1

nkT

)R.JV(qexpJJ S

0

Add a shunt resistance

Sshsh RJVRi ..

JL

LS J

nkT

RJVqJJ

1

).(exp 0

Under illumination

VOC

JSC

- JL

4TH Quadrant

J = I/A

VReverse

Forward0

Solar cell in the dark

1

).(exp0 nkT

RJVqJJ S

D

Dp

ip

An

in

NL

nD

NL

nDqJ

22

0

J. RS

(Voltage drop)

V

Dark characteristics being shifted down by photocurrent which depend on light

intensity.

P

N

Slope -1/RLoad

Photogenerated carriers can also flow through the crystal surfaces or grain boundaries in polycrystalline devices

Two diodes model / Equivalent Circuit

R

J.RV

Sh

S

1

).(exp1

).(exp

202

101 kTn

RJVqJ

kTn

RJVqJJ SS

RLoad

J +

-

RS

VJ

01,n1

J02

,n2

Rsh

JL

LJ -

R

J.RV

Sh

S

1

).(exp1

).(exp

202

101 kTn

RJVqJ

kTn

RJVqJJJ SS

L

1st Quadrant

4th Quadrant

1st Quadrant

4th Quadrant

J

V

A. Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie

Photocurrent analysis: Quantum efficiency measurments

Acce

ptor

Voc

x = 0 La= 1/x = Lnx = W

EJ dx

dpDp

Don

or

Rec

h

eE p

Load

• How much light converted?• Limited information on the electronic properties• Information on the optical properties of the device

)(R

1

EQEIQE

λ

hc

e

J

ΦEQE

)(

)(

1

This ratio can be measured


0 x R

0

Joulehν

Watt/cmΦN

2photons

in

Coulombe

A/cmJN

2electronsout Electrons

collected

Photons absorbed

0 x R

h(c/) < EG

x0 ).eR.(1ΦΦ α

λ

0

EQE and and absorption coefficient

Photon absorptiondirect band-gap

GG21

E)E(hν vs. .hν α

2G )E(h

hνB

να

Direct Bandgap Eg

EC

EV

Photon

ConductionBand

ValenceBand

E(k)

GaAs e.g.

+k-k

Photon absorptionindirect band-gap

GG2 E)E(h vs. .h ννα

21

G )E(hh

A ν

να

Photon

+k-k

Eg

EC

EV

ConductionBand

ValenceBand

PhononEG+Ep

Ep

E(k)

Si e.g.

Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie and IRESEN

Cut-off vs. EG [eV]E

1.24m][μλ

GG

dEQEq Jsc )()(

λ

hc

e

J

ΦEQE

)(

)(

1

h

Band Gap - absorption coefficient - absorption length

Temperature changes: EG as T

Changing the absorption edge


A(T)(0)E(T)E gG

Si Ge GaAs

EG (eV) 1.12 0.66 1.42

TAR100%

)R.(1Φ

Φln .

d

1 α

λ0

αx-o R).α).-(E).(1Φ

dx

dΦx)G(E,

Absorptionx

0 ).eR.(1ΦΦ αλ

Generation

Φ

ΦΦΦΦ TAR0

Quantum efficiency measurements

2 – Cell Measurement

2CELLCELLsc .Φq.EQEJ

2MONMON,2sc .aΦq.EQEJ

.a.EQEJ

J.aEQE MONMON,2

sc

CELLsc

CELL

3 – Final Result

REFREFsc

MON,1sc

MON,2sc

CELLsc

CELL EQEJ

J.

JJ

EQE

Monochromator equipped with more gratings*Chopper

Beam splitter

*Gratings should have line density as high as possible for achieving high resolution and high power throughput. (600 – 3000 lines/mm).

EG

EQE vs.

1REFREFsc .Φq.EQEJ

1MONMON,1sc .aΦq.EQEJ

1

MON,1sc

MON qΦ

J.aEQE

1 - Reference measurement

photon 1 ofrgy photon/ene of power Total

electron 1 ofarge current/chEQE"" Efficiency Quantum External


Design to high efficiency solar cells

Light trapping

Reflection Loss: ARC

Material Parameter absorption

Important cost factor €/kg

αW

p

eαL1

11 R)(1 η

λ

hc

e

)J(

Φ(λ)

1

Decisive Material ParameterThe band gap

0.3 0.5 0.7 0.9 1.1

20

0

40

60

80

100

0

1

2

3

4

5

Num

ber o

f Sun

light

Pho

tons

(m-2

s-1m

icro

n-1) E

+19

R E

xter

nal Q

uant

um E

ffici

ency

, % c-Si:H junctiona-Si:H junction

AM 1.5 global spectrum

Wavelength, microns

a-Si:H/c-Si:H Cell Spectral Response

Textured TCO

a-Si Top cell

Back Reflector

Glass substrate

Thin film mc-SiBottom cell

GE

λ0λsc dλ .dα-exp . )().ΦR(1 . η(λ). qJ

Light from the sun

Ahmed Ennaoui / Helmholtz-Zentrum Berlin für Materialien und Energie and IRESEN

Power output characteristics

Jsc VOC Pmax

Sun

OCSC

P

.FF.VJEFF.

Vmpp

Pmpp= Impp x Vmpp

OCSC

mppmpp

.VJ

.VJ

Inverse of slope Vmpp/Impp

is characteristic resistance

Jmpp mmp

Rmpp

V

J

mpp = Maximum Power Point

P=I.V

Fill Factor

OCSC

mppmpp

.VJ

Vx J

Sun

mppmpp

P

V . JEFF


Solar cell efficiency under simulated sun light

Earth´ s Surface

AM1AM0

AM1.5

d=1.5 atmos d=1 atmos

Challenges To simulate a spectrum as similar as possible to the sun spectrum with excellent homogeneity over relatively large areas


Principle of a sun simulator

The unit of the photon flux


Reference cell

solar cell

Sources: Thomas FU-Berlin

Contactgrid

TotalArea

Includinggrid

Iluminated Area (2)

JSC is rather accurately determined by EQE measurements

0.5 cm

1 cm

Iluminated Area (1)

0.5 cm

1 cm

dEQEq )( )( J 0sc

Frommonochromator

Performance measurement standard conditions


(1) effective area or

(2) total area


Photons to electrons, solar power to electrical powerYou need a computer for this exercise

Physical constants: elementary charge, e = 1.60 x 10-19 C Planck’s constant, = 6.63 × 10-34 J s speed of light, c = 3.00 x 108 m s-1

Exercice: An ideal solar cell has a band gap energy . The solar cell absorbs 100% of photons with energy and 0% of photons with energy . All absorbed photons are converted to current with 100% quantum efficiency. The solar cell has a fill factor of 70% and an active area of 1 cm2. The external quantum efficiency (EQE) spectrum and current-voltage (I-V) curves are sketched below:

0

20

40

60

80

100

120

Eg

Curr

ent

Voltage VOC

ISC

Vmpp

EQE

(%)

a) The international standard AM1.5 solar spectrum is provided in the text file “Solar spectral irradiance.txt” (from NREL.gov). Use it to calculate the short circuit current, ISC, for the ideal solar cell made from:

Crystalline silicon Si, EG = 1.1 eV; Germanium Ge, EG = 0.67 eV ; Gallium arsenide GaAs EG = 1.42 eVAmorphous Si, EG = 1.75 eV.b) If the open-circuit voltage is given by Voc = EG/e, what is the maximum power conversion efficiency of each of the four cells? (The total terrestrial irradiance is 1000 W m -2.).c) What is the optimum band gap for an ideal solar cell?

0

0.5

1

1.5

2

2.5

0 500 1000 1500 2000 Spec

tral

irra

dian

ce (W

m- 2

nm

-1)

Solar spectral irradiance Extraterrestrial

Terrestrial

From Cells to a Module

The basic building block for PV applications is a module consisting of a number of pre-wired cells in series.

Typical module Silicon technolog/ 36 cells in series referred to as 12V.

Large 72-cell modules are now quite common.

Multiple modules can be wired in series to increase voltage and in parallel to increase current. Such combinations of modules are referred to as an array

Cells wired in series


0.6 V each cell

N°1

N° 36

4 cells

4 x 0.6V36 x36 x 0.6V = 21.6 V

Adding cells in series

Vmodule = n (Vd – I.RS)Series resistance RS

Cell 1 Cell 2 Cell 36. . . . .

+ - + - + -


A parallel association of n cells is possible and enhances the output current of the generator created. In a group of identical cells connected in parallel, the cells are subjected to the same voltage and the the resulting group is obtained by adding currents

VSC,nCell n

n Cells

Cell 1

n Cells in parallele

n x ISC

ISC,n

From Module to array

For modules in series, the I –V curves are simply added along the voltage axis at any given current which flows through each of the modules), the total voltage is just the sum of the individual module voltages.

For modules in parallel, the same voltage is across each module and the totalcurrent is the sum of the currents at any given voltage, the I –V curve of the parallel combination is just the sum of the individual module currents at that voltage.


Two ways to wire an array with three modules in series and two modules in parallel.

The series modules may be wired as strings, and the strings wired in parallel.

The parallel modules may be wired together first and those units combined in series

V V

If an entire string is removed from service for some reason, the array can still deliver whatever voltage is needed by the load, though the current is diminished, which is not the case when a parallel group of modules is removed.


Two ways to wire an array with three modules in series and two modules in parallel.

The series modules may be wired as strings, and the strings wired in parallel.

The parallel modules may be wired together first and those units combined in series

V V

If an entire string is removed from service for some reason, the array can still deliver whatever voltage is needed by the load, though the current is diminished, which is not the case when a parallel group of modules is removed.


Standard conditions of your PV module

Standard Test Conditions:• 1 kW/m2, AM 1.5, 25°C Cell Temperature• Solar irradiance of 1 kW/m2 (1 sun)• Air mass ratio of 1.5 (AM 1.5).• Key parameter: rated power PDC,STC

• I –V curves at different insolation and cell temperature• NOCT: Nominal Operating Cell Temperature (T = 20°C,Solar Irradiation= 0.8 kW/m2, winds speed 1 m/s.)

.S0.8

C20NOCTTT ambCell

cell temperature (°C)ambient temperature (°C)

Insolation(1 kW/m2 )

VMPP

MPP

VMPP V

MPP



Impact of Cell Temperature on Power for a PV Module.Estimate cell temperature, open-circuit voltage, and maximum power output for the 150-W BP2150S module under conditions of 1-sun insolation and ambient temperature 30°C. The module has a NOCT of 47°C.

C64.10.8

C2043.S

0.8

C20NOCTTT ambCell

70

From The table for this module at the standard T = 25°C, VOC = 42.8VVOC drops by about 0.37% per °C , the new VOC = 42.8[1 − 0.0037(64 − 25)] = 36.7 Vwith decrease in maximum power available of about 0.5%/°C.With maximum power expected to drop about 0.5%/°C, this 150-W module atits maximum power point will deliver: Pmax = 150 W· [1 − 0.005(64 − 25)] = 121 WThis is a significant drop of 19% from its rated power.


• Module with Power of 240 WC• 240 Wc and efficiency 14.8%• 1.64×0.99=1.6236 m².• ηSTC=240/(1000×1.6236) = 14.78 % 14.8 %



Siliken modules were awarded the Number one test modules 2010 and Number two test modules 2011.



• Module with Power of 240 WC• 240 Wc and efficiency 14.8%• 1.64×0.99=1.6236 m².• ηSTC=240/(1000×1.6236) = 14.78 % 14.8 %• KT(P) = -0.41 %/°C Power decreases by (0.41% × 240W) = 0.984 W /°C• KT(Uco) = -0.356 %/°C Load voltage decreases by (0.356 × 37V) = 0.13 V / °C.• KT(Icc) = 0.062 %/°C Isc enhanced by (0.062% × 8.61 = 0.0053 A / °C• NOCT = 49°C (±2°C).

).S(kW/m0.8

C20C249C)(TC)(T 2

ambCell

NOCT terms:Level of illumination: 800 W / m²Outdoor temperature: 20 ° CWind speed: 1 m / sAir mass AM = 1.5

Siliken modules were awarded the Number one test modules 2010 and Number two test modules 2011.


Exercice: Electronic Structure of Semiconductors and Doping

Physical constants: Planck’s constant, h = 6.63 × 10-34 J s Boltzmann’s constant, k = 1.38 × 10-23 J K-1 = 8.62 x 10-5 eV K-1

speed of light, c = 3.00 x 108 m s-1 Rest mass of an electron, m0 = 9.11 x 10−31 kg Elementary charge, e = 1.60 x 10-19 C

1) Germanium has an effective density of states (DOS) NC = 1019 cm-3 for the conduction band and a band gap EG = 0.66 eV. The intrinsic carrier density at 300 K is 1.8 x 1013 cm-3. i) What is the effective DOS for the valence band, NV ? ii) If the material is n-doped to give an electron density of ne = 1018 cm-3, what is the hole density? iii) What is the intrinsic carrier density at 100 K? You can assume that the effective DOS do not change with temperature.

2) (Only attempt this question if you like calculus or use a program like Mathematica)

The conduction-band DOS in a direct band gap semiconductor is given by

where is the conduction band minimum and is the electron effective mass. Show that the conduction band electron density can be approximated by:

where EF is the Fermi level and is the effective DOS.


Exercice: Electronic Structure of Semiconductors and Doping

3) The effective electron mass in crystalline GaAs is . The effective hole mass is = 0.47 m0 , and the band gap is EG = 1.42 eV. i) Sketch the band structure (energy versus momentum) for GaAs. ii) Using the expression for the effective DOS given in question 2, determine the intrinsic carrier density at 300K. iii) A GaAs crystal is doped with 1016 cm-3 Si atoms, acting as electron donors by replacing Ga atoms in the lattice.What is the electron and hole density, assuming that all dopants are ionised? iv) What is the position of the Fermi-level relative to the conduction band onset? (Give your answer in electron volts.)

4) Crystalline silicon has an effective DOS of NC = 3 x 1019 cm-3 for the conduction band and NV = 2 x 1019 cm-3 for valence band, and a band gap EG = 1.1 eV. A silicon crystal is doped with 1017 cm-3 boron (B) atoms. (Boron is a group III element.) i) What is the position of the Fermi-level relative to the valence band maximum, EV, and conduction band maximum, EC, at 300 K?

ii) If the acceptor state energy, ED, is 0.05 eV above the valence band maximum (see diagram), use the Fermi-Dirac

distribution and the Fermi level calculated in (i) to calculate the fraction of dopant atoms that are ionized.

iii) Using the same approximations, calculate the Fermi-level and fraction of ionized dopants at 77 K. Is the assumption of complete ionization still valid?

iVI Roughly sketch the variation of hole density with temperature over a wide temperature range.

energy

EV

ED

EC

0.05 eV


At wavelength λ = 1050 nm, the refractive index of silicon is n = 3.6 and the absorption coefficient is α = 15 cm-1. i)A Si wafer of thickness d = 0.25 mm is illumined by light at wavelength λ = 1050 nm at normal incidence. What fraction of light is reflected and what fraction of light is absorbed? ii)A perfect reflective surface is added to the back side of the wafer. What is the absorptivity now? iii)An estimate for the absorptivity of a wafer with a light-trapping surface is given by Würfel as:

(P. Würfel, Physics of Solar Cells, p144) where R is the reflectivity of the surface. By what factor would you expect the external quantum efficiency at 1050 nm of the corresponding solar cell to be improved by a light-trapping surface?

Use the absorption coefficient and refractive index for silicon as a function of wavelength and the solar irradiance spectrum to calculate the reflectivity and absorptivity spectra for a 0.25 mm-thick Si solar cell with a reflective back side and no light trapping (assume normally incident light). Plot these spectra as functions of wavelength. Assuming that each absorbed photon generates one electron in the external circuit (external quantum efficiency = absorptivity), calculate the short-circuit current for the cell under AM1.5 illumination.

Exercice: Charge transport and p-n diodes

Physical constants: Reduced Planck’s constant = 1.05 × 10-34 J s = 6.58 × 10-16 eV s

Boltzmann’s constant, k = 1.38 × 10-23 J K-1 = 8.62 x 10-5 eV K-1 speed of light, c = 3.00 x 108 m s-1

elementary charge, e = 1.60 x 10-19 C

1. A crystalline silicon wafer, has a band gap EG = 1.1 eV and an intrinsic carrier density of ni = 1.3 x 1010 cm-3 at 300 K.

The wafer is 200 µm thick and has an area of 1 cm -2. The electron mobility is µe = 1000 cm2 V-1 s-1, and the hole

mobility is µh = 100 cm2 V-1 s-1.

i) What is the conductivity of the undoped wafer?

ii) The wafer is doped with a donor density ND = 1018 cm-3. Is the doped wafer n-type or ptype? Which

carrier types (electron or hole) are the minority and majority carriers?

iii) A voltage of 1.0 V is applied across the wafer. Sketch the energy band diagram (energy vs depth), indicating the direction of travel of holes and electrons. How large is the drift current?

iv) The minority carrier lifetime is 1 µs. On average how far does a minority carrier travel (under 1.0 V applied bias) before recombining? How does this affect the photocurrent?

v) Why is the n-type region made thin relative to the p-type region in typical crystalline silicon solar cells?

Exercise : Crystalline silicon solar cells

2. A 250 micrometer-thick crystalline silicon wafer is doped with 5×1016 acceptors per cubic centimetre. A 1 micrometer-

thick emitter layer is formed at the surface of this wafer with a uniform concentration of 3×10 19 cm-3 donors. Assume that all doping atoms are ionized. The intrinsic carrier concentration in silicon at 300 K is ni = 1.3 x 1010 cm-3. How large is (at

300 K and thermal equilibrium):

i)The electron and hole concentration in the p-type region and n-type region? Which charge carriers are the majority carriers in the p-type region and what is their concentration?

ii)What is the position of the Fermi level (in eV) in respect to the conduction band in the ptype and n-type region, respectively?

iii)The built-in voltage of the p-n junction? iv) Draw the corresponding band diagram of the p-n junction.

iv)The width of the depletion region of the p-n junction. Compare it with the total thickness of the Si wafer.

3. A 200 micrometer-thick multicrystalline silicon cell is doped with 5×1017 acceptors per cubic centimetre. A 1 micrometer-

thick n-type emitter layer is formed at the surface of this cell with a uniform concentration of 3×10 19 cm-3 donors. Assume that all doping atoms are ionized. The intrinsic carrier concentration in silicon at 300 K is ni = 1.3 x 1010 cm-3, and the

dielectric constant is ε = 11.7. At 300 K and thermal equilibrium:

i) The electron mobility is µe = 500 cm2V-1s-1, and the hole mobility is µh = 50 cm2V-1s-1. The minority

carrier lifetime for electrons is τe = 400 ns and τh = 100 ns for holes. The diffusion constant is given

by the Einstein relation, D

ii) What are the minority carrier diffusion lengths for electrons and holes?

iii) The width of the depletion zone in the p-type region is given by:

Calculate this.

Exercice: Charge transport and p-n diodes

iVI) Estimate the saturation current density for the cell, neglecting recombination in the depletion zone. How does the saturation current affect the open-circuit voltage of the cell?

iV) Minority carriers generated within one diffusion length of the depletion zone will be collected and will contribute to the measured photocurrent. Those generated outside of this region will recombine and will not contribute to the current. The absorption coefficient for silicon at 950 nm is α(950nm) = 104 m-1. Using the Beer-Lambert law for absorption, estimate the quantum efficiency for this cell at 950 nm. (The light has normal incidence and shines on the n-type side of the cell.)

Vi) Sketch the energy band diagram for the cell, labelling all relevant distances. Explain why

reducing the doping in the p-type region might increase the short-circuit current of the cell. How

might this affect the open-circuit voltage?

PV module made up of 36 identical cells, all wired in series. With 1-sun insolation (1 kW/m2), each cell has short-circuit current ISC = 3.4 A and at 25°C its reverse saturation current is I0 = 6 × 10−10 A. Parallel resistance RP = 6.6 and series resistance RS = 0.005 .

a) Find the voltage, current, and power delivered when the junction voltage of each cell is 0.50 V.b) Set up a spreadsheet for I and V and present a few lines of output to show how it works.

Using Vd = 0.50 V along with the other data

The voltage produced by the 36-cell module:Vmodule = n(Vd − I x RS ) = 36(0.50 − 3.16 x 0.005) = 17.43 VPower dilevred: P(watts) = Vmodule x I = 17.43 × 3.16 = 55.0 W

R

I.RV 1

n.k.T

)I . Rq(Vexp.-III

p

SS0ph

p

dV9.380ph R

V 1e .-III d

A6.36.6

5.0 1e .10x6-4.3I 5.0x9.3810

Voltage and Current from a PV Module

A spreadsheet might look something like the following:


Gonçalves et al., Dye-sensitized solar cells, Energy Environ. Sci. 1, 655 (2008), is a very nice summary of the current state of DSSCs. Use it as a reference to answer the following questions: (only brief answers required)

What is the main reason for the lower efficiency of DSSCs compared to crystalline silicon cells? What is the main difference in the physical process of charge generation and transport compared to silicon cells? After excitation, what prevents the dye from returning to its ground state via fluorescence? What are the main requirements when choosing a dye? What are the main requirements that the semiconductor (TiO2) layer must satisfy to in order to make an efficient cell? What causes the lack of stability of DSSCs? How can this potentially be solved?

Exercise : Tandem Solar Cells

A tandem cell is made from two sub-cells, A and B. The individual sub cells are ideal diodes, with current-voltage (J-V) characteristics given by:

Where J0 is the reverse saturation current density, and Jph is the photocurrent density. These have values of J0,A = 10-10 mA/cm2 , Jph,A= 25 mA/cm2 and J0,B = 10-18 mA/cm2 , Jph,B= 20 mA/cm2 for sub-cells A and B respectively at temperature T = 300 K.Calculate the open-circuit voltage for each sub-cell. Which sub cell do you suppose has the highest band gap? The two sub-cells can be connected together in series or in parallel to make a tandem cell. Sketch the J-V characteristics of the individual sub-cells as well as the two possible configurations of tandem cell. Write an expression for the J-V characteristic of the parallel-connected tandem cell. Calculate the short-circuit current and the open-circuit voltage. Calculate the short-circuit current and open-circuit voltage for the series-connected tandem cell. (optional) Using a computer or otherwise, calculate the fill-factor for each sub-cell and the two possible tandem-cell configurations. (Hint: it is simpler to calculate power as a function of current for the series-connected cell.) Assuming the J-V curves were generated with AM1.5 radiation (100 mW/cm2 ), what are the corresponding power conversion efficiencies? The series configuration is more efficient than the parallel configuration. Why? Light passes through sub-cell B before reaching sub-cell A. The band gaps of each sub-cell can be adjusted to optimise the overall efficiency. How are the J-V curves of sub-cells A and B affected by changing the band gaps of the two materials? What is an important criterion for optimising the efficiency of a series-connected stacked tandem cell?

Lecture Conference Ourzazate ennaoui

Technology

silicon technology

absorption length

short circuit current

photo generationlight

absorption coefficient

photo generation direct

silicon nitride layer

metallurgical grade