An NSF/DOE Engineering Research Center

QUANTUM ENERGY AND SUSTAINABLE QUANTUM ENERGY AND SUSTAINABLE SOLAR TECHNOLOGYSOLAR TECHNOLOGY

Ultrafast Carrier Dynamics and

Third Generation Photovoltaics

Stephen M. Goodnick, Executive Director, ASU Lightworks

Christiana Honsberg, Director, QESST ERC

School of Electrical, Computer and Energy Engineering

Arizona State University

Photovoltaics

First Generation single crystal Si PV technology

2

Solar Energy Conversion Efficiencies

• Losses primarily arise from large range of photon energies in

incident spectrum and ability to only utilize energy = band gap.

• In a solar cell, detailed balance calculations quantify these losses,

giving single junction efficiency = 30.8% under one sun and 40.8%

under max concentration (Shockley-Queisser)

3

Single Gap Solar Cell Efficiencies

4

New physics concepts to take PV efficiencies closer to thermodynamic limits

Third Generation (3G) Solar Electric

New Physical MechanismsAssumption in Shockley-Queisser

Approach which circumvents assumption Examples

Input is solar spectrum

Multiple spectrum solar cells: transform the input spectrum to one with same energy but narrower wavelength range

Up/down conversionThermophotonics

One photon = one electron-hole pair

Multiple absorption path solar cells: any absorption path in which one photon ≠≠≠≠one-electron hole pair

Impact ionizationTwo-photon absorption

One quasi-Fermi Multiple energy level solar cells: Existence Intermediate band

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One quasi-Fermi level separation

Multiple energy level solar cells: Existence of multiple meta-stable light-generated carrier populations within a single device

Intermediate bandQuantum well solar cells

Constant temperature = cell temperature = carrier temperature

Multiple temperature solar cells. Any device in which energy is extracted from a difference in carrier or lattice temperatures

Hot carrier solar cells

Steady state (≈≈≈≈ equilibrium)

AC solar cells: Rectification of electromagnetic wave.

Rectenna solar cells

Nano-Enabled 3G Solar Cells

Third Generation Concepts

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Intermediate BandMulti-Exciton Generation

Hot Carrier Solar Cell

Multiple Exciton Generation• Physical process involves transfer of energy to another electron in lower energy

state rather than thermalization

• In bulk materials, requires momentum change as well as energy change: lower

Eth

• Quantum confined (particularly QD) materials, rates of thermalization is

reduced (particularly with no allowed stated between energy levels as in QDs)

and rates of impact ionization are increased.

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A.J. Nozik, “Multiple exciton generation in semiconductor quantum dots,” Chemical Physics Letters, vol. 457, no. 1, p. 3-11, (2008).

R.D. Schaller, and V.I. Klimov, “High efficiency carrier multiplication in PbSe nanocrystals: implications for solar energy conversion,” Physical Review Letters, vol. 92, no. 18, p. 186601/1-4, (2004).

• Detailed balance analysis used to calculate efficiency assuming integer increase in quantum efficiency as threshold for MEG crossed

• Optimum band gap for MEG devices increase as M (the maximum number of excitonsgenerated from a single photon) decreases.

Multiexciton Generation Solar Cells

0 0

( ) ( 1) 1,2,3...g

g g

E E

Q E m mE E m E m

< <= < < + =

• Experimentally, initial results indicated M up to 7, but more recent results show smaller M values.

• Silicon MEG is close to optimum for M=2, and retains 90% of maximum efficiency for M= 4.

g g

gM E ME ≥

Detailed balance one-sun black

body efficiency for MEG solar

cell showing the optimum band

gap for different values of M

Hot Carrier Solar Cells• Energy of electron (hole) extracted before thermal relaxation occurs;

optimal Te,h is on order of 3000K

• Energy selective contacts (wide bandgap, resonant tunneling QW, QDOTs)

• Efficiency improves with concentration, absorber electron temperature

• Suppression of energy loss critical: reduced dimensionality,

nonequilibrium phonons

Schematic of a hot-carrier solar cell (Würfel 2005)

Ross and Nozik, JAP 53, 3813

(1982)

( ) ( ) )/1(/// HaextphHaHphout TTqITTqIP −+∆= εµ

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(Würfel 2005)( ) ( ) )/1(/// HaextphHaHphout TTqITTqIP −+∆= εµ

Energy Selective Contacts• Implementation of energy selective contacts requires some sort of

tunneling scheme or narrow band semiconductor • Quantum dots or impurities in a high barrier material may act as

effective resonant tunneling site.

Relaxation Dynamics in SemiconductorsEnergy Relaxation Processes

• Intercarrier scattering: e-e, e-h, hh, e-plasmon

• Polar optical phonons: Ionic compounds (III-V, II-VI)

• Deformation potential optical

• Dissipative acoustic modes

• Impact Ionization

• Auger Recombination

Main Effects

• Carrier-carrier scattering effective exchanges energy

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• Carrier-carrier scattering effective exchanges energy

between electrons and holes.

• Carrier-carrier drives the distribution function towards

a heated Maxwellian or Fermi-Dirac distribution

(Boltzmann H-theorem)

• Optical phonon emission results in a phonon cascade,

with peaks in the distribution function separated by

the phonon energy

Relaxation Dynamics in Semiconductors

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Polar Optical Phonon Relaxation QWs

Quantum Well

Total scattering rate due to POP scattering

for a 15 nm well for electrons in subband 1*

*Goodnick and Lugli, in Hot Carriers in Semiconductor Nanostructures, (J. Shah, Ed., 1992)

pp. 191-234.

Ultrafast Carrier Relaxation in QWs

Ensemble Monte Carlo simulation of the carrier distribution function and tabulated scattering rate versus time during photoemission of optical phonon emission, absorption, and carrier-carrier scattering (S. M. Goodnick and P. Lugli, 1988)

Hot Carrier Solar Cells• Requires slowed cooling, so that carriers extracted from TH, not Ta

Nonequilibrium Phonons

High Electric Field

Optical Phonon Emission

Acoustic Phonon Emission

τ τ τ τ ~ 0.1ps τ τ τ τ ~ 0.1ps

τ τ τ τ ~ 10ps

τ τ τ τ ~ 10ps

Hot Electron Transport

Heat Conduction in Semiconductor

Nonequilibrium LO phonon distribution and carrier temperature in a GaAs/AlGaAs QW at several different times after photoexcitation from Monte Carlo simulation (P. Lugli and S. Goodnick, PRL 1987).

Hot Carrier Solar Cell Realization in Nanostructures

• In order to realize sufficiently high TH, must have greatly reduced electron-phonon relaxation time

• Quantum dot absorbers have been proposed as way of reducing cooling

• Nonequilbrium phonons with long LO phonon lifetime currently being investigated

In steady state, under optical illumination, the energy input into the coupled electron-hole system is balanced by the energy loss due optical phonon emission, and extraction of carriers from the system:

Energy Balance Model for QW Hot Carrier Devices

EEE ∂=∂+∂

The excess kinetic energy from photons is:

( ) exce

Davgg

optical

En

EhGt

E

τυ 2∆=−=

∂∂

opticalrecextrphonons t

E

t

E

t

E

∂∂=

∂∂+

∂∂

/

Energy Balance ModelIn the limit that a phonon bottleneck due to hot phonons occurs, the energy loss rate for electrons and holes to optical phonons is governed by the phonon lifetime, which is much longer than the LO phonon emission time (< 1 ps):

The energy loss due to recombination removes k T per

DLO

LBB

phonons

nTkTk

t

E H

2∆−

=∂∂

τThe energy loss due to recombination removes kBTH per carrier

Selective energy contacts remove excess carrier energy at the net selective contact energy

HTkn

t

EB

e

D

rec τ2∆=

∂∂

( ) '22s

e

Dgs

e

D

extr

En

EEn

t

E

ττ∆=−∆=

∂∂

Energy Balance ModelCombining equations and eliminating the excess carrierdensity, the hot carrier temperature is given in the limit ofrecombination limited extraction by:

+

+

+

=

e

LO

L

LO

e

BexcH

TkET

ττ

ττ 11

/

And in the limit of selective contact limited extraction by

which places a limit on the selective energy contacts

( )L

e

BsexcLOH T

kEET +−=

ττ /'

Energy Balance Model

Average excess kinetic energy, Eexc, available for carrier heating as a function of bandgap based on the blackbody solar spectrum.

Energy Balance Model

Calculated hot carrier temperature versus bandgapfor various phonon lifetimes assuming a 1 ns recombination time.

EMC Simulation in Quantum Wells

MODEL

-Nonequilibrium POP

-Deformation potential

-Acoustic dissipative

-e-e, e-h, h-h (intrasub,

Intersubband)

• 10 nm QW• 10 nm QW

• GaAs material

paramteters

• 1000 sun illumination

around peak energy

(2900/Ts )

• 5 ps phonon lifetime

Summary• Third generation concepts such as multiexciton

generation, hot carrier extraction, and intermediateband solar cells depend critically on hot carrierrelaxation dynamics

• Hot carrier extraction requires strong suppression ofdissipative relaxation processes

• Coupled carrier-nonequilibrium phonon dynamics canlead to sufficient hot carrier distributions to realizeimproved efficiencies, but only with phonon lifetimesmuch larger than presently exist in bulk systems >10ps

Thank You!