04-GR Transport

8/12/2019 04-GR Transport

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Introduction

EEE 598: Fundamentals of Solar Cell Design and Fabrication Fall 2010 Honsberg 1

What semiconductor basics are important for solar cells?

carrier generation, loss, and transpor t

p-n junction

metal semiconductor contacts


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2

Outline Semiconductor basics classes

Need to know how many carriers at what energy and where in the device

Properties of Semiconductors

Band gap & band diagrams

Density of states

Fermi-levels

Carrier Concentration: Intrinsic and doped

Recombination and Generation Transport properties and mechanisms

PN junctions

Built-in electric field

Current flow mechanisms under voltage and light bias

Diode equation Metal semiconductor contacts

Schottky

Ohmic

I

2

3

4

EEE 598: Fundamentals of Solar Cell Design and Fabrication Fall 2010 Honsberg


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Outline Basics part II

3

Recombination

-Types

- Lifetime

- Diffusion length

- Surface recombination

Generation-Types

- Photons

Transport properties and mechanisms

- Diffusion

- Drift



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Motivation

Part I described how to calculate the carrier concentration in bulkmaterial in equil ibrium

Part II discusses how carrier concentrations are altered from

equilibrium by two factors:

Generation and recombination of carriers

Transport of carriers f rom one region to another. Need to determine processes for recombination and generation,

and their rates.

Need to determine the processes for transport, and how they

depend on the carrier concentrations.

We wi ll consider drift and diffusion as the transport processes.



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Continuity equation

5

Powerful general equation widely used in many fields

SVt

=+

The change in a quantity depends on thegeneration or removal rate (S) and the vector

function describing the transport ofV

Apply this to carriers in a semiconductor

RGJqt

tzyxnn +=

1),,,( For electrons. is the electron currentand G and R are the generation and

recombination rates, respectively

nJ



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Generation & Recombination

Even with no external inputs, carriers are continuouslymoving from band to band, but at equilibrium, the carrierconcentration does not change as a result of theseprocesses.

Generation refers to any process by which electrons

move from valence band to conduction band toconduction band, leavingbehind a hole in valence band.

Recombination is any processby which electrons fromconduction band moveback into the valence band,thereby removing a holefrom the valence band.



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Recombination

7

There are three basic types of recombination in the bulk of a single-crystal

semiconductor:

Band to band recombination (radiative transition in direct bandgapsemiconductors)

Shockley-Read-Hall (SRH) recombination. Also called trap assisted

recombination

Auger recombinat ion

E

Et

Band to band SRH Auger



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Recombination Band to Band

8

Band-to-Band recombination usually emits a photon (radiative)

The emitted photon has an energy similar to the band gap

Dominates in direct bandgap semiconductor devices (e.g.,

LEDs and concentrator or space solar cells made from GaAs)

Can be neglected for silicon solar cells since Si is an indirect

bandgap semiconductor and radiative recombination is

extremely low



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Recombination - Shockley-Read-Hall

Recombination through a defect is calledShockley-Read Hall Recombination (SRH

recombination) The defects, either foreign atoms or structural

defects, may be unintentional or deliberate

Does not occur in perfectly pure, defect freematerial.

The defect introduces an additional state into

the forbidden gap. Energy levels near mid-gapare veryeffective for recombination whereas defectstates close to either band edge are not aseffective

SRH recombination is a two-step process: An

electron (or hole) is captured in the defect state.If a hole (or electron) moves to the sameenergy state before the first carrier is thermallyre-emitted, then recombination occurs.

SRH recombination dominates in indirectsemiconductors



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Recombination - Auger

Involves three carriers

An electron and a hole recombine, but

rather than emitting the energy as heat

or as a photon, the energy is given to

a third carrier, an electron in the

conduction band.

Auger recombination is most important

in heavily doped or heavily excited

material



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Recombination lifetime

11

Recombination rate is proport ional to the excess carrier density (ie, no net

recombination at thermal equilibr ium)

Recombination rates for majority carriers equals that of minority carriers Rate (R) is proportional to the product of n and p

Assuming low level in jected mater ial (where the number of minori ty carriers is less

than the doping) we define the minority carrier lifetime () which is related to therecombination rate

)(

2

innpdt

dp

dt

dn

R ==

o

n

nnnn

R =

= ,

o

p

pppp

R =

= ,

in n-type material in p-type material

1 1 1 1

= + +

rad SRH aug

Think of the lifetime as the average time a carrier can spend in an excited state after electron-

hole generation before it recombines

Lifetimes are defined for each of the recombination mechanisms

The total recombination rate is given by:

augSRHrad

and,,



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Diffusion length

12

The "minority carrier dif fusion length" is the average distance a carrier can

move from point of generation until it recombines.The diffusion length is related to the carrier lifetime by the diffusivity

where L is the diffusion length (cm), D is the diffus ivity (cm/s ) and t is the

lifetime (s)

Example calculation of L for silicon (assume p type, doping 5x1016/cm -3)

De=23 cm/s ; assume a lifetime of 1 msec; L = 1500 microns

This is a large distance, considering a typical solar cell wafer is only 200 to

300 microns thick, and suggests we need to consider the effect of wafer

surfaces on lifetime

DL = eeq

kTD =



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Surface Recombination

13

By definition, bonds are disrupted at the surface of a semiconductor

material and there is a high probability of dangling bonds and defectsunless special efforts are made to terminate and passivate that surface

Similarly to SRH recombination due to defects in the bulk, surface defects

can lead to very rapid recombination of minori ty carriers

Characterized by a surface recombination velocity (s) which depends on

the two dimensional density of traps at the surface (Nt) and the

recombination cross section () which is on the order of 10-15 cm2

th is the carrier thermal velocity (approx. 107 cm/sec)Typical values:

-unpassivated silicon surface: 107 cm/sec

-carefully prepared thermally oxidized si licon: < 10 cm/sec

tthNvsnsR == ;



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Generation: Basic Processes

In order to move from one band to another, there are several requirements:

Carrier must gain enough energy to move from one band to another There must be an electron in the valence band or at another low energy

level.

There must be an unoccupied space to which the electron can move.

Energy can come from thermal energy or f rom photons.

Unless there is a thermal gradient across the material, thermal energydoes not cause a net generation rate, as it is balanced by recombination.

Hence, wi ll only consider generation due to photons.

Every recombination process has an inverse generation process, but not allare practically observed.

In most photovol taic devices, the number of light-generated carriers are oforders of magnitude less than the number of majority carriers already presentdue to doping. Thus, the number of majority carriers in an illuminated

semiconductor does not alter signi ficantly. However, the number of photo-generated minority carriers outweighs the number of minority carriersexisting in the solar cell in the dark, and therefore the number of minor itycarriers in an illuminated solar cell can be approximated by the number oflight generated carriers.



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Generation: Photons

Photons are quantum mechanical particle that describes electromagnetic

radiation. Properties of photons:

Photons have small momentum, but large energies.

Energy given by either energy (usually in eV) or by wavelength orfrequency.

Photon flux gives number of photons/sec.cm

Can convert between photon flux and power density (for a monochromaticsource) by:

=

= hhc

E

in microns



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Generation: Photons

The energy of a photon has a major impact on how the

photon interacts with the semiconductor. If the photon = EG, then photon can be absorbed.

Excess energy above EG generally given offas heat



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Absorption coefficient , , (units cm-1) is a measure of the probability ofabsorbing a given photon.

intensity of light (Io)at any distance (x) into the material is

where Io is the light intensity at the top surface.

Absorption depends on the likelihood of the transition occurr ing lower for

processes near the band edge, increasing for higher photon energies. For band-to-band transitions, the absorption

coefficient has the form

Temperature changes in amaterial cause a change inthe band gap (EG as T ),hence changing theabsorption edge in a material.

Generation: Absorption coefficient

21)( GE

x

oeII

=



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Generation Rate

Generation rate given by the number of photonsabsorbed in a material, and usually assumed to alter

the number of carriers in the energy bands.

Number of photons at a given distance x into a material

given by:

Generation rate given by:

x

sph eNN

=

Nph is the number of photons in the material

Ns is the number of photons at the surface is the absorption coefficient and depends on x is the distance into the material

x

s

pheN

dx

dNG

==



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Generation Rate

Generation rate depends on the wavelength of incident light

(different ) and also varies with posi tion in the material.

Large means light absorbed close to surface, small means

light absorbed relatively uniformly in entire material.

If x


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Sample Calculation

Given 100 W/m2 of monochromatic light (=1000nm) on a silicon substrate

200 microns thick, calculate the generation rate at the surface and at x=100

microns

Ns=100w/m2 (1/1.6x10-19)(1/1.24)J-1=5x1016cm-2sec-1

From the plots, is approx. 100 cm-1, so 1/ = 100 microns G not

constant with depth

At the surface:

G=Ns=100 cm-1 (5x1016cm-2sec-1)= 5x1018cm-3sec-1

At 100 microns deep into the silicon:

G=Nse(-x)=100 cm-1 (5x1016cm-2sec-1)e[(-100cm-1)(0.01cm)]

= 1.8x1018cm-3sec-1


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Transport

Electrons (holes) in the conduction (valence) band are free and can move

throughout the crystal. We will consider two transport mechanisms: Drift and

diffusion.

Both these transport mechanisms depend on constant, random motion of electrons.

Electron moves in a given direction until it scatters due to an interaction with the

crystal lattice.

Electrons have a distribution of velocities around an average thermal velocity Vthdetermined by the temperature T

The net motion in the absence of an external influence is zero

Thermal velocities are fast (on the order of 107 cm/sec)

Drift transport: In the presence of an electric field, carrier movement due to thepresence of the E-field is superimposed on the random motion

Diffusion transport: In the presence of a concentration gradient, carrier movement

due to the presence of the gradient is superimposed on the random motion

kTvm the2

3

2

1 2*= k = Boltzmanns constant, m* is

the effective mass for conductivity



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Transport-Drift

An applied electric field E results in a net carriervelocity called the drift velocity, Vd. The carriers are

accelerated during the time t between latticescattering events so we can write the followingexpression:

Define the mobility of the carriers as

Current due to electric field

Note that usually only one of the components in thisequation for conductivity is significant because of thelarge ratio between the two carrier densities

( )

= = +1

q n pn p

*

n

nmqt=

EqnqnvJ ndn== EqpqpvJ pdp

==

( ) EEpnqJJJ pnpntotal =+=+=

*

*

n

d

dn

m

qEtv

vmqEt

=

=

and



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Transport-Drift Si resistivity / mobility data

Electron mobil ity vs. doping

Hole mobility vs. doping

Resistivity vs. doping density


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Transport-Diffusive

Diffusive transport: the random thermal motion of charged particles in

a concentration gradient results in a net particle flow and thus a

current

J qD dn

dxn n= + for electrons

J qD dp

dxp p= for holes.

DpkTq p

= for holes

DnkTq n

= for electrons.

Dn, Dp are the diffusivities for

electrons and holes, respectively

and can be related to the mobility

values by the Einstein

relationship:



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Transport-Drift + Diffusive

If both an electric field and a concentration gradient are present, the total current

density is the sum of both drift and diffusive components:

dx

dpqDEqpJ

dx

dnqDEqnJ

pxppx

nxnnx

=

+=

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04-GR Transport