solar cells stanford unit 2

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MSE 156/256 - Solar Cells, Fuel Cells andBatteries: Materials for the Energy Solution

Stanford University

Autumn 2012

Unit 2: Semiconductors Crystalline structure Electrical transport

Resistance, resistivity and conductance Materials classification

Metals, insulators, semiconductors Conductivity: mobility and carrier density Electronic states

Energy, occupancy and bands Free electron picture

Electron energy and momentum Density of electron states Filling of electronic states

Semiconductors and band gap Electrons and holes


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Diamond

cubic crystal

lattice The structure for C, Si, Ge, Sn (grey tin) May be visualized as 2 fccs with one

translated along the body diagonal

Lattice is relatively loosely packed Atomic packing factor = 34%

Compound semiconductors, often have avariation of diamond cubic called

zincblende (named after ZnS) where theIII-V (e.g. Ga-As) atoms alternate

Crystallographic Structure

Many semiconductor elements and compounds are:

Group 4 elements or average of group 4 (i.e. III-V, II-VI) Covalently bonded Have structure with tetravalent units with 4 nearest neighbors

Example: Diamond Cubic Structure

H.K.D.H. Bhadeshia: Yes, anyone can use it, I createdit and am happy with this... and there is no need for

acknowledgement.

Electrical Properties of Solids

Resistivity ~ ohm-length

Resistance R~ ohm = volt/amp

Ohms Law

Voltage

Current

Resistance AL

I

V

Cross section

area

Length

Resistance is a device property (depends on whatthe device is made of and its physical dimensions)

We can relate this to a material property


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Electrical Properties of SolidsOhms Law

Voltage

Current

Resistance

Microscopic Ohms Law

Electric field ~ (Volts/meter)

Conductivity = 1/

Currentdensity

AL

I

V

Cross section

area

Length

More generally

Materials Classified by Conductivity

Semiconductors:

The conductivity is controllable by addition of impurities called dopants

The conductivity is strongly temperature dependent and increases as thetemperature increases

101010510010-510-1010-1510-20

Insulators Semiconductors Metals

GraphiteCu

AgAu

GermaniumSiliconNylon

Polystyreneteflon

SiO2

Conductivity


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Conductivity: A Closer Look

Conductivity ~ (A/Vm) or (m)-1

Current density ~(A/m2)

Electric field ~ (V/m)

Charge per carrier (q = - e for electrons)

Application of field E = V/L produces force on carriers

Charge carrier number density

Physics of conductivity in solids

L

V

Motion of electrons is responsible for electrical current in conventional metals andsemiconductors

Conductivity: A Closer Look

Application of field E = V/L produces force on carriers

Carrier mobility

Important material property

Drifting charges Current density

Force results in a drift velocity

Physics of conductivity in solids

L

V

Relationship between material properties

Conductivity related to: Carrier density

Carrier mobility

Units on mobility

Recall microscopic Ohms Law


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Describing Electrons in Solids

Electrons are described by quantum mechanical

states

These states describe- the energy of the electron

- its momentum(more on this later)

- the probability of finding it at a given location

- the property of an electron known as spin (its

either up or down)

Energy

Important characteristics of electron states:

Occupancy Each state can be occupied by either zero or one electron Electron with different spin are different states States with a given energy can have a fractional average

occupancy between zero and one

Energy This gives the energy of the electron that occupies a given

state

Electron states in a quantum corral made ofFe atoms on a Cu surface. This depiction is

a picture of a gilded wooden block carved by

artist-physicist Julian Voss-Andreae from

data taken in 1993 by Lutz et al. Creative

Commons Attribution-ShareAlike License.http://en.wikipedia.org/wiki/File:The_Well_

%28Quantum_Corral%29.jpg

Electron Energy Bands: Isolated Atoms to Crystals

Energy

Isolated atom Isolated atom

Two atoms

Energy

Four atoms

Bring atomstogether

Bring atomstogether

bonding

Anti bonding

Atomic electronstates split (and

sometimeshybridize)

Energy

A lot of atoms

As many atoms are brought together to make a crystal Atomic electron states are split to have different energies New crystal electron levels are grouped into bands of narrowly-spaced energy

levels

Anti bonding states become the conduction band Bonding states become the valence band

Bring atoms

together

Valence

Conduction


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Free Electron PictureBand theory of solids

Atoms give up outer electrons, creating electron sea and charged remaining atomcores

Electrons behave as though they are particles in a box,

- Must each occupy its own quantum state (electrons are fermions)- Interactions with positive atom cores and with each other

Free electron model

No interaction between

electrons and ion cores

Electron have only kinetic energy

Quantum Mechanically:de Broglie wavelength

Classically, Momentum

+ + +

+ + +

+ + +

-

--

--

--

-

- -

-

Positive Ion Cores

Electron Cloud

Free Electron PictureBand theory of solids

Quantum Mechanically:de Broglie wavelength

Classically, Momentum

wavenumber

Free electron energy

5

4

3

2

1

0-2 -1 0 1 2

a = Lattice parameter

Free electrons Electron (kinetic) energy


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Density of states (DOS) is the numberof electronquantum mechanical states pervolume per

energy

Free electron density of states

Electron mass

Density of States in a Band

Bands can have differentnumber of states per energy

We call this density of states

Energy

Energy

Low DOS High DOS

For free-electron bands in solids, the density of statesvaries with energy within the band

Energy

= number of states between and

Density of states

Energy

Fill states in order of energy (lowest energy first)

Filling of Free Electron States: T = 0 K

For T=0 K

Imagine we put in n electrons per volume electrons fill states in order of energy

What is energy of highest filled state?

Invert to findFermi energy

Energy

Densityofstates

Energy

Cu example: One electron per atom


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Filling of Free Electron States: T 0 K

For T0 K

Electron states are occupied according tothe Fermi-Dirac Distribution

- Electron chemical potential alsocalled Fermi level (T dependent)

(T=0) Fermi energy

1.0

0.8

0.6

0.4

0.2

0.02.241.120.00-1.12

0 K300 K

600 K

1000 K

1500 K

2000 K

Density

ofstates

Energy

kBT

f( T)D()

Material Classification

ValenceBand

ConductionBand

ValenceBand

ConductionBand

ValenceBand

ConductionBand

Fermi Level

Metal

SemiconductorInsulator

Electron Energy

Semiconductors, insulators have a gap between valence band and conduction band The Fermi level lies in the gap between these bands At T = 0 K the electronic levels in the valence band are completely occupied by

electrons

At T = 0 K the electron levels in the conduction band are completely unoccupied At T > 0 K the some electrons are promoted from the valence band to the conduction

band

Eg

So for any practical temperatures

Semiconductors


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Band Gaps of Common PV Materials

Material Band Gap (eV) Type of Gap

Crystalline Si 1.12 Indirect

Amorphous Si 1.75 Direct

CdTe 1.45 Direct

CuInSe2 (CIS) 1.05 Direct

Cu2InGaSe4 (CIGS) 1.0 1.7 DIrect

Cu2ZnSn(SSe)4 (CZTS) 1.0 1.5 Direct

GaAs 1.42 Direct

InP 1.34 Direct

4

3

2

1

0

43210

AM1.5

5960 K SpectraPhotons with energyabove the band gap can

excite carriers fromvalance to conduction

band

ConductionBand

ValenceBand

Ec

EvEg

ElectronEn

ergy

MSE 156/256 - Solar Cells, Fuel Cells and

Batteries: Materials for the Energy SolutionStanford University

Autumn 2012

Unit 3: Transport and carrierconcentration in

semiconductors

Coming Up:Unit 2: Semiconductors Crystalline structure Electrical transport

Resistance, resistivity and conductance Materials classification

Metals, insulators, semiconductors Conductivity: mobility and carrier density Electronic states

Energy, occupancy and bands Free electron picture

Electron energy and momentum Density of electron states Filling of electronic states

Semiconductors and band gap Electrons and holes

solar cells stanford unit 2

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