Basic Fundamentalsof

Solar Cell Semiconductor Physicsfor

High School Level Physics

Review Topics

Wavelength and Frequency

Period (sec)

time

amplitude

Frequency () = 1/Period [cycles/sec or Hertz]Wavelength () = length of one Period [meters]For an electromagnetic wave c = ,where c is the speedof light (2.998 x 108 m/sec)

Spectrum

Frequency ()

Range of frequency (or wavelength, c/) responses or source emissions.The human eye has a response spectrum ranging from a wavelength of 0.4 microns (0.4 x 10-6 meters) (purple) to 0.8 microns (red)

Intensity

Energy and Power

Electromagnetic waves (light, x-rays, heat) transport energy.

E = h or hc/[Joules or eV (electron-volts)]1 eV = 1.6 x 10-19 Joulesh = Plank’s constant (6.625 x 10-34 Joule-sec or4.135 x 10-15 eV-sec) = frequencyc = speed of light= wavelength

Power is the amount of energy delivered per unit time.P = E/t [Joules/sec or Watts]

Photons

A light particle having energy. Sunlight is a spectrum of photons. X-rays and heat are photons also.

Photon EnergyE = h or hc/[Joules or eV (electron-volts)]

(higher frequency = higher energy)

(lower energy)

Irradiance

Amount of power over a given area, Watts/m2

Area = 2.00 m2

4 red photons every second

Energy of 1 red photon = hc/ = (6.63 x 10-34 J-s)(2.99 x 108 m/s)/(0.80 x 10-6 meters) = 2.48 x 10-19 J = 1.55 eVIrradiance = Power/Area = (4 photons/sec)(Energy of 1 photon)/2.00 m2

= 4.96 x 10-19 W/m2 Typical sunlight irradiance is 0.093 W/cm2 = 930 W/m2 at = .55 m

Solar Spectrum at Earth Surface (noon time)

E (eV) = hc/ = hc/E

Visable range.75 m (red) - .4 m (purple)1.6 eV - 3.1 eV

Solar Spectrum at Earth Surface.5 eV - 3.6 eVm (infrared) - 0.34 m (ultraviolet)

visible

ultravioletinrfared

Solar Spectrum at Earth Surface

(noon time)

925 W/m2

Transmission, Reflection, and Absorption

air

material

incident light

reflectance (R)

transmittance (T) + absorptance (A)

• Incident light = T + R + A = 100%• Non-transparent materials have either very high reflection or very high absorption.• Absorption decreases transmission intensity with increasing depth into material.

Polarization

Unpolarized light(e.g. sunlight) Linearly polarized light

Polarizer

Only one plane of vibration passes

Basics of Semiconductor Physics

Semiconductor Crystal Lattice

Simple Cubic Structure

atomcovalent bond

Silicon has a more complex lattice structurebut a lattice structure exists nevertheless.

Si atom (Group IV)

Crystalline Silicon Bonds

covalent bond(electron sharing)

=

valanceelectrons

Breaking of Covalent Bond CreatingElectron-Hole Pair

Si atom

covalent bond+

e-free electron movingthrough lattice

created hole(missing electron)

Photon (light, heat)

Photon hits valance electron with enough energy tocreate free electron

Movement of a Hole in a Semiconductor

+

Thermal energy causes valance electron to jump to existing holeleaving a hole behind

+

Valance and Conduction Energy Bands

covalent bonds

+

e-

free electron moving inlattice structure

ConductionEnergy Band

ValanceEnergy Band

Band Gap Energy, Eg = Ec - Ev

Hole within valance band

Ec

Ev

Valance and Conduction Energy BandsThermal Equalibrium

covalent bonds

+

e-

free electron withinlattice structure

Heat energyabsorbed

Energy absorbed = Energy given up

ConductionEnergy Band

ValanceEnergy Band

Eg

Hole created within valance band

+

e-

Heat enerygiven up

Ec

Ev

free electron combineswith hole

Intrinsic (pure) Silicon Electron-Hole PairsThermal Equalibrium

covalent bonds

+

e-

ni = 1.5 x 1010 cm-3

at 300° K

•Number of electron-hole pairs increase with increasing temperature•The thermal voltage, Vt is equal to kT/e (k = 8.62 x 10-5 eV/K, T = [Kelvin])

ConductionBand

ValanceBand

Eg = 1.12 eV

pi = 1.5 x 1010 cm-3

at 300° K

hole density = electron densitynumber of holes per cubic centimeter =

number of free electrons per cubic centimeterpi = ni = 1.5 x 1010 cm-3

Ec

Ev

Creating a Semiconductor

Doping or Substitutional ImpuritiesGroup V Atom (Donor or N-type Doping)

Si atom (Group IV)

covalent bond

e-

The donor electron is not part of a covalent bond soless energy is required to create a free electron

Phospherous (Group V)

P atom

Energy Band Diagram of Phospherous Doping

covalent bonds

+

e-

N-type Semiconductor

ConductionBand

ValanceBand

Eg

n > p (more electrons in conduction band)A small amount of thermal energy (300° K) elevatesthe donor electron to the conduction band

Donor ElectronEnergy

e-

intrinsic hole

intrinsic free electron donor free electron

Ec

Ev

Doping or Substitutional ImpuritiesGroup III Atom (Acceptor or P-type Doping)

Si atom

covalent bond

Boron (Group III)

B atom

+

- covalent bond

created hole

Boron atom attacts a momentarily free valanceelectron creating a hole in the Valance Band

Energy Band Diagram of Boron Doping

covalent bonds

+

e-

P-type Semicondutor

ConductionBand

ValanceBand

Eg

p > n (more holes in valance band)A small amount of thermal energy (300° K) elevatesthe acceptor electron to the Acceptor band

Acceptor ElectronEnergy e-

intrinsic hole

intrinsic free electron

acceptor electron

+

created hole

Ec

Ev

Charge Transport Mechanismswithin a Semiconductor

• Drift Current Density• Diffusion Current Density

y

x

+

Current The number of holes or electrons passing through

a cross sectional area, A, in one second

+ +

++

+

+

+

+

Applied Electric Field

e-

e-e-

e-

e-e-

e-

I = q/t[I] = [coulombs/sec] = [amps]

e-

e-

and Direction of Current

• holes move in Current direction• electrons move in opposite direction

y

x

+

Current DensityThe number of holes or electrons passing through

a cross sectional area, A, in one second divided by A

A (area) = xy cm2

+ +

++

+

+

+

+

Applied Electric Field

e-

e-e-

e-

e-e-

e-

I (amps) = coulombs/secJ (current density) = I/A[J] =[amps/cm2]

e-

e-

and Direction of Current

Drift VelocityThe average velocity of a hole (vp) or electon (ve) moving

through a conducting material

Applied Electric Field

• Scattering Sites are caused by impurities and thermal lattice vibrations• Electrons typically move faster than holes (ve>vp)

+e-

Scattering Sitesvp = dp/t1

ve = dn/t1

dp

dn

Drift Velocity and Applied Electric Field

Newton’s Second Law of MotionF = ma

Analogy with Electic Fieldsm q (mass charge)a E (accelerating field applied electric field)

F = qE

Without scattering sites, the charged particlewould undergo a constant acceleration.

Scattering sites create an average drift velocity.Similar to the terminal velocity of a falling object caused by air friction.

Drift Velocity and Applied Electric Field (cont’d)

• F = qE• The force, F, on a charged partical is proportional to the electric field, E

• Scattering sites create an average drift velocity, vp or ve

• The average drift velocity is proportional to the applied electric field

• vp = μpE• ve = -μnE (negative sign due to electrons moving in opposite direction of applied electric field)

where μp and μn are constants of proportionality

Hole and Electron Mobility

μp is the hole mobility in the conducting materialμn is the electron mobility in the conducting material

The units of mobility, μ, are

v = μE[cm/sec] = [μ] [volts/cm][μ] = [cm2/volt-sec]

Typical mobility values in Silicon at 300° K:

μp = 480 cm2/volt-secμn = 1350 cm2/volt-sec

Mobility and Current Density Relation

CurrentI = q/tq = number of charged particles passing through a cross sectional areat = timeCurrent DensityJ = I/A = (q/t)/AA = cross sectional area

p = number of holes per cubic centimeter (hole density [1/cm3])n = number of electrons per cubic centimeter (electron density [1/cm3])

Each hole has an average velocity of vp

Each electron has an average velocity of ve

++

Mobility and Current Density for Holes

Each hole has traveled a distance z in a time t = z/vp

The number of holes in the volume is pV (hole density x volume)The charge of each hole is e (1.6 x 10-19 coulombs)I = q/t = e(pV)/(z/vp) = ep(xyz)/(z/vp) = ep(xy)vp = epA μpEJp|drf = Ip/A = epμpE

E

x

y

z

x

y

z

vp+

+

+

+

+

+

+

+

vp

veve

e-

e-

Mobility and Current Density for Electrons

Replacing p with n and vp with ve gives:The charge of each electron is -e (-1.6 x 10-19 coulombs)I = q/t = -epV/(z/ve) = -ep(xyz)/(z/ve) = -ep(xy)ve = -epA(-μnE)I = epA(μnE)Jn |drf = In/A = enμnE

Ex

y

z

x

y

z

e-

e-e-

e-

e-

e-

e-e-

Drift Current Density Expressions

Jp|drf = Ip/A = enμpEJn|drf = In/A = enμnE

Jp|drf and Jn|drf are in same direction

Total Drift Current = Jp|drf + Jn|drf

Diffusion Process

gas filled chamber empty chamber

sealed membrane After seal is broken

Gas molecules move from high concentration region to lowconcentration region after membrane is broken

If gas molecules are replaced by charge then a current existsduring charge transport creating a Diffusion Current

gas

Electron Diffusion Current

distance

Ele

ctro

n co

ncen

trat

ion,

n

electron flow

Electron diffusioncurrent density

x

slope = n/x

• electron flow is from high to low concentration (-x direction)• electron diffusion current density is in positive x direction• Jn|dif = eDnn/x where Dn is the electron diffusion constant

Hole Diffusion Current

distance

Hol

e co

ncen

trat

ion,

p hole flow

Hole diffusioncurrent density

x

slope = p/x

• hole flow is from high to low concentration (-x direction)• hole diffusion current density is in negative x direction• Jp|dif = -eDnp/x where Dp is the hole diffusion constant

Diffusion Currents

• Jn|dif = eDnn/x• Jp|dif = -eDnp/x• Electron and hole diffusion currents are in opposite directions for the same direction of increasing concentration

Total Diffusion Current = Jn|dif - Jp|dif

Formation and Basic Physicsof

PN Junctions

PN Junction Formation

Phophorous AtomDoping

• Doping Atoms are accelerated towards Silicon Wafer• Doping Atoms are implanted into Silicon Wafer• Wafer is heated to provide necessary energy for Doping Atoms to become part of Silicon lattice structure

Intrinsic Silicon Wafer

Masking Barrier

Boron AtomDoping

PN Junction in Thermal Equilibrium(No Applied Electric Field)

metallurgicaljunction

• Free electrons from n-region diffuse to p-region leaving donor atoms behind.• Holes from p-region diffuse to n-region leaving acceptor atoms behind.• Internal Electric Field is created within Space Charge Region.

P-type N-Type

metallurgicaljunction

E field

Space Charge Region

p n

Initial Condition

Equilibrium Condition

++++

----

PN Junction in Thermal Equilibrium(No Applied Electric Field)

Diffusion Forces = E Field Forcesmetallurgical

junction

E field

Space Charge Region

p n

++++

----

Diffusion forceon holes

Diffusion forceon electrons

E field forceon electrons

E field forceon holes

Definition of Electric Potential Difference (Volts)

Work (energy) per test charge required to move a positive test charge, +q, a distance x=d against an electric field,

E field

x=a x=b

Positive test charge, +q0

V = (Vb - Va) = Wab/q0 = E(b - a) = Ed [volts or Joules/coulomb]

d

PN Junction in Thermal EquilibriumElectric Field

metallurgicaljunction

Internal E field direction

Space Charge Region

p n

- - - - - - - - -- - - - - - - - -- - - - - - - - -- - - - - - - - -- - - - - - - - -

+ + + + + + + + ++ + + + + + + + ++ + + + + + + + ++ + + + + + + + ++ + + + + + + + +

E

- xp + xnx = 0

E = 0E = 0

metallurgicaljunction

Internal E field direction

Space Charge Region

p n

- - - - - - - - -- - - - - - - - -- - - - - - - - -- - - - - - - - -- - - - - - - - -

+ + + + + + + + ++ + + + + + + + ++ + + + + + + + ++ + + + + + + + ++ + + + + + + + +

Positive test charge, +q0

E = 0E = 0

V

- xp + xnx = 0

V = Vbi

PN Junction in Thermal EquilibriumBuilt-in Potential, Vbi

Conduction and Valance Band Diagram for PN Junctionin Thermal Equilibrium

Built-in Potential, Vbi

- xp + xnx = 0

eVbi

Ec

Ev

p region n regionspace charge region

Ec

Ev

Conduction Band Diagram for PN Junctionin Thermal Equilibrium

- xp + xnx = 0

eVbi

Ec

p region n regionspace charge region

Ec---------------

Work or Energy is required to move electrons fromn region to p region (going uphill)

Electron Energy

Applying a Voltage Across a PN JunctionNon-Equilibrium Condition (external voltage applied)

Reverse Bias Shown

• Eapplied is created by bias voltage source Vapplied.• E field exists in p-region and n-region.• Space Charge Region width changes.• Vtotal = Vbi + Vapplied

metallurgicaljunction

E field

Increased Space Charge Region

p n

E applied

Vapplied

-

+

+ ++ ++ ++ ++ +

- -- -- -- -- -

+

-

ForwardBias

ReverseBias

Reverse Bias PN JunctionNon-Equilibrium Condition (external voltage applied)

• ER is created by reverse bias voltage source VR.• ER is in same direction as internal E field.• Space Charge Region width increases.• Vtotal = Vbi + VR

• Ireverse is created from diffusion currents in the space charge region

metallurgicaljunction

E field

Increased Space Charge Region

p n

E R

VR

- +

+ ++ ++ ++ ++ +

- -- -- -- -- -

Ireverse

Conduction and Valance Band Diagram for PN JunctionReverse Bias Voltage Applied

Vtotal = Vbi + VR

- xp + xnx = 0

eVbi + eVR

Ec

Ev

p region n region

space charge region Ec

Ev

Forward Bias PN Junction (Diode)Non-Equilibrium Condition

• Eapplied is created by voltage source Va.• Eapplied must be greater than internal E field for IForwad to exist.• When Eapplied = E field, Va is called the “turn on” voltage.

metallurgicaljunction

E field

Space Charge Region

p n

E applied

Va

IForward

+ -

Forward Bias PN Junction(Applied Electric Field > Internal Electric Field)

Diffusion Forces > E Field Forcesmetallurgical

junction

E field

Space Charge Region

p n

+++

---

Diffusion forceon holes

Diffusion forceon electrons

Net E field forceon electrons

Net E field forceon holes

Applied E field

Forward Bias PN JunctionDiffusion Forces > E Field Forces

Creates Hole and Electron Injectionin Space Charge Region

E field

p

Diffusion forceon holes

Diffusion forceon electrons

Net E field forceon electrons

Net E field forceon holes

Applied E field

n

Hole Injectionacross

Space charge regionfrom Diffusion force

Electron Injectionacross

Space charge regionfrom Diffusion force

Forward Bias PN JunctionDiffusion Forces > E Field Forces

Creates Hole and Electron Injectionin Space Charge Region

p n

Hole Injectionacross

Space charge regionfrom Diffusion force

Jp|inj

Electron Injectionacross

Space charge regionfrom Diffusion force

Jn|inj

Currentdensity

Total Current density

Jtotal

Jtotal = Jp|inj + Jn|inj

Forward Bias PN JunctionElectron and Hole Current

Components

p n

hole diffusioncurrent

Jp|dif

electron diffusioncurrent

Jn|dif

Currentdensity

Total Current density

Jtotal

hole driftcurrent

Jp|drf

electron driftcurrent

Jn|drf

hole injectioncurrent

Jp|inj

electron injectioncurrent

Jn|inj

Forward Bias PN JunctionElectron and Hole Current

Components

p n

Jp|difJn|dif

Currentdensity

Jtotal

p-region: Jtotal = Jp|drf + Jn|dif

n-region: Jtotal = Jn|drf + Jp|dif

space charge region: Jtotal = Jn|inj + Jp|inj

Jp|drf Jn|drf

Jp|inj

Jn|inj

Ideal PN JunctionCurrent-Voltage Relationship

JS

Jtotal

JS = Reverse Bias Current DensityVa = Applied VoltageJtotal = JS[exp(eVa/(kT) - 1]

Va

turn on voltage

Key Concepts of PN Junction

• Thermal Equalibrium (no voltage source applied)• Internal E field created by diffusion currents• Built in potential, Vbi, exists• Space charge region created• E field is zero outside of space charge region• No current flow

• Forward Bias Applied• Hole and electron injection in space charge region• Total current density is constant through out semiconductor• Diffusion, injection, and drift currents exist• E field is not zero outside of space charge region

• Reverse Bias Applied• A constant reverse bias current exists for large applied voltages due to diffusion currents

PN Junction Hole and Electron InjectionReversible Process

Forward biased voltage applied to a PN junction creates hole and electron injection carriers within the space charge region.

External photon energy absorbed in space charge region creates holeand electron injection carriers that are swept out by the internalE field creating a voltage potential.

PN Junction Solar Cell OperationStep 1Photon

h > EgSpace Charge Region

+

+

+

+

+

E field

p n

e-e-e-e-e-

• Photons create hole-electron pairs in space charge region

• Created hole-electron pairs swepted out by internal E field

PN Junction Solar Cell OperationStep 2

• Created hole-electron pairs are swept out by the E field.• creates excess holes in p-region• creates excess electrons in n-region• Einjected is created by excess holes and electrons

• Photocurrent, IL, is in reverse bias direction

Photonh > Eg

Space Charge Region

E field

p nIL

E injected

+

+

+

+

+

e-e-e-e-e-

PN Junction Solar Cell OperationStep 3

• Attaching a resistive load with wires to the PN Junction allows current flow to/from p-n regions• Photocurrent, IL, is in reverse bias direction• Iforwad is created by Einjected

• Icell = IL - Iforward

Photonh > Eg

Space Charge Region

E field

p n

Resistor

Vcell

IL

Icell

IForwad

+ -

E injected

+

+

+

+

+

e-e-e-e-e-

PN Junction Solar Cell OperationStep 3

• Icell = IL - Iforward

• Icell = IL - IS[exp(eVcell/(kT) -1]• Icell is always in reverse bias direction

Photonh > Eg

Space Charge Region

E field

p n

Resistor

Vcell

IL

Icell

IForwad

+ -

E injected

+

+

+

+

+

e-e-e-e-e-

heat

Typical Silicon Solar Cell Design

N-typeSiliconWafer

P-typeDoping

Protective High Transmission Layer

To load

Wires

4-6 inches

0.6 mm

Photons

• Photons transmit through thin protective layer and thin P-type doped layer and create hole-electron pairs in space charge region• Typical Silicon Single Cell Voltage Output = ~ 0.5 volts

Silicon Solar Cell 6 Volt Panel Series-Parallel Design

12 cells in series = 6 volts

6 volts

p to n connection

-

+

External Factors Influencing Solar Cell Effeciency

• Photon transmission, reflection, and absorption of protective layer• Maximum transmission desired• Minimum reflection and absorption desired

• Polarization of protective layer• Minimum polarized transmission desired

• Photon Intensity• Increased intensity (more photons) increases cell current, Icell

• Cell voltage, Vcell, increases only slightly• Larger cell area produces larger current (more incident photons)

• Theoretical Silicon Solar Cell Maximum Efficiency = 28%• Typical Silicon Solar Cell Efficiency = 10-15%