Basic Fundamentals of Solar Cell Semiconductor Physics for High School Level Physics

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Basic Fundamentals of Solar Cell Semiconductor Physics for High School Level Physics. Review Topics. Wavelength and Frequency. Period (sec). amplitude. time. Frequency ( n ) = 1/Period [cycles/sec or Hertz] Wavelength ( l ) = length of one Period [meters]

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Basic Fundamentals

of

Solar Cell Semiconductor Physics

for

High School Level Physics

Wavelength and Frequency

Period (sec)

amplitude

time

Frequency (n) = 1/Period [cycles/sec or Hertz]

Wavelength (l) = length of one Period [meters]

For an electromagnetic wave c = nl,where c is the speed

of light (2.998 x 108 m/sec)

Spectrum

Intensity

Frequency (n)

Range of frequency (or wavelength, c/n) 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)

Energy and Power

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

energy.

E = hn or hc/l [Joules or eV (electron-volts)]

1 eV = 1.6 x 10-19 Joules

h = Plank’s constant (6.625 x 10-34 Joule-sec or

4.135 x 10-15 eV-sec)

n = frequency

c = speed of light

l = 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 Energy

E = hn or hc/l [Joules or eV (electron-volts)]

(higher frequency = higher energy)

(lower energy)

Amount of power over a given area, Watts/m2

4 red photons every second

Area = 2.00 m2

Energy of 1 red photon = hc/l = (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 eV

Irradiance = 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 l = .55 mm

Transmission, Reflection, and Absorption

incident light

reflectance (R)

air

transmittance (T) + absorptance (A)

material

• 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

Polarizer

Unpolarized light

(e.g. sunlight)

Linearly polarized light

Only one plane of vibration passes

Semiconductor Crystal Lattice

atom

covalent bond

Simple Cubic Structure

Silicon has a more complex lattice structure

but a lattice structure exists nevertheless.

Crystalline Silicon Bonds

valance

electrons

Si atom (Group IV)

=

covalent bond

(electron sharing)

+

Breaking of Covalent Bond Creating

Electron-Hole Pair

free electron moving

through lattice

e-

created hole

(missing electron)

covalent bond

Si atom

Photon (light, heat)

Photon hits valance electron with enough energy to

create free electron

+

+

Movement of a Hole in a Semiconductor

leaving a hole behind

e-

+

Valance and Conduction Energy Bands

free electron moving in

lattice structure

Conduction

Energy Band

Ec

Band Gap Energy, Eg = Ec - Ev

Valance

Energy Band

Ev

Hole within valance band

covalent bonds

Valance and Conduction Energy Bands

Thermal Equalibrium

e-

e-

+

+

free electron combines

with hole

free electron within

lattice structure

Conduction

Energy Band

Ec

Eg

Heat enery

given up

Heat energy

absorbed

Valance

Energy Band

Ev

Hole created within valance band

covalent bonds

Energy absorbed = Energy given up

e-

+

Intrinsic (pure) Silicon Electron-Hole Pairs

Thermal Equalibrium

ni = 1.5 x 1010 cm-3

at 300° K

Conduction

Band

Ec

hole density = electron density

number of holes per cubic centimeter =

number of free electrons per cubic centimeter

pi = ni = 1.5 x 1010 cm-3

Eg = 1.12 eV

pi = 1.5 x 1010 cm-3

at 300° K

Valance

Band

Ev

covalent bonds

• 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])

Doping or Substitutional Impurities

Group V Atom (Donor or N-type Doping)

Phospherous (Group V)

P atom

e-

covalent bond

Si atom (Group IV)

The donor electron is not part of a covalent bond so

less energy is required to create a free electron

e-

e-

+

Energy Band Diagram of Phospherous Doping

intrinsic free electron

donor free electron

Conduction

Band

Ec

Donor Electron

Energy

n > p (more electrons in conduction band)

A small amount of thermal energy (300° K) elevates

the donor electron to the conduction band

Eg

Ev

Valance

Band

intrinsic hole

covalent bonds

N-type Semiconductor

-

+

Doping or Substitutional Impurities

Group III Atom (Acceptor or P-type Doping)

Boron (Group III)

B atom

covalent bond

created hole

covalent bond

Si atom

Boron atom attacts a momentarily free valance

electron creating a hole in the Valance Band

e-

e-

+

+

Energy Band Diagram of Boron Doping

intrinsic free electron

Conduction

Band

Ec

p > n (more holes in valance band)

A small amount of thermal energy (300° K) elevates

the acceptor electron to the Acceptor band

Eg

acceptor electron

Acceptor Electron

Energy

Ev

Valance

Band

created hole

intrinsic hole

covalent bonds

P-type Semicondutor

Charge Transport Mechanisms

within a Semiconductor

• Drift Current Density
• Diffusion Current Density

e-

e-

e-

e-

e-

e-

e-

e-

e-

+

+

+

+

+

+

+

+

+

Applied Electric Field

Current

The number of holes or electrons passing through

a cross sectional area, A, in one second

x

y

I = q/t

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

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

and Direction of Current

e-

e-

e-

e-

e-

e-

e-

e-

e-

+

+

+

+

+

+

+

+

+

Applied Electric Field

Current Density

The number of holes or electrons passing through

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

x

A (area) = xy cm2

y

I (amps) = coulombs/sec

J (current density) = I/A

[J] =[amps/cm2]

and Direction of Current

e-

+

Applied Electric Field

Drift Velocity

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

through a conducting material

dp

Scattering Sites

vp = dp/t1

dn

ve = dn/t1

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

Drift Velocity and Applied Electric Field

• Newton’s Second Law of Motion
• F = ma
• Analogy with Electic Fields
• m q (mass charge)
• a E (accelerating field applied electric field)
• F = qE
• Without scattering sites, the charged particle
• would 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 material

μn 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-sec

μn = 1350 cm2/volt-sec

Mobility and Current Density Relation

• Current
• I = q/t
• q = number of charged particles passing through a cross sectional
• area
• t = time
• Current Density
• J = I/A = (q/t)/A
• A = 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

vp

+

+

+

+

+

+

+

+

+

+

Mobility and Current Density for Holes

E

x

x

vp

y

y

z

z

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 μpE

Jp|drf = Ip/A = epμpE

ve

ve

e-

e-

e-

e-

e-

e-

e-

e-

e-

e-

E

Mobility and Current Density for Electrons

x

x

y

y

z

z

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

Drift Current Density Expressions

Jp|drf = Ip/A = enμpE

Jn|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

gas

sealed membrane

After seal is broken

Gas molecules move from high concentration region to low

concentration region after membrane is broken

If gas molecules are replaced by charge then a current exists

during charge transport creating a Diffusion Current

Electron Diffusion Current

electron flow

slope = Dn/Dx

Electron concentration, n

Electron diffusion

current density

x

distance

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

Hole Diffusion Current

hole flow

slope = Dp/Dx

Hole concentration, p

Hole diffusion

current density

x

distance

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

Diffusion Currents

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

Total Diffusion Current =Jn|dif - Jp|dif

PN Junction Formation

Boron Atom

Doping

Phophorous Atom

Doping

Intrinsic Silicon Wafer

• 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

PN Junction in Thermal Equilibrium

(No Applied Electric Field)

Space Charge Region

metallurgical

junction

metallurgical

junction

-

-

-

-

+

+

+

+

P-type

N-Type

p

n

Initial Condition

E field

Equilibrium Condition

• 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.

PN Junction in Thermal Equilibrium

(No Applied Electric Field)

Diffusion Forces = E Field Forces

Space Charge Region

metallurgical

junction

-

-

-

-

+

+

+

+

p

n

E field

Diffusion force

on holes

Diffusion force

on electrons

E field force

on holes

E field force

on electrons

Definition of Electric Potential Difference (Volts)

d

Positive test charge, +q0

E field

x=a

x=b

Work (energy) per test charge required to move a positive test charge, +q,

a distance x=d against an electric field,

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

PN Junction in Thermal Equilibrium

Electric Field

metallurgical

junction

Space Charge Region

p

n

- - - - - - - - -

+ + + + + + + + +

- - - - - - - - -

+ + + + + + + + +

- - - - - - - - -

+ + + + + + + + +

E = 0

E = 0

- - - - - - - - -

+ + + + + + + + +

- - - - - - - - -

+ + + + + + + + +

Internal E field direction

E

- xp

x = 0

+ xn

PN Junction in Thermal Equilibrium

Built-in Potential, Vbi

metallurgical

junction

Space Charge Region

p

n

- - - - - - - - -

+ + + + + + + + +

- - - - - - - - -

+ + + + + + + + +

- - - - - - - - -

+ + + + + + + + +

E = 0

E = 0

- - - - - - - - -

+ + + + + + + + +

- - - - - - - - -

+ + + + + + + + +

Internal E field direction

V

Positive test charge, +q0

DV = Vbi

- xp

x = 0

+ xn

Conduction and Valance Band Diagram for PN Junction

in Thermal Equilibrium

Built-in Potential, Vbi

Ec

eVbi

Ec

Ev

Ev

p region

space charge region

n region

- xp

x = 0

+ xn

------

-----

----

Conduction Band Diagram for PN Junction

in Thermal Equilibrium

Electron Energy

Ec

eVbi

Ec

- xp

x = 0

+ xn

p region

space charge region

n region

Work or Energy is required to move electrons from

n region to p region (going uphill)

Applying a Voltage Across a PN Junction

Non-Equilibrium Condition (external voltage applied)

Reverse Bias Shown

Increased Space Charge Region

metallurgical

junction

- -

+ +

+ +

+ ++ ++ +

- -

- -

n

p

- -

E field

Forward

Bias

- -

E applied

+

-

Reverse

Bias

Vapplied

+

-

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

Reverse Bias PN Junction

Non-Equilibrium Condition (external voltage applied)

Increased Space Charge Region

metallurgical

junction

- -

+ +

+ +

+ ++ ++ +

- -

- -

n

p

- -

E field

- -

Ireverse

E R

+

-

VR

• 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

Conduction and Valance Band Diagram for PN Junction

Reverse Bias Voltage Applied

Vtotal = Vbi + VR

Ec

eVbi + eVR

Ec

space charge region

Ev

p region

n region

Ev

- xp

x = 0

+ xn

Forward Bias PN Junction (Diode)

Non-Equilibrium Condition

metallurgical

junction

Space Charge Region

n

p

E field

IForward

E applied

-

+

Va

• 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.

Forward Bias PN Junction

(Applied Electric Field > Internal Electric Field)

Diffusion Forces > E Field Forces

Space Charge Region

metallurgical

junction

-

-

-

+

+

+

p

n

Applied E field

E field

Diffusion force

on holes

Diffusion force

on electrons

Net E field force

on holes

Net E field force

on electrons

Forward Bias PN Junction

Diffusion Forces > E Field Forces

Creates Hole and Electron Injection

in Space Charge Region

Hole Injection

across

Space charge region

from Diffusion force

Electron Injection

across

Space charge region

from Diffusion force

p

n

Applied E field

E field

Diffusion force

on holes

Diffusion force

on electrons

Net E field force

on holes

Net E field force

on electrons

Forward Bias PN Junction

Diffusion Forces > E Field Forces

Creates Hole and Electron Injection

in Space Charge Region

Total Current density

Jtotal

Current

density

Electron Injection

across

Space charge region

from Diffusion force

Jn|inj

Hole Injection

across

Space charge region

from Diffusion force

Jp|inj

p

n

Jtotal = Jp|inj + Jn|inj

Forward Bias PN Junction

Electron and Hole Current

Components

hole injection

current

Jp|inj

Total Current density

Jtotal

Current

density

p

n

hole drift

current

Jp|drf

electron drift

current

Jn|drf

electron diffusion

current

Jn|dif

hole diffusion

current

Jp|dif

electron injection

current

Jn|inj

Forward Bias PN Junction

Electron and Hole Current

Components

Jtotal

Jp|inj

Current

density

p

n

Jp|drf

Jn|drf

Jn|inj

Jp|dif

Jn|dif

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

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

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

Ideal PN Junction

Current-Voltage Relationship

Jtotal

turn on voltage

Va

JS

JS = Reverse Bias Current Density

Va = Applied Voltage

Jtotal = JS[exp(eVa/(kT) - 1]

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 Injection

Reversible 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 hole

and electron injection carriers that are swept out by the internal

E field creating a voltage potential.

e-

e-

e-

e-

e-

+

+

+

+

+

PN Junction Solar Cell Operation

Step 1

Photon

hn > Eg

Space Charge Region

E field

p

n

• Photons create hole-electron pairs in space charge region
• Created hole-electron pairs swepted out by internal E field

e-

e-

e-

e-

e-

+

+

+

+

+

PN Junction Solar Cell Operation

Step 2

Photon

hn > Eg

Space Charge Region

E field

IL

p

n

E injected

• 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

e-

e-

e-

e-

e-

+

+

+

+

+

PN Junction Solar Cell Operation

Step 3

Photon

hn > Eg

Space Charge Region

E field

IL

p

n

E injected

Icell

Resistor

-

+

Vcell

• 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

e-

e-

e-

e-

e-

+

+

+

+

+

PN Junction Solar Cell Operation

Step 3

Photon

hn > Eg

Space Charge Region

E field

IL

p

n

E injected

Icell

Resistor

-

+

Vcell

heat

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

Typical Silicon Solar Cell Design

Photons

Protective High Transmission Layer

P-type

Doping

Wires

N-type

Silicon

Wafer

0.6 mm

4-6 inches

• 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

p to n connection

-

6 volts

+

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%