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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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slide1

Basic Fundamentals

of

Solar Cell Semiconductor Physics

for

High School Level Physics

slide3

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)

slide4

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)

slide5

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]

slide6

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)

slide7

Irradiance

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

slide9

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.
slide10

Polarization

Polarizer

Unpolarized light

(e.g. sunlight)

Linearly polarized light

Only one plane of vibration passes

slide12

Semiconductor Crystal Lattice

atom

covalent bond

Simple Cubic Structure

Silicon has a more complex lattice structure

but a lattice structure exists nevertheless.

slide13

Crystalline Silicon Bonds

valance

electrons

Si atom (Group IV)

=

covalent bond

(electron sharing)

slide14

+

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

slide15

+

+

Movement of a Hole in a Semiconductor

Thermal energy causes valance electron to jump to existing hole

leaving a hole behind

slide16

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

slide17

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

slide18

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])
slide20

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

slide21

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

slide22

-

+

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

slide23

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

slide24

Charge Transport Mechanisms

within a Semiconductor

  • Drift Current Density
  • Diffusion Current Density
slide25

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

slide26

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

slide27

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)
slide28

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.
slide29

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
slide30

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

slide31

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
slide32

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

slide33

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

slide34

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

slide35

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

slide36

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
slide37

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
slide38

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

slide40

PN Junction Formation

Masking Barrier

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
slide41

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.
slide42

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

slide43

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]

slide44

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

slide45

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

slide46

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

slide47

------

-----

----

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)

slide48

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
slide49

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
slide50

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

slide51

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.
slide52

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

slide53

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

slide54

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

slide55

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

slide56

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

slide57

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]

slide58

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
slide59

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.

slide60

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
slide61

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
slide62

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

IForwad

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
slide63

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

IForwad

Icell

Resistor

-

+

Vcell

heat

  • Icell = IL - Iforward
  • Icell = IL - IS[exp(eVcell/(kT) -1]
  • Icell is always in reverse bias direction
slide64

Typical Silicon Solar Cell Design

Photons

Protective High Transmission Layer

P-type

Doping

Wires

N-type

Silicon

Wafer

0.6 mm

4-6 inches

To load

  • 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
slide65

Silicon Solar Cell 6 Volt Panel Series-Parallel Design

12 cells in series = 6 volts

p to n connection

-

6 volts

+

slide66

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%
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