High School Slides

8/12/2019 High School Slides

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Basic Fundamentals

ofSolar Cell Semiconductor Physics

for

High School Level Physics


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Review Topics


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Wavelength and Frequency

Period (sec)

time

amplitude

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 108m/sec)


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Spectrum

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 10-6meters) (purple) to 0.8 microns (red)

Intensity


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Energy and Power

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

energy.

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

1 eV = 1.6 x 10-19Joulesh = Planks constant (6.625 x 10-34Joule-sec or

4.135 x 10-15eV-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]


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Photons

A light particle having energy. Sunlight is a spectrum of

photons. X-rays and heat are photons also.

Photon Energy

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

(higher frequency = higher energy)

(lower energy)


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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/l= (6.63 x 10-34J-s)(2.99 x 108m/s)/(0.80 x 10-6meters)

= 2.48 x 10-19J = 1.55 eV

Irradiance = Power/Area = (4 photons/sec)(Energy of 1 photon)/2.00 m2

= 4.96 x 10-19W/m2

Typical sunlight irradiance is 0.093 W/cm2= 930 W/m2at l= .55 mm


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Solar Spectrum at Earth Surface (noon time)

E (eV) = hc/ll= hc/E

Visable range

.75 mm (red) - .4 mm (purple)

1.6 eV - 3.1 eV

Solar Spectrum at Earth Surface

.5 eV - 3.6 eV

mm (infrared) - 0.34 mm (ultraviolet)

visible

ultravioletinrfared

Solar Spectrum

at Earth Surface

(noon time)

925 W/m2


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Polarization

Unpolarized light

(e.g. sunlight)Linearly polarized light

Polarizer

Only one plane of vibration passes


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Basics of Semiconductor Physics


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Si atom (Group IV)

Crystalline Silicon Bonds

covalent bond

(electron sharing)

=

valance

electrons


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Breaking of Covalent Bond Creating

Electron-Hole Pair

Si atom

covalent bond+

e-free electron moving

through lattice

created hole

(missing electron)

Photon (light, heat)

Photon hits valance electron with enough energy to

create free electron


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Movement of a Hole in a Semiconductor

+

Thermal energy causes valance electron to jump to existing hole

leaving a hole behind

+


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Valance and Conduction Energy Bands

Thermal Equalibrium

covalent bonds

+

e-

free electron within

lattice structure

Heat energy

absorbed

Energy absorbed = Energy given up

ConductionEnergy Band

Valance

Energy Band

Eg

Hole created within valance band

+

e-

Heat enery

given up

Ec

Ev

free electron combines

with hole


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Intrinsic (pure) Silicon Electron-Hole Pairs

Thermal Equalibrium

covalent bonds

+

e-

ni= 1.5 x 1010cm-3

at 300 K

Number of electron-hole pairs increase with increasing temperature

The thermal voltage, Vtis equal to kT/e (k = 8.62 x 10-5eV/K, T = [Kelvin])

ConductionBand

Valance

Band

Eg= 1.12 eV

pi= 1.5 x 1010cm-3

at 300 K

hole density = electron density

number of holes per cubic centimeter =number of free electrons per cubic centimeter

pi = ni= 1.5 x 1010cm-3

Ec

Ev


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Creating a Semiconductor


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Doping or Substitutional Impurities

Group V Atom (Donor or N-type Doping)

Si atom (Group IV)

covalent bond

e-

The donor electron is not part of a covalent bond so

less energy is required to create a free electron

Phospherous (Group V)

P atom


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Energy Band Diagram of Phospherous Doping

covalent bonds

+

e-

N-type Semiconductor

ConductionBand

Valance

Band

Eg

n > p (more electrons in conduction band)A small amount of thermal energy (300 K) elevates

the donor electron to the conduction band

Donor Electron

Energy

e-

intrinsic hole

intrinsic free electron donor free electron

Ec

Ev


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Doping or Substitutional Impurities

Group 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 valance

electron creating a hole in the Valance Band


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Drift Velocity

The 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


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Drift Velocity and Applied Electric Field

Newtons 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.


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Hole and Electron Mobility

pis the hole mobility in the conducting materialnis the electron mobility in the conducting material

The units of mobility, , are

v = E

[cm/sec] = [] [volts/cm]

[] = [cm2/volt-sec]

Typical mobility values in Silicon at 300 K:

p = 480 cm2/volt-sec

n = 1350 cm2/volt-sec


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++

Mobility and Current Density for Holes

Each hole has traveled a distance z in a time t = z/vpThe number of holes in the volume is pV (hole density x volume)

The charge of each hole is e (1.6 x 10-19coulombs)

I = q/t = e(pV)/(z/vp) = ep(xyz)/(z/vp) = ep(xy)vp= epA pE

Jp|drf= Ip/A = eppE

E

x

y

z

x

y

z

vp+

+

+

+

+

+

+

+

vp


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ve ve

e-

e-

Mobility and Current Density for Electrons

Replacing p with n and vpwith vegives:The charge of each electron is -e (-1.6 x 10-19coulombs)

I = q/t = -epV/(z/ve) = -ep(xyz)/(z/ve) = -ep(xy)ve= -epA(-nE)

I = epA(nE)

Jn |drf= In/A = ennE

E

x

y

z

x

y

z

e-

e-e-

e-

e-

e-

e-e-


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Diffusion Process

gas filled chamber empty chamber

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

gas


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Electron Diffusion Current

distance

Electron

concentration,n

electron flow

Electron diffusion

current density

x

slope = Dn/Dx

electron flow is from high to low concentration (-x direction)

electron diffusion current density is in positive x direction

Jn|dif= eDn

n/

xwhere Dnis the electron diffusion constant


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Hole Diffusion Current

distance

Holecon

centration,p hole flow

Hole diffusion

current density

x

slope = Dp/Dx

hole flow is from high to low concentration (-x direction)

hole diffusion current density is in negative x direction

Jp|dif= -eDn

p/

xwhere Dpis the hole diffusion constant


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Diffusion Currents

Jn|dif= eDnn/xJp|dif= -eDnp/xElectron and hole diffusion currents are in opposite directions

for the same direction of increasing concentration

Total Diffusion Current =Jn|dif- Jp|dif


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Formation and Basic Physicsof

PN Junctions

PN Junction Formation


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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 Atom

Doping


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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

+

++

+

-

--

-


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(No Applied Electric Field)

Diffusion Forces = E Field Forces

metallurgical

junction

E field

Space Charge Region

p n

+

++

+

-

--

-

Diffusion force

on holesDiffusion force

on electrons

E field force

on electrons

E field force

on holes


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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


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Electric Fieldmetallurgical

junction

Internal E field direction

Space Charge Region

p n

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

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

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

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

E

- xp + xnx = 0

E = 0E = 0


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metallurgical

junction

Internal E field direction

Space Charge Region

p n

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

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

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

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

Positive test charge, +q0

E = 0E = 0

V

- xp + xnx = 0

V = Vbi


Built-in Potential, Vbi


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Conduction and Valance Band Diagram for PN Junction

in Thermal Equilibrium

Built-in Potential, Vbi

- xp + xnx = 0

eVbi

Ec

Ev

p region n regionspace charge region

Ec

Ev


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Conduction Band Diagram for PN Junction

in 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 Junction


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Applying a Voltage Across a PN Junction

Non-Equilibrium Condition (external voltage applied)

Reverse Bias Shown

Eappliedis created by bias voltage source Vapplied.

Efield exists in p-region and n-region.

Space Charge Region width changes.

Vtotal= Vbi+ Vapplied

metallurgical

junction

E field

Increased Space Charge Region

p n

E applied

Vapplied

-

+

+ +

+ +

+ +

+ ++ +

- -- -- -- -- -

+

-

Forward

Bias

Reverse

Bias

R Bi PN J ti


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Reverse Bias PN Junction

Non-Equilibrium Condition (external voltage applied)

ERis created by reverse bias voltage source VR.

ERis in same direction as internal E field.

Space Charge Region width increases.

Vtotal= Vbi+ VRIreverseis created from diffusion currents in the space charge region

metallurgical

junction

E field

Increased Space Charge Region

p n

E R

VR

- +

+ +

+ +

+ +

+ ++ +

- -- -- -- -- -

Ireverse


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Forward Bias PN Junction

(Applied Electric Field > Internal Electric Field)

Diffusion Forces > E Field Forces

metallurgical

junction

E field

Space Charge Region

p n

+

++

-

--

Diffusion force


on electrons

Net E field force

on electrons

Net E field force

on holes

Applied E field


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Creates Hole and Electron Injection

in Space Charge Region

E field

p

Diffusion force


on electrons

Net E field force

on electrons

Net E field force

on holes

Applied E field

n

Hole Injection

across

Space charge region

from Diffusion force

Electron Injection

across

Space charge region



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Creates Hole and Electron Injection

in Space Charge Region

p n

Hole Injection

across

Space charge region


Jp|inj

Electron Injectionacross

Space charge region


Jn|inj

Current

density

Total Current density

Jtotal

Jtotal= Jp|inj+ Jn|inj


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Electron and Hole Current

Components

p n

hole diffusion

current

Jp|dif

electron diffusioncurrent

Jn|dif

Current

density

Total Current density

Jtotal

hole drift

current

Jp|drf

electron drift

current

Jn|drf

hole injectioncurrent

Jp|inj

electron injection

current

Jn|inj



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Current-Voltage Relationship

JS

Jtotal

JS = Reverse Bias Current Density

Va= Applied Voltage

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

Va

turn on voltage


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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


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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.

PN Junction Solar Cell Operation


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p

Step 1Photonhn> Eg Space 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



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Step 2

Created hole-electron pairs are swept out by the E field.

creates excess holes in p-region

creates excess electrons in n-region

Einjectedis created by excess holes and electrons

Photocurrent, IL, is in reverse bias direction

Photon

hn> Eg Space Charge Region

E field

p nIL

Einjected

+

+

+

+

+

e-

e-

e-

e-

e-



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Step 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

Iforwadis created by Einjected

Icell= IL- Iforward

Photon

hn> Eg Space Charge Region

E field

p n

Resistor

Vcell

IL

IcellIForwad

+ -

Einjected

+

+

+

+

+

e-

e-

e-

e-

e-


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Typical Silicon Solar Cell Design


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Typical Silicon Solar Cell Design

N-type

Silicon

Wafer

P-type

Doping

Protective High

Transmission Layer

To load

Wires

4-6 inches

0.6 mm

Photons

Photons transmit through thin protective layer andthin 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


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g

12 cells in series = 6 volts

6 volts

p to n connection

-

+


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External Factors Influencing Solar Cell Effeciency

Photon transmission, reflection, and absorption of protective layerMaximum transmission desired

Minimum reflection and absorption desired

Polarization of protective layer

Minimum polarized transmission desiredPhoton Intensity

Increased intensity (more photons) increases cell current, IcellCell 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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