Download H.S. Semiconductor Physics of Solar Cells Advanced

Basic Fundamentals
of
Solar Cell Semiconductor Physics
for
High School Level Physics
Review Topics
Wavelength and Frequency
amplitude
Period (sec)
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)
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
Solar Spectrum at Earth Surface (noon time)
925 W/m2
E (eV) = hc/l
l = 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
inrfared
ultraviolet
Solar Spectrum
at Earth Surface
(noon time)
Transmission, Reflection, and Absorption
incident light
air
material
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
Polarizer
Unpolarized light
(e.g. sunlight)
Linearly polarized light
Only one plane of vibration passes
Basics of Semiconductor Physics
Semiconductor Crystal Lattice
covalent bond
atom
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
e- through lattice
+
covalent bond
created hole
(missing electron)
Si atom
Photon (light, heat)
Photon hits valance electron with enough energy to
create free electron
Movement of a Hole in a Semiconductor
+
+
Thermal energy causes valance electron to jump to existing hole
leaving a hole behind
Valance and Conduction Energy Bands
free electron moving in
lattice structure
Conduction
eEnergy Band
Ec
Band Gap Energy, Eg = Ec - Ev
Valance
Energy Band
covalent bonds
+
Ev
Hole within valance band
Valance and Conduction Energy Bands
Thermal Equalibrium
free electron combines
free electron within
with hole
lattice structure
Conduction
eeEnergy Band
Ec
Eg
Heat enery
given up
Valance
Energy Band
covalent bonds
Heat energy
absorbed
+
+
Ev
Hole created within valance band
Energy absorbed = Energy given up
Intrinsic (pure) Silicon Electron-Hole Pairs
Thermal Equalibrium ni = 1.5 x 1010 cm-3
at 300° K
Conduction
eBand
Ec
Eg = 1.12 eV
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
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])
Creating a Semiconductor
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
Energy Band Diagram of Phospherous Doping
intrinsic free electron
Conduction
Band
donor free electron
e-
eEc
Donor Electron
Energy
n > p (more electrons in conduction band)
Eg
Valance
Band
covalent bonds
A small amount of thermal energy (300° K) elevates
the donor electron to the conduction band
+
intrinsic hole
N-type Semiconductor
Ev
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
Energy Band Diagram of Boron Doping
intrinsic free electron
Conduction
Band
eEc
p > n (more holes in valance band)
Eg
A small amount of thermal energy (300° K) elevates
the acceptor electron to the Acceptor band
acceptor electron
Acceptor Electron
Energy
Valance
Band
e+
+
Ev
created hole
covalent bonds
intrinsic hole
P-type Semicondutor
Charge Transport Mechanisms
within a Semiconductor
• Drift Current Density
• Diffusion Current Density
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]
+
+
Applied Electric Field
and Direction of Current
eee-
• holes move in Current direction
• electrons move in opposite direction
e-
eee-
ee-
+
+
+
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]
Applied Electric Field
and Direction of Current
eee-
e-
eee-
ee-
Drift Velocity
The average velocity of a hole (vp) or electon (ve) moving
through a conducting material
Applied Electric Field
e-
+
dp
vp = dp/t1
Scattering Sites
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
Mobility and Current Density for Holes
E
x
x
+
+
y
+
vp
+
+
+
+
vp
+
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
Mobility and Current Density for Electrons
E
x
x
e-
ve
y
ee-
eve
y
ee-
eeee-
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
sealed membrane
empty chamber
gas
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 concentration, n
Electron Diffusion Current
electron flow
slope = Dn/Dx
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 concentration, p
Hole Diffusion Current
hole flow
slope = Dp/Dx
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
Formation and Basic Physics
of
PN Junctions
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
PN Junction in Thermal Equilibrium
(No Applied Electric Field)
metallurgical
junction
P-type
Space Charge Region
metallurgical
junction
N-Type
Initial Condition
p
-
+
+
+
+
n
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
E field force
on holes
Diffusion force
on electrons
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
E=0
-----------------------------------------
n
+++++++++
+++++++++
+++++++++
+++++++++
+++++++++
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
E=0
-----------------------------------------
n
+++++++++
+++++++++
+++++++++
+++++++++
+++++++++
E=0
Internal E field direction
Positive test charge, +q0
V
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
- xp
x=0
n region
+ xn
Conduction Band Diagram for PN Junction
in Thermal Equilibrium
Electron Energy
Ec
------------- xp
p region
x=0
space charge region
+ xn
eVbi
Ec
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
p
Forward
Bias
Reverse
Bias
------
++
++
++
E field
++
++
n
+ E applied Vapplied
-
+
• 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
Reverse Bias PN Junction
Non-Equilibrium Condition (external voltage applied)
Increased Space Charge Region
metallurgical
junction
p
------
++
++
++
E field
++
++
Ireverse
n
ER
+
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
Net E field force
on holes
Diffusion force
on electrons
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
p
n
Electron Injection
across
Space charge region
from Diffusion force
Applied E field
E field
Diffusion force
on holes
Net E field force
on holes
Diffusion force
on electrons
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
Current
density
Jtotal
Hole Injection
across
Space charge region
from Diffusion force
Jp|inj
p
n
Jtotal = Jp|inj + Jn|inj
Electron Injection
across
Space charge region
from Diffusion force
Jn|inj
Forward Bias PN Junction
Electron and Hole Current
Components
hole injection
current
Total Current density
p
n
hole drift
current
electron drift
current
Jp|drf
electron diffusion
current
Jn|dif
Jp|inj
Current
density
Jtotal
Jn|drf
electron injection
current
Jn|inj
hole diffusion
current
Jp|dif
Jtotal
Forward Bias PN Junction
Electron and Hole Current
Components
Current
Jp|inj
density
p
n
Jp|drf
Jn|drf
Jn|dif
Jn|inj
Jp|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.
PN Junction Solar Cell Operation
Photon
Step 1
Space Charge Region
hn > Eg
p
+
+
+
+
+
E field
eeeee-
n
• Photons create hole-electron pairs in space charge region
• Created hole-electron pairs swepted out by internal E field
PN Junction Solar Cell Operation
Photon
Step 2
Space Charge Region
hn > Eg
p
+
+
+
+
+
E field
IL
E injected
eeeee-
n
• 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
PN Junction Solar Cell Operation
Photon
Step 3
Space Charge Region
hn > Eg
p
IForwad
+
+
+
+
+
E field
eeeee-
IL
E injected
Icell
n
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
PN Junction Solar Cell Operation
Photon
Step 3
Space Charge Region
hn > Eg
p
IForwad
+
+
+
+
+
E field
eeeee-
IL
E injected
Icell
n
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
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
0.6 mm
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%