The Illuminated p-n Junction
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
The Illuminated pn Junction
•
Generation re-visited
– Basic requirements
– Optical Generation
– Absorption Coefficient
– Optical Generation Rate
•
The Illuminated pn Junction
– IV equation
– Physical Meaning of I0
– What is going on?
•
Different Operating Conditions
– Short circuit condition
– Open circuit condition
– Forward bias
– Reverse bias
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Generation revisited
Basic requirements:
• Need to move carriers from one band to the other, so require:
– Energy increase greater than the band gap
– Must be a carrier available for excitation
– Must be a vacant state available for carrier to move to
•
Energy can be provided by any means, however:
– Thermal energy only gives nett increase with thermal gradients across
device.
– Optical absorption does not have such a restriction – will consider ONLY
optical absorption
•
Important to remember that each absorption process has its own inverse
process (we may not be able to observe them easily but they are there)
– In thermal equilibrium they balance exactly
– Steady state they are both present though one will be much stronger than the
other
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Optical Generation
•
Absorption of photons where the energy of each photon is given by:
•
Energy of photon is primary determinant of what happens when it
hits the semiconductor
– If E < EG then (ideally) no absorption
– If E ≥ EG then absorption
•
•
Energy above the band gap
is lost as heat to the crystal
lattice (phonons)
Major fundamental losses
for a solar cell
excess holes
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Optical Generation
•
Recall that the bands are actually more complex and vary with
crystal momentum
– Direct and indirect band gaps arise
– Absorption for indirect band gap requires phonons, a three particle
process meaning lower absorption
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Absorption Coefficient
•
Absorption coefficient, α, is a measure of the probability that a photon is
absorbed
– Varies with wavelength
– Material specific
•
Absorption depends on likelihood of transition – lower around the band
edge increasing further away
•
Direct band gap materials generally
have more rapid increase in the
absorption – higher α
•
Absorption depth 1/α is often
defined – intensity of light has
dropped to 1/e of initial
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Absorption Coefficient
•
Absorption coefficient of direct materials
has the form:
(hν − EG )
1
2
•
Not so straight-forward for indirect band
gap materials, like Si, also get
absorption below EG
•
Temperature of the material shifts the
band gap.
– As T increase EG decreases and vice
versa
– Since band gap is shifted so is the
absorption coefficient
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Generation Rate
•
•
Need to know how many photons have been absorbed by a material at a
particular depth x
Given by the following:
•
NS is number of photons at surface (x = 0), α is absorption coefficient
•
Generation rate can then be found:
•
Important to distinguish between two – remember which is a rate and
which is a total number
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Generation Rate
•
Generation rate depends on the
wavelength of light and the depth
in the material
•
Larger absorption coefficient
means generation is predominantly
near the surface
Small absorption coefficient means
generation is more uniform
•
•
If x << 1/α then generation can be
assumed to be constant
Remember
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Illuminated pn junction
•
•
•
pn junction has optical generation of carriers that may be swept across the
junction by the drift field
Optical generated carriers are swept from being minority carriers on one side to
being majority carriers on the other
How is the IV equation affected by the optical generation?
minority
carriers
majority
carriers
majority
carriers
minority
carriers
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Illuminated IV equation
•
•
•
•
We can solve for the IV equation in exactly the same manner as
previously but this time don’t assume G = 0
This means the differential equation to be solved for the carrier
concentration increase is given by:
We simplify by assuming that the generation is constant (solving it
otherwise is a nightmare)
Means we get the following simple solution to the differential equation:
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Illuminated IV equation
•
We can proceed in an identical manner as for the un-illuminated case
i.e. differentiate the carrier concentration increase to find the current
and then equating the currents on the p and n sides of the junction, we
then end up with:
•
This means the light generated current is simply a superposition on top
of what we get for the un-illumined case!
We bundle this information up in the following expression:
•
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Meaning of I0
• We want to extract the light generated current with a forward
bias meaning the diode current determined by I0 works
AGAINST the light generated current
• The first term is a recombination current found by
considering the diode without illumination – often referred to
as the dark current
• We therefore want to reduce I0 to as low a value as possible
in order to be able to extract as much light generated
current as possible
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Short Circuit
• Means no load attached but current can flow
• Recombination is essentially what we expect for thermal
equilibrium and can be ignored
J SC = J 0 (e
q .0
kT
− 1) − J L = J 0 (1 − 1) − J L = − J L
• Short circuit current is therefore the light generated current
• This makes the short circuit current VERY important
because it tells us how much light generated current there is
• Gives us good idea about absorption of the light but carriers
still have to get to contacts without recombining
• Can be measured as function of wavelength to give the
quantum efficiency
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Open Circuit
• Infinite load attached – no current flow
J = J 0 (e
VOC
qVOC
nkT
− 1) − J L = 0
⎛ JL ⎞
nkT ⎛ J L ⎞
=
ln⎜⎜ − 1⎟⎟ ≈ ln⎜⎜ ⎟⎟
q
⎝ J0 ⎠
⎝ J0 ⎠
• Tells us about the light generated current AND the “dark”
current
• Lower dark current means higher open circuit voltage but it
scales logarithmically not linearly
• Harder to “fix” than short circuit current
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
IV Curves
• When illuminated the diodes ‘dark’ I-V characteristic is
shifted
• Note short circuit current and open circuit voltages for the
illuminated case
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Reverse bias
•
Deliberately reverse bias the diode that is under illumination –
diffusion current is switched off
•
Current seen is essentially equal to the light generated current –
slight increase seen but if I0 is low we can neglect
•
Assuming that we get ~100%
extraction of photons absorbed
and absorption is good then the
current is proportional to the
number of photons with energy
above the band gap
•
•
Reverse bias
This is how a photodetector works
Note it doesn’t tell us what the photon
energy is, just that it is above the band
gap
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Reverse bias
• Recall from the dark diode case that when we apply a reverse or
negative bias the built-in field at the junction increases – this is an
increase in the barrier to diffusion
• Note that the drift current (light generated) is not increased but the
diffusion current is made negligible
• The slight increase in drift current is related to I0 and so we want this
to be low
• Obviously we will run at a voltage
that ensures negligible diffusion
current
• Requirements for a photodetector
- high absorption
- high collection probability
- low diffusion current
are the same as for a solar cell
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Forward Bias
• More than meets the eye to case of diode in the dark
• If radiative recombination is efficient than we can get
significant light emission when bias is applied
• Direct band gap materials such as GaAs
work best
• Device designed to enhance
recombination
• This is the basis of light emitting
diodes (LEDs)
• Can even get a laser diode
– This requires a bit more work
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Forward bias
• What if we deliberately make the recombination of carriers
very unlikely and shine light on it?
• According to the IV characteristic we need a forward bias to
raise the dark current to kill off the light generated current –
this is VOC
• This implies power is being
generated by the diode
- we have a current
- we have a bias
• We have a solar cell!
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
What is going on?
• Light generates excess minority carriers
• Carriers swept across junction by electric field –
electrons and holes are separated
• Do we get a voltage? Depends…..
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
What is going on?
….. on the load
• We are sending carriers to opposite sides of the junction
– if not extracted we have a build up of charge
– get an electric field and potential difference between p and n
regions
– this corresponds to a forward bias across the p-n junction
• So we can get both current and voltage extraction when
illuminating the pn junction – can get power out!
• We have a solar cell – i.e. it converts solar energy
directly to electrical energy
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Conventions
•
•
The light generated current being negative is simply a convention
based upon it being in the direction opposite to the flow for a biased
diode
We are talking of power generation so we think of the light generated
current as being positive and the diffusion current as being negative
J = J L − J 0 (e
•
•
•
qV
kT
− 1)
Burn this into your brain
Think of the IV curve as
what is shown here
Power is simply I.V
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Circuit model
• Simple circuit model can be used to understand the solar
cell and how it operates
• Need to add some more parts to make it ‘realistic’
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Power Extracted
• To find power simply multiply I by V
• Get an increase as V is increased until a maximum and
then get drop off until VOC when power is zero
Pmax = Imp.Vmp
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Efficiency
• We can easily find the power output and should be able to
find the input power
• Energy conversion efficiency is output divided by input
power
Pmax I mpVmp
η=
=
Pin
Pin
• For unconcentrated sunlight the typical input power will be
1kW/m2 (what does this mean for units of ISC and VOC?)
• How do the short circuit current and the open circuit voltage
relate to the efficiency?
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Efficiency
• Can also write the efficiency in the following way:
η=
•
I mpVmp
Pin
I SCVOC
= FF
Pin
FF =
I mpVmp
I SCVOC
Fill factor is a measure of how
‘ideal’ the IV curve is – it is a
measure of how much of area
described by ISC and VOC is
filled by the area described by
Imp and Vmp
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner
Fill Factor
Glossary
• ISC or JSC: Short circuit current – direct measure of light
absorption and collection probability
• VOC: Open circuit voltage – measure of ‘dark’ current as well
as light current, scales logarithmically
• FF: Fill factor – measure of how ‘ideal’ maximum power
point is in filling power area defined by ISC and VOC
• Dark current: diffusion current across pn junction due to bias
– carriers recombine and are lost
To make a good solar cell we must do the following:
- Maximize JSC
- Maximize VOC, this means minimize the dark current
- Maximize FF, bit trickier as it involves non-idealities
ELEG620: Solar Electric Systems University of Delaware, ECE Spring 2009 S. Bremner