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Chapter 6
Photodetectors
H-Alpha Solar
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Section 6.1 Solar Energy Spectrum
Photovoltaic devices or solar cells convert the incident solar
radiation energy into electrical energy.
The intensity of the radiation emitted from the sun has a spectrum
that resembles a black body radiation at a temperature of about
6,000 K.
Incident photons are absorbed to photogenerate charge carriers that
pass through an external load to do electrical work.
0
Black body radiation at 6000 K AM
AM1.
0.2 0.4^ 0.6^ 0.8^ 1.0 1.2 1.4^ 1.6 1.8^ 2.
0
Wavelength (μm)
Spectral Intensity dW cm-2^ (μm) -
or kW m-2^ (μm) -
The spectrum of the solar energy represented as spectral intensity ( I λ) vs wavelength above the earth's atmosphere (AM0 radiation) and at the earth's surface (AM1. radiation). Black body radiation at 6000 K is shown for comparison (After H.J. Möller, Semiconductors for Solar Cells , Artech House Press, Boston, 1993, p.10)
From S.O. Kasap, Optoelectronics and Photonics: Principles and Practices (Prentice Hall)
Figure 6.
Space = Air Mass Zero
Earth’s surface = AM 1.
Solar Energy Spectrum
The earth’s atmosphere absorbs and scatters the solar radiation
depending on the wavelength. Thus the space value (AM0) is not
available at the earth’s surface.
Iλ δλ is the intensity in a small interval δλ. Integration over the
whole spectrum give the total intensity I.
Light intensity variation with wavelength is typically represented
by intensity per unit wavelength, called spectral intensity Iλ.
This total intensity I gives the total power flow through a unit area
perpendicular to the direction of the sun. This quantity is called
solar constant or air-mass zero (AM0) radiation = 1,353 W/m
2
Solar Energy Spectrum
The actual intensity spectrum on the earth’s surface depends on the
absorption and scattering effect of the atmosphere. The
atmosphere’s composition (pollutants, airborne particulates, and so
on) and on the path length through the atmosphere.
Note on the next figure the effects of angle of the device with
respect to the sun and diffuse (cloudy) versus clear sky.
All of these effects depend on the spectral wavelength. Indeed
laser spectroscopy and atmospheric interferometry depends on this
effect.
Direct Diffuse
(a) Illustration of the effect of the angle of incidence θ on the ray path length and the
definitions of AM0, AM1 and AM(sec θ). The angle α between the sun beam and the horizon
is the solar latitude (b) Scattering reduces the intensity and gives rise to a diffused radiation
Atmosphere
AM
AM
θ
AM(sec θ)
h 0^ h
α
(a) (b)
α
Tilted PV device
Earth
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Figure 6.2 Example 6.1.1 on page 256 Solar energy conversion
Suppose a family house in a sunny geographic location consumes a
daily average electrical power of 500 W.
Let the annual average solar intensity incident per day (daylight
intensity averaged for 24 hour day) is 6 kW hours/m
2
. This is about
7 hours of direct sunlight per day.
Lastly let the efficiency of the solar cell be about 15%. Space borne
solar cells achieve about 30% efficiency at a cost of about
$100,000/m^2. The 15% efficient cell is around $500/m2.
What is the required solar cell area to supply this required power?
Energy per house
Incident solar energy per unit area × Efficiency
Area =
2
sec (500 )(86, 400 )
3600sec (6000 )( )(0.15)
W day
W hour
m day hour
= ⋅
2 =13.3 m
Example 6.1.1 on page 256 Solar energy conversion
So the space capable system would cost about 1.5 million dollars,
but would receive/convert more power by about a factor of 4.
The terrestrial installed solar cell at 15% would cost about $6,700.
Obviously, this solar system cannot match the peak power
requirements. Storage batteries and energy transfer to the power
grid add cost and complexity.
The payback period for a solar device is between 3 and 30 years
with 5 years considered the current average.
Section 6.2 Photovoltaic Device Principles
Consider a pn junction with a very narrow and more heavily doped
n-region. The illumination is through the thin n-side.
Neutral n -region Neutral p -region
W
Eo
Voc
Medium λ
Long λ
Depletion region
Drift Diffusion
Finger electrode
Back electrode
A n A p
Le
The principle of operation of the solar cell (exaggerated features to highlight principles)
Lh
Short λ
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
The depletion region W extends
primarily into the p-side. As in any
pn junction there is a built-in field
(and voltage) E 0.
The necessary current collection
electrodes attached to the n-side must
allow illumination to enter the device
and still result in a small series
resistance. Finger electrodes are the
device structure commonly used.
Finger electrodes
p
n
Bus electrode for current collection
Finger electrodes on the surface of a solar cell reduce the series resistance
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Figure 6.
Monocrystaline
Polycrystaline
Photovoltaic Device Principles
A thin antireflection coating on the surface reduces reflections
from the surface and allows more light to enter the device.
Neutral n -region Neutral p -region
W
Eo
Voc
Medium λ
Long λ
Depletion region
Drift Diffusion
Finger electrode
Back electrode
A n A p
Le
The principle of operation of the solar cell (exaggerated features to highlight principles)
Lh
Short λ
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
EHPs generated in the depletion
regions are immediately separated by
the built-in field to the bulk regions
where the charges can form an
external current.
For long wavelength photons, only
those EHPs created within a minority
carrier diffusion length of the
depletion region contribute to an
external current.
pn Junction Photovoltaic I-V Characteristics
By the text’s definitions used for the solar cell, the load resistor
appears to be delivering power since the current is not in accordance to
the power sign convention.
The author solved this notation dilemma by using the relationship
as negative resistance.
Thus we can find a specific (-R) that solves for the Vand I
required. The load line approach solves this problem graphically.
V
I
R
V
I (mA)
0.2 0.4 0.
0
Voc
Isc = – Iph
V ′
The Load Line for R = 30 ž ( I-V for the load)
I-V for a solar cell under an illumination of 600 Wm-2.
Operating Point
Slope = – 1/ R
P
I ′
(a) When a solar cell drives a load R , R has the same voltage as the solar cell but the current through it is in the opposite direction to the convention that current flows from high to low potential. (b) The current I ′ and voltage V ′ in the circuit of (a) can be found from a load line construction. Point P is the operating point ( I ′, V ′). The load line is for R = 30 ž.
Light I
R
V
I
(a) (b)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Figure 6.
pn Junction Photovoltaic I-V Characteristics
Another approach is the solve the P = VI equation and take the
derivative for maximum power. Let the ideality factor n = 1.
ph 0 exp^ k TB^1 e
V P I V I V V I
⎡ (^) ⎛ ⎞ ⎤ = ⋅ = − + ⋅ (^) ⎢ (^) ⎜ ⎟−⎥ ⎢⎣ ⎝ ⎠ ⎥⎦
max max (^0) ph 0 exp (^) k TB (^1 0) max exp k TB e b e
dP V e V I I I V dV k T
Now define the thermal voltage as V t = k BT/e
max max max 0
exp 1 exp
ph
t t t
V V I
V
V V V I
⎢ ⎜ ⎟ −^ ⎥+^ ⎜ ⎟ ⎜ ⎟=
max max
0
1 exp 1
ph
t t
V V I
V V I
⎜ +^ ⎟ ⎜ ⎟=^ +
max max
0
exp see homework 6.
ph
t t
V V I
V V I
pn Junction Photovoltaic I-V Characteristics
This last relationship can be solved by trial and error over the limited
voltages (typically 0.4 < Vmax < 0.6 for silicon) of a solar cell.
The current I ph will depend on the illumination and I 0 will be parameter
for the particular pn junction solar cell.
max max
0
1 exp 1
ph
t t
V V I
V V I
⎜ +^ ⎟ ⎜ ⎟=^ +
Since the open circuit voltage is the maximum voltage possible, and
short circuit current Isc is the maximum current possible, the
unachievable maximum power = Isc V oc.
The fill factor is a measure of how close to the maximum power is a
particular operating point.
m m
sc oc
I V FF I V
=
Problem 6.3 A solar cell driving a resistive load
A solar cell of area A = 4 cm^2 in connected to drive a load R.
Illumination = 600 W/m^2 behavior is shown in the figure.
Let the load R = 20 Ω and the intensity change to 1 kW/m^2.
What are the current and voltage in the circuit?
V
I (mA)
0.2 0.4 0.
0
Voc
V ′
The Load Line for( I-V for the load) R = 30 ž
I-V for a solar cell under an illumination of 600 Wm-2. Operating Point
Slope = – 1/ R
P
I ′
The solar cell is now used under an illumination of 1 kW/m^2. The short circuit
current Isc must be scaled by a factor of 1,000/600 = 1.67.
V ′ (^) V
I (mA)
0.4 0.
0
The load line for R = 20 ž ( I-V for the load)
I-V for a solar cell under an illumination of 1000 Wm -.
P
I ′
M
The figure shows the load line for R = 20 Ω.
The corresponding current I’= 22.5 mA.
The voltage V’ = 0.45 V.
Problem 6.3 A solar cell driving a resistive load
What is the power delivered to the load?
Pin = (Light Intensity)(Surface Area)
What is the efficiency of the solar cell in this circuit?
The efficiency η is given by
' ' 3 Poutput I V (22.5 10 A )(0.45 V ) 10.1 mW
− = = × =
4 2 2 2
2 10 in (1, 000^ W^ )(4^ m ) m cm
P cm
−
100%
out
in
P
P
η = ×
= 0.4 W
= × =
Problem 6.4 Open Circuit voltage and illumination
A solar cell under an illumination of 100W/m^2.
Short circuit current Isc = 50 mA Open circuit voltage Voc = 0.55 V.
What is Isc and Voc when the light intensity is halved?
Example 6.3.2 showed (We will assume the ideality constant n = 1.)
2 2 1 1
oc oc t ln
Intensity V V nV Intensity
2 2 1 1
sc sc
Intensity I I Intensity
2 2 1 1
sc sc
I
I I mA I
⎝ ⎠ ⎝^ ⎠
= 25 mA
2 2 1 1
ln 0.55 (0.0259) ln 2
oc oc t
I
V V V
I
⎝ ⎠ ⎝^ ⎠
= 0.55 − 0.018 =0.53 V
Section 6.4 Series Resistance and Equivalent Circuit
Practical devices can deviate substantially from the ideal pn
junction solar cell behavior considered so far.
The finger electrodes introduce an effective series resistance Rs
into the photovoltaic circuit. Small thin electrodes (the better for
light to pass through) further increase this series resistance.
A fraction of the current can flow through the crystal surfaces
(edges of the device) or through grain boundaries in
polycrystalline devices. This is represented as a shunt (or parallel)
resistance Rp.
Neutral n -region
Neutral p -region
Finger electrode
Back electrode
Depletion region
R (^) L
R (^) s
R (^) p
Series and shunt resistances and various fates of photegenerated EHPs.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Figure 6.
A
Iph
R p V R^ L
Iph I
Id
Solar cell Load
B
R s
The equivalent circuit of a solar cell
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Figure 6.
I (mA)
V
0 0
0.2 0.4 0.
5
10
Vo c
I (^) s c
Rs = 0
Rs = 20 Ω
Rs = 50 Ω
I (^) p h
The series resistance broadens the I-V curve and reduces the maximum available power and hence the overall efficiency of the solar cell. The example is a Si solar cell with n ≈ 1.5 and Io ≈ 3 × 10 -6^ mA. Illumination is such that the photocurrent I (^) ph = 10 mA.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Figure 6.11 Effect of Series and parallel resistance to the operating point. Problem 6.6 Series Connected Solar Cells
Consider two identical solar cells subject to the same illumination Iph = 10 mA.
I 0 = 25 x 10-6^ mA
RS = 20 Ω Ideality constant n = 1
Find the maximum power that can be delivered by two cells in series.
In this case there are two RS = 20 Ω in series and two pn junctions is series.
Thus the current is
Let I be the current through both and Vd the voltage across one pn junction then
(2 ) 2
s d
V I R V
−
0 exp^1
d ph t
V I I I V
⎡ ⎛ ⎞ ⎤ = − + (^) ⎢ ⎜ ⎟−⎥ ⎢⎣ (^) ⎝ ⎠ ⎥⎦
0
(2 ) exp 1 2
s ph t
V I R I I V
⎡ ⎛ − ⎞ ⎤ = − + (^) ⎢ ⎜ ⎟−⎥ ⎢⎣ (^) ⎝ ⎠ ⎥⎦
0
(2 ) exp 2
s ph t
V I R I I V
⎛ − ⎞ ≈ − + (^) ⎜ ⎟ ⎝ ⎠
Solar One Project – Mojave, California
First generation directly heated steam for the generator for power in
Second generation heated molten salts then transferred the heat to a
steam generator for power.
SEGS Project – Kramer Junction, California
SEGS – solar-thermal-electric generating system still in operation.
The parabolic reflectors heat oil which is used to generate steam for a
conventional turbine generator since 1985.
Stirling Engines
These are closed cycle regenerative gas engines.
Dish concentrators by Stirling Engine Systems.
R.D. McConnell, J. Thompson, National Renewable Energy Laboratory
Concentrator Photovoltaic Systems
Spectrolab has teamed up with the Arizona Public Service (APS) to develop and
deploy the first grid-connected concentrator system that utilizes Spectrolab’s
GaInP/GaAs/Ge triple-junction solar cells.
This module is operational at the APS Solar Test and Research (STAR) facility in
Tempe, Arizona under 500-sun concentration and has been operational since April
Concentrator Cell on Cooling Plate
Arionza Public Service (^) Solar Cells Materials, Devices and Efficiencies
Concentrator PV relies on gathering light over some area and then
focusing it down onto a photovoltaic cell.
Since the net area density of the photovoltaic material is much
smaller than for flat-plate PV, its is economically possible to use
newer generation higher efficiency cells.
A three junction cell made by Boeing-Spectrolab Inc. claims
efficiencies of 39% at 236 suns.
There are thermal management issues with these concentrator PV
systems and continued research is addressing this issue.
R.D. McConnell, J. Thompson, National Renewable Energy Laboratory
Best Research-Cell Efficiencies Dye Solar Cell
Swiss Federal Institute of Technology
Dye Sensitized Nanocrystalline Solar Cell (DYSC)
Swiss Federal Institute of Technology
Solar Flight!
HELIOS prototype close-up on the lakebed, August 18, 2001, Photo Tom Tschida;
NASA Dryden Flight Research Center
End of Chapter 6
