Optical Devices: Solar cells and photo-detectors

OPTICAL DEVICES: SOLAR CELLS AND
PHOTODETECTORS
22th June 2020
Manmohan Dash

Solar Cells
❖ p-n Junction Solar Cell
❖ Conversion Efficiency and
Solar Concn
❖ Nonuniform Absorption
Effects
❖ Heterojunction Solar Cell
❖ Amorphous Silicon Solar
Cells
Photodetectors
❖ Photoconductor
❖ Photodiode
❖ PIN Photodiode
❖ Avalanche Photodiode
❖ Phototransistor
We will discuss >>

Solar Cell
❖ Solar cell is a p-n junction device where no V is
applied directly across jn
❖ It converts photon power into electrical power and
delivers this power to a load
❖ They have long been used for power supply of
satellites, space vehicles, and some calculators

Solar Cell
❖ We will 1st consider simple p-n junction solar
cell with uniform generation of excess carriers
❖ We will discuss briefly heterojunction and
amorphous silicon solar cells

p-n Junction Solar Cell
❖ Zero bias is applied to the
junction, an E-field exists in
the Depletion (D) - region
❖ Incident photon creates e-
– hole pair (EHP) in D-
region; leads to
photocurrent IL in R-biased
direction
a p-n junction is shown with a
resistive load (R)

❖ IL produces a voltage drop across R, this forward biases p-n
junction, F-bias V produces a F-bias current IF given by:
(using ideal diode equation)
❖ When diode becomes F-biased, E-field in D-region
decreases, but does not go to zero or change direction
❖ IL is always in R-biased direction; net current is always in R-
biased direction

❖ 1st limiting case; short-circuit condition,
when R = 0 so that V = 0, short-circuit
current is given by: I = Isc = IL
❖ 2nd limiting case; open-circuit
condition, when R → ∞, net current is
zero, photocurrent is balanced by F-
biased jn current

❖ Power delivered to the load is
❖ Current, Voltage which deliver maxm
power to load; derivative of power P wrt
voltage V is equal to zero, or dP/dV = 0,
Vm is voltage producing maxm power
Vm can be determined
by trial and error

Conversion Efficiency, Solar Concentration
❖ Conversion efficiency; ratio of output electrical power to
incident optical power, for maxm power output
❖ Maxm possible I and V in solar cell; Isc and Voc. ImVm/IscVoc is
called “fill factor” a measure of realizable power, typically b/w
0.7 and 0.8
❖ Conventional p-n jn solar cell; single semicon Eg, upon exposure
to solar spectrum, photons of energy < Eg no effect on electrical
output power, ones of energy > Eg contribute to output power,
latter’s energy eventually dissipated as heat

❖ Solar spectral irradiance; power
per unit area per unit wavelength,
for air mass zero is solar spectrum
outside earth’s atmosphere and
for air mass one is solar spectrum
at earth’s surface at noon
❖ Maxm efficiency of Si p-n jn solar
cell is ~ 28 %. Nonideal factors,
e.g. series resistance and
reflection from semicon surface,
lowers  typically to 10 - 15 %
Solar spectral irradiance

❖ Large optical lens; used to focus sunlight onto a
solar cell
❖ This increases light intensity up to several 100 times
❖ ISC increases linearly with light concn
❖ VOC increases slightly with concn

❖ We see  increases slightly with
optical concn
❖ Primary use of concn techniques
is cost effectiveness
❖ Optical lens is less expensive than
equivalent area of solar cells
ideal solar cell efficiency ()

❖ Photon absorption coefficient () in a
semicon is a very strong fn of incident
photon energy or wavelength 
❖ As  increases, more photon energy is
absorbed near surface than in depth of
semicon, this leads to non-uniform excess
carrier generation in a solar cell
❖ # of photons absorbed per cm3 per
second, given as a fn of distance x from
surface: 0 is incident photon flux (cm2s-1)
on surface of semicon
 as function of 

❖ To account for reflection of
photons from surface, let R() be
fraction of reflected photon (Bare
Si, R ≈ 35 %)
❖ If each absorbed photon creates
1 EHP, generation rate of EHP as a
fn of distance x from surface is
❖ Each parameter is a fn of incident

Steady-state, photon-induced
normalized minority carrier concn
in p-n jn solar cell for 2 values of
incident photon 

Heterojunction Solar Cell
❖ Heterojunction is formed b/w 2
semicons with different Eg
values
❖ Photons are incident on a wide
bandgap material, those with
energy < EgN pass through the
material, which acts as an
optical window
❖ Photons with energy > Egp is
absorbed in the narrow
bandgap material
pN heterojunction EB diagram in thermal
equilibrium

❖ On the average, excess carriers created in D-region within a diffusion
length of jn, is collected and contributes to photocurrent
❖ Photons with energy > EgN is absorbed in the wide-bandgap material,
excess carriers generated within 1 diffusion length of jn is collected
❖ If EgN is large enough, high-energy photons are absorbed in the D-region
of the narrow-bandgap material
❖ Heterojunction solar cell should have better characteristics than a
homojunction cell, especially at shorter wavelengths

❖ A p-n homojunction forms, and a
wide-bandgap material is grown on
top. Wide bandgap material acts as
optical window for h < Eg1
❖ Photons with Eg2 < h < Eg1 create
excess carriers in the homojunction,
photons with energies h > Eg1 create
excess carriers in the window type
material
❖ If  in narrow bandgap material is
high, almost all excess carriers are
generated within a diffusion length of
jn, collection efficiency is very high
normalized spectral response
for various mole fractions x in
AlxGa1-xAs

Amorphous Silicon Solar Cells
❖ Single-crystal Si solar cells are expensive and limited to ≈ 6″ in diameter, a
system powered by solar cells requires, a very large area solar cell array
for required power
❖ Amorphous Si solar cells provide possibility of fabricating large area and
are relatively inexpensive solar cell systems
❖ When Si is deposited by CVD techniques below 600 0C, an amorphous
film is formed, order is very short range, no crystalline regions are seen
❖ Hydrogenated amorphous Si: H may be incorporated in Si to reduce # of
dangling bonds

❖ Amorphous Si contains large numbers of
electronic energy states within normal
bandgap of single-crystal Si
❖ Due to shortrange order, effective
mobility () is quite small, typically b/w 10-6
and 10-3 cm2/V-s, for states above EC and
below EV b/w 1 and 10 cm2/V-s,
❖ So conduction in energy states b/w EC
and EV is negligible due to low mobility
density of states vs
energy, amorphous Si

❖ Due to difference in  values, EC and EV are known as
mobility edges and energy b/w EC and EV is known as
mobility gap
❖ Mobility gap can be modified by adding specific
types of impurities, typically, mobility gap is of the
order of 1.7 eV

❖ Si has a very high optical ,
most sunlight is absorbed within
approximately 1 m of surface,
so a very thin layer of
amorphous Si is needed
❖ Amorphous Si is deposited on
an optically transparent ITO–
coated glass substrate, if Al is
used as back contact, it reflects
any transmitted photons back
through the PIN device
Amorphous Si solar cell is a PIN
device

❖ n+ and p+ regions can be quite
thin, intrinsic region b/w 0.5 to
1.0 m thick, excess carriers
generated in intrinsic region are
separated by E-field and
produce photocurrent
❖ ’s are smaller than in single-
crystal Si, but reduced cost
makes this technology
attractive, amorphous Si solar
cells are ~ 40 cm wide and
many meters long
EB diagram @ thermal
equilibrium
EB diagram @ illumination

Photodetectors
❖ Photodetectors are semicon devices used to detect photons;
they convert optical signals into electrical signals
❖ Excess e- and holes generated in a semicon, increase its
conductivity , change in  is the basis of photoconductor, the
simplest type of photodetector
❖ If e- and holes are generated in D-region of a p-n jn, then they
are separated by E-field and a current is produced, p-n jn is basis
of several photodetector devices such as photodiode and
phototransistor

❖ Initial thermal-equilibrium
conductivity
❖ If excess carriers are
generated in the semicon, 
becomes,
here n and p are excess e-
and hole concn, respectively
bar of semicon material
with ohmic contacts at
each end and a V applied
b/w terminals
Photoconductor

❖ For n-type semicon, with charge neutrality, n = p  p, we use
p as excess carrier concn
❖ In steady state, p is given by p = GLp, where GL is generation
rate of excess carriers (cm-3-s-1) and p is excess minority carrier
lifetime
❖ Rewrite equation for 
❖ Change in  due to optical excitation, (called photoconductivity)
is
Photoconductor

❖ E-field is induced in semicon by applied voltage, producing a
current, current density is
❖ J0 is current density in semicon prior to optical excitation and JL is
photocurrent density, the latter given by
❖ If excess carriers are generated uniformly throughout semicon,
photocurrent is given by
❖ A is cross-sectional area of device, photocurrent is  to excess
carrier generation rate, which is  to incident photon flux
Photoconductor

❖ If excess carriers are not generated uniformly throughout
semicon, total photocurrent is found by integrating
photoconductivity over cross-sectional area
❖ Since nE is e- drift velocity, e- transit time: time required
for an e- to flow through photoconductor, is
❖ Photocurrent, can be rewritten
Photoconductor

❖ We define photocon gain, ph, as ratio of rate at which charge is
collected by contacts to rate at which charge is generated
within photocon, we can write the gain as
Physically what happens to a photon-generated e-?
❖ After excess e- is generated, it drifts very quickly out of photocon
at anode terminal, to maintain charge neutrality throughout
photocon
❖ another e- immediately enters photocon at cathode and drifts
toward anode
Photoconductor

❖ This process continues during a time period equal to mean
carrier lifetime
❖ At the end of this period, on the average, photo-e- recombines
with a hole
❖ e- transit time, is calculated to be, tn = 7.4110-9 s
❖ In a simplistic sense, photo- e- circulate around photocon circuit
135 times during 10-6 s time duration, which is mean carrier
lifetime
Photoconductor

❖ For photon-generated hole, total number of charges collected at photocon
contacts for every e- generated is 183
❖ When optical signal ends, photocurrent decays exponentially with a time
constant equal to minority carrier lifetime
❖ With photocon gain in mind, we like a large minority carrier lifetime, but
switching speed is enhanced by a small minority carrier lifetime, there is a
trade-off b/w gain and speed
❖ In general, performance of a photodiode is superior to that of a
photoconductor
Photoconductor

❖ Photodiode; a p-n junction
diode operated with an
applied R-biased V
❖ Lets consider a long diode
where excess carriers are
generated uniformly
throughout semicon device
Photodiode
R-biased p-n jn diode

❖ GL is generation rate of excess
carriers, within D-region, and
swept out very quickly by E-field
❖ e- are swept into n region, holes
into p region
❖ Photon-generated current
density from D-region is given
by
Photodiode
minority carrier distribution
prior to photon illumination

❖ Integral is over space charge region width, if GL is
constant throughout, then, with W as space charge
width
❖ JL1 is in R-biased direction through p-n jn, this component
of photocurrent responds very quickly to photon
illumination: so known as prompt photocurrent
❖ Comparing prompt photocurrent and photocon gain:
photodiode gain is unity
Photodiode

❖ Speed of photodiode is limited by carrier transport
through D-region
❖ If saturation drift velocity is 107 cm/s and depletion
width is 2 m, transit time is t = 20 ps. The ideal
modulating frequency has a period of 2t, so frequency
is f = 25 GHz
❖ This frequency response is substantially higher than that
of photoconductors
Photodiode

❖ Excess carriers also generated within neutral n and p regions,
excess minority carrier e- distribution in p region is found from
ambipolar transport equation
❖ Assuming E-field = 0, in neutral regions, in steady state
with:
❖ solution to above is sum of homogeneous and particular
solutions, homogeneous solution is found from
Photodiode

❖ One boundary condition is nph must remain finite, which implies
that B0 for the “long” diode
❖ Particular solution is found from
❖ Total steady-state solution for excess minority carrier e- concn in
p region is
Photodiode

❖ Total e- concn is zero at x = 0 for
R-biased jn. Excess e- concn at x =
0 is then
❖ Using above boundary
condition, e- concn becomes
❖ Excess minority carrier hole
concn in n region uses same type
of analysis. Using x’ notation
shown
Photodiode

❖ Gradient in minority carrier concn produce diffusion currents in
p-n jn. Diffusion current density at x = 0 due to minority carrier e- is
❖ This can be written as
❖ 1st term is steady-state photocurrent density, 2nd term is ideal
reverse saturation current density due to minority carrier e-
Photodiode

❖ Diffusion current density (in x
direction) at x’ = 0 due to minority
carrier holes is
❖ 1st term is steady-state
photocurrent density, 2nd term is
ideal reverse saturation current
density
❖ Total steady-state photocurrent
density for the long diode
Photodiode
Photocurrent is in R-biased
direction in diode. Last formula for
photocurrent is result of assuming
uniform generation of excess
carriers, a long diode, and steady
state.
Time response of diffusion
components of photocurrent is
relatively slow, as currents are
results of diffusion of minority
carriers towards D-region.
Diffusion components of
photocurrent are known as
delayed photocurrent.

❖ In many photodetector appln,
speed of response is important; only
prompt photocurrent generated in
D-region is of interest
❖ To increase photodetector
sensitivity, D-region width should be
made as large as possible;
achieved in PIN photodiode
❖ I-region width W >> D-width of a
normal p-n jn
PIN Photodiode
PIN diode consists of a p-region
and n-region separated by an
intrinsic (I) region
D-region spans entire I-region, if
R-bias is applied to PIN diode

❖ If photon flux 0 falls on p+ region,
whose width Wp is very thin, then
0, as a fn of distance, in intrinsic
region is (x) = 0e-x, where  is
photon absorption coefficient
❖ Photocurrent density generated
in I-region, eqn based on; no e–
hole recombination within D-
region and each absorbed
photon creating 1 EHP
PIN Photodiode
Nonlinear photon absorption

❖ Avalanche photodiode ~ p-n or PIN photodiode except bias
applied to avalanche photodiode is sufficiently large to cause
impact ionization
❖ EHP are generated in D-region by photon absorption. Photon-
generated e- and holes generate additional EHP by impact
ionization. Avalanche photodiode has a current gain due to
avalanche multiplication factor
❖ EHP generated by photon absorption and by impact ionization
are swept out of D-region very quickly
Avalanche Photodiode

❖ If saturation velocity is 107 cm/s in a D-region that is 10 m wide,
then transit time is t = 107/(1010-4) = 100 ps
❖ Period of modulation signal would be 2t, so that the frequency
would be f = 1/ 2t = 1/(20010-12) = 5 GHz
❖ If avalanche photodiode current gain is 20, then gain-
bandwidth product is 100 GHz
❖ Avalanche photodiode can respond to light waves modulated
at microwave frequencies
Avalanche Photodiode

❖ Bipolar transistor can be
used as photodetector.
Phototransistor can have
high gain through transistor
action
❖ An n-p-n bipolar
phototransistor, has a large
base–collector jn area;
usually operated with the
base open circuited
Phototransistor
n-p-n bipolar phototransistor

❖ e- and holes generated in R-biased
B–C jn are swept out of D-region,
producing a photocurrent IL
❖ Holes are swept into p-type base
(B), making base +ve wrt emitter (E).
Since B–E becomes F-biased, e- are
injected from E back into B, leading
to normal transistor action
❖ From figure IE = IE + IL where IL is
photon-generated current and  is
common base current gain
Phototransistor
block diagram of the
phototransistor

❖ Since base is open circuit, we have IC = IE so IC = IC + IL
❖ Solving for IC we get IC = IL/(1-), relating  to , the dc common
emitter current gain IC = (1+ )IL
❖ This shows that basic B–C photocurrent is multiplied by factor (1+
 ),
❖ Phototransistor, thus, amplifies basic photocurrent
Phototransistor

❖ With relatively large B–C jn area, frequency response of
phototransistor is limited by B–C jn capacitance
❖ Since base is essentially input to device, large B–C capacitance
is multiplied by Miller effect, so frequency response of
phototransistor is further reduced
❖ As an advantage phototransistor is a lower-noise device than
avalanche photodiode
Phototransistor

❖ Phototransistors can also be fabricated in heterostructures
❖ Injection efficiency is increased as a result of bandgap
differences
❖ With bandgap difference, lightly doped base restriction no
longer applies
❖ A fairly heavily doped, narrow-base device can be fabricated
with a high blocking voltage and a high gain
Phototransistor

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