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PN-Junction
Formation of a PN-Junction
Joining n-type material with p-type material causes excess electrons in the n-type
material to diffuse to the p-type side and excess holes from the p-type material to
diffuse to the n-type side.
Movement of electrons to the p-type side exposes positive ion cores in the n-type
side while movement of holes to the n-type side exposes negative ion cores in the
p-type side, resulting in an electron field at the junction and forming the depletion
region.
A voltage results from the electric field formed at the junction.
The PN diode is indispensable for the operation of all electronic devices,
counting on all forms of carrier transport, generation and recombination.
In equilibrium, the net current (diffusion and entrainment) is zero for both
electrons and holes, because the diffusion current is equal and opposite to the
drag current for both carriers.
Junction diodes pn are the basis not only of solar cells, but many other electronic
devices, such as LEDs, laser diodes and bipolar junction transistors (BJTs).
When that imaginary boundary is removed, electrons and holes diffuse into the
others side.
Semiconductor devices have three modes of operation:
1. Thermal Equilibrium
At thermal equilibrium there are no external inputs such as light or applied
voltage. The currents balance each other out so there is no net current within the
device.
2. Steady State
Under steady state there are external inputs such as light or applied voltage, but
the conditions do not change with time. Devices typically operate in steady state
and are either in forward or reverse bias.
3. Transient
If the applied voltage changes rapidly, there will be a short delay before the solar
cell responds. As solar cells are not used for high speed operation there are few
extra transient effects that need to be taken into account.
Bias of PN Junctions
Forward Bias PN Junctions
Forward bias occurs when a voltage is applied across the solar cell such that the
electric field formed by the P-N junction is decreased. It eases carrier diffusion across
the depletion region, and leads to increased diffusion current.
In the presence of an
external
circuit
that
continually
provides
majority
carriers,
recombination increases
which constantly depletes
the influx of carriers into
the solar cell. This
increases diffusion and
ultimately
increases
current
across
the
depletion region.
Reversed Bias PN Junctions
Reverse bias occurs when a voltage is applied across the solar cell such that
the electric field formed by the P-N junction is increased. Diffusion current
decreases.
Diode Equation
Ideal Diodes
The diode equation gives an expression for the current through a diode as a
function of voltage. The Ideal Diode Law, expressed as:
where:
I = the net current flowing through the diode;
I0 = "dark saturation current", the diode leakage current density in the absence of
light;
V = applied voltage across the terminals of the diode;
q = absolute value of electron charge;
k = Boltzmann's constant; and
T = absolute temperature (K).
The "dark saturation current" (I0) is an extremely important parameter which
differentiates one diode from another. I0 is a measure of the recombination in a
device. A diode with a larger recombination will have a larger I0.
Note that:
I0 increases as T increases; and
I0 decreases as material quality increases.
At 300K, kT/q = 25.85 mV, the "thermal voltage".
Non-Ideal Diodes
For actual diodes, the expression becomes:
where:
n = ideality factor, a number between 1 and 2 which typically
increases as the current decreases.
Solar Cell Structure
The basic steps in the operation of a
solar cell are:
the generation of light-generated
carriers;
the collection of the light-generated
carries to generate a current;
the generation of a large voltage
across the solar cell; and
the dissipation of power in the load
and in parasitic resistances.
Light Generated Current
The generation of current in a solar cell, known as the "light-generated current",
involves two key processes.
The first process is the absorption of incident photons to create electron-hole
pairs. Electron-hole pairs will be generated in the solar cell provided that the
incident photon has an energy greater than that of the band gap. However,
electrons (in the p-type material), and holes (in the n-type material) are metastable and will only exist, on average, for a length of time equal to the minority
carrier lifetime before they recombine. If the carrier recombines, then the lightgenerated electron-hole pair is lost and no current or power can be generated.
A second process, the collection of these carriers by the p-n junction, prevents
this recombination by using a p-n junction to spatially separate the electron and the
hole. The carriers are separated by the action of the electric field existing at the pn junction. If the light-generated minority carrier reaches the p-n junction, it is swept
across the junction by the electric field at the junction, where it is now a majority
carrier. If the emitter and base of the solar cell are connected together (i.e., if the
solar cell is short-circuited), the the light-generated carriers flow through the
external circuit.
The ideal flow at short circuit is shown in the animation below.
The ideal short circuit flow of electrons and holes at a p-n junction. Minority
carriers cannot cross a semiconductor-metal boundary and to prevent
recombination they must be collected by the junction if they are to contribute to
current flow.
Collection Probability
The "collection probability" describes the probability that a carrier generated by
light absorption in a certain region of the device will be collected by the p-n junction
and therefore contribute to the light-generated current, but probability depends on
the distance that a light-generated carrier must travel compared to the diffusion
length.
The collection probability in conjunction with the generation rate in the solar cell
determine the light-generated current from the solar cell.
The light-generated current is the integration over the entire device thickness of the
generation rate at a particular point in the device, multiplied by the collection
probability at that point.
The equation for the light-generated current density (JL), with an arbitrary
generation rate (G(x))and collection probability (CP(x)), is shown below, as is the
generation rate in silicon due to the AM1.5 solar spectrum:
where:
q is the electronic charge;
W is the thickness of the device;
α(λ) is the absorption coefficient;
H0 is the number of photons at each wavelength.
Quantum Efficiency
The "quantum efficiency" (Q.E.) is the ratio of the number of carriers collected by
the solar cell to the number of photons of a given energy incident on the solar cell.
The quantum efficiency may be given either as a function of wavelength or as
energy. If all photons of a certain wavelength are absorbed and the resulting
minority carriers are collected, then the quantum efficiency at that particular
wavelength is unity.
The quantum efficiency for photons with energy below the band gap is zero. A
quantum efficiency curve for an ideal solar cell is shown below.
Photocurrent and Quantum Efficiency
The photocurrent generated by a solar cell under illumination at short circuit is
dependent On the incident light. To relate the photocurrent density, Jsc, to the incident
spectrum we need the cell’s quantum efficiency (QE).
QE (E) is the probability that an incident photon of energy E will deliver one electron to
the external circuit.
J sc  q  bs ( E )QE ( E ) dE
Where bs(E) is the incident spectral photon flux density, i.e., the number of photon of
energy in the range E and E+dE which are incident on unit area in unit time and q is
electronic charge.
QE depends upon the absorption coefficient of the solar cell material, the efficiency of
charge separation and the efficiency of charge collection in the device but does not
depend on the incident spectrum.
Two types of QE are used:
External quantum efficiency (EQE): Loss of photons due to reflection and
transmission is not considered.
Internal quantum efficiency (IQE): Only absorbed photons are considered.
The difference between EQE and IQE is that loss of photons due to reflection and
transmission is not considered in EQE.
However, only those photons which are absorbed (excluding reflected and transmitted)
contribute to the solar cell current. Due to this IQE is most commonly used to study cell
performance.
EQE
IQE 
1  R ( )  T ( )
QE ( E )  EQE 
current density collected
q x incident photon flux density
Spectral Response
The spectral response is conceptually similar to the quantum efficiency. The quantum
efficiency gives the number of electrons output by the solar cell compared to the number
of photons incident on the device, while the spectral response is the ratio of the current
generated by the solar cell to the power incident on the solar cell. A spectral response
curve is shown below.
Spectral response is important since it is the spectral response that is measured
from a solar cell, and from this the quantum efficiency is calculated.
The quantum efficiency can be determined from the spectral response by replacing
the power of the light at a particular wavelength with the photon flux for that
wavelength. This gives:
SR( A / W ) 
QE .  (nm)
1239.8
The photovoltaic effect
The collection of light-generated carriers does not by itself give rise to power
generation. In order to generate power, a voltage must be generated as well as a
current.
Voltage is generated in a solar cell by a process known as the "photovoltaic effect".
The collection of light-generated carriers by the p-n junction causes a movement of
electrons to the n-type side and holes to the p-type side of the junction.
Under short circuit conditions, there is no build up of charge, as the carriers exit the
device as light-generated current.
However, if the light-generated carriers are prevented from leaving the solar cell,
then the collection of light-generated carriers causes an increase in the number of
electrons on the n-type side of the p-n junction and a similar increase in holes in
the p-type material.
This separation of charge creates an electric field at the junction which is in
opposition to that already existing at the junction, thereby reducing the net electric
field. Since the electric field represents a barrier to the flow of the forward bias
diffusion current, the reduction of the electric field increases the diffusion current. A
new equilibrium is reached in which a voltage exists across the p-n junction.
The current from the solar cell is the difference between IL and the forward bias
current. Under open circuit conditions, the forward bias of the junction increases to a
point where the light-generated current is exactly balanced by the forward bias
diffusion current, and the net current is zero. The voltage required to cause these two
currents to balance is called the "open-circuit voltage".
Solar Cell Parameters
I-V Curve
The IV curve of a solar cell is the superposition of the IV curve of the solar cell diode
in the dark with the light-generated current. The light has the effect of shifting the IV
curve down into the fourth quadrant where power can be extracted from the diode.
Illuminating a cell adds to the normal "dark" currents in the diode so that the diode
law becomes:
where IL = light generated current.
The equation for the IV curve in the first quadrant is:
The -1 term in the above equation can usually be neglected. The exponential term
is usually >> 1 except for voltages below 100 mV. Further, at low voltages the light
generated current IL dominates the I0 (...) term so the -1 term is not needed under
illumination.
The short-circuit current (ISC), the open-circuit voltage (VOC), the fill factor (FF) and
the efficiency are all parameters determined from the IV curve.
Solar cell I-V curve
Solar cell I-V curve
Short-Circuit Current
The short-circuit current is the current through the solar cell when the voltage across
the solar cell is zero (i.e., when the solar cell is short circuited). Usually written as ISC,
the short-circuit current is shown on the IV curve below.
The short-circuit current is due to the generation and collection of light-generated
carriers. For an ideal solar cell at most moderate resistive loss mechanisms, the
short-circuit current and the light-generated current are identical. Therefore, the
short-circuit current is the largest current which may be drawn from the solar cell.
The short-circuit current depends on a number of factors which are described
below:
the area of the solar cell. To remove the dependence of the solar cell area, it is
more common to list the short-circuit current density (Jsc in mA/cm2) rather than
the short-circuit current;
the number of photons (i.e., the power of the incident light source). Isc from a
solar cell is directly dependant on the light intensity;
the spectrum of the incident light. For most solar cell measurement, the
spectrum is standardised to the AM1.5 spectrum;
the optical properties (absorption and reflection) of the solar cell (discussed
in Optical Losses); and
the collection probability of the solar cell, which depends chiefly on the
surface passivation and the minority carrier lifetime in the base.
When comparing solar cells of the same material type, the most critical material
parameter is the diffusion length and surface passivation. In a cell with perfectly
passivated surface and uniform generation, the equation for the short-circuit current
can be approximated as:
where G is the generation rate, and Ln and Lp are the electron and hole diffusion
lengths respectively. Although this equation makes several assumptions which are
not true for the conditions encountered in most solar cells, the above equation
nevertheless indicates that the short-circuit current depends strongly on the
generation rate and the diffusion length.
Illuminated Current and Short Circuit Current (IL or Isc ?)
IL is the light generated current inside the solar cell and is the correct term to use in
the solar cell equation.
At short circuit conditions the externally measured current is Isc. Since Isc is usually
equal to IL, the two are used interchangeably and for simplicity and the solar cell
equation is written with Isc in place of IL.
In the case of very high series resistance (> 10 Ωcm2) Isc is less than IL and writing the
solar cell equation with Isc is incorrect.
Another assumption is that the illumination current IL is solely dependent on the
incoming light and is independent of voltage across the cell. However, IL varies with
voltage in the case of drift-field solar cells and where carrier lifetime is a function of
injection level such as defected multicrystalline materials.
Open-Circuit Voltage
The open-circuit voltage, VOC, is the maximum voltage available from a solar cell,
and this occurs at zero current. The open-circuit voltage corresponds to the amount
of forward bias on the solar cell due to the bias of the solar cell junction with the
light-generated current. The open-circuit voltage is shown on the IV curve below.
An equation for Voc is found by setting the net current equal to zero in the solar
cell equation to give:
The above equation shows that Voc depends on the saturation current of the solar
cell and the light-generated current.
While Isc typically has a small variation, the key effect is the saturation current,
since this may vary by orders of magnitude.
The saturation current, I0 depends on recombination in the solar cell. Open-circuit
voltage is then a measure of the amount of recombination in the device.
Silicon solar cells on high quality single crystalline material have open-circuit
voltages of up to 730 mV under one sun and AM1.5 conditions, while commercial
devices on multicrystalline silicon typically have open-circuit voltages around 600
mV.
The VOC can also be determined from the carrier concentration
where kT/q is the thermal voltage, NA is the doping concentration, Δn is the
excess carrier concentration and ni is the intrinsic carrier concentration. The
determination of VOC from the carrier concentration is also termed Implied VOC.
Voc as a Function of Band gap, EG
Where the short-circuit current (ISC) decreases with increasing bandgap, the opencircuit voltage increases as the band gap increases. In an ideal device the VOC is
limited by radiative recombination and the analysis uses the principle of detailed
balance to determine the minimum possible value for J0.
The minimum value of the diode saturation current is given by
where q is the electronic charge, σ is the Stefan–Boltzman constant, k is Boltmann
constant, T is the temperature and
Fill Factor
The "fill factor", more commonly known by its abbreviation "FF", is a parameter which,
in conjunction with Voc and Isc, determines the maximum power from a solar cell.
The FF is defined as the ratio of the maximum power from the solar cell to the product
of Voc and Isc. Graphically, the FF is a measure of the "squareness" of the solar cell IV curve and is also the area of the largest rectangle which will fit in the IV curve.
As FF is a measure of the "squareness" of the IV curve, a solar cell with a higher
voltage has a larger possible FF since the "rounded" portion of the IV curve takes up
less area. The maximum theoretical FF from a solar cell can be determined by
differentiating the power from a solar cell with respect to voltage and finding where
this is equal to zero. Hence:
However, the above technique does not yield a simple or closed form equation,
and extra equations are needed to find Imp and FF.
A more commonly used expression for the FF can be determined empirically as
where voc is defined as a "normalized Voc":
A key limitation in the equations described above is that they represent a maximum
possible FF, although in practice the FF will be lower due to the presence of parasitic
resistive losses.
Therefore, the FF is most commonly determined from measurement of the IV curve
and is defined as the maximum power divided by the product of Isc*Voc, i.e.:
Solar Cell Efficiency
The efficiency of a solar cell is determined as the fraction of incident power which
is converted to electricity and is defined as:
Where:
Voc is the open-circuit voltage;
Isc is the short-circuit current;
FF is the fill factor and
η is the efficiency.
The input power for efficiency calculations is 1 kW/m2 or 100 mW/cm2. Thus the
input power for a 100 × 100 mm2 cell is 10 W and for a 156 × 156 mm2 cell is
24.3 W
Efficiency as a function of band gap
To find the efficiency as a function of band gap, the above procedure is repeated
for each band gap. There is a range of bandgaps for the optimum cell efficiency
as shown in the graph below.
Tandem Cells
One method to increase the efficiency of a solar cell is to split the spectrum and use
a solar cell that is optimised to each section of the spectrum.
Tandem solar cells can either be individual cells or connected in series. Series
connected cells are simpler to fabricate but the current is the same though each cell
so this contrains the band gaps that can be used. The most common arrangement for
tandem cells is to grow them monolithically so that all the cells are grown as layers on
the on substrate and tunnel junctions connect the individual cells.
As the number of bandgaps increases the efficiency of the stack also potentially
increases. In reality, the semiconductor materials do not exist to allow for arbitrary
materials with a specific bandgap and of high quality.