# Definitions of Some Terms related to Solar Cell

**Efficiency **– Ratio of energy output from the solar cell to the input energy from the Sun.

**External Radiative Efficiency (ERE)** – Fraction of total dark recombination current that results in the emission of light.

**Photon Recycling **– Multiple reabsorption and reconversion in free charges of photons emitted by charge recombination in the active layer.

**Luminous efficiency **– Measure how well a light source produces visible light and the ratio of luminous flux to power.

**Operational loss **– Difference between the optical band gap of the absorber and the maximum power point voltage when the cell is operating under sunlight.

**Fill Factor (FF) **– Ratio of actual maximum obtainable power to the product of open circuit voltage and short circuit current. The key parameter in evaluating PV performance is a measure of the squareness of the I-V curve. Fill Factor in conjunction with V_{OC} and I_{SC} determines the maximum power from the solar cell.

**Optical Loss **– Consists of light that could have generated an electron-hole pair, but does not, because the light is reflected from the front surface, or because it is not absorbed in the solar cell.

**Collection probability** – describes the probability that the carrier generated by light absorption in a certain region of the device will be collected by the p-n junction and therefore contribute to light-generated current.

**Diffusion length **– Average length a carrier moves between generation and recombination.

**Absorption coefficient **– Measure of rate of decrease in the intensity of the electromagnetic radiation as it passes through a given substance, a fraction of incident radiation energy absorbed per unit mass, or thickness of an absorber.

**Quantum efficiency **– 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.

**Spectral Response **– Ratio of the current generated by the solar cell to the power incident on the solar cell.

**Short-Circuit Current **– Current through the solar cell when the voltage across the solar cell is zero (i.e., when the solar cell is short-circuited).

**Open-Circuit Voltage **– It is the maximum voltage available from a solar cell, and this occurs at zero current.

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# Solar Cell structure

A solar cell is an electronic device that directly converts sunlight into electricity. Light shining on solar cells produces both current and voltage. Absorption of light raises electrons to a higher energy state, this higher energy electron from the solar cell into the external circuit.

The electron dissipates its energy in the external circuit and returns to the solar cell. Basic steps in the operation of solar cells – generation of light-generated carriers, collection of light-generated carriers to generate a current, generation of large voltage across solar cell, dissipation of power in the load, and parasitic resistances.

# Light Generated Current in a Solar Cell

There is an absorption of incident photons to create electron-hole pairs. Electron-hole pairs will be generated in the solar cell if the energy of the incident photon > band gap. Electrons and holes are meta-stable and will only exist, on average, for the length of time equal to the minority carrier lifetime before they recombine.

If the carriers recombine, then the light-generated electron-hole pair is lost and no current or power can be generated. The collection of these carriers by the p-n junction prevents recombination by using the p-n junction to spatially separate the electron and the hole.

Carriers are separated by the action of the electric field existing at the p-n junction. If the light-generated minority carrier reaches the p-n junction, it is swept across the p-n junction by the electric field, where it is now a majority carrier.

If the emitter and the base of the solar cell are connected together (i.e if the solar cell is short-circuited), the light-generated carriers flow through the external circuit. 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 the current flow.

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# Collection Probability of a Solar Cell

Collection probability describes the probability that the carrier generated by light absorption in a certain region of the device will be collected by the p-n junction and therefore contribute to light-generated current.

Depends on the distance that a light-generated carrier must travel compared to the diffusion length. Also depends on surface properties. The collection probability in the depletion region is 1 because electron-hole pairs are quickly swept apart by the electric field and collected.

Away from the junction collection probability drops. If the carrier is generated more than a diffusion length from the junction, the collection probability is low. Similarly, if the carrier is generated closer to a region with high recombination rates such as the surface, then collection probability is low.

Collection probability along with generation rate determine the light-generated current. Light-generation 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 the point.

**I _{L} = q _{0}^{W}∫G(x) CP(x) dx = q _{0}^{W}∫[∫ α(λ) H_{0} exp(-α(λ)x) dλ] CP(x) dx ** where, q = electronic charge, W = thickness of the device, α(λ) = absorption coefficient, H

_{0}= number of photons at each wavelength, G(x) = generation rate, CP(x) = collection probability.

Carrier generation is highest at the surface of the solar cell, thus PV devices are very sensitive to surface properties. Non-uniform collection probability will cause spectral dependence in the light-generated current.

Collection probability is lower on the surface than in bulk. Among the colors, blue light is nearly completely absorbed in the first few tenths of a micron in silicon. So if the collection probability at the front surface is low, any blue light does not contribute to the light-generated current.

The blue light of 0.45µm has a high absorption coefficient of 10^{5}cm^{-1} and is absorbed very close to the front surface, Red light at 0.8µm has an absorption coefficient of 10^{3}cm^{-1} is absorbed deeper into the cell, infrared light at 1.1µm with an absorption coefficient of 10^{3}cm^{-1} is barely absorbed since it is close to the band gap of silicon.

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# Quantum efficiency of a Solar Cell

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. It can be a function of wavelength or energy. If all photons of a certain wavelength are absorbed and the resulting minority carriers are collected, then the quantum efficiency is 1.

The Quantum efficiency of photons below the band gap is zero. Quantum efficiency from blue light is reduced due to front surface recombination. Reduction in quantum efficiency is caused by reflection and low diffusion length.

Quantum efficiency from red light is reduced due to rear surface combination, reduced absorption at long wavelengths, and low diffusion lengths.

No light is absorbed in long wavelengths, the quantum efficiency is zero. High front surface recombination affects quantum efficiency from blue light. External quantum efficiency depends on the optical losses such as transmission and reflection.

Internal quantum efficiency refers to the efficiency with which the photons that are not reflected or transmitted out of the cell can generate collectible carriers.

# Spectral Response of a Solar Cell

It is the ratio of the current generated by the solar cell to the power incident on the solar cell. At short wavelengths, glass absorbs most of the light and the cell response is very low. At intermediate wavelengths, the spectral response approaches ideal.

At longer wavelengths, it falls back to zero, due to the inabilities of the semiconductor to absorb photons with energies below the band gap. Any energy above the band gap energy is not utilized by the solar cell and instead goes on to heat the solar cell.

The inability to fully utilize the incident energy at high energies and the inability to absorb low energies of light represents a significant power loss in solar cells consisting of the single p-n junction. 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.

**SR = (qλ/hc) QE**

# Series Resistance of a Solar Cell

In addition to maximizing absorption and minimizing recombination, the final condition necessary to design a high-efficiency solar cell is to minimize parasitic resistive losses. Shunt and series resistance losses decrease fill factor and efficiency.

Low shunt resistance is a processing defect rather than a design parameter. Series resistance, controlled by top contact design and emitter resistance, needs to be carefully designed for each type and size in order to maximize cell efficiency.

Series resistance consists of several components, emitter, and top grid dominate overall series resistance and are heavily optimized in solar cell design. Metallic top contacts are necessary to collect the current generated by the solar cell.

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# Photovoltaic Effect in a Solar Cell

Light-generated carriers do not give power by themselves. To generate power a voltage must be generated along with a current. Voltage is generated in solar cells by a process known as the photovoltaic effect. The collection of light-generated carriers in the junction causes a movement of electrons to the n-side and holes to the p-side.

Under short circuit conditions, there is no build-up of charge, as the carriers exit the device as light-generated current. If the light-generated carriers are prevented from leaving the solar cell, then the collection of light-generated carriers causes an increase in the electrons on the n-side and holes in the p-side.

The separation of charges creates an electric field at the junction which is opposite to the electric field already existing in the junction, thereby reducing the net electric field. The electric field in the junction is a barrier to the flow of forward bias diffusion current.

The reduction of the electric field at the junction increases the forward bias diffusion current. An equilibrium state is reached. Current from the solar cell is the difference between the light-generated current and the forward bias current.

Under open circuit conditions, the forward bias of the junction increases to the 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 balance these two currents is called ‘open-circuit voltage’.

# I-V Curve of a Solar Cell

The I-V curve of the solar cell is the superposition of the I-V curve of the solar cell diode in the dark with the light-generated current. Light shifts I-V curve down into the fourth quadrant where power can be extracted from the diode.

Diode law becomes **I = I _{0}[exp(qV/nkT) – 1] – I_{L}**, where IL is the light-generated current. In the first quadrant, the equation is

**I = I**, -1 term in the equation can usually be neglected. The exponential term is >>1 except for below 100mV.

_{L}– I_{0}[exp(qV/nkT) – 1]**Solar System: How it Formed Will Make You Fascinated**

Under illumination at low voltages -1 term is not needed, so **I = I _{L} – I_{0}[exp(qV/nkT)]**. In the power curve, there is a maximum denoted as PMP where the solar cell should be operated to give maximum power output. It is also denoted as a maximum power point (MPP), the voltage is V

_{MP }and the current is I

_{MP}.

From the I-V curve, important parameters such as short-circuit current (I_{SC}), open-circuit voltage (V_{OC}), fill factor (FF) and efficiency are determined. In terms of voltage, the equation is **V = (nkT/q) ln((I _{L} – I)/I_{o})**.

When I>I_{L}, the number in ln() becomes negative and undefined. Actually what happens is that the solar cell goes into reverse bias (negative voltage) and either the non-idealities in the solar cell limit the voltage or the supply limits the voltage. In either case, solar cells will dissipate power.

If there is no limit on the supply then a solar cell close to ideal (very high R_{SHUNT} in reverse bias) will be destroyed almost instantly. Other cells will be destroyed due to heating.

# Short-Circuit Current Through a Solar Cell

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). It is the maximum current from a solar cell and occurs when the voltage across the device is zero. 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 light-generated current are identical. Short-Circuit current is the largest current that may be drawn from the solar cell.

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Short-Circuit current depends on a number of factors; the area of the solar cell (if you want to remove the dependence on solar cell area, you can use short-circuit current density (J_{SC}) rather than short-circuit current; the number of photons (I_{SC} is directly dependent on light intensity); the spectrum of incident light; the optical properties (absorption and reflection); the collection probability (depends on surface passivation and minority carrier lifetime).

When comparing solar cells of the same material, the most important parameters are diffusion length and surface passivation. Equation for a cell with perfectly passivated surface and uniform generation **I _{SC} = qG(L_{n}+L_{p})**, G = generation rate, L

_{n }= electron diffusion length, L

_{p}= hole diffusion length.

Short-Circuit current depends strongly on the generation rate and diffusion length. In an ideal device, every photon above the bandgap gives one charge carrier in the external circuit so the highest current is for the lowest bandgap.

I_{L} 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 I_{SC}. Since I_{SC} is usually equal to I_{L}, the two are used interchangeably. In the case of very high series resistance, I_{SC} is less than I_{L}.

I_{L} is not solely dependent on incoming light, it varies with voltage in the case of drift-field solar cells and where the carrier lifetime is a function of injection level such as defected multi-crystalline materials._{ }

# Open-Circuit Voltage of Solar Cell

Open-Circuit voltage is the maximum voltage available from a solar cell, and this occurs at zero current.

**V _{OC} = (nkT/q) ln((I_{L}/I_{0})+1)**

The effect of temperature is not linear as in the equation, because I_{0} increases rapidly with temperature primarily due to changes in the intrinsic carrier concentration n_{i}. The effect of temperature is complicated. V_{OC} decreases with temperature.

The saturation current I_{0} depends on the recombination in the solar cell. Open-Circuit voltage is a measure of the amount of recombination in the device. Open-circuit voltage can also be determined from carrier concentration **V _{OC} = (kT/q) ln[{(N_{A}+Δn)Δn}/n_{i}^{2}]**, kT/q = thermal voltage, N

_{A}= doping concentration, Δn = excess carrier concentration, n

_{i}= intrinsic carrier concentration.

Open-Circuit voltage increases as the bandgap increases. Minimum value of diode saturation current, **J _{0} = (q15σT^{3}/kπ^{4})_{u}^{∞}∫(x^{2}/e^{x} – 1)dx**, q = electronic charge, σ = Stefan-Boltzmann constant, k = Boltzmann constant, T = temperature, u = E

_{G}/kT.

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# Fill Factor of a Solar Cell

The ratio of actual maximum obtainable power to the product of open circuit voltage and short circuit current. **FF = P _{MP}/(V_{OC }X I_{SC}) = (V_{MP}I_{MP})/(V_{OC}I_{SC})**. Fill Factor in conjunction with V

_{OC}and I

_{SC}determines the maximum power from the solar cell.

A key parameter in evaluating PV performance is a measure of the squareness of the I-V curve. Maximum theoretical FF from a solar cell can be determined by differentiating power from a solar cell wrt voltage and finding where this is equal to zero. **V _{MP} = V_{OC} – (nkT/q) ln{(qV_{MP}/nkT)+1}**.

The ideality factor n is a measure of junction quality and the type of recombination in the solar cell. A high n value will degrade FF. The key limitation of the equation is that it gives the maximum possible FF while in practice FF will be lower due to parasitic resistive losses, therefore FF is commonly determined from the measurement of the I-V curve.

**VMP = nVtW(exp(VOC/nVt))**, VMP is when the derivative of the power wrt V is zero, and** **W is the Lambert function. The expression inside W() is always real and positive, and we need only the principle branch of the Lambert W function, W_{0}. Lambert W is a transcendental function much like a logarithm function.

# Solar Cell Efficiency

It is the ratio of energy output from the solar cell to the input energy from the Sun. Depends on the spectrum, the intensity of incident light, and temperature.

**P _{max} = V_{OC}I_{SC}FF**

Efficiency,** ɳ = (V _{OC}I_{SC}FF/P_{in})**.

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