Reciprocity (optoelectronic)

A light emitting diode is operated at an applied forward bias (without external illumination).

While a solar cell converts the energy contained in the electromagnetic waves of the incoming solar radiation into electric power (voltage x current) a light-emitting diode does the inverse, namely converting electrical power into electromagnetic radiation.

A solar cell and a light emitting diode are typically made from different materials and optimized for different purposes; however, conceptually every solar cell could be operated as a light emitting diode and vice versa.

Given that the operation principles have a high symmetry it is fair to assume that the key figures of merit that are used to characterize photovoltaic and luminescent operation of diodes are related to each other.

These relations become particularly simple in a situation, where recombination rates scale linearly with minority carrier density and are explained below.

is a spectral quantity that is generally measured as a function of photon energy (or wavelength).

This simple relation is useful for the analysis of solar cells using luminescence-based characterization methods.

Luminescence used for characterization of solar cells is useful because of the ability to image the luminescence of solar cells and modules in short periods of times, while spatially resolved measurements of photovoltaic properties (such as photocurrent or photovoltage) would be very time-consuming and technically difficult.

Equation (1) is valid for the practically relevant situation, where the neutral base region of a pn-junction makes up most of the volume of the diode.

Typically, the thickness of a crystalline Si solar cell is ~ 200 μm while the thickness of the emitter and space charge region is only on the order of hundreds of nanometers, i.e. three orders of magnitude thinner.

In the base of a pn-junction, recombination is typically linear with minority carrier concentration over a large range of injection conditions and charge carrier transport is by diffusion.

Further away from the edge of the space charge region, the collection efficiency will be smaller than one depending on the distance and the amount of recombination happening in the neutral zone.

Here, the electron concentration will also decrease from the edge of the space charge region towards the back contact.

This decrease as well as the collection efficiency will be approximately exponential (with the diffusion length controlling the decay).

The Donolato theorem is based on the principle of detailed balance and connects the processes of charge carrier injection (relevant in the luminescent mode of operation) and charge carrier extraction (relevant in the photovoltaic mode of operation).

In addition, the detailed balance between absorption of photons and radiative recombination can be mathematically expressed using the van Roosbroeck–Shockley[3] equation as Here,

(1)) is only valid if absorption and emission is dominated by the neutral region of the pn-junction shown in the adjacent figure.

However the equations has limitations when applied to solar cells where the space charge region is of comparable size to the total absorber volume.

This limitation is relevant for microcrystalline and amorphous silicon solar cells.

The voltage that can build up in such as situation is directly connected to the density of electrons and holes in the device.

The rate of photogeneration is usually determined by the typically used illumination with white light with a power density of 100 mW/cm2 (called one sun) and by the band gap of the solar cell and does not change much between different devices of the same type.

The rate of recombination however might vary over orders of magnitude depending on the quality of the material and the interfaces.

Thus, the open-circuit voltage depends quite drastically on the rates of recombination at a given concentration of charge carriers.

However, since absorption is a key requirement for a solar cell and necessary to achieve a high concentration of electrons and holes as well, radiative recombination is a necessity (see van Roosbroeck-Shockley equation [3]).

This leads to a second reciprocity relation between the photovoltaic and the luminescent operation mode of a solar cell because the ratio of radiative to total (radiative and non-radiative) recombination currents is the external luminescence quantum efficiency

Mathematically, this relation is expressed as,[7][1] Thus, any reduction in the external luminescence quantum efficiency by one order of magnitude would lead to a reduction in open-circuit voltage (relative to

Illustration of the basic underlying principles of the reciprocity relation between photovoltaic quantum efficiency and external luminescence quantum efficiency of a light emitting diode. On the left, the band diagram of a p-n junction solar cell is depicted with a thin n-type region on the left and a thicker p-type region on the right. Light absorption in the p-type base leads to free electrons that have to be collected by diffusing to the edge of the space charge region between the n and p-type regions of the diode. On the right, a forward voltage is applied to the same diode. Electron injection will lead to recombination and consequently light emission. The emission spectrum of the luminescence emitted in the situation on the right is directly related to the quantum efficiency of photocurrent in the photovoltaic situation on the left. The relation between the two situations is based on the principle of detailed balance that relates absorption and radiative recombination via the van Roosbroeck-Shockley equation and charge collection and injection via the Donolato theorem.