 Open Circuit Voltage

Definition of Open Circuit Voltage

Open circuit voltage is a common term  in solar cell applications. VOC  is the open circuit voltage, which is the maximum voltage that is available for drawing out from a solar cell, and occurs at zero current. The open circuit voltage resembles the forward bias amount on the solar cell as a result of the bias of the solar cell junction with light generated current. A Voc equation can be defined by making the net current to equal zero in solar cell equation to be: Effects of different factors on Open Voltage current

From the above equation it might seem that VOC increases linearly with temperature. Yet, this is not true as I0 quickly increases with temperature mainly as a result of changes in the  ni  which is intrinsic carrier concentration. The temperature effect is complex and changes with different cell technology. VOC decreases with decrease of temperature. When temperature changes, I0 changes as well.

While Isc normally has small variation, the main effect is saturation current, as it may vary with orders of magnitude. The saturation current, I0 relies on recombination of the solar cell. Open circuit voltage then measures the recombination amount in the device. Open circuit voltages of silicon solar cells of high quality single crystal material  is up to nearly 764 mV under one sun and AM1.5 conditions, while commercial devices usually have open circuit voltages of around 600 mV.

The VOC can be also determined from carrier concentration and the equation is shown below: Where:

kT/q: the thermal voltage

NA: the doping concentration

Δn: the excess carrier concentration

ni: the intrinsic carrier concentration.

The VOC determines the carrier concentration

Voc as a Function of Bandgap, EG

The short circuit current ISC decreases when the bandgap increases, the open circuit voltage increases when the bandgap increases. In a perfect device radiative recombination limits VOC and the analysis uses the detailed balance principle to determine the minimum possible J0 value.

The minimum value for the diode saturation current is : Where the terms

q: defines the electronic charge

σ: defines the Stefan Boltzmann constant

k: is the Boltzmann constant

T: is the temperature

And u= EG / kT

The evaluation of the above integral in the equation is fairly complex. The calculated J0 from above can be plugged directly into the standard solar cell equation previously provided to be used to determine the VOC as long as the voltage remains equal to less than the band gap, as is the normal case and conditions known under one sun illumination.

References:

https://www.pveducation.org/pvcdrom/solar-cell-operation/open-circuit-voltage

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