Open Circuit Voltage

Definition of Open Circuit Voltage

Open circuit voltage is a common term  in solar cell applications. V_OC  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 V_oc 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 V_OC increases linearly with temperature. Yet, this is not true as I₀ quickly increases with temperature mainly as a result of changes in the  n_i  which is intrinsic carrier concentration. The temperature effect is complex and changes with different cell technology. V_OC decreases with decrease of temperature. When temperature changes, I₀ changes as well. While I_sc 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 V_OC can be also determined from carrier concentration and the equation is shown below:   Where: kT/q: the thermal voltage  N_A: the doping concentration  Δn: the excess carrier concentration n_i: the intrinsic carrier concentration. The V_OC determines the carrier concentration  

Voc as a Function of Bandgap, E_G

The short circuit current I_SC decreases when the bandgap increases, the open circuit voltage increases when the bandgap increases. In a perfect device radiative recombination limits V_OC 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= E_G / 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 V_OC 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.