Open-Circuit Voltage

The open-circuit voltage, V_OC, 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.

IV curve of a solar cell showing the open-circuit voltage.

An equation for V_oc is found by setting the net current equal to zero in the solar cell equation to give:

$$V_{OC}=\frac{n k T}{q} \ln \left(\frac{I_{L}}{I_{0}}+1\right)$$

A casual inspection of the above equation might indicate that V_OC goes up linearly with temperature. However, this is not the case as I₀ increases rapidly with temperature primarily due to changes in the intrinsic carrier concentration n_i. The effect of temperature is complicated and varies with cell technology. See the page “Effect of Temperature” for more details

V_OC decreases with temperature. If temperature changes, I₀ also changes.

The above equation shows that V_oc depends on the saturation current of the solar cell and the light-generated current. While I_sc 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 764 mV under one sun and AM1.5 conditions1, while commercial silicon devices typically have open-circuit voltages around 690 mV.

The V_OC can also be determined from the carrier concentration 2:

$$V_{OC}=\frac{k T}{q} \ln \left[\frac{\left(N_{A}+\Delta n\right) \Delta n}{n_{i}^{2}}\right]$$

where kT/q is the thermal voltage, N_A is the doping concentration, Δn is the excess carrier concentration and n_i is the intrinsic carrier concentration. The determination of V_OC from the carrier concentration is also termed Implied V_OC.

Voc as a Function of Bandgap, E_G

Where the short-circuit current (I_SC) decreases with increasing bandgap, the open-circuit voltage increases as the band gap increases. In an ideal device the V_OC 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 3:

$$J_{0}=\frac{q}{k} \frac{15 \sigma}{\pi^{4}} T^{3} \int_{u}^{\infty} \frac{x^{2}}{e^{x}-1} d x$$,

where q is the electronic charge, σ is the Stefan–Boltzmann constant, k is Boltzmann constant, T is the temperature and

$$u=\frac{E_{G}}{k T}$$

Evaluating the integral in the above equation is quite complex. The graph below uses the method outlined in 4 

Diode saturation current as a function of band gap. The values are determined from detailed balance and place a limit on the open circuit voltage of a solar cell.

The J₀ calculated above can be directly plugged into the standard solar cell equation given at the top of the page to determine the V_OC so long as the voltage is less than the band gap, as is the case under one sun illumination.

V_OC as function of bandgap for a cell with AM 0 and AM 1.5. The V_OC increases with bandgap as the recombination current falls. There is drop off in V_OC at very high band gaps due to the very low I_SC.

• 1. “Analysis of the recombination mechanisms of a silicon solar cell with low bandgap-voltage offset”, Journal of Applied Physics, vol 121, 호 20, p 205704, 2017.
• 2. R. A. Sinton 와/과 Cuevas, A., “Contactless determination of current–voltage characteristics and minority-carrier lifetimes in semiconductors from quasi-steady-state photoconductance data”, Applied Physics Letters, vol 69, pp 2510-2512, 1996.
• 3. P. Baruch, De Vos, A., Landsberg, P. T., 와/과 Parrott, J. E., “On some thermodynamic aspects of photovoltaic solar energy conversion”, Solar Energy Materials and Solar Cells, vol 36, pp 201-222, 1995.
• 4. M. Y. Levy 와/과 Honsberg, C. B., “Rapid and precise calculations of energy and particle flux for detailed-balance photovoltaic applications”, Solid-State Electronics, vol 50, pp 1400-1405, 2006.