Dear Omar

An upper limit for the open circuit voltage of a solar cell will obviously be the band gap. Lower values are due to recombination processes in the cell. Even in an otherwise ideal material, black body radiation will present a minimum amout of unavoidable radiative recomibation, simply because we operate the solar cell at some finite temperature. The assumption that all light with energy higher than the band gap energy is ideally absorbed defines the solar cell as a black body for this spectral region. As such it will also emit black body radiation because it operates at some non-zero temperature and it is in equilibrium with its environment and the solar irradiation. This concept is called detailed balance [Schockley1961].

We will consider a less general case which is more illustrative. Assume that the charge transport is purely by diffusion of minority carriers. Then, the relationship between current density and voltage yields the following approximate expression between open circuit voltage Voc and short circuit current density jsc:

VOC=(Eg/q)-kT/q (JSC/J00)

Here, Eg is the bandgap and jsc the short circuit current. The current prefactor j00 for the diffusion current of minority carriers in a p-type absorber involves the effective densities of states NC and NV, the doping concentration NA, the minority carrier diffusion constant Dn, and the minority diffusion length Ln.

For the material constants of silicon and germanium and a typical doping concentration of about 1016 cm-3 we obtain j00 in the range from 108 to 109 mA/cm2. After putting this into the above equations we find that the open circuit voltages are about 400 mV lower than the band gap energy. Indeed, the open circuit voltages for high efficiency germanium, silicon and gallium arsenide solar cells are up to 245, 706 and 1020 mV, respectively, with their respective bangaps of 0.67, 1.12 and 1.43 eV.

Note that the diffusive transport is already a very ideal assumption, even in the best cells other recombination mechanisms are present which lower the maximum open circuit voltages below the discussed limits.

Dear Omar

An upper limit for the open circuit voltage of a solar cell will obviously be the band gap. Lower values are due to recombination processes in the cell. Even in an otherwise ideal material, black body radiation will present a minimum amout of unavoidable radiative recomibation, simply because we operate the solar cell at some finite temperature. The assumption that all light with energy higher than the band gap energy is ideally absorbed defines the solar cell as a black body for this spectral region. As such it will also emit black body radiation because it operates at some non-zero temperature and it is in equilibrium with its environment and the solar irradiation. This concept is called detailed balance [Schockley1961].

We will consider a less general case which is more illustrative. Assume that the charge transport is purely by diffusion of minority carriers. Then, the relationship between current density and voltage yields the following approximate expression between open circuit voltage Voc and short circuit current density jsc:

VOC=(Eg/q)-kT/q (JSC/J00)

Here, Eg is the bandgap and jsc the short circuit current. The current prefactor j00 for the diffusion current of minority carriers in a p-type absorber involves the effective densities of states NC and NV, the doping concentration NA, the minority carrier diffusion constant Dn, and the minority diffusion length Ln.

For the material constants of silicon and germanium and a typical doping concentration of about 1016 cm-3 we obtain j00 in the range from 108 to 109 mA/cm2. After putting this into the above equations we find that the open circuit voltages are about 400 mV lower than the band gap energy. Indeed, the open circuit voltages for high efficiency germanium, silicon and gallium arsenide solar cells are up to 245, 706 and 1020 mV, respectively, with their respective bangaps of 0.67, 1.12 and 1.43 eV.

Note that the diffusive transport is already a very ideal assumption, even in the best cells other recombination mechanisms are present which lower the maximum open circuit voltages below the discussed limits.

the eqn. you wrote is approximated under certain conditions, write completely to know the other parameters can reduce the value of Voc to be less than Eg. it is different for thin film devices, for a=Si and for Organic. 

Dr. Vasilopoulou is absolutely right. If you want details on the thermodynamics of solar cells I recommend Peter Würfel's book "Physics of Solar Cells".

Thank you Dr. Vasilopoulou for your well-put and valuable breakdown.

And thank you Dr. Schnabel for the reference.

The open-circuit voltage of a solar cell has as such nothing directly to do with the band-gap. The open-circuit voltage is that voltage for which the diode current equals the light-generated current. So, for a given semiconductor and given insolation, it depends only upon the diode current-voltage relation or the diode I-V characteristics. For example in the case of a Schottky barrier junction, the open-circuit voltage is related to the barrier height; higher the barrier, higher is the open-circuit voltage. 

However, Voc cannot exceed the band-gap equivalent voltage, because in that case the band-bending at the junction will be such that the photo-generated carriers will move in the opposite direction. 

The unit of open circuit voltage and bandgap are volt and eV (or Joule or Coulomb-Volt) respectively. The open circuit voltage is proportional to the bandgap of the PV materials and photo-sensitivity. The relation between open circuit voltage and bandgap should be (EFn-EFp ) = Eg = eVoc for the case of the homo-junction of perfect photosensitive materials in which all radiation has been used to produce electron hole pairs. Possibility of the open circuit voltage is larger for the case of type-I pn junction for their larger common part of bandgap, and for the high photo-sensitive materials. Another important cause of less open circuit voltage is matching problems to the n and p type materials for the case of the heterojunction.

i am not able to calculate values of Voc for Si, Ge and GaAs as per the formula, please help me out with this problem

after I agree with what's writen above, I will try to provide also my explaination in a more simple way ( I hope so!). As a start for my arguments I will state that I am worried only about the material which absorbs light (absorber), being a semiconductor with a defined bandgap, and I am not referring to (any kind of) junctions which help to separate charges and drive them selectively towards the electrodes. This is another story, most of the times, the built-in voltage at the junction drives charge separation and thus limits Voc. But again, in my opinion, this has nothing to do with Eg of the absorber. So here I briefly present two things: 1) thermodynamically, a solar cell is an energy converter: from solar to electricity. The solar energy is what the system receives, in the case of a semiconductor a photon of adequate energy is absorbed by a valence electron, gaining kinetic energy to move to the conduction band (if the energy is higher than bandgap, we dont care, the electron will thermalize at the conduction band edge anyway- unless it is hot). Thus, the maximum energy that the system can convert (otherwise stated free Gibbs energy) is obviously that of the bandgap: the electron will arrive at the electrode with this energy (neglecting EVERY energy limitation such as recombination). It cannot arrive with a higher energy, it is thermodynamically impossible! 2) As Dr. Md. Muhibbullah states above, the origin of the photovoltaic effect is the Fermi level splitting. The higher the splitting, the higher the Voc. In a semiconductor, the maximum splitting of Fermi levels OBVIOUSLY happens when EFn attaches Ec and, simultaneously, EFp attaches Ev, thus BANDGAP.         

It means that the thermally generated  minority carrier if contribute to optimize the diffusion current then the variation between the band gap Eg  and open circuit voltage , Voc  should be minimum.  It has also influenced by the binding energy of the materials that may relate to the dielectric constant. Therefore higher dielectric constant materials moderate binding energy may influence the carrier diffusion process and frequency dependent  relaxation and permittivity might have good relation to influence the minority carrier generation and diffusion current, thus minimize the gap between Eg-Voc