I fabricated different band gaps CH3NH3PbIxBr3-x active layers on mesoscopic NIP junction (FTO/bl-TiO2/mp-TiO2/CH3NH3PbIxBr3-x/spiro-MeOTAD/Au) and I found that Voc is increased as Eg become larger. Why is that?
The thermodynamic limit of the open circuit voltage is essentially determined by the band gap, temperature of the sun and temperature of the solar cell. You can think of the solar cell as a heat engine, with a Carnot limit. There are many references in the literature which explain this, but one convenient place is in: https://search.proquest.com/openview/740ae11f677e7369e90bda7b32f4f2da/1?pq-origsite=gscholar&cbl=27576 . : see equation 1.
Essentially, the solar cell Voc is given by the bandgap minus some fixed voltage penalties, determined by the luminescence yield, temperature and solid angle of emission. Another way to think about this is in terms of detailed balance. In the detailed balance efficiency limit at open circuit, every photon absorbed by the solar cell needs to produce an externally emitted photon. You can check that the radiative emission rate for a small bandgap material is larger at the same fermi level split, than the radiative emission rate of a wide bandgap material. For the same radiative emission rate (= detailed balance absorption rate), the small bandgap material needs a smaller fermi level split compared to the wide bandgap material. This Fermi level split translates into Voc for the solar cell..
You may determine the max. value of Open circuit voltage from the following general equation
E=qV hence, Voc=Eg/q
Of course there should be a other part using ln function, which is subtracted from the maximum value in order to get the practical result
The open circuit voltage is related to the bandgap of the active material. It is so that as the bandgap increases the opencircuit voltage increases so your observation is right.
For more details of relation between Voc and the energy gap please see my detailed answer below which i introduced to answer a similar question on the RG:
From the basic point of view a solar cell is composed of a device having a built in field region and solar photons absorbing material for generating electron hole pairs that will be separated by the field region where the electrons accumulates on the cathode and the holes on the anode.
The built in electric field is formed by the contact difference of potential which is the difference of the work function of the the two contacting material. Assuming the two materials a are n-type and ptype with doping ND and NA, then the contact differnce of potential phi= Vt ln NA NA /ni^2, the highest value of this potential is Eg and it will be achieved when the fermi level of the n material coincides with the conduction band edge ECand the fermi level of the p type material coincides with valence band edge Ev. The solar cell can not operated at such high doping since the junction will be a tunneling one and the transport properties will be detracted. ONE SIDE ONLY CAN BE OPERATED AT SUCH HIGH DOPING IT IS THE EMITTER LAYER WHILE THE BASE LAYER IS OPERATED AT ABOUT 10^17/CM^3.
If the solar cell is illuminated by solar radiation electron hole pair will be generated and separated by the built in field associated with the contact difference of potential.
As consequence electrons will be accumulated on the n-side and the holes on the p-side resulting in an opposite electric field to the built in field and the net electric field decreases. This is one effect, the other effect is that there will be an opposite current to the collection current where there will be a back flow of electrons and holes where they recombine and limit the upper bound of the accumulate charges on the opposite electrodes. As a thought experiment if one assumes that there is no recombination, the process of accumulation would continue till the the net electric field becomes zero and therefore the collection ceases. This means that the maximum open circuit voltage would be equal to the built in potential or the contact difference of potential. Therefore, the struggle is against the recombination to reduce it. The maximum theoretical open circuit voltage is material property.
Best wishes
VOC as function of bandgap for a cell with AM 0 and AM 1.5. The VOC increases with bandgap as the recombination current falls. There is drop off in VOC at very high band gaps due to the very low ISC.
from first equation intrinsic carrier concentration(ni) decreasing with increase in Eg and from second equation you will find that reverse saturation current Jo will decrease with decrease in (ni), hence from third equation Voc will increase as Jo decreases so conclusion Voc increases with increase in Eg and vice versa is true.
Open circuit voltage is directly related to material’s bandgap. Hence, it’s fine for your case
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