Question

a)A photodiode used in a solar cell is designed to absorb light with a wavelength less than or equal to 1 µm. What is the minimum energy band gap (in eV) for the material making up the photodiode?

eV

(b)What If? Gallium arsenide (GaAs) has an energy gap at 300 K of 1.42 eV. What maximum wavelength of sunlight (in nm) could be absorbed by a solar cell consisting of GaAs?

nm

Answer 1

a) It is given that the photodiode in a solar cell is designed to absorb light with a wavelength less than or equal to .

So, in order for the photodiode to be responsive for a particular wavelength or less than a particular wavelength of light, it should have energy bandgap corresponding to that particular wavelength.

We know that the energy is emitted in discrete particles of quanta with a particular frequency and the energy associated with each quanta of energy is given by, , where is the Planck's constant.

So, the energy bandgap of a semiconductor is energy gap between the valence band and the conduction band. So, when an electron in the conduction band (Higher energy band) makes a transition to the valence band (lower energy band) it emits energy as quanta which will have a frequency corresponding to the energy band difference divided by the Planck's constant. So, when a photodiode is designed to absorb a certain frequency range from the solar cell, it should have a minimum bandgap corresponding to the frequency or the wavelength it is absorbing from the solar cell.

So, in the question it is given that the photodiode is supposed to absorb all the wavelengths equal to or less than . So, is the maximum wavelength in the range, so if we find the energy corresponding to this wavelength, we will get the minimum band gap of the photodiode. This is beacuse the energy is proportional to the frequency which is mentioned above, but frequency is inversely proportional to the wavelength. Hence energy will be inversely proportional to the wavelength, so the maximum wavelength and wavelengths below it will correpond to minimum energy of the photodiode and the energy above it.

Where c is the velocity of light.

... Equation(1)

So, the minimum bandgap of the photodiode will be,

.... Equation(2)

In terms of electron volts we can write,

b) In the second question, the energy bandgap of Galium Arsenide at 300K is given, we have to find the maximum wavelength.

So, from equation (2), we can write,

Where is the energy bandgap at 300K.

PLease note, the energy bandgap decreases as temperature increases in a semiconductor.

So, at 300K, the maximum wavelength of sunlight that can be measured as,