It may helpful

https://www.researchgate.net/post/What_is_the_basic_difference_between_optical_band_gap_and_electrical_band_gap

It may helpful

https://www.researchgate.net/post/What_is_the_basic_difference_between_optical_band_gap_and_electrical_band_gap

Dear Md. Mahabub,

the optical bandgap is the difference between the band minima or the difference between states within the gap-region. This is usual the exciton gap (difference between band minima minus exciton binding energies. The electrical gap describes the difference between band states. Very often (as an example in p-n-diodes) you have to consider the difference between the quasi fermi level. There, you transport an hole from the valence band (at fermi level) into the band of conductivity.

With Regard

R. Mitdank

What I describe below is not the full story -- it is partly rigorous and partly based on a hand-waving argument.

Let EM;s denote the energy of the M-particle eigenstate of an interacting Hamiltonian, characterised by the compound index s, with s = 0 denoting the ground state and s = 1 the first excited state. For an N-particle ground state,

(1) εv = EN;0 - EN-1;0

is the energy of the top of the valence band, and

(2) εc = EN+1;0 - EN;0

the energy of the bottom of the conduction band [1,2]. The electronic energy gap εg;e is therefore equal to

(3) εg;e = εc - εv ≡ EN+1;0 + EN-1;0 -2EN;0.

In contrast, for the optical energy gap εg;o one has [2]

(4) εg;o = EN;1 - EN;0.

Theoretically, the results (1)-(3) follow from the spectral representation (the Lehmann representation [1]) of the one-particle Green function G1, and the result in (4) from that of the density-density response function χ, which is related to the two-particle Green function G2 [1,2]. Clearly, theoretically εg;e and εg;o are two different quantities. Physically, εg;e is the difference of two lowest-lying charged excitation energies (note the N±1), while εg;o is the lowest-lying neutral excitation energy.

Considering a system of non-interacting particles, where the total energy EM;s is equal to a sum of M one-particle eigen energies, one has εg;o = εg;e [2]. For an interacting system of electrons, the condition εg;o ≤ εg;e is, following Eqs. (3) and (4), tantamount to the condition

(5) EN;1 - EN;0 ≤ EN+1;0 + EN-1;0 -2EN;0 ⇔ EN;1 + EN;0 ≤ EN+1;0 + EN-1;0,

the proof of which is non-trivial. The hand-waving argument to which I referred above is that by considering at first glance the N-particle excited state to which EN;1 corresponds as consisting of an 'electron' promoted from the valence band into the conduction band and a 'hole' left behind, these two particles with opposite charges attract each other (think of an exciton, the bound state of an electron-hole pair) and the inequality in Eq. (5) reflects the attractive force between the two.

It is interesting to note that the stability of the ground state implies that EM;s should be a convex function of M, implying the Jensen inequality (see appendix B in [3])

(6) EN;0 ≤ (EN+1;0 + EN-1;0)/2,

in conformity with the condition

(7) εg;e ≥ 0.

With reference to Eqs (5) and (6), two cases can arise: (i) EN;1 + EN;0 ≤ 2EN;0, and (ii) 2EN;0 ≤ EN;1 + EN;0. Case (i) is contradictory, and case (ii) is trivially true -- since by definition EN;1 ≥ EN;0.

_____

[1] AL Fetter, and JD Walecka, Quantum Theory of Many-Particle Systems (Dover, New York, 2003).

[2]

Chapter Ground and Low-Lying Excited States of Interacting Electron ...

[3]

Article On the Luttinger theorem concerning number of particles in t...

Dear Md.

Adding to the colleagues above, there is the optical emission bandgap which is the difference between the lowest occupied level of the conduction band to highest empty level in the top of the valence band. While the electrical band gap is that associated with the thermal generation of the electron hole pair. This will be the difference between the highest empty level in the conduction band to highest occupied level in the valence band. Since in the room temperature the the bottom of the conduction band is filled with free electrons and the top of the valence band is occupied by holes. It follows that the electrical band gap will be basically greater than the emission optical band gap.

For more information please follow the paper: https://www.researchgate.net/publication/235941372_A_New_and_Simple_Model_for_Plasma_and_Doping_induced_Band_Gap_Narrowing

Best wishes

The optical bandgap is the measure of the band-to-band (CB to VB) gap at constant k (momentum) - the threshold for photons to be absorber. Similarly the electrical bandgap is the threshold for free electron and hole pairs (i.e., electrons and holes are not bound). This is depend on the exciton binding energy and depending on the exciton binding energy this threshold will be different. So optical bandgap and electrical bandgap could be different in different systems. For semiconductor, the good measurement should be temperature dependent conductivity measurement at high temperature regime in which the semiconductor behave like an intrinsic semiconductor and the electrical bandgap should be double for conductivity activation energy (using Arrhenius equation).

I always see the optical bandgap is higher than the electrical bandgap.

Dear Sanjoy Paul Sir,

Thank you very much for adding your answer. I've just learned a new lesson. Could you please give reference(s) regarding the fact that "The optical band-gap is higher than the electrical band-gap". Thanks again.

its not always electrical band gap is higher then optical band gap.

if the semiconductor is a non degenerated semiconductor, in this case with the presence of small amount of defects (suppose n-type defect) that leads to create new localized states under the conduction band ( some cases show donor levels above the valence band) and the optical band gap in this case is from the valence band until the new localized states while the electrical band gap is from the valence band until the conduction band, which results that optical band gap is lower then the electrical band gap.

but if you have a degenerated semiconductor the fermi level is located above the conduction band due to high carrier charges concentration. and in this case the optical band gap is from the valence band maximum to the fermi level, and the electrical band gap is always from the valence to the conduction band. and this phenomena results that the optical band gap become higher then the electrical band gap.

in resume, the optical band gap depends with the carrier charge concentration that may come from intrinsic defect of doping while the electrical band gap is depend with the crystalline structure of the material.

please have a look to our paper in which we have studied both electrical and optical band gap of Na doped ZnO.

Article Impact of position and concentration of sodium on the photov...