SRH model is largely depicted in Grove's book Physics and Technology of Semiconductor Devices (Wiley International) and is suitable especially for Si or for those semiconductors with indirect transitions from VB in CB with one intermediary center.

About Langevin model, I am sure you find all details in the Atlas guide. The generation process in Organic materials fundamental differs from generation process in inorganic Si substrate. 

@Cristtian Ravariu, Thank you so much for your concern and giving the reply, but I would like know more and why we are not using SRH model in organic semiconductor materils.

Organic semiconductors are characterized by low mobility. Consequently, the electrons and holes move slowly and the  chance for a hole to capture a neighboring electron will be higher than if they moving fast. Langevin gave the theory of such process. In fact, it is analogous of the direct band to band recombination in metalic semiconductors. I mean it is a direct capture of electrons bu holes as they attract each other by Coulomb force.

So, the recombination rate will be proportional to the pn where p is the hole concentration and n the electron concentration.

The SRH recombination mechanisms that may be dominant in  indirect band gap material,is based on the recombination of electrons and holes via traps having energy levels lying in energy gap. The traps act as a catalytic for recombination process.The recombination occurs on two steps. The fall the electron in a trap then the fall of the electron from the trap into hole in the valence band.

There is also the Auger recombination mechanism which more probable in materials having high carrier concentration.

In principle, in a semiconductor all these recombination mechanisms exist a they are probable and the resultant recombination rate is the sum of all the possible rates. All mechanisms are acting  in parallel but the nature of the semiconductor and its operating conditions leads to the dominance of one or more recombination mechanism.

Foe example, the SRH mechanism is dominant in the indirect bandgap materials, while the radiative band to band recombination dominates in direct bandgap materials such as gallium arsenide while the Langevin mechanism may be dominant in low mobility materials.

Every mechanism has its statistics and rates, and one has to to judge before deciding on the dominant mechanism or perhaps mechanisms.

This is my experience with the recombination processes in semiconductors.

For more information please revert to:

http://www.roderickmackenzie.eu/finland_answers.pdf

and: https://www.researchgate.net/publication/236003006_Electronic_Devices

Wish you success

Book Electronic Devices

nice answer

Thank you Xingang. You are welcome. In fact, you encouraged me to return again to the answer of the question with more details about the Langevin recombination rate as i treated it within the scope of my question to compare the organic and metallic semiconductors. So, i copied part of my answer from there here:

Now let us resume the comparison this time about the recombination mechanisms in both types of materials.

The recombination is the disappearance of a mobile electron in a hole. This process leads to the loss of mobile charge carriers and thereby affect much the electrical characteristics of the  semiconductor devices including solar cells and light emitting diodes.

The recombination mechanisms were studied intensively in metallic semiconductors and to less extent in the organic semiconductors.

From the conceptual point of view, the recombination mechanisms occurring in the the metallic semiconductor also occur in the organic semiconductors.These mechanisms can be classified into radiative and nonradative types. Radiative recombination is a consequence of the direct fall of electrons from the conduction band to the valence band band while the nonradiative one when the fall of the electrons occurs through trap levels in the bandgap. These trap levels are called recombination centers.

Every recombination mechanism has its specific dependence on the hole and electron concentrations and its rate constants.

There is a recombination mechanism which exists in the organic semiconductors.

It is the Langevin mechanism which occurs as direct consequence of an electron and holes comes in the field of the other.  They get this chance when they meet while moving with low mobility.  Its recombination rate r lv can be expressed by the expression:

r lv=q (mun+mup) pn/ epsilon,

where mun, mup are the electron and hole mobilities, p,n are the hole and electron concentrations, epsilon is the permitivity and q is the electron charge.

It is found that this mechanism is applicable in case of the organic LEDs, where it must be reduced by an appreciable factor when applied to organic solar cells.

Generally the rate can be expressed by r lv= kr pn, where kr is the recombination rate constant that can be determined experimentally.

Best wishes

It is required to compare organic and inorganic semiconductors?. Available from: https://www.researchgate.net/post/It_is_required_to_compare_organic_and_inorganic_semiconductors [accessed Aug 8, 2017].

Thank you sir

Does titanium dioxide have direct gap bands or indirect bands? Does titanium dioxide follow the Langevin model?

One important observation in Langevin recombination is the temperature effect. It increases with temperature. Inorganic binding energy is less than K/q thus temperature does not impact but organic materials the temperature influence in carrier mobility and recombination after e-h pair separation from excitonic binding effect is predominant.

Titanium dioxide is an inorganic material and its electrical permittivity is huge > 10, so it does not possess similar nature as organic of very low permittivity