Dear Xiaorong,

The organic material preserves its molecular nature because the very weak bond among the adjacent molecules. Accordingly the energy band  is the resultant of molecular energy band levels modified by weak interaction from the neighboring molecules. This weak interaction leads to small splitting of the molecular levels. Accordingly the LUMO and Homo levels will slightly broaden forming narrow energy bands. A consequence of the narrow band, is a small curvature of the energy momentum relation resulting in large effective mass. Simply expressed the electrons are localized in molecules. In long term ordered materials such as in silicon materials the valence electrons are delocalized and can move easily among the valence structure. The energy level splitting will be much larger and the width of the energy bands will be much larger than in the organic molecular materials.

This is a qualitative explanation of the shape of the energy band structure in the two types of materials. There are quantitative models through the solution of the wave mechanical equations as well as the measurements.

Best wishes

This is the first time I came to know about organic semiconductor. Interesting.

A very good book on organic semiconductors

Book Physics of Organic Semiconductors

I can't understand "because of the short order the energy width of the valence band and the conduction band are narrow rendering the effective mass appreciably large. Consequently the mobility of these materials are normally very small compared to the metallic semiconductors.", In my opinion, the smaller the energy gap, the better the conductivity?

Dear Xiaorong,

The organic material preserves its molecular nature because the very weak bond among the adjacent molecules. Accordingly the energy band  is the resultant of molecular energy band levels modified by weak interaction from the neighboring molecules. This weak interaction leads to small splitting of the molecular levels. Accordingly the LUMO and Homo levels will slightly broaden forming narrow energy bands. A consequence of the narrow band, is a small curvature of the energy momentum relation resulting in large effective mass. Simply expressed the electrons are localized in molecules. In long term ordered materials such as in silicon materials the valence electrons are delocalized and can move easily among the valence structure. The energy level splitting will be much larger and the width of the energy bands will be much larger than in the organic molecular materials.

This is a qualitative explanation of the shape of the energy band structure in the two types of materials. There are quantitative models through the solution of the wave mechanical equations as well as the measurements.

Best wishes

I would like to express my gratitude to the colleagues who gave an answer to my question. However, i want to discuss the conduction in the organic semiconductors and how current can be expressed under different operating conditions of such materials.

Basically the drift current density can be expressed by J= q un n + qup p where q is the electronic charge, un and up the electron and hole mobility an n and p are the electron and hole concentration. Based on this equation we want to discuss all terms and their origin in the organic materials. While the movement of the electrons and holes are limited by their effective masses, the barriers at boundaries of the molecules the temperature and the applied electric field, where n and p are coming from?

The electrons and holes can come from thermal generation giving the intrinsic concentration ni. This concentration is negligible in the organic materials because of the large energy gap. It can come by doping where the doping can be atomic or molecular. Mostly the doping is molecular. In this case one material will be p-type and the other will be n-type. That is donor molecules will be p-type and the acceptor molecules will be p- type. Also, the electrons can be injected by electrodes contacting the organic materials. If the contact material injects holes the organic material will be p-type , and if it injects electrons the material will be n-type.

If organic material is contacted from both sides with two contacts one injecting holes and the other injects electrons, there will be electrons and holes in the material and the conduction will be bipolar. This is the case of organic LEDs.

According to this description the organic material will be unipolar except  injected from both sides by electrons

and holes simultaneously.

Electrons and holes can be generated simultaneously by subjecting the material to photons with proper energy. However the generated electron hole pairs are not free but are still bound and called excitons. This because of the relatively low dielectric constant of the organic material. These excitons diffuse in the material and finally recombine after elapsing their lifetime. In this lifetime they diffuse a length equal about the molecule lemgth of about 10 nanometers.

In order to free electron and holes from the excitons one must extract the electrons by acceptor molecules. Therefore the active material in an organic solar cell consists of an acceptor donor junction. Where the donor absorbs the light and the  acceptor separates the electrons from the excitons at the interface of the two materials.

This is an outline of the origin of conduction in organic materials. 

It is required to discuss the conduction models at first in the solar cell then in the organic LEDs.

Dear Colleagues,

I would like to thank you for following this question. really , i intend to introduce the most important features of the organic electronic materials because of their impact on the advancement in electronics. Also, i would like to encourage the researchers to ask questions or to add their insights

Prof. Samaras asked about the common organic semiconductors used in fabricating or developing the organic semiconductor devices and there electronic properties. The most useful data about the materials can be obtained from the material suppliers themselves. To now about the most common materials for the organic semiconductor electronics and the devices made from them please refer to the Link: https://www.sigmaaldrich.com/content/dam/sigma-aldrich/materials-science/material-matters/material_matters_v2n3.pdf

In the coming post , the expression of the mobility as a function of the temperature and electric field will be discussed.

Best wishes

Dear Xiaorong Gan,

organic semiconductors might have quite a high[1] optical mobility. However, a "high DC" mobility remains a challenge. Also, the achievement of OS (organic semiconductors) with both high optical and near DC mobility is a higher challenge, today.

1. High mobility emissive organic semiconductor  http://www.nature.com/articles/ncomms10032.pdf

Mobility model in organic semiconductors:

The mobility of the charge carriers in amorphous organic semiconductors is modeled by hopping motion between energy sites separated by potential barriers with help of the applied electric field and the thermal energy. allowed sites are irregularly spaced from each other with an average distance (a) and disorder factor gamma. The energy distribution of the allowed sites follow a Gaussian distribution with a standard deviation sigma.

According to this hopping model the mobility is given by

u = uinf exp[ -( 3sima/5kBT)^2+ 0.78((sigma/kBT)^3/2 - gamma)  sq. root ( qaF/ sigmma)

where uinf is the mobility in the limit T tends to infinity, sigma gives the width of the Gaussian distribution of the density of states, kB is Boltzmann's constant and T the temperature. gamma gives the positional disorder of transport sites, a is the intersite spacing, and q and F are the elementary charge and the field strength, respectively.

One sees from the given expression that the mobility increases by increasing the electric field and temperature.

For more information plese refer to the thesis:Device Physics of All-Polymer

Solar Cells,Maria Magdalena.

In the next post the curents in the metal organic metal diodes will be outlined.

Best wishes

Dear colleagues;

I would like to thank all the colleagues who followed this question and invite them to continue the discussion on the topic of current mechanisms in organic semiconductor to the new question in the link:https://www.researchgate.net/post/How_is_the_current_limited_in_metal_organic_semiconductor_metal_MOSM_diode#view=58474c593d7f4b08b336dd71

I will be happy to see you there.

Best wishes