For diodes, as you said, both the electric field and the charge carrier density are highly non-uniform. The local field has to be taken into account for the calculation of the current/mobility.

For single carrier devices one can calculate the drift and diffusion currents as a function of applied voltage analytically (in a reasonable field range). For OLEDs and solar cells one has to solve numerically, calculating the local electric field (potential basically) and solving the Poisson/current continuity equations (Koster et. al Physical Review B 72, 085205 2005) point by point across the layer. 

In the end, no matter how one does it, the current is going to be a function of the applied bias, which is used for the comparison with the experimental data. The comparison then can also be made through the average applied field (an example: Organic Electronics 14, 1591, 2013)

For diodes, as you said, both the electric field and the charge carrier density are highly non-uniform. The local field has to be taken into account for the calculation of the current/mobility.

For single carrier devices one can calculate the drift and diffusion currents as a function of applied voltage analytically (in a reasonable field range). For OLEDs and solar cells one has to solve numerically, calculating the local electric field (potential basically) and solving the Poisson/current continuity equations (Koster et. al Physical Review B 72, 085205 2005) point by point across the layer. 

In the end, no matter how one does it, the current is going to be a function of the applied bias, which is used for the comparison with the experimental data. The comparison then can also be made through the average applied field (an example: Organic Electronics 14, 1591, 2013)

Dear M. V. Bogdanova, Your question is a basic question concerning the drift motion of mobile charge carriers.

By definition, the mobility is the ability of mobile charge carriers to drift in the solid materials upon the application of an external electric field on it. By applying an external electric field on the material the mobile charges acquire certain steady state velocity called the drift velocity vd, which is dependent on the external applies electric field E.

The vd versus E is a characteristic curve for a given solid material. There are the total mobility  u= vd/E or the incremental mobility ui= delta vd/ delta E.The incremental mobility is equal to the slope of the vd versus E curve.

This relation is affected by the internal electric fields in the material including the periodic potential of the crystal and  all the scattering forces impeding the motion of the mobile charge carriers such as crystallographic defect and chemical defects.

In order to be measurable the mobility describes the motion of the mobile charge carriers with the external applied field. The internal fields affect the shape of the vd-E curve.

For more information follow the link:

https://www.researchgate.net/publication/236003006_Electronic_Devices?ev=prf_pub

Best wishes.

Book Electronic Devices

The electric field in question is of course the macroscopic electric field across the diode. Because charge transport in organic semiconductors is mainly governed by hopping mechanisms, the mobility is low. Accordingly, the materials behave much like an insulator, and the electric field is simpky given by the bias divided by the thickness of the diode.

Dear Prof. Horowitz, in general terms, I agree with your comment, but let me express some objection: precisely due to the low mobility in organic materials, injected charge under an applied voltage tends to accumulate close to the metal/organic interfaces, hence generating a strong space charge effect in these regions, which contributes to a significant non-homogeneity in the internal electric field. So the question by M. V. Bogdanova still remains. In fact, I consider comments by Ilias as more accurate.

This is my contribution to the discussion: Mobility is defined, in principle, as an average magnitude for many particles. Do not forget that, under an applied external fiel, ONE particle should move faster and faster, I mean, it should accelerate. Since we externaly measure a stationary current and NOT an increasing current, we realize that carriers have thermalised by scattering (a sort of friction) and they have finally acquired a CONSTANT speed. So we can affirm: < v > = mu · E.  If carriers in a spatial local region have enough time to achieve thermal equilibrium, I think that the electric field E of the previous formula is the field at that local point. If E is not homogeneous across the sample, you should assume you have a dispersion of carrier velocities. And you have to be careful with your calculations.

You are perfectly correct, Angel. This space charge would result in a reduction of the electric field in the bulk of the diode. However, I would like to note that when charge injection is hampered by large barrier height (which is often the case in organic diodes) the space charge become negligible.

 The electric field  as defined here is that electric field strength in a location x of the material caused by an external  applied voltage on the semiconductor material. If the material is homogeneous and the metallic contacts to the material are  ohmic and the voltage drop on them is negligible, the external electric field will be homogeneous and= The applied voltage divided by the  distance between the electrodes. If the material is non homogeneous  the external electric field will be position dependent and also does the mobility such that

vd= mu (x)Ee(x). Such linear relation is valid only for the very small applied electric field. For larger electric field one has to consider the concept of the nonlinear mobility as the relation between vd and Ee.  In general, the concept of the mobility is valid in the ohmic neutral regions of the semiconductors

At the end i would hint that what prof. Angel said is in agreement with mine and my comment is very precise..