voltage drop behavior

[nazi]

Dear experts,

In many systems, the voltage drop across to the transport direction is not a linear ramp, and it has convex or concave shapes. My question is that what is the meaning of this behavior?

What is the main difference between two systems where the voltage of one of them drops linearly across the central scattering region, but the other one does not drop linearly?

Thank you very much in advance.
Nazi

[Petr Khomyakov]

The potential profile is given by the dielectric response of the material in the central/scattering region, as well as by the boundary conditions imposed on the boundaries between the electrodes and central region.

For metals, the potential is flat across the central region, since ideal metals fully screen the electric field, i.e., it is zero in metals, whereas it is linear for insulators, which have a finite dielectric constant. In reality, the central region is a kind of in-homogeneous material, in general, and the dielectric function has a spacial dependence, meaning that the potential profile is in-homogeneous accordingly.

I would suggest reading some textbooks on the electrodynamics to understand this issue, i.e., Electrodynamics of Continuous Media
by L.D. Landau & E.M. Lifshitz., or any other book. 

[nazi]

Dear Petr,

Thank you for your answer. let me ask my question in other words. If the voltage drops linearly (nonlinearly), may I conclude that the system is a semiconductor (metal)?

I calculated the voltage drop of two 2D systems in the same bias voltage; the voltage drop of the system which shows higher conductivity (current) drops linearly but the voltage drop of another system with a very weak current intensity has a concave shape.

Thanks in advance.
Nazi 

[Petr Khomyakov]

Thank you for your answer. let me ask my question in other words. If the voltage drops linearly (nonlinearly), may I conclude that the system is a semiconductor (metal)?

I would not make a conclusion about the semiconducting or metallic nature of the scattering region, just using the potential profile. For example, a heavily doped semiconductor would behave similarly to metals in that regards, but it is still semiconductor.  Also, in-homogeneous ("nonlinear") profile does not mean metallic-like, it should be just flat for a perfect metal.