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Homogenous conductors like silver or semiconductors like pure germanium or germanium containing impurities obey ohm's law within some range of electric field values.

but if the field becomes too strong, there is a departure from Ohm's law in all cases. why?

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    $\begingroup$ First you can wonder why Ohm's law is valid. Why is the drift velocity proportional to the field at low fields? $\endgroup$ – Pieter Sep 2 '19 at 16:15
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    $\begingroup$ oh thanks! I got u point sir. $\endgroup$ – Garima Singh Sep 2 '19 at 16:17
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There are many different mechanisms causing non-ohmic charge transport in materials. Here are just a few examples:

  • In metals, the (steady-state) resistance typically increases with the applied voltage (or current), as a result of the Joule heating caused by the current. The reason for the higher resistance at high temperatures is usually the more frequent interactions of electrons with the vibrating lattice of metal ions. This is also often called phonon scattering.

  • In semiconductors, as the material gets hotter, the resistance can actually decrease. This is because in the intrinsic regime, the carrier concentration increases with temperature.

  • In semiconductors, as the E-field (which depends on the voltage) is increased beyond the point where the electron energies in between collisions exceed the energy required to excite high-energy lattice vibration modes (i.e. emit optical phonons), electrons undergo more lattice scattering, which increases the resistance. This effect is called velocity saturation.

  • In certain semiconductors such as some III-V's, which have accessible conduction band valleys that are higher in energy than the one normally populated in equilibrium, the electric field can provide this energy, moving electrons to these upper valleys. These valleys usually have a higher effective mass than at the conduction band edge, and hence a lower average group velocity. This causes the resistance to increase with an increasing E-field. This effect is more gradual than the previous one, so the average carrier velocity can actually have an overshoot that peaks at a certain E-field.

  • It can happen, often in insulators or intrinsic semiconductors, that the charge injected between two contacts results in a space-charge not neutralized by the material. The I-V relation in this case is given by the Mott-Gurney law. The resulting current is called space charge limited current, and varies superlinearly with voltage, corresponding to a static resistance that decreases with voltage.

There is also a host of interface-related effects resulting in non-ohmic behavior I won't even go into here, because I'm assuming you are asking about the resistance of a material and not a combination of materials.

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  • $\begingroup$ Quite interesting! If you feel like I'd love to read something on contact resistance between different metals too. $\endgroup$ – carloc Sep 2 '19 at 19:09
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the resistance depends not so much from the voltage, but from the current, the hotter the metallic material gets, the greater the resistance. but different materials have different behavior, so you find materials with positive or negativ temperature dependence.

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  • $\begingroup$ Why would you say the resistance depends on the current but not so much the voltage? Voltage and current are interdependent. Moreover, the rate of heat generation is the product of voltage and current. $\endgroup$ – Puk Sep 2 '19 at 18:38
  • $\begingroup$ you are right. of cause, the Voltage gives rise to the current, but the moving electrons cause the heat. But you have a much better answer from Puk $\endgroup$ – trula Sep 5 '19 at 9:03

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