3

Ohm's law is valid for metals, but is it valid for semiconductors? Does it work there?

I am not talking about a PN junction here.

If I have a block of silicon and pass voltage across it, will I see current flowing, in accordance with Ohm's law?

Hearth
  • 27,177
  • 3
  • 51
  • 115
Wonder
  • 155
  • 5
  • Yes. In fact, the very first chapter of any book on microelectronics starts out at the beginning analyzing semiconductor behavior with the assumption of the Drude model and the application of Ohm's Law (though you'd have to put some of the equations together to produce Ohm's law, since they will be using volts/meter, usually.) – jonk Apr 27 '19 at 14:02
  • 1
    You would need a block of silicon doped with either a N-type or P-type to make it a conductor. Silicon on it's own wouldn't conduct current because there is no transfer of electrons/holes. – Rajesh Shashi Kumar Apr 27 '19 at 16:24
  • The relationship between voltage, current, and resistance always applies; the confusing parts are situations where these have interdependence, such that the effective resistance at one voltage or current is different from that at another. But the relationship between those in any given situation holds. – Chris Stratton Apr 27 '19 at 17:55
  • 3
    @RajeshS Pure silicon is still conductive, just much less so. – Hearth Apr 27 '19 at 17:55
  • 4
    Possible duplicate of [Does a diode really follow Ohm's Law?](https://electronics.stackexchange.com/questions/339055/does-a-diode-really-follow-ohms-law) –  Apr 27 '19 at 21:29
  • @vaxquis Please, it's not. I have clearly mentioned that I am NOT talking about a pn junction, as in a diode. – Wonder Apr 28 '19 at 05:13
  • A diode has a depletion region, thats why the I-V curve shows a threshold voltage. A chunk of semiconductor doesn't have one, right? But it has a small band gap. So will there be a threshold voltage due to this little energy gap? If the semiconductor is doped, then there will be enough electrons in the conduction band. It will behave like an ohmic conductor. But an undoped one? That's where my doubt lay. – Wonder Apr 28 '19 at 05:20
  • @ShaonaBose IMVHO the crux of the answer lies not in the distinction between diode/semiconductor/whatever, but about understanding *what Ohm's Law is really about*, and why this question makes little sense. tl;dr currently used form of Ohm's law is an empirical law, and the original statement by Ohm was that in *a circuit in permanent state*, I = E/(r+Rl). Thus, the real answer here is, *what are you actually asking about?* 1) can we effectively approximate the behaviour of a block of semiconductor with U = IR? **or** 2) does a block of semiconductor exhibit ohmic behaviour at all? –  Apr 28 '19 at 11:02
  • @vaxquis Hehe, both. – Wonder Apr 28 '19 at 11:29
  • Are you assuming Is a block of pure Silicon a Semiconductor? It's an insulator. So in practical terms it is a dielectric that becomes a capacitor between probes. – Tony Stewart EE75 Apr 30 '19 at 22:43
  • Okay. I see. And what if it's n-doped? – Wonder May 01 '19 at 04:37

2 Answers2

8

Yes. All materials under normal conditions and at fixed temperature follow* ohm's law, though it becomes less useful in good insulators where breakdown occurs before any substantial amount of current can flow.

Non-ohmic effects occur at boundaries between different materials, such as pn junctions, schottky junctions, thermocouples, electrochemical cells, et cetera. They can also be observed in discharge phenomena, where the flow of current causes ionization and chemical changes in the conducting material.

*Here, "follow" means "behave in a way closely approximated by". Depending on how precisely you're measuring things, it may matter that it's not quite exact.

Edit: it's worth mentioning that the presence of (changing) magnetic fields can complicate things. Transformers and inductors are not generally considered to obey ohm's law under dynamic conditions, for instance.

For further information on where it gets murky, see this question.

Hearth
  • 27,177
  • 3
  • 51
  • 115
  • 2
    To be accurate, I'd phrase it "nearly all materials under normal conditions **closely approximate** Ohm's law". As engineers, we tend to separate the exceptions into nicely explained phenomena, such as resistance change due to heating, or thermoelectric effects, or rectification, etc., etc., etc. If you're going into a 16-bit ADC, then in general you only just barely start to worry. If you're going into a 24-bit ADC and the last eight aren't just there to boost your ego, then worry. – TimWescott Apr 27 '19 at 16:29
  • 1
    Velocity saturation... – sstobbe Apr 27 '19 at 17:39
  • @sstobbe Would you consider velocity saturation to be "under normal conditions"? – Hearth Apr 27 '19 at 17:42
  • @TimWescott Good point. I'll add that note. – Hearth Apr 27 '19 at 17:42
  • I guess normal is relative to application. Certainly agree ohms law always is true in differential form – sstobbe Apr 27 '19 at 18:07
  • With the sort of work I do, I've certainly never had occasion to take velocity saturation into consideration. I don't honestly even know that much about what it is. – Hearth Apr 27 '19 at 18:12
  • @Hearth If I have an undoped semiconductor, will the band gap of the semiconductor cause a knee voltage to appear on the I-V curve? – Wonder Apr 28 '19 at 05:22
0

Ohm's law is just an approximation. It says that voltage and current are linearly related with a constant called (DC) resistance. This may be true over a wide range of applied voltage, or only over a small range. In some cases the concept is used to describe small changes around a particular point (dynamic impedance -- R = dV/di around a particular bias point).

Metallic conductors follow it very well because the movement of electrons caused by reasonable currents is small compared to their pre-existing thermal random movements. If the current is so high that heating occurs, then 'Ohm's law' isn't followed exactly.

Semiconductors have more constraints. There can be a limited number of carriers available so their velocity is significant compared to thermal motion -- and then Ohm's law is not followed. In addition, higher voltages affect boundary conditions at the surfaces of the semiconductor and this also affects the DC resistance (large signal resistance).

jp314
  • 18,395
  • 17
  • 46