Resistance & temperature of semiconductor

Question

From what I have read about semiconductors, the reason their IV characteristic shows a decrease in resistance is because as voltage is increased, current is increased. However, the reason for the disproportionate increase in current is because any increase in current causes joule heating as describe by P = I^2R - current has a strong dependency on heating effect. This means the temperature increases. This causes more electrons to be freed as they have more energy (from the thermal energy) to cross the band gap. This causes a further increase in current than would occur with an ohmic conductor. This further increase in current reduces the resistance. Powerlines use this ohmic heating effect to there advantage by ramping up the voltage and therefore reducing the current so their is little joule heating. Could someone clarify if this logic is correct as this is what I have gathered from reading around various websites.

This brings up several problems for me: 1) Take a simple circuit with a loop of resistive wire, a transformer and a fixed power source. The power can either be put in as high current, low voltage or low current, high voltage. If the high voltage, low current combination causes less joule heating, where would the energy go in this circuit? 2) Ohmic conductors show that voltage is proportional to current and this holds across a range of temperatures. This means that if you increase the voltage, the current increases but the resistance remains constant. I don't get how this can happen? In a filament bulb, an increase in current causes a greater joule heating (and temperature rise) leading to an increase in resistance. What is it about an ohmic conductor that stops this from happening to it?

Answer 1

The I-V characteristics of materials and devices should always be measured at the same thermodynamic conditions, i.e. at the same temperature. Mixing the actual isothermal I-V characteristic with the temperature dependence doesn't lead to any useful data for the purposes of physics (but it is occasionally done in electrical engineering and electronics design for certain parts like NTC heaters and breakers).

A pure semiconductor at a constant temperature would be a pretty good Ohmic conductor, i.e. the current will be proportional to the applied voltage. This is a lot harder to measure properly on semiconductors than on metals, though, because of junctions formed with the metal wires that one has to attach for the measurement.

The conduction characteristics of semiconductor devices with one or multiple different materials forming junctions, on the other hand, is highly non-linear and can be made very complex. These devices will also have a temperature dependence, but it can be tuned very finely with appropriate material combinations and geometries.

Pure metals have typically increasing resistance with increasing temperature, but alloys can be made that have almost constant temperature characteristic (i.e. they are both Ohmic and temperature independent). One can also make metal alloys with negative characteristics, if necessary. Both constant and negative temperature characteristic is of enormous importance for the design of electronics, almost none of which would function properly if we couldn't make these near zero-TC metal alloys for resistors and NTC's for temperature measurement and compensation.

Non-metallic materials with very strong negative temperature characteristics often use percolation phenomena, i.e. on grain boundaries in sintered crystal powders, where conduction can only happen in very few narrow points in the material. As the material expands, these points of contact may get lost and the resistance may increase by many orders of magnitude over the technical temperature range of the material. The physics of these systems is very different from that of metals and semiconductors.

I think it would be better to say that power lines are designed to avoid ohmic heating rather than that they make use of it. I am not sure about the potential advantages of the heating for lines that may otherwise be weighed down and damaged or destroyed by snow and ice in cold climates, though. One would have to look at the design requirements for these power systems to understand if their designers make explicit use of these otherwise unwanted losses.

You are correct that one can trade current for voltage and vice versa by adjusting the resistance in circuits. Much of electronics design is a repeated application of that principle.

As for the question of how to design materials that have nearly temperature independent characteristics, that would require a very deep dive into solid state physics and materials research and I will leave that to someone who actually has the necessary detail knowledge. The guiding principle in many of these practical applications is that one tries to offset a positive gradient of one material with the negative gradient of another or one tries to combine multiple materials in such a way that the physical effects (like the formation of defects in the mixed material) offset bulk effects like the increase in the number of conduction band electrons in either of the constituents.