Why does MOSFET RDS (ON) increase with temperature? - Page 1
Forum section: electronics / beginners

author: Enrique.Garcia
author_rank: Newbie
timestamp: May 03, 2021, 09:57:06 am
content: Hallo EEV community,Why does MOSFET RDS (ON) increase with temperature? If I understand correctly, resistance should decrease with temperature.Thanks!

author: golden_labels
author_rank: Super Contributor
timestamp: May 03, 2021, 11:31:22 am
content: Despite MOSFETs are semiconductors, there is still purely resistive component involved that works similarly to how a standard resistor works. The hotter it gets, the higher is the resistance.If you are confused, because MOSFET can also undergo thermal runaway: the temperature is the key. At low temperatures it’s the resistive, positive temperature coefficient; at much higher temperatures the negative temperature coefficient of the semiconductor takes over. At this point it must be stressed, that “much higher temperature” refers to very localized temperature in spots inside the semiconductor, not the overall junction or case temperature, which will usually be considerably lower. At a tiny spot temperature will rise, negative temperature coefficient takes over and that tiny spot starts to channel more and more current, heating up the surrounding area and causing a kind of chain reaction that ends up in a thermal runaway damaging the whole junction.In MOSFETs designed to work with high currents this is actually used to stabilize them. They are much better cooled and the temperature inside the semiconductor is kept in the region where resistive component plays the major role. If a spot gets too hot, it simply becomes more resistive and current is diverged to the rest of the junction, evenly distributing load.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 03, 2021, 01:29:21 pm
content: Semiconductors have competing effects of increased density of states, increased thermal voltage, and decreased mobility.As it happens, for diodes and BJTs where Ebers-Moll holds, we have:(If or Ic) = Is * (exp(Vf / Vth) - 1)where If is the diode or base forward current, or Ic is the BJT collector current; Is, saturation current; Vf, forward/applied voltage; and Vth, thermal voltage, k_B T / q.Is depends on carrier concentration (intrinsic and extrinsic (dopant caused) electrons and holes), which in turn depends on bandgap, Fermi level and so on. It goes up ~exponentially with temperature.Vth goes up proportionally of course (with absolute temperature).For a constant If, Is can be brought inside the exponent and adds to (Vf / Vth). Thus as Is goes up with temperature, Vf goes down, roughly proportional to 1/T.A similar mechanism governs FET threshold voltage, so you get a negative tempco in Vgs(th) and Id(Vgs), though whether current or transconductance overall has a negative or positive tempco depends on construction; and which one is important, depends on application. (Most switching transistors are strongly NTC in any practical linear operating range; some old or obscure types (lateral, SIT, etc.?) can be paralleled with ease as the PTC region extends down to normal operation.)So this is why diodes, BJTs and FETs are generally difficult to wire in parallel, and need some ballasting resistance to behave.This isn't what you asked about, but it's related and fills out the whole picture. On to that specifically:FET Rds(on) is governed by the resistivity of doped semiconductor. As long as the doping is stronger than the intrinsic carrier concentration, the carrier concentration is fairly constant with temperature. (Over the commercial temperature range in silicon, n_i < 10^15 cm^-3 while N_D is higher. This is, roughly speaking, the lowest practical dopant concentration, and semiconductor design consists of clever ways to arrange that doping or higher, to achieve higher voltage ratings, lower capacitance, etc. These are minute amounts -- the number of atoms in the same volume is on the order of 10^23.) Instead, thermal scattering dominates -- charge carriers occasionally rebound off atoms, and rebound stronger when that atom happens to have a lot of energy (vibration). The energy transfer scatters the charge carrier, sending it off course and dissipating its kinetic energy -- overall, charge carriers drift through the material very slowly at typical current densities (~m/s), and electric field is proportional to current density.This is a very roundabout way of saying...it looks like a resistor. But the quantum mechanical explanation shows us both why it's a resistance in the first place, and also what happens with temperature. Temperature is lattice vibrations (phonons), in terms of density and energy distribution. Higher temperature causes more scattering, increasing resistance.Typically, over commercial temperature range (say from 25 to 150°C), the resistance increases 2-3 times. This is less noticeable in very short channels -- for Vds(max) < 30V, the tempco is lower, which may give some preference to lower voltage devices, when the choice is possible (say for peak voltages <= 12V).This relates to carrier mobility, which is a diffusion effect, how fast charge carriers spread out (alone, without electric field pushing them around). Hole mobility is lower than electron mobility, so we expect higher resistance from P-type semiconductor -- and indeed, P-ch FETs perform about 2.5 times worse than N-ch. (That is, higher Rds(on) for the same area or capacitance.)Okay, so that's technically correct, but rather low level. For a more beginner-oriented explanation, some analogies are in order.Semiconductors exhibit Fermi-Dirac statistics. (This has so far all been about statistical mechanics: what happens on a very small scale, averaged over a very large scale. Atoms and electrons are particles and waves, and we sum up their behaviors (mechanics) to get an overall statistical model of the system. Stat mech itself is notoriously difficult to do actual work in, and I'm probably misremembering a few things already...) This is analogous to electrons filling up energy levels, as balls fill up positions in a ball pit -- they start from the bottom and stack up to a mean level. The balls at the bottom are trapped by the weight of all the balls above them, so cannot move -- they essentially do not participate in any interesting (dynamic) behavior of the system. There is some distribution in play, where balls can be stacked on top of, or away from, each other, to some extent -- the mean level is what's important, but the fact that these distributions can happen at all means there's something to play with up here; the surface is free to move, and rise or fall subject to gravity.Now imagine a ball pit being shaken violently. Atoms are very small, and thermal energy in solids is essentially vibration. Using a ball pit analogy, we'd have to shake it pretty hard -- balls being made of quite a few atoms themselves. Well, with that shaking, at first (slight shake) it disturbs balls in precarious positions, and tends to flatten out the surface; you can't really get anything stacked up like this, but if you work at it, you can still make an especially stable stacking (a bit of a hexagonal pile, perhaps). Well, one thing to note already: there aren't many arrangements of those balls, that will randomly fall into that hexagonal pattern -- most of the time they'll be disordered and you won't be able to stack anything very high. (Mind, I'm already assuming one imaginary property: that the balls do not spontaneously form into hexagonal grids; as it happens, they really do, and it's very easy to make crystalline structures in sheets or piles of uniform granular material like this, even given random motion to drive them into those locations. This is more descriptive of crystallization of solids, than of the electrons within them.)If we continue to shake it harder and harder, first the surface levels out as it becomes impossible for any ordered stacking to persist, at least more than transiently (by random chance, for merely an instant). Soon, it becomes so violent that balls start bouncing entirely up into the air, and we start to get something like a "mist" of boiling balls, instead of a "surface". At this point, we have two things:1. The statistics of that "mist", depend on vibration intensity -- temperature. The distribution is wider (taller, more numerous) at higher temperature, and thinner at lower temperature.2. The bulk of balls, at some depth, will actually be moving around a significant amount (despite what I asserted above). Suppose you started with a ball pit perfectly divided into blue balls on one side, and red balls on the other: shaken this way, we expect the surface to mix fairly quickly, and the mixing rate drops with increasing depth. (If this is a shallow ball pit, probably the whole thing mixes pretty well, but a deep enough one will eventually go to zero at some depth, at least as long as the peak downward acceleration does not exceed gravity.)Now we cannot avoid talking about the quantum mechanical properties of semiconductors. The band gap is a prohibited region, where there are no states for electrons to sit at those energy levels. It's like we put a low ceiling over our ball pit; except that, if a ball happens to smack into the ceiling with enough energy, it is magically transported through the ceiling to the next floor, where it can roll or bounce around, and has some chance of falling back through again (because again, it's at a higher energy there -- so it can gain kinetic energy by falling through, and in physicst-speak, it "wants" to -- it's just that the band gap prohibits this from happening along the continuous path we expect a thrown ball to follow... weird, I know).With this setup, now all balls with insufficient energy, stay below the ceiling, and only those energetic enough to tunnel through, escape to the next floor, momentarily.We notice two things:1. Because the ceiling is low, the balls in the pit are really well trapped. Like, clamped in place almost. The only way any room is freed up, is if some balls escape to the next floor.2. When there are more vacancies, the balls can move around more. Like a sliding block puzzle, it's like the vacancy itself is moving. Which actually... isn't a bad way to think about it, hmm.If we apply an electric field to this ball pit (assuming the balls are electrically charged so they respond to the influence...), or perhaps more aptly, if we tilt the pit so there's a sideways element of gravity -- then at low temperature when there's not enough energy to form vacancies and promotions, nothing moves, no current flows (no balls spill over the side). It's temperature that makes it do anything at all.So we come to the explanation of intrinsic charge carriers. Promoted electrons are in the conduction band, where they flow relatively freely (higher mobility), and vacancies allow electrons to flow in around them -- we track the negative space as holes. Vacancies are in the valence band (that is, electrons that make up atoms themselves, or bind them together -- mostly stuck in place for those reasons), and have lower mobility due to a combination of lower energy, and more moving parts (I think the effective mass is higher but I forget exactly how that works?).Incidentally, if you're curious what, if anything, happens at even higher temperatures? The conduction band is only so wide itself, and there's another ceiling on top of that. Well, this time it's the roof -- an electron with enough energy to kick entirely out of the building, is free-as-in-beer to move anywhere in space. This is the vacuum state: free unbound electrons, able to move outside the material itself. This is essentially irrelevant in semiconductors, but makes their predecessors possible: vacuum tubes work by "boiling" electrons off a material with a low work function, and once free in vacuum, they are subject to electric fields, and it happens we can control their flow with a small field (a few volts) while accelerating them into a stronger field (hundreds of volts). The downside is, because the electrons are free, they aren't charge-balanced by the material they're embedded in -- the electron density in the beam is very much lower, greatly limiting performance (by a factor of perhaps ten to thousands, depending on how you count it)."Work function" is an odd term. It originates from the study of photoemission: hit with light of sufficient energy, electrons can be pushed out of a material. Typically visible to UV light. It was the subject of a Nobel prize awarded to... some famous guy with crazy hair I guess? Anyway, it doesn't matter what the energy source is, just that the energy gets there -- so light works as well as heat.Anyway, so we get the statistics of balls bouncing around, right? Now we average over that, abstracting away all the irrelevant particle motions, and derive the diffusion rate (mobility), and how much promotion occurs with temperature, and how much current flow occurs under bias. Cool. Now we don't need to know about Fermi levels and band gaps and such, we just have amounts of charge carriers, and how they can move.So we can fit this into the earlier explanation of resistivity. Effectively, both valence holes and conduction electrons are bouncing around (if you like, the floor is lumpy, so it's not just smooth rolling up there), bonking into things and exchanging momentum with thermal vibration. It happens that, for most semiconductors, thermal vibration dominates -- with a mean thermal velocity around 10^5 cm/s (or is that m/s, I forget -- semiconductors use cgs units a lot so probably it was cm?) and a drift velocity of ~cm/s, they're being bounced around a hell of a lot more. So it's very much a resistance dominated flow.There are, in fact, semiconductors where this needn't apply: gallium arsenide has higher electron mobility and breakdown electric field strength, high enough in fact that drift velocity can exceed thermal velocity. In this regime, ballistic transport takes over -- that is, velocity accelerates in a field, ala Newtonian mechanics -- and it's not so much a fixed velocity as a velocity depending on field strength and distance. Well, the effect on V/I characteristics at the terminals (we put metal pads on either end of an N-doped bar of GaAs) is to cause negative resistance: that is, as voltage rises, at some point current actually starts to drop off. And this effect acts very quickly, because it's simply how electrons are flowing through the material -- on the order of picoseconds if that. If we put this negative resistance inside a resonator, it will oscillate at the resonant frequency: this is a Gunn diode (poorly named, it's actually a monode -- no PN junction, remember?), capable of oscillation up to 100s of GHz!We just don't observe this effect in silicon, because impact ionization occurs sooner. That is, when electrons of enough energy smack into atoms or defects, that energy liberates additional electrons/holes, which can make more in turn, and so on -- avalanche breakdown. (In the ball-pit analogy, this would be like a ball falling in with such velocity that it kicks out extra balls from the pit (valence band) -- thus freeing more electrons and holes, and so on.)Oh, one last thing, doping: impurity atoms add an energy level within the bandgap, with an attendant electron or hole initially bound to that atom. These levels are more accessible by thermal energy, so the electron/hole is easily displaced into the conduction/valence band. Thus, dopant atoms effectively leak charge carriers into the surrounding semiconductor, providing a concentration in excess of the intrinsic carrier level. N-type dopants have an electron very near the conduction band (so just a little thermal energy easily promotes it to the conduction band), while P-type have a hole near the valence band (so just a little thermal energy easily promotes a valence electron to it, leaving a hole behind). Dopants with energy levels near the middle of the band, tend to act as traps to generate or recombine electrons and holes equally -- this tends to worsen performance (lower breakdown voltage and hFE), but can prove beneficial in certain cases (the old 2N2369 switching transistor has very fast switching speed due to gold doping hastening recombination -- a BJT switches on and off due to free charges; likewise, high speed rectifiers achieve short reverse-recovery times with gold, platinum or other dopings; this is irrelevant for FETs however, which modulate the conduction/valance band with an electric field rather than causing charge promotion).Tim