# Drain current as a function of temperature

I was working on the temperature dependence of the Mosfet and I obtained the following characteristics shown below. Interestingly the drain current decreases with increasing temperature. But thought that temperature increases the energy of the electrons thereby it should cause a higher current is it not ? Why would it be otherwise ? In the graph shown below Vgs was constant and the Vds was varied for different temperature values and you can see that the current decreases for higher temperatures.

those look like you have saturation and a high gate voltage above Vt, so VDSat approx is sqrt(Is *Isat)/Ut (that's the behavior, not the complete equation), where Ut is the thermal voltage. The drain current would decrease as the temperature goes up.

As the temperature increases, the meantime of collisions goes up, which causes those "higher order effects" that slows down mobility.

If we had a benefit from higher temperatures, we wouldn't need heatsinks.

• Okay, now I get it but could you explain a bit on what, Is and Isat are ? and also what do you mean b higher order effects ?? I thought temperature increase would iimprove the conductivity of silicon. – Bhuvanesh Narayanan Jan 12 '16 at 1:50
• Explaining this in detail would take a whole lecture series, but I can point you at references. Firstly, there's a low point called "freeze out" where you do not have enough entropy to conduct, and then you have "chaos" where you don't have enough free states due to energy. Electricity does not actually "flow", it more of rattles: as you remove one electron, another fills the space. The most succinct discussion I know about this exists in the Semiconductor Physics book by Andy Grove from 1967. "Analog VLSI: Circuits and Principles" by Shih-Chii Liu will be more available. – b degnan Jan 12 '16 at 15:14

The drain current depends on carrier mobility (which decreases with increasing temperature by about -0.3 %/deg C); carrier concentration (which increases negligible with temperature), and threshold voltage (which decrease with temperature by about -2 mV/deg. C).

At gate voltages just above the threshold voltage (say < 500 mV above), the threshold variation dominates, and drain current increases with temperature. Conversely, at significantly higher gate voltages (say more than 1 V above threshold), the mobility term dominates, and drain current decreases with temperature.

IN MOSFETs, generally it works in inversion mode in which (for n channel mosfet) electrons make a channel due to high electric field between gate terminal to substrate . when temperature increases, electrons will gain kinetic energy and this will be a barrier for electrons moving towards channel in the influence of electric field to create channel which means now either we need to increase gate voltage to get the same amount of current (current at previous temperature). or if we make gate voltage constant then current will decrease due to extra gained kinetic energy which decreases the influence of electric field .

Are you sure that is a MOSFET? Silicon devices like BJTs have negative temperature coefficients (conductivity goes up as a function of temperature) which describes the phenomenona you see.

• Yes this is a MOSFET for sure. – Bhuvanesh Narayanan Jan 12 '16 at 2:13
• Wrong. These are silicon -- not silicone. In doped silicon, conductivity decreases with temperature (because mobility decreases -- more collisions) . In unroped (intrinsic) silicon, conductivity increases (more carriers generated), but undoped silicon is not an active portion of a FET. – jp314 Jan 12 '16 at 2:19
• Lol thanks. Did a little more reading and see that negative coefficients happen for MOSFET at very low currents... usually they are positive. I am power guy and rarely deal with MOSFETs at only 25mA. – OneSolver.com Jan 12 '16 at 2:22
• I just read the OnSemi Application Note ... it says a bunch of times MOSFETs have positive temperature coefficients.... – OneSolver.com Jan 12 '16 at 2:37
• Look at their Fig. 1 -- below 6.2 VGS it's positive, above it it's negative. However, they are talking about RDSON -- since current depends inversely on this (I = VDS/RDSON), RDSON has a negative tempo at low VGS (RDSON decreases); and the opposite at high VGS. – jp314 Jan 12 '16 at 3:30