understanding high temperature currents and thermal run away in npn power transistors

I want to better understand the nature of the increase in npn collector current with increasing temperature.

For Vbe held constant we know that this current approximately doubles with every 10 degree C increase in temperature. I believe there are two sources of this current increase and that they add to each other (they are in the same direction, and they do not partly cancel each other). Both depend on the temperature dependence of Is. The first is that more base-emitter current will flow. This is just an increased forward biasing of the base-emitter junction with temperature (Vbe held constant). This is normal transistor action. In the equation for Ic, Is increases with temp, and so Ic increases with temp. The second source of current is due to EHP generation across the reverse biased collector base junction. In this case, the appropriate equation is the diode equation under reverse bias. In this case Is is still increasing with temperature. Here we can think of the increase in current as coming from an increase in thermally generated electron-hole pairs (EHPs) in the depletion region. Now for the key point: at the reverse biased collector base junction, the thermally generated holes will follow the depletion region electric field and will flow into the neutral base. This flow of holes back into the base and of electrons back into the collector is what we would normally call reverse current or leakage current in a diode. In this case, what do the holes do when they move into the neutral base? Do they stimulate more emitter current? Is this process similar to the beta multiplication that we see in Vceo breakdown? What is the magnitude of this leakage current compared to first current component described above (the further forward biasing of the base-emitter junction)? If it is insignificant, then the whole description of "leakage current" as describing what happens to an npn with increased temperature is confusing, because strictly speaking, "leakage current" is in the direction of reverse (diode) current. So, finally, is the doubling of Ic with temp mainly due to the enhanced base-emitter conduction, and what role does the collector-base leakage current play in this doubling of Ic with temp?

Don't worry about the E-B junction and constant Vbe
so much.

Worry about the much larger and lighter-doped C-B
junction and its larger depletion volume in which to
capture increased (and usually unmodeled) generation
currents which roll on big-time at high temp. Worry
about the worsening Rb, which will reduce the base
shunt effectiveness on that excess base current. And
worry about the increasing / improving low current hFE
which will do its best to gain up that excess current,
against a lowered Vf on the E-B junction (double
whammy on the base current extraction, in a case
where the best you can do is B=E=gnd).

Which of these effects dominate, depends a lot on
your operating point and device dopings. And the
device theory for high temp stuff, which ignores (or
used to) generation and recombination currents at
standard temps, isn't as much help as you'd hope
when it comes down to cases.

Good papers to be found in the HiTEC / HiTEN
High Temperature Electronics Conference proceedings,
now part of or managed by IMAPS.

Thank you Richard!

I am new to this website and I am amazed at the quality of the information that is available here.

Let me make sure I completely understand your reply.

It appears that the component that I thought was the main contributor is only a minor contributor, and what I thought was the minor contributor is actually the main source of increased current.

1. In the npn, the primary source of increased conduction as T rises are the thermally generated carriers in the C-B depletion region.

2. These carriers, specifically the holes, are driven back into the base, and act as base current, forcing the npn into higher Ic conduction.

3. The Rb which will also rise with temp, limits a possible shunt path for these holes (a shunt path would prevent them from acting as base current)

This makes good sense to me now. Thank you so much. I now feel comfortable calling these high temp currents "leakage" currents.

We are looking at designing power amps that must survive at the high underground temps in the oil & gas industry. We are looking at increased reliability at 200 C.

The product is a hybrid. The front end can be an IC amplifier specifically designed for high temp. Honeywell has an SOI process and they claim a 5 year lifetime at 225 C. We can purchase that die. My concern is in the temperature performance of the output transistors. They are a Darlington pair and need to supply around 10A. A previous design with this output stage shows a resistor connecting base to emitter. This external B-E resistor is shown for both transistors (the pre-driver and the driver) in the Darlington pair. Before your reply, I had read of two reasons for the B-E resistor in the driver: first it is known as a turn-off resistor; next it provides a shunt path for leakage currents from the pre-driver so that those leakage currents don't go entirely into the base of the driver. To those reasons, I can now also add that the external R provides a shunt path for the above discussed thermally generated holes.

Here are two follow up questions:

1.The external B-E turn-off resistor. I will run a simulation, but I wanted to reply to you asap monday morning, so before running that sim, my thoughts on understanding the turn-off are as follows: in saturation the base is full of holes. The external resistor allows these holes to conduct out of the base. Is this correct? To verify this, I should see current flowing out of the base at turn-off. Without this shunting resistor, we have to wait for recombination in the base before the base is cleared of holes.

2. ok, so the increased diffusion currents in the E-B junction are not the main source of higher currents in the npn. But what about in the diode? For the diode, as I run Id vesus Vd sweeps (Vd > 0) with temp as a parameter, the currents are much larger, as T increases. Here, the only possible current is forward biased current, and they are sensitive to temp. It is for this reason that I thought the E-B conduction might be the dominant source in the npn. Not really a question here, but more an opportunity for further comment.

Thanks for the reference for furhter reading.

Best,

David