beta at low currents

Goes to hell on a motorcycle (see my prior posts on beta versus current and current mirror accuracy). From a modeling point of view it's parameter NE... degradation of beta at low currents due to recombination (and dirt and surface leakage ;-)

Probably, since you're dealing with beta/(beta + 1)

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IME, which only extends down to nA, you get lower beta. The obsolete

2N929 was recommended as having decent beta at 50nA Ic.

Fundamentals of Solid-State Electronics By Chih-Tang Sah indicates that you might expect a beta of around 1 at 10pA and worse at lower currents, but maybe modern transistors are not quite the same.

Maybe a job for an optoisolator?

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Yes, or a FET, since it's inside a loop.

Cheers, James Arthur

Since base current has shot noise, a beta of 1 is very bad news.

I guess I'll have to try something else. But maybe I'll test a few modern high-beta transistors just to see.

Hmmm... some low-capacitance PIN photodiodes might be interesting. Again, I'd have to see how bad the shot noise would be.

John

As you reduce the current, HFE goes down. At Vbe=3D0 you still have some leakage current flowing in the collector. This current will tend to decrease further if you put a small back bias on the emitter junction. In this situation you are sinking current out of the base and the more you sink, the less collector current flows. The collector leakage current depends weakly on the collector voltage and strongly on the temperature.

Beta goes kaputt unless you have devices made at a lab, small, very low defect rate and very low parasitic current. It's not something you can order at Digikey. Winfield Hill would be a good person to ask. If he doesn't know anyone who can make them for you then there probably isn't anyone in the world.

Honestly, I'd try to find another solution.

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Really small devices e.g. BFT25A have betas that hold up pretty well down to the 100 pA level. You'll need a pretty big sense resistor, like

10**10 ohms, because you need to drop at least 50 mV across it to get the shot noise to dominate the Johnson noise.

How about a charge pump? You can make the mutual capacitance between two nodes as low as you like by adding a bit of shielding around them, so you can use a big swing, a couple of LEDs as steering diodes (femtoamp leakage, typically), and a second set with a bigger mutual capacitance as a check or local feedback loop.

Cheers

Phil Hobbs

Never tried at such low currents, but for picoamp collector currents, one would think that leakage currents to the base would be in a similar range of magnitude (or worse) and thus "kill" the beta seen in real life. ...and keep the transistor cool, man (yah hip?).

Try selected part types made by Zetex...ZTX1051A, ZTX689A, ZXTN25015DFHTA, ZTX457, FCX458TA, ZTX696A.

?? Red LEDs to generate voltage / current? Illuminate as one sees fit; gives rather decent isolation.

What about an LED-to-LED optocoupler? That would sure make tiny, poorly controlled currents. A couple LEDs as steering diodes would let you temporarily divert that current to a measurement node, e.g. to an integrating cap., whereupon you could adjust the current quite accurately, then steer that back to the load.

And/or you could use the steering to PWM the current--once you'd measured it--to make smaller values. A multiplying D/A.

Cheers, James Arthur

Good catch, and to my surprise Digikey has them.

I guess it depends on what John really wants to do.

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Yeah, we're all kinda shootin' in the dark. But it's fun.

Cheers, James Arthur

I really wish I could present the entire problem - it's deliciously difficult - but there might be legal problems down the road. For now, I just want to learn more about signal slinging at the pA level.

As Phil notes in his book, diodes look like resistors at zero bias. Ro = 40 mV / Is is a cruel equation. And transistors don't work well at these currents. Some fets might, but they have a lot of capacitance. Resistors have Johnson and shot noise.

Sigh.

John

How about something at a more reasonable current, and a resistive current divider?

Have Fun! Rich

Could you define the pF-number for "a lot"?

Look at the bright side: As you said it's deliciously difficult so it's fun, challenging and best of all, puts food on the table :-)

Or in your case, has paid for the brat's Jeep ...

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Resistors make Johnson noise. A 1T resistor generates 128 microvolts RMS per root Hertz of system bandwidth. That's huge in a system that would benefit from a few nV/rthz noise floor.

Tee networks can be even worse.

John

One trick to controlling a tiny current is to use the collector current to control the base current. I don't know how this looks from a noise perspective.

Find a neon lamp with no Kr-85, ie a camera flash indicator from a disposable camera.

Illuminate one electrode with a UV led. Enjoy your teeny-weenie photoelectron current source.

Don't ask how I know.....

One of those strange things they asked me to do at the university. That was a solution I came up with.

Steve