Measuring the Boltmann constant by the IV curve of a diode

[GuitarDean]

So the current through a diode as a function of applied voltage is:

I = I₀ [ exp( V q / K_B T) - 1 ]

where V is the voltage (independent variable), q is the charge of the electron (constant), T is temperature (constant over each trial), I₀ is some parameter that's measured to be really tiny (I don't know why it exists, but I'm sure semiconductor theory can explain it), and K_B is Boltzmann's constant.

The circuit I built was just a diode and a resister in series. A voltage sweep from 0 - 10V was applied. The voltage is measure before and after the resister, and V<sub>applied{/SUB] - Vdrop over the resister is V across the diode. I is determined by Ohm's law applied to the voltage drop across the resister.

So I fit the above equation to an I vs. V graph, and tried it with a bunch of temperatures and got several roughly equal values for KB, and did a weighted average over them. The problem is, it's almost exactly double the real value of KB.

My lab report has already been marked and handed back, and the mark was pretty good; the TA made a note saying: "This KB is exactly what you should've gotten with this experimental setup."

I totally don't understand what that means though. What might've gone wrong with my measurement technique? Or is this "mistake" actually intrinsic to the diode? The note certainly implied that the data analysis is all correct.</sub>

 

[Bob S]

I have used diodes (actually diode-connected npn transistors) for gain elements in log-response amplifiers (feedback element), and have had to keep the diode current in the 1 microamp range. I got a good log-response gain.
Bob S

 

[f95toli]

I think the explanation is that that you are not using the full equation.
The equation for a real diode also involved an ideality factor which is in the range 1-2. This is probably the reason for your missing factor of 2.

 

[GuitarDean]

Ah. I just looked up the Shockley equation, and indeed there is an ideality factor between 1 and 2 multiplying k_B. The lab manual gave us the equation without that factor.. Bastards eh? A few other people in my class said they also got a k_B value that's about twice the actual value.

In any case, for any specific diode, is it possible to determine its ideality factor? The article I was reading about the Shockley equation just said "in most situations, the ideality factor is assumed to be 1" with no further explanation. It seems that if that's not possible, then the this experiment can't really get more accurate than it is now, so this is a pretty awful way of measuring k_B.

 

[f95toli]

The ideality factor depends on the forward voltage, it is indeed close to one for large bias but that was presumably not the case in your setup (for low bias it is about 2 which is what you got).

But yes, as a method for measuring kb it is pretty useless.