Measuring the Boltmann constant by the IV curve of a diode

In summary, the current through a diode as a function of applied voltage follows the equation I = I0 [ exp( V q / KB T) - 1 ], where V is the voltage, q is the charge of the electron, T is temperature, and KB is Boltzmann's constant. The equation also involves an ideality factor, which is usually assumed to be 1, but can range from 1-2 for different diodes. The circuit used to measure this equation includes a diode and a resistor in series, with a voltage sweep applied. After fitting the equation to an I vs. V graph and taking a weighted average of several trials, it was found that the calculated value for KB was almost exactly
  • #1
GuitarDean
7
0
So the current through a diode as a function of applied voltage is:

I = I0 [ exp( V q / KB 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 KB 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 Vapplied{/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.
 
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  • #2
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
 
  • #3
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.
 
  • #4
Ah. I just looked up the Shockley equation, and indeed there is an ideality factor between 1 and 2 multiplying kB. The lab manual gave us the equation without that factor.. Bastards eh? A few other people in my class said they also got a kB 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 kB.
 
  • #5
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.
 

FAQ: Measuring the Boltmann constant by the IV curve of a diode

What is the Boltzmann constant?

The Boltzmann constant, denoted as k, is a fundamental physical constant that relates the average kinetic energy of particles in a gas to the temperature of the gas. It is named after Austrian physicist Ludwig Boltzmann and has a value of approximately 1.38 x 10^-23 Joules/Kelvin.

Why is it important to measure the Boltzmann constant?

The Boltzmann constant is used in many areas of physics and engineering, particularly in thermodynamics and statistical mechanics. It is a crucial factor in understanding the behavior of particles in a gas and determining the thermodynamic properties of materials. Accurate measurements of the Boltzmann constant are essential for advancing our understanding of these fields.

How is the Boltzmann constant measured using the IV curve of a diode?

The IV (current-voltage) curve of a diode can be used to determine the diode's forward voltage at different temperatures. By measuring the forward voltage at known temperatures, the relationship between voltage and temperature can be used to calculate the Boltzmann constant.

What are the advantages of using the IV curve method to measure the Boltzmann constant?

The IV curve method is a relatively simple and cost-effective way to measure the Boltzmann constant. It does not require sophisticated equipment and can be performed with commercially available diodes. Additionally, this method does not require any specialized knowledge or expertise, making it accessible to a wide range of researchers.

Are there any limitations to using the IV curve method to measure the Boltzmann constant?

While the IV curve method is a useful tool for measuring the Boltzmann constant, it is not as accurate as other methods such as Johnson noise thermometry. The accuracy of the IV curve method can also be affected by factors such as the quality of the diode and external factors like temperature fluctuations. Therefore, it is important to carefully control and account for these factors to obtain accurate measurements.

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