Johnson Noise and Shot Noise: The Boltzmann Constant, Absolute Zero, and the Electron Charge

Electrons in conductors at finite nonzero temperatures produce measurable voltages due to thermal noise, even if the conductor is not driven by any other external voltage. The thermal noise voltage, called Johnson noise, is posited to depend only on the frequency width of the signal, as well as the temperature and resistance of the material. From the measurement of Johnson noise voltages for resistors of many different resistances at the same temperature, the proportionality constant, which is the Boltzmann constant, can be found. In addition, from the measurement of Johnson noise voltages for a single resistor at many different temperatures, the Boltzmann constant as well as the absolute zero temperature can be found. Electrons in conductors are discrete particles rather than a continuous fluid of charges. This means that in addition to Johnson noise, electrons produce fluctuations in any current passing through a conductor solely because they are discrete charges rather than a continuous charge density; these fluctuations constitute shot noise. Measuring unamplified and amplified voltages from a specialized circuit allows for the determination of the value of the electron charge.