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kT (also written as k B T) is the product of the Boltzmann constant, k (or k B), and the temperature, T.This product is used in physics as a scale factor for energy values in molecular-scale systems (sometimes it is used as a unit of energy), as the rates and frequencies of many processes and phenomena depend not on their energy alone, but on the ratio of that energy and kT, that is, on E ...
Boltzmann constant: The Boltzmann constant, k, is one of seven fixed constants defining the International System of Units, the SI, with k = 1.380 649 x 10 −23 J K −1.The Boltzmann constant is a proportionality constant between the quantities temperature (with unit kelvin) and energy (with unit joule).
Any system in thermal equilibrium has state variables with a mean energy of kT / 2 per degree of freedom. Using the formula for energy on a capacitor (E = 1 / 2 CV 2), mean noise energy on a capacitor can be seen to also be 1 / 2 C kT / C = kT / 2 . Thermal noise on a capacitor can be derived from this ...
Boltzmann's distribution is an exponential distribution. Boltzmann factor (vertical axis) as a function of temperature T for several energy differences ε i − ε j.. In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution [1]) is a probability distribution or probability measure that gives the probability that a system will be in a certain ...
For the example above, diatomic nitrogen (approximating air) at 300 K, = [note 2] and = % % /, the true value for air can be approximated by using the average molar weight of air (29 g/mol), yielding 347 m/s at 300 K (corrections for variable humidity are of the order of 0.1% to 0.6%).
The minimum subthreshold swing of a conventional device can be found by letting and/or , which yield , = (known as thermionic limit) and 60 mV/dec at room temperature (300 K). A typical experimental subthreshold swing for a scaled MOSFET at room temperature is ~70 mV/dec, slightly degraded due to short-channel MOSFET parasitics.
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In this case ΔE = E 2 − E 1 ≈ 2.07 eV, and kT ≈ 0.026 eV. Since E 2 − E 1 ≫ kT, it follows that the argument of the exponential in the equation above is a large negative number, and as such N 2 /N 1 is vanishingly small; i.e., there are almost no atoms in the excited state. When in thermal equilibrium, then, it is seen that the lower ...