Noise in Semiconductors

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Presentation transcript:

Noise in Semiconductors Noise is a reflection of current fluctuations. The measured power spectrum is: Current Autocorrelation Function

Types of Noise Spectrum Uncorrelated in time. (velocity in random walk) Highly correlated “integral of white noise”. (position in random walk) Highly correlated but less than 1/2. “1/f noise”

Examples of Noise Thermal Noise (Johnson-Nyquist) Due to electron thermal motion. Shot Noise Due to discreteness of electric charge. Generation-Recombination Due to fluctuations in the number of charge carriers. 1/f Noise ??? Ec Ev

Typical Noise spectrum We are interested in the change of the thermal noise under large external electric fields.  Hot Electron Noise

Calculating the Noise Spectrum Use a Boltzmann-like equation to calculate the conditional probability = probability of finding electron with velocity v at (x,t) given the electron had velocity v’ at (x’,t’). Then: f(v’) is the steady state distribution function Collision Integral Boltzmann-Green Function Method PRB 35, 9722 (1987).

Constant Relaxation Time Collision Integral Parabolic Energy Band: Current is linear in E. Noise increases with E 2 . Heating of the electron gas by the electric field.

k-dependent Relaxation Time. Dependence of noise on electric field is more complicated. Basic results are: Electric field increase  heating or increased variance of the velocity distribution  noise increases. Electric field increase can increase scattering rates  correlation time decreases  noise decreases. Scattering rate increases  less heating of electron gas. area under the correlation function  t

Monte Carlo Results of L. Reggianni Optic Phonon Model The rapid turn on of the scattering rate at the optic phonon emission threshold decreases the correlation time and the noise. At higher fields, heating of the electron gas dominates. Monte Carlo Results of L. Reggianni

Noise in Non-parabolic Semiconductors Narrow gap, compound semiconductors: InAs, InSb From Georgia Tech, EPICS Lab Graphene Systems

Effect of nonparabolicity on the noise Relaxation time approximation can be solved exactly for the noise: Since the velocity saturates at high field, k-state fluctuations do not lead to velocity (current) fluctuations and the noise decreases! constant relaxation time E≠0 E=0

Noise Summary Graphene systems should have very good noise properties. Hot electron noise is reduced at large E fields. Fluctuations in k states do not lead to fluctuations in current.