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

2. 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”

3. 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

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

5. 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).

6. 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.

7. 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

8. 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

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

10. 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

11. 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.