Terahertz Optoelectronic Devices

Noise is a reflection of current fluctuations.

The measured power spectrum is:Noise in Semiconductors

Current Autocorrelation Function

Types of Noise SpectrumUncorrelated 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 NoiseThermal Noise (Johnson-Nyquist)Due to electron thermal motion.

Shot NoiseDue to discreteness of electric charge.

Generation-RecombinationDue to fluctuations in the number of charge carriers.

1/f Noise ???

EcEvTypical Noise spectrum

We are interested in the change of the thermal noise under large external electric fields. Hot Electron Noise Calculating the Noise SpectrumUse 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

Boltzmann-Green Function Method PRB 35, 9722 (1987). Collision IntegralConstant Relaxation Time

Parabolic Energy Band:

Current is linear in E.

Noise increases with E 2 .

Heating of the electron gas by the electric field.Collision Integral

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 functiont

Optic Phonon Model

Monte Carlo Results of L. ReggianniThe 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.

Noise in Non-parabolic Semiconductors

From Georgia Tech, EPICS LabNarrow gap, compound semiconductors: InAs, InSbGraphene 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!E=0E0constant relaxation timeNoise SummaryGraphene 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.