On the theory of 1/f noise of semi-insulating materials

The 1/f noise phenomena associated with devices involving semi-insulating materials, for instance GaAs MESFET´s on semi-insulating GaAs, has long been a perplexing problem. In this particular case the 1/f noise corner frequency can be up to 100 MHz before the mean square noise current at the drain is dominated by the Nyquist noise associated with the channel conductance. No reasonable explanation has ever been given, although there are many different theories. 1/f noise is a common phenomena in nature and other devices involving semi-insulating materials. We propose here that this 1/f noise is a bulk phenomena associated with localized high frequency variations and long range low frequency fluctuations, the lowest frequency being limited only by the volume of the material. Specifically the proposal here is that injection of a current I into a semi-insulating material will result in a mean square noise voltage at the point of injection given by v_n²~=2(kT/q)qΔfR(ω_c/ω) Volts² where ω_c=1/t_t, for the radian frequencies, ω, larger than ω_c which is the reciprocal of the transit time of the carriers. For a long sample and long transit times then this 1/f noise voltage due to current injection will be larger than the Nyquist mean square noise of the sample alone as long as the DC voltage developed across the semi-insulating sample exceeds ((2kT/q)l²(ω/μ))¹2/. This theory then gives the 1/f or 1/ω frequency dependence. The dc current I might be injected for instance by the substrate current in a GaAs MESFET being injected into the semi-insulating substrate, or gate current in an IGET being injected into the gate insulator.