Conductance fluctuations near the localized-to-extended transition in narrow Si metal-oxide-semiconductor field-effect transistors

A unified theoretical picture has emerged to explain the fluctuations in the conductance of disordered, one-dimensional resistors. At zero temperature T, and if the localization length ξ is shorter than the sample length L, current is carried by resonant tunneling which gives rise to exponentially large conductance fluctuations as the Fermi energy is varied. On the other hand, if ξ>L, the fluctuations are always of size $e^2$/h. As T is raised, the fluctuations at first remain exponentially large for L>ξ, but are the result of one-dimensional phonon-assisted hopping. At still higher T, the inelastic diffusion length $L_{\mathrm{in}}$ plays the role of sample length, and when $L_{\mathrm{in}}$ becomes as short as the localization length the states become delocalized. For temperatures above this localized-to-extended transition, the fluctuations of conductance are always of order $e^2$/h in a sample of length $L_{\mathrm{in}}$. We present the results of experiments on narrow (∼70 nm) inversion layers in Si metal-oxide-semiconductor field-effect transistors. At low T there are exponentially large fluctuations at low conductance and $e^2$/h fluctuations at high conductance. It is shown that the dependence of current on Fermi energy, temperature, and source-drain voltage for low conductance can be explained by one-dimensional phonon-assisted hopping. The samples are too long to observe resonant tunneling. It is pointed out, however, that several predicted features are not observed in the limited temperature range studied. At high conductance the fluctuations are of size $e^2$/h in a sample of length $L_{\mathrm{in}}$. An estimate is made of the value of the conductance at which the localized-to-extended transition occurs: That is, the value at which the conductance and its fluctuations are both ∼$e^2$/h in a sample of length $L_{\mathrm{in}}$.