Cryogenic Field-Effect Transistors for the Study of Semiconductor Nanostructures.

This thesis presents an experimental study of low-noise cryogenic field-effect transistors. The devices are fabricated in GaAs/AlGaAs heterostructure material grown by molecular beam epitaxy and are patterned using electron beam lithography. A mesa etch is used to define channels in the two-dimensional electron gas in the heterostructure; metallic gates are deposited by thermal evaporation of chrome and gold. We have measured the performance of these cryogenic devices at liquid helium temperatures between 0.38 K and 4.2 K. At T = 1.3 K these FETs display a charge sensitivity of less than 10^{-2} e/ surdHz and a charge resolution of approximately 0.4 electronic charges. The power dissipated in these devices is less than 1 muW and the operating bandwidth extends to 1 MHz and above. The input impedance of the FETs is equal to approximately 0.4 pF in parallel with a leakage resistance exceeding 10 ^{15} Omega. The channels are matched for devices built on the same chip, allowing the possibility of multi-FET cryogenic circuits. We demonstrate this with a simple differential amplifier built from cryogenic FETs. We demonstrate sensitive and low-leakage operation of the cryogenic FETs by using them to study the Fermi level of a two-dimensional electron gas in a microstructure. Using a floating gate arrangement the electrochemical potential is measured as a function of applied magnetic field; the experiment is a non-perturbative probe of the thermodynamic density of states of the electron gas. We observe oscillations corresponding to Landau level depopulation and large spikes due to persistent currents when the sample is in the quantum limit.