| The density of states (DOS) in both the two-dimensional (2d) electron gas and arrays of "quantum dots" is studied using capacitive and tunneling techniques. A capacitance bridge described in this thesis is used to make high sensitivity capacitance measurements on GaAs samples produced using molecular beam epitaxy.;The "single-particle" DOS is measured in the same samples. Zero bias tunneling of electrons between a quantum well and an ;We laterally confine electrons in a quantum well into arrays of quantum dots using a technique which requires only slight (300A) surface corrugation of the sample. Electron beam lithography and reactive ion etching techniques are used to produce this corrugation. These samples are studied using a capacitance method which has allowed us to determine the lateral area of dots. Further, on the femto-Farad scale, quasi-periodic capacitance fluctuations are observed. We show, through comparisons with simulated results, that these fluctuations arise as due to an almost regular spectrum for adding single electrons to the dots which develops as a consequence of the Coulomb blockade.;We have made quantitative determinations of the "thermodynamic" DOS of Landau levels in a 2d system whose electronic density can be varied by means of a gate bias. A novel technique which, by taking advantage of two normalization conditions based on knowledge of the Landau level degeneracy and level spacing, allows extraction of the DOS from capacitance data using no sample parameters. The method yields the DOS as a function of Fermi energy in the 2d electron gas. We find that Lorentzian lineshapes give an excellent fit to the Landau level lineshapes observed. Further, the widths of these lineshapes are independent of the strength of the magnetic field. In high fields, the exchange enhanced spin splitting is observed and the exchange energy is determined. |
