Theoretical Investigation of Resonant-Tunneling Structures

Sammanfattning: Resonant-tunneling structures are generally of great interest, both for technological applications and for basic theoretical research. This work focuses on the Double-Barrier Resonant-Tunneling Structure (DBRTS). We investigate both unipolar and bipolar DBRTSs. The unipolar DBRTS has been thoroughly investigated in the literature and the DC properties are well understood, while there are still controversy regarding the AC response. The bipolar DBRTS has not received the same attention as the unipolar, and neither DC or AC properties are much studied in the literature. For the unipolar DBRTS we therefore focus on the small signal AC properties, while for the bipolar we investigate both the steady state and the AC properties. We also investigate, principally, the use of the multiband effective mass approximation on semiconductor heterostructures.Starting with the investigations of the steady state we perform a theoretical analysis on bipolar DBRTSs using a two-band model, by solving self-consistently eight equations: the Poisson equation, two Schrodinger equations, four equations for quantum transport of electrons and holes, and the equation for electron-hole radiative recombination. All physical parameters are calculated from first principle, except the electron-hole recombination time ? , which is treated as an empirical parameter. We investigate in details the physical processes relevant to the three conditions for optimizing a bipolar DBRT light emitting diode: (1) the charge carriers are entirely trapped in the well as the only light source, (2) electrons and holes tunnel resonantly into the quantum well simultaneously, and (3) in the well it is nearly zero-field. We study the electroluminescence spectrum within a wide temperature range, and investigate the origin of its temperature dependence. Finally, we consider ?  as a varying parameter, to examine the dynamical aspects of the electroluminescence spectrum. To investigate the AC response of the DBRTS we choose to start with the much simpler unipolar system. Following the definition of admittance, we perform a first principle theoretical analysis of the total intrinsic admittance of unipolar DBRTSs. The theory includes contributions from the tunneling currents through the barriers, as well as from the charge distribution. We solve the problem numerically for small AC voltage amplitudes in the framework of linear response. The calculations are fully quantum mechanical in the Hartree approximation. In linear response, and at frequencies much smaller than the internal frequencies of the system, the susceptance is found to be entirely of capacitive nature. We found that the susceptance-voltage characteristic depends strongly on both frequency and temperature. A ?-shaped peak  in the susceptance is found in the negative differential resistance (NDR) region, where the conductance also depends strongly on frequency.The theoretical investigation of the intrinsic admittance of bipolar DBRTSs takes the same starting point as for the unipolar DBRTS. In addition to the tunneling of electrons we also have to take into account the tunneling currents of holes and there combination of electrons and holes in the quantum well. Based on our steady state calculations for the bipolar DBRTS we solve the problem fully quantum mechanically for small AC voltage amplitudes in the framework of linear response. We find the same ?-shaped peak in the susceptance in the NDR region here as for the unipolar DBRTS. Both conductance and susceptance are found to be strongly frequency dependent, and the recombination of electrons and holes plays an important role for the AC response of the bipolar DBRTS.While the use of the single band effective mass equation on semiconductor heterostructures is much studied and well justified, the use of multiband effective mass equations still remains controversial. To establish a firm basis for the use of multiband effective mass equations on semiconductor heterostructures we consider the Luttinger Hamiltonian for the degenerate Γ8 valence bands. Based on the bulk Hamiltonian we develop a Hermitian Hamiltonian for heterostructures, where the Luttinger parameters are spatially varying. The correct boundary conditions are derived from the minimal mathematical restrictions on the resulting coupled set of second order differential equations. The equations can be generally written , with the effective mass tensor fulfilling the symmetry property . This requires and  continuous in the effective mass equation. These boundary conditions automatically imply the conservation of current in the sample.