Theoretical Study Of Resonant Tunneling Characteristics In Multi-Barrier Quantum Well Structures

There have been remarkable advances in science and technological applications of resonant tunneling since the pioneering work of Chang, Tsu and Esaki on resonant tunneling phenomena of super-lattices in 1974. With the modern development on growth of semiconductor devices by using the molecular beam epitaxy and metal-organic chemical vapor deposition techniques, multi-barrier quantum well structures are becoming the basic building blocks of modern semiconductor devices. In order to design new devices or optimize the device performance, one needs to know the whole information about the quasi-bound states, the lifetimes of quasibound states and the current-voltage characteristics in multi-barrier quantum well structures; to find out resonant tunneling characteristics in multi-barrier quantum well structures at bias or magnetic field or the situation taking into account the coupling between the transverse and the longitudinal wave-vector component of an electron; to acquire the knowledge of the resonant tunneling characteristics in different potential profiles multi-barrier quantum well structures. From the intrinsic quantum mechanics point of view, the quasi-bound states and the lifetimes of quasibound states of the tunneling process in these devices has been the heart of much research in the last decades. For the case of understanding the tunneling dynamics in high-speed devices, the lifetimes of quasibound states is one of the key parameters for ultimate performance evaluation of different kind of electronic devices. In addition, through current-voltage characteristics, we can evaluate the negative differential resistance behaviors. As we know, negative differential resistance behaviors are the most attractive phenomenon in tunneling questions. It is the basis of a series of high-frequent and high-speed micro-electron devices. Therefore, studying the resonant tunneling characteristics in multi-barrier quantum well structures is very important not only in understanding basic physics of semiconductor devices but also in device application.This dissertation specializes the resonant tunneling characteristics in multi-barrier quantum well structures.(1) Based on time-independent Schr?dinger equation and the Energy Uncertainty Condition in Quasi-bound States Method, the elaborate dependence of the quasi-bound states and the lifetimes of quasibound states in symmetrical double-barrier quantum well structures on structure parameters, such as well width, barrier width and composition mole fraction, have been investigated elaborately. The calculation results show that the lifetimes of lowest and higher quasibound states vary with structure parameters as a simple and exact function, and that the lifetimes of lowest and higher quasibound states increase exponentially with structure parameters. In addition, except quasi-bound states saturate when barrier width increases to some value,the effect of well width and composition mole fraction on quasi-bound states is remarkable.(2) By use of Airy Function and Transfer Matrix Method, one-dimensional Schr?dinger equation has been calculated exactly and correct analytical expression of transmission coefficient in biased/unbiased multi-barrier quantum well structures has been derived. Its validity and accuracy has been proved by comparisons with other currently used techniques. A few of mistakes made in transfer matrix method of Airy functions in previous literatures have been pointed out. By using the transfer matrix method of Airy functions, quasi-bound state dependence upon carrier effective masses, bias, well width, barrier width and height have been investigated systematically for several biased/unbiased double/multi-barrier quantum well structures. It is shown that the transfer matrix method of Airy functions is more promising for evaluating and designing intra-band transition far-infrared detectors and quantum cascade lasers.(3) By use of Transfer Matrix Method and the Energy Uncertainty Condition in Quasi-bound States Method, the effect of transverse wave vector of an electron and magnetic fields on resonant tunneling times in double-barrier structures, which is significant but has been frequently omitted in previous theoretical methods, has been reported. The analytical expressions of the longitudinal energies of quasibound states and the lifetimes of quasibound states in symmetrical double-barrier structures have been derived as a function of transverse wave vector of an electron and longitudinal magnetic fields perpendicular to interfaces. Based on our derived analytical expressions, the longitudinal energies of quasibound states and the lifetimes of quasibound states dependence upon transverse wave vector of an electron and longitudinal magnetic fields has been explored numerically for a symmetrical double-barrier structure. Model calculations show that the longitudinal energies of quasibound states decrease monotonically and the lifetimes of quasibound states shorten with increasing transverse wave vector of an electron, and each original longitudinal energy of quasibound state splits to a series of sub-longitudinal energies of quasibound state which shift nearly linearly toward the well bottom and the lifetimes of quasibound state series shorten with increasing Landau-level indices and magnetic fields.(4) By use of Airy Function and Transfer Matrix Method as well as the Energy Uncertainty Condition in Quasi-bound States Method to solve time-independent Schr?dinger function in triangular double-barrier quantum well structures, resonant tunneling characteristics of triangular double-barrier diodes have been investigated systematically. Originally, the exactly analytical expressions of the quasi-bound states and the lifetimes of quasibound states in symmetrical triangular double-barrier quantum well structures have been derived within the effective-mass approximation as a function of structure parameters including well width, slope width and barrier height. Based on our derived analytical expressions, the influence of structure parameters on quasi-bound states and lifetimes of quasibound states has been investigated and the numerical results show that well width, slope width and barrier height play an important role on quasi-bound states and lifetimes of quasibound states. Furthermore, according to the improved transmission coefficient of triangular double-barrier structures under external electric field, the current densities of triangular double-barrier diodes with different slope width at 0K have been calculated numerically. It is shown from the calculations that the N-shaped negative differential resistance behaviors have been observed in current-voltage characteristics due to the resonant tunneling effect and current-voltage characteristics have been found to be sensitive to the slope width.This work is supported by National Basic Research Program of China No.2006CB300406,and Shanghai Science and Technology Grant No.05nm0533, and National Natural Science Foundation of China No.60576064.