N. C. Kluksdahl

Investigation of ballistic transport through resonant-tunnelling quantum wells using wigner function approach

Abstract We present a Wigner function study of quantum ballistic transport through resanant-tunneling quantum wells, as found in devices which employ a double barrier formed by layers of GaAs and AlGaAs. The Wigner equation-of-motion is numerically solved, in an effective-mass Hamiltonian formulation. The inclusion of scattering is also attempted using a simple relaxation term.

Wigner function study of a double quantum barrier resonant tunnelling diode

Abstract Resonant tunnelling structures are receiving attention as a testbed for theoretical approaches to quantum transport. We present a Wigner function study of a double quantum barrier resonant tunnelling device formed by layers of AlGaAs in GaAs. Our study deals with the influence of the boundary conditions on the initial distribution as well as on the time-evolution of the system. We use a Gaussian wave packet to study the numerical effects of the boundaries. We attempt to solve the system in both the time-evolution and steady-state cases, including self-consistency in the potential.

Quantum tunneling properties from a Wigner function study

Abstract We use a Wigner function description of a Gaussian wave packet to study tunneling through single and double quantum barriers. We note a tunneling time proportional to 1/k and a constant delay time associated with tunneling for the single barrier. The resonant structure gives rise to peaks in tunneling time associated with the resonant energy of the system. We study the initial distribution for the resonant tunneling diode. This is computed from a scattering state basis. Time evolution of the resonant tunneling system is then performed, yielding transient and steady-state results for the I–V curves.

Absorbing boundary conditions for the simulation of quantum transport phenomena

Abstract Absorbing boundary conditions for the transport equation governing the time evolution of the Wigner distribution function are derived. Local approximations are given which can be used to simulate quantum transport phenomena numerically on a finite domain and a numerical test example is presented.

Transient switching behavior of the resonant-tunneling diode

A quantum mechanical analysis is used to treat the transient behavior of the resonant-tunneling diode (RTD). The use of the Wigner formalism permits inclusion of the quantum mechanics inherent in the device, while offering a Boltzmann-like equation that is rather easily implemented. Self-consistent treatment of the potential introduces plasma oscillations in the distribution, which leads to the oscillatory current transient. Fourier analysis of this transient indicates that the RTD behaves inductively at frequencies under 2 THz, consistent with the ballistic nature of the carriers. At higher frequencies, the dominant mechanism is the capacitive charging and discharging of the quantum well, which leads to capacitive behavior of the device. The real part of the conductance is negative for frequencies under 1.5 THz, and positive for higher frequencies. The critical frequencies are shown to be independent of the relaxation time used to model dissipation, although the magnitude of the conductance decreases as the dissipation increases.<<ETX>>

Wigner function simulation of quantum tunneling

Abstract The quantum mechanical phenomenon of tunneling time has been the subject of much debate. We use a Wigner function description of a Guassian wave packet to study the tunneling process. By adjusting the parameters of the barrier and wave packet, a variety of cases can be studied. For the multiple barrier case, the tunneling time shows peaks at energies corresponding to resonant states of the system. This charge storage within the well is also found to be significant in studying the resonant tunneling diode, giving rise to kinks in the negative differential conductivity region of the I–V characteristic.

Intrinsic bistability in the resonant tunneling diode

Abstract Quantum transport in the resonant tunneling diode is modeled here with the Wigner formalism including self-consistent potentials for the first time. The calculated I–V characteristics show an intrinsic bistability in the negative differential conductivity region of the curve. We show that intrinsic bistability results from charge storage and the subsequent shifting of the internal potential of the device. The effect of undoped spacer layers is investigated. The cathode region of the RTD shows a strong depletion and quantization of electrons in a deep triangular potential well if no spacer layer is present. The potential drop in the cathode well reduces the barrier height to ballistic electron injected from the cathode, enhancing the valley current and reducing the peak-valley ratio. A finite relaxation time for the electrons increases the negative resistance, reduces the peak to valley ratio of the current, and causes a ‘soft’ hysteresis in the bistable region. The spacer layer prevents the formation of a deep quantum well at the cathode barrier, and the distribution does not deplete as sharply as without the spacer layer.

The role of visualisation in the simulation of quantum electronic transport in semiconductors

Using the Wigner function to simulate semiconductor processes and depicting the results graphically is leading to new insights concerning these devices. The Wigner function, which uses a formalism that correctly incorporates all the quantum mechanics inherent in a problem, is the Fourier transform of the density matrix, taken with respect to a difference variable. The tunneling problem and the simulation of the resonant tunneling diode are discussed.<<ETX>>

Role of structure sizes in determining the characteristics of the resonant tunneling diode

Abstract Using the Wigner function formalism, we study the effects of structural parameters on the DC I-V characteristics and on the large-signal transient response of the resonant tunneling diode. We model two types of structures of GaAs/Al x Ga 1-x As; first, with symmetric barriers ranging from 3 to 8 nanometers in thickness separated by a 5 nanometer well, and second with a well varying from 3 to 8 nanometers between 3 nanometer barriers. Experimental variation of the barrier thickness and height changes the peak-to-valley ratio in the I-V curve, as predicted by elementary models of tunneling structures. This stems directly from the changes in tunneling probabilities. For the DC studies, we show that the peak-to-valley ratio in the I-V curve is a function of the resonance width, which depends both on the well and barrier thickness. The location of the peak on the I-V curve depends on the location of the resonant energy, which is a function of the well width. Transient switching behavior is compared to earlier numerical studies of tunneling times of wave packets. Charge storage stabilizes the position of the resonant state, thus damping the transients. Consequently, wider barriers yield faster transient settling times, in agreement with the tunneling time results which predicted longer charge storage times for thicker barriers.

Effective potential for moment-method simulation of quantum devices

Abstract In the simulation of submicron devices, complete quantum descriptions can be extremely computationally intensive, and reduced descriptions are desirable. One such description utilizes a few low-order moments of the momentum distribution that are defined by the Wigner function. Two major difficulties occur in applying this moment method: (i) An independent calculation is required to find quantum mechanically accurate initial conditions. (ii) For a system in a mixed state, the hierarchy of time evolution equations for the moments does not close. We describe an approach to solve these problems. The initial distribution is determined in equilibrium by means of a new effective potential, chosen for its ability to treat the sharp potential features which occur in heterostructures. It accurately describes barrier penetration and repulsion, as well as quantum broadening of the momentum distribution. The moment equation hierarchy is closed at the level of the second-moment time evolution equation, using a closure that is exact for a shifted Fermi distribution. Band-bending is included by simultaneous self-consistent determination of all the moments.