Alfred M. Kriman

Molecular dynamics extensions of Monte Carlo simulation in semiconductor device modeling

Abstract The modeling of relaxation and transport is semiconductors is often performed using Monte Carlo techniques in which electrons follow free trajectories between discrete scattering events, the scattering events being defined to include carrier-phonon interactions and Coulomb interactions among various carrier species and the ionized impurities. We consider situations in which this approach is inappropriate, and describe corresponding implementations of a more accurate technique in which the usual Monte Carlo technique is combined with a molecular dynamics time evolution between scattering events. In these approaches, the Coulomb interaction is not approximated as screened scattering between pairs of particles, but instead is treated explicitly by allowing the carriers to follow trajectories accelerated by the electric field of the other charges in the system. In one implementation, the particle dynamics incorporates quantum corrections such as exchange interaction.

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.

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>>

Quantum molecular dynamics treatment for the electronic relaxation of high‐density plasmas in two‐dimensional structures

We examine effects of the exchange interaction on the thermalization dynamics of high‐density photogenerated plasmas in quantum wells. A technique for simulating the transient dynamics is presented which combines the conventional Ensemble Monte Carlo method for the carrier‐phonon scattering, with a molecular dynamics scheme for treating the many‐body contributions to the long‐range Coulomb potentials. Account is taken of the exchange‐energy interactions in keeping with the exclusion principle and the Fermi nature of the system. Our results indicate that the exchange corrections slow the cooling of the photogenerated plasma at carrier densities above 1012 cm−2. The effect is due primarily to a weakening of the direct Colomb force, and demonstrates that calculations based on simple carrier–carrier scattering alone would underestimate thermalization time constants.

Analysis of electron diffraction in a novel field-effect transistor

We analyze a field effect transistor whose operation utilizes the quantum diffraction of electrons by a narrow slit in the gate. Calculations are performed using a low-energy conformal mapping technique which does not assume small-angle scattering. It is shown that the device will exhibit far-field quantum diffraction similar in appearance to the Fraunhofer patterns observed in optics. The diffraction pattern can be detected as current collected at a number of narrow Schottky contacts which together comprise a “viewing screen”. Fringe visibilities on the order of 0.5 are predicted. A number of applications of the device are discussed.

Overshoot saturation in ultra-submicron fets due to minimum acceleration lengths

Abstract Ultra-submicron GaAs MESFETs have been fabricated with gate lengths ranging from 25 nm to 80 nm, using an electron-beam lithography process, in order to examine the operating characteristics as a function of gate length. The MESFETs were fabricated on wafers doped at 2×10 17 cm −3 and 1.5×10 18 cm −3 with active layer thicknesses of 250 nm and 60 nm, respectively. Measurements of the transconductance, and the inferred transit velocity, as a function of the effective gate length show a minimum in these quantities near 55 nm. The rise in transconductance below this gate length is attributed to the onset of velocity overshoot in the channel region, and both the inferred transit velocity and the variations between the lightly doped samples and the heavily doped samples support this interpretation. For gate lengths below about 40 nm, however, the transconductance again drops. We attribute this drop to the existence of a minimum acceleration length needed for the carriers to reach the high values of the overshoot velocity. We have investigated this behavior with a transient transport model based upon a parameterized velocity autocorrelation function incorporating both energy and momentum relaxation rates. The results of this model yield qualitative agreement with both the measurements and the interpretation given above.

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.

Statistical properties of hard-wall potentials

Abstract We develop an effective potential for calculating the quantum statistical properties of potentials having high, sharp barriers. Accurate results are obtained for an infinite square well potential at all temperatures.

Magnetoconductance in Lateral Surface Superlattices

Microfabrication through the use of electron-beam lithography has allowed the creation of nanostructures with interesting and novel properties, and it is now possible to create potential-induced lateral surface superlattices. The magnetoconductance in such structures can be expected to be significantly different from that of normal quasi-two-dimensional systems. Here, we discuss the theoretical understanding and experimental studies that show the presence of the Aharonov-Bohm effect, universal conductance fluctuations, and structure in VH and σxx with h/e and 2h/e periodicity in the flux coupled through each quantum well of the superlattice. At high VSD, we have seen evidence for negative differential conductivity, which might be attributable to Bloch oscillations.

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.