Analytical Expressions for Tunneling Time through Single and Double Barrier Structures

In the past, the quantum mechanical tunneling time through simple rectangular barrier has been obtained by various theoretical approaches including the dwell time, the phase delay time, the Larmor clock time and also using the numerical analysis of wave packets. The agreement among these approaches over a range of incident electron energy is far from satisfactory. In this manuscript, analytical expressions for the tunneling time are derived based on the group velocity approach (referred hereafter as the average particle time, τAPT) for single and double rectangular potential barriers under zero bias. The results of the single barrier case, including the limiting value of the tunneling time for various energy limits, are compared with these previous tunneling time calculations. The τAPT results provide physically meaningful tunneling times for zero and infinite incident energy limits of the electron. The τAPT for the double barrier structure is computed from the analytical solution as a function of the incident energy of the electron for two experimentally studied resonant tunneling structures. For both the single and double barrier cases, the effect of the structure parameters such as barrier width, height, and well width on the τAPT are obtained and reported

Measurement of Superluminal optical tunneling times in double-barrier photonic bandgaps

Tunneling of optical pulses at 1.5 micron wavelength through double-barrier periodic fiber Bragg gratings is experimentally investigated. Tunneling time measurements as a function of barrier distance show that, far from the resonances of the structure, the transit time is paradoxically short, implying Superluminal propagation, and almost independent of the distance between the barriers. These results are in agreement with theoretical predictions based on phase time analysis and also provide an experimental evidence, in the optical context, of the analogous phenomenon expected in Quantum Mechanics for non-resonant superluminal tunneling of particles across two successive potential barriers. [Attention is called, in particular, to our last Figure]. PACS nos.: 42.50.Wm, 03.65.Xp, 42.70.Qs, 03.50.De, 03.65.-w, 73.40.GkComment: LaTeX file (8 pages), plus 5 figure

Clinical Neuroimaging Findings in Catatonia: Neuroradiological Reports of MRI Scans of Psychiatric Inpatients With and Without Catatonia

OBJECTIVE: Catatonia is a debilitating psychomotor disorder. Previous neuroimaging studies have used small samples with inconsistent results. The authors aimed to describe the structural neuroradiological abnormalities in clinical magnetic resonance imaging (MRI) brain scans of patients with catatonia, comparing them with scans of psychiatric inpatients without catatonia. They report the largest study of catatonia neuroimaging to date. METHODS: In this retrospective case-control study, neuroradiological reports of psychiatric inpatients who had undergone MRI brain scans for clinical reasons were examined. Abnormalities were classified by lateralization, localization, and pathology. The primary analysis was prediction of catatonia by presence of an abnormal MRI scan, adjusted for age, sex, Black race-ethnicity, and psychiatric diagnosis. RESULTS: Scan reports from 79 patients with catatonia and 711 other psychiatric inpatients were obtained. Mean age was 36.4 (SD=17.3) for the cases and 44.5 (SD=19.9) for the comparison group. Radiological abnormalities were reported in 27 of 79 cases (34.2%) and in 338 of 711 in the comparison group (47.5%) (odds ratio [OR]=0.57, 95% confidence interval [CI]=0.35, 0.93; adjusted OR=1.11, 95% CI=0.58, 2.14). Among the cases, most abnormal scans had bilateral abnormalities (N=23, 29.1%) and involved the forebrain (N=25, 31.6%) and atrophy (N=17, 21.5%). CONCLUSIONS: Patients with catatonia were commonly reported to have brain MRI abnormalities, which largely consisted of diffuse cerebral atrophy rather than focal lesions. No evidence was found that these abnormalities were more common than in other psychiatric inpatients undergoing neuroimaging, after adjustment for demographic variables. Study limitations included a heterogeneous control group and selection bias in requesting scans

Quantum Mechanical Tunneling Time and its Relation to the Tsu-Esaki Formula

Various approaches have been used to calculate the quantum-mechanical tunneling time through potential barriers including the phase-delay method first introduced by Bohm and Wigner, Buttiker\u27s analysis of the Larmor clock and its generalization, the dwell time of Smith, and numerical studies of wavepacket propagation through potential barriers among others. Most of those previous estimates have only dealt with the tunneling time through simple obstacles, including delta-potential scatterers and simple rectangular barriers under zero bias condition. Even for these simple cases, the agreement among the various estimates is far from being satisfactory. In this manuscript, the transmission line technique is employed to solve the time-dependent Schrodinger equation and an expression of the quantum-mechanical tunneling time is derived for an arbitrary potential profile under non zero bias condition. An exact analytical expression of the tunneling time through a rectangular barrier is derived and shown to be identical to the one obtained recently by Spiller et. al. using the Bohm\u27s quantum potential approach. The tunneling time through resonant tunneling structures under zero bias is also calculated and is shown to be minimum at the quasi-boundstate energy. Finally, the quantum-mechanical tunneling time through the emitter-base junction of a typical heterojunction bipolar transistor is shown to be larger than its semiclassical counterpart

Dynamics of thermal growth of silicon oxide films on Si

Thermal growth of silicon oxide films on Si in dry O₂ is modeled as a dynamical system, assuming that it is basically a reaction-diffusion phenomenon. Relevant findings of the last decade are incorporated, as structure and composition of the oxide/Si interface and O₂ transport and reaction at initial stages of growth. The present model departs from the well-established Deal and Grove framework [B. E. Deal and A. S. Grove, J. Appl. Phys. 36, 3770 (1965)] indicating that its basic assumptions, steady-state regime, and reaction between O₂ and Si at a sharp oxide/Si interface are only attained asymptotically. Scaling properties of these model equations are explored, and experimental growth kinetics, obtained for a wide range of growth parameters including the small thickness range, are shown to be well described by the model