Tunneling Lifetime Research Articles

Observation of dissociative and radiative states of N2H by neutralized ion beam techniques

The N2 H(D) radical has been studied experimentally by measurement of the kinetic energy release in its unimolecular dissociation following formation by electron transfer from metal atoms to high velocity, mass-resolved ion beams and theoretically by ab initio techniques. Calculations of the dissociation coordinate of the ground state radical at the MP4/6-311G**//MP3/6-311G** level of theory indicate that the radical is unstable with respect to N2 and H by 0.6 eV but separated from the dissociation products by a 0.4 eV barrier. One dimensional tunneling lifetimes are determined to be 7.0×10−12 s for N2 H and 3.6×10−10 s for N2 D. Neutralization of the ion by Zn targets produces predominantly radicals in the 2 A′ ground state with dissociative lifetimes τ<0.5 μs, in agreement with the calculations. Mg targets produce the radical in a mixture of the 2A′ ground and 2A″(π) excited states with a branching ratio dependent on the internal energy of the precursor ion. A higher excited state of the radical, suggested to be an n=3 Rydberg level, is produced with K targets and is inferred to undergo radiative transitions, probably containing some discrete structure, to the lower 2A′ and 2A″(π) states in the wavelength range of 2700–4500 Å. Observations of these transitions may constitute the first spectroscopic observation of the radical.

Theory of resonant tunneling in heterostructures.

For a parallel-plane barrier heterostructure of any form or composition, it is shown by considering the electron quantum states as functions of complex values of the energy that the full linewidth of a resonant peak in the coherent transmission probability, 2 \ensuremath{\Delta}E, and the tunneling lifetime of the quasilevel giving rise to the resonance, \ensuremath{\tau}, are necessarily related by (2 \ensuremath{\Delta}E)\ensuremath{\tau}=\ensuremath{\Elzxh}, and the conventional wave-packet transit time is 2\ensuremath{\tau} at the resonance energy. A formula is obtained for the peak transmission probability in terms of the ratio of the two outward currents for an electron escaping from the quasilevel.

Exciton-tunneling-lifetime enhancement by the Coulomb interaction in a quantum well with a perpendicular field.

The tunneling lifetime of an exciton in a semiconductor quantum well in the presence of a perpendicular electric field is calculated by using the Wentzel-Kramers-Brillouin method. The confining effect of the electron-hole Coulomb interaction is included for the first time. An effective one-dimensional Schr\"odinger equation describing the motion of each carrier (electron or hole) relative to the well is constructed from the variational solution of the exciton ground state. For quantum wells with small band offsets, the carrier lifetime against tunneling out of the well is significantly enhanced by the Coulomb interaction. Numerical results are in qualitative agreement with the recent experiment on ZnSe/${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Se heterostructures.

Tunneling study of GaAs/GaAlAs heterostructures

In the vertical transport through heterojunction barriers, the emitting states are often quasi-two-dimensional space charge layers. Here a study on the fundamental quantum processes underlying the tunneling from quasi-bound states is presented. We discuss: (a) the stationary tunneling lifetime of the 2D bound state, (b) a highly accurate quasi-free approximation for the 2D states, (c) nonparabolicity and interferences in the GaAs/GaAlAs system, (d) scattering broadening of 2D-2D and 2D-3D subband resonances, (e) new experimental evidence for resonant subband tunneling.

The role of the electron-hole coulomb interaction in quantum confined stark effect

The luminescence peak energy and tunneling lifetime of an exciton in a semiconductor quantum well with a small valence band offset in the presence of a perpendicular electric field is calculated by generalizing the variational approach of quantum confined Stark effect normally used for systems of GaAs/AlGaAs quantum wells. At a finite electric field, the electron-hole Coulomb interaction provides additional confinement to each of the carriers and significantly enhances the Stark shift and the exciton lifetime against field ionization. Numerical results are presented for ZnSe/Zn 1−xMn xSe heterostructures studies in recent experiments.

Electric field dependence of optical absorption near the band gap of quantum-well structures.

We report experiments and theory on the effects of electric fields on the optical absorption near the band edge in GaAs/AlGaAs quantum-well structures. We find distinct physical effects for fields parallel and perpendicular to the quantum-well layers. In both cases, we observe large changes in the absorption near the exciton peaks. In the parallel-field case, the excitons broaden with field, disappearing at fields \ensuremath{\sim}${10}^{4}$ V/cm; this behavior is in qualitative agreement with previous theory and in order-of-magnitude agreement with direct theoretical calculations of field ionization rates reported in this paper. This behavior is also qualitatively similar to that seen with three-dimensional semiconductors. For the perpendicular-field case, we see shifts of the exciton peaks to lower energies by up to 2.5 times the zero-field binding energy with the excitons remaining resolved at up to \ensuremath{\sim}${10}^{5}$ V/cm: This behavior is qualitatively different from that of bulk semiconductors and is explained through a mechanism previously briefly described by us [D. A. B. Miller et al., Phys. Rev. Lett. 53, 2173 (1984)] called the quantum-confined Stark effect. In this mechanism the quantum confinement of carriers inhibits the exciton field ionization. To support this mechanism we present detailed calculations of the shift of exciton peaks including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations of exciton binding energy in a field. We also calculate the tunneling lifetimes of particles in the wells to check the inhibition of field ionization. The calculations are performed using both the 85:15 split of band-gap discontinuity between conduction and valence bands and the recently proposed 57:43 split. Although the detailed calculations differ in the two cases, the overall shift of the exciton peaks is not very sensitive to split ratio. We find excellent agreement with experiment with no fitted parameters.

Competition between autoionisation and predissociation in the Rydberg series approaching the c4Σu-state of O2+

The competing modes of decay of the Rydberg series approaching the c4 Sigma u- state of O2+ have been studied using photoelectron spectroscopy and time-of-flight spectrometry. The predissociation was detected in the case of the low series members via the photon emission from the excited oxygen atoms and in the case of the high series members by field ionisation. These experiments provide an estimate of 1*10-13 s for the tunnelling lifetime of the nu =1 level of the c state that is more than two orders of magnitude less than a previously calculated semi-empirical value.

Tunneling from Metal to Semiconductors

Conductance and differential capacitance have been measured as a function of frequency and of bias on a number of silicon-silicon-dioxide-aluminum sandwiches. The results indicate that information about the density and energy of states near the silicon-silicon-dioxide interface may be deduced from these measurements. Conductance is due to electron tunneling transitions between the aluminum and silicon. Analysis of the tunnel current is given in terms of a single-particle WKB approximation. A simplified formula is derived to explain tunneling between the metal and the intrinsic semiconductor bands. A preliminary analysis of tunneling to impurity bands is discussed. Experimental data are shown which display details of impurity-band spreading near the valence-band edge of silicon samples containing ${10}^{18}$ and ${10}^{19}$ boron atoms/${\mathrm{cm}}^{3}$. Tunneling from silicon-silicon-dioxide interface states is analyzed by defining a tunneling lifetime and using this concept to explain the observed frequency dependence of the conductance and capacitance measurements. Quantitative experimental values are obtained giving the density of interface states versus energy. These results are in close agreement with those obtained by Statz et al., from inversion-layer conductance studies.