In-plane Mass Research Articles

Photocurrent spectroscopy of a (001)- and a (111)-oriented GaAs/Al0.33Ga0.67As quantum-well structure.

Photocurrent (PC) spectroscopy was used to study exciton oscillator strengths in a (001)- and a (111)-oriented GaAs/${\mathrm{Al}}_{0.33}$${\mathrm{Ga}}_{0.67}$As quantum-well structure (QWS) as a function of the electric field. In the (111) quantum well, an extremely large oscillator strength of the ${\mathit{e}}_{1}$-${\mathrm{hh}}_{2}$ forbidden-transition exciton was observed that was larger than that of the ${\mathit{e}}_{1}$-${\mathrm{lh}}_{1}$ exciton, even at low electric fields. [The notation ${\mathit{e}}_{\mathit{n}}$-hh(lh${)}_{\mathit{m}}$ represents a transition between the nth electron and the mth heavy- (light-) hole subband.] The exciton oscillator strength ratios estimated from the PC spectra were compared with those calculated theoretically with the exciton reduced-mass ratio used as a parameter. The comparison revealed that, whereas the reduced masses of the ${\mathit{e}}_{1}$-${\mathrm{hh}}_{1}$ and ${\mathit{e}}_{1}$-${\mathrm{hh}}_{2}$ heavy-hole exciton are lighter than that of the ${\mathit{e}}_{1}$-${\mathrm{lh}}_{1}$ light-hole exciton in the (001) QWS, reflecting the mass reversal effect in the (001) QWS, it is not so in the (111) QWS; especially, the reduced mass of the ${\mathit{e}}_{1}$-${\mathrm{hh}}_{2}$ exciton was revealed to be as much as 1.5 times larger than that of the ${\mathit{e}}_{1}$-${\mathrm{lh}}_{1}$ exciton in the (111) QWS. This difference between the (001) and the (111) QWS is discussed, taking valence-band coupling into account; it is attributed to a difference in order between the ${\mathrm{lh}}_{1}$ and the ${\mathrm{hh}}_{2}$ subband, since a strong repulsion between the two subbands is expected to give either a large or a negative in-plane mass to the upper subband of the two.

The in-plane effective mass in strained-layer quantum wells

The problem of calculating the valence-band structure of strained-layer quantum wells in the effective-mass approximation is reviewed. Using the spherical approximation and exploiting the simplicity of the infinitely deep well model we show that the in-plane effective mass is determined by two factors—a splitting contribution which is dominant at large strains, and a quantum confinement contribution. A model for finite-depth wells is presented which gives analytic expressions for the zone-center in-plane mass and associated nonparabolicity factor, and it is applied to the system InxGa1−xAs/GaAs. The model allows the computation of valence-band structure using no more than a pocket calculator. It is shown to give results in reasonable agreement with experiment.

Pressure dependence of light-hole transport in strained InGaAs/GaAs

A single modulation p-doped InGaAs/GaAs quantum well, 90 Å wide, was grown by MBE. The hole effective mass, m h ∗, at the Fermi energy was measured to be 0.155 from cyclotron resonance experiments. The valence Landau level dispersion was calculated and, in contrast to unstrained quantum wells, showed an approximately linear dependence on magnetic field, in agreement with the cyclotron resonance data. Transport measurements as a function of temperature (4–300 K) and hydrostatic pressure (4–8 kbar) show for the first time that the valence subband structure of strained structures is sensitive to pressure, reflecting the low in-plane mass at the valence band maximum.

High-field mobility of light holes in strained InGaAs quantum wells

The small in-plane mass of light holes in strained quantum wells leads to high mobility at low electric fields. An analysis shows that the high-field mobility in high quality samples primarily depends on Δ, the strain splitting of the light and heavy holes, and ħω 0, the optical phonon energy. Monte Carlo calculations show that the carrier drift velocity versus electric field characteristic can be optimized for Δ ≈ ħω 0. In this case, the low field mobility is enhanced but a Gunn effect is avoided at high fields. Pulsed field measurements on a p-doped GaAs/InGaAs/GaAs sample show that the drift velocity lies below the theoretical predictions. Further calculations in which interface roughness scattering is included show that interface roughness scattering can reduce the drift velocity. Comparison with the data suggests the roughness fluctuation length Δ ≈ 10 nm.

Valence subband structure and optical gain of GaAs-AlGaAs (111) quantum wells

The authors use the envelope function method to calculate the hole confinement energies and valence subband dispersion energies of (111) GaAs-AlGaAs quantum wells of varying widths. The heavy-hole mass is significantly larger along (111) than along the conventional (001) growth direction. This increases the number of heavy-hole confined states for a given well width. Away from the zone centre, the subband dispersion shows less mixing between heavy- and light-hole bands than for (001) growth and, in thin wells, the highest subband has a low in-plane effective mass over a greater energy range ( approximately 25 meV for a 50 AA well). It has recently been shown that (111) GaAs-AlGaAs quantum well lasers can have a lower threshold current density than equivalent (001) lasers. They perform laser gain calculations which show that this reduced threshold current density can be explained by the enhanced light-hole behaviour at the valence band maximum of (111) quantum wells. No theoretical evidence is found to support an increased in-plane heavy-hole mass or enhanced optical matrix element, as have been deduced from recent experiments on (111) quantum well structures.

Optical, vibrational and electronic properties of short period GaAsAlAs superlattices

We have explored the effect of electronic coupling on the low temperature (∼ 6K) photoluminescence excitation spectrum observed from GaAsAlAs superlattices. In particular a decrease in the continuum contribution to the luminescence signal can be correlated with increased coupling between the ⌜ electron states. Oscillations due to the interaction of photoexcited electrons and optical phonons can be observed in the photoluminescence excitation spectrum of both type-I and type-II samples. The period of the oscillations allows a determination of the in-plane hole mass, which gets heavier as the AlAs thickness is reduced. For one sample, a 25Å-8Å GaAsAlAs superlattice, we estimate the heavy hole exciton binding energy to be ∼8.5 meV. A comparison of the observed direct ⌜-⌜ and pseudo-direct X z−⌜ transition with calculations using a rudimentary effective mass type of calculation shows surprisingly good agreement down to a period of about 12 monolayers.

A transition from quantum well to superlattice behaviour in GaAsAlAs short period superlattices

Interband photoconductivity and reflectivity measurements have been performed on thin barrier GaAsAlAs superlattices up to 15 Tesla. Oscillatory photoconductivity due to the resonant emission of LO phonons is observed. The period allows as to determine the in-plane hole mass. Excitonic Landau levels seen in reflectivity are fitted using the masses determined from the oscillatory photoconductivity. Applying the magnetic field parallel to the superlattice layers allows a determination of the perpendicular miniband mass and hence illustrates the mass anisotropy due to the miniband structure.

Nonlinear panel flutter using high-order triangular finite elements

A 54 degree-of-freedom, high-order triangular plate finite element extended for geometrically nonlinear static and dynamic analysis is used to formulate and analyze the supersonic nonlinear panel flutter problems. The finite element formulation is based on Kirchhoffs theory of thin plates. The quasisteady aerodynamic theory is used. Numerical solution procedures are presented. The limit cycle oscillation analyses are performed for twodimensional and square panels with all edges simply supported and clamped, respectively. The effects of in-plane compressive force, mass ratio, and in-plane edge stress free condition are considered. Stress distributions for the limit cycle oscillation of a two-dimensional panel are plotted. For the case of panels under static pressure differential, the results for the steady mean amplitude and flutter dynamic pressure are obtained for the twodimensional and square panels, respectively. The effect of biaxial in-plane compressive stress for a simply supported square panel is studied and boundaries among the flat and stable region, dynamically stable buckled region, and the limit cycle oscillation region are found. Alternative analytical and numerical solutions are available for most of the examples for comparison and all are in excellent agreement.

Thermal expansion and lattice anharmonicity of alkali-graphite intercalation compounds

We have measured the $c$-axis and $a$-axis thermal expansion of several alkalimetal---graphite intercalation compounds by means of x-ray scattering between 10 and 300 K. The $c$-axis thermal expansion depends strongly on the in-plane mass density of the alkali-metal atoms and the stage of the compound, and is largest for K${\mathrm{C}}_{8}$. The $a$-axis thermal expansion of K${\mathrm{C}}_{8}$ and K${\mathrm{C}}_{24}$ is negative in the considered temperature region and the room-temperature coefficient is twice as large as for pristine graphite. We have analyzed the $c$-axis data in terms of a one-dimensional quasiharmonic approximation, which yields Gr\uneisen parameters 2 or 3 times as large as those for graphite.

Influence of non-linear inertia on the parametric response of rectangular plates

A simply supported rectangular plate is subjected to a distributed periodic in-plane load of the form P = P 0 + d φ( t), where φ( t) is a periodic function of time t with period T. Using a large deflection theory in-plane and lateral (parametric) vibrations of a simply supported plate have been analyzed. The effects of the distributed in-plane mass of the plate and of a concentrated end mass have been included in the analysis. It is shown that the in-plane mass influences the frequencies associated with the principal instability zone and with the resonance zone. When the in-plane inertia terms are included in the analysis, a coupling may occur between the in-plane deflections and the lateral deflection to produce an additional resonance. The shape of the deflected plate is found to change as the amplitude of vibration increases.