Gain Maximum Frequency Research Articles

Parametric Amplification of Ultrasound in Strong Magnetic Fields

When ultrasound propagates in a piezoelectric semiconductor, the acoustoelectric interaction between the acoustic flux and the conduction electrons leads to parametric amplification of acoustic waves offrequencies different from that of the initial ultrasonic wave. The acousto-electric interaction between the electrons and the ultrasound can be modified by applying a strong magnetic field transverse to the direction of propagation of the ultrasound. The application of the magnetic field is shown to lead to the enhancement of the parametric-amplification process for waves whose frequency lies in the vicinity or below the frequency of maximum linear gain (or loss) in high-mobility semiconductors such as InSb or GaAs. However, the threshold strain necessary to have the parametric amplification exceed the linear loss also increases with magnetic field owing to the large enhancement of the linear electronic losses with magnetic field.

Ultrasonic Harmonic Generation in Magnetic Fields

Second-harmonic generation of ultrasound propagating transverse to a dc magnetic field in a piezoelectric semiconductor is treated using a phenomenological approach which is valid when either $\mathrm{qR}\ensuremath{\ll}1$ or $\mathrm{ql}\ensuremath{\ll}1$. We find that the magnetic field can change both the magnitude of the harmonic generation and the frequency at which the harmonic generation has its peak value. It is found that at frequencies near or below the frequency of maximum gain the magnitude of the harmonic generation has a maximum as a function of magnetic field. Therefore, the application of a transverse magnetic field can lead to an enhancement of second-harmonic generation in a piezoelectric semiconductor.

Reduced Phonon Noise in the Acoustoelectric Amplifier

In long acoustoelectric amplifiers, the phonon noise at a frequency of maximum acoustoelectric gain in the gigahertz regime is reduced to 110 of the thermal noise level if GaAs is used as the amplifying material and to ½ of the thermal level for CdS. The reduction is quantitatively measured by a double-pulse technique. In order to obtain a large gain within the linear regime of the device, long and thin piezoelectric semiconductor rods having a high mobility and a weak piezoelectric coupling, must be used for the amplifier. In a GaAs amplifier an over-all linear gain of 90 dB can be obtained, before nonlinear effects set in.

Nonlinear Frequency Shift in Acoustoelectric Domains in GaAs

Abstract A Bommel-Dransfeld technique is used to analyse the frequency spectrum in GaAs acousto­ electric domains up to 8 GHz. Parametric frequency conversion is found to be only dominant at the very onset of domain formation. In the strongly nonlinear regime, the amplified noise is mainly concentrated around the shifting frequency of maximum nonlinear gain. The shift of the maximum gain frequency is generally discussed by a theory of nonlinear ultrasound amplification. An evaluation of the measured frequency shifts by this theory leads to the simple relation |x| ≈ 2 y between the domain electric field and the bunching rate.

X-RAY DIFFRACTION FROM PIEZOELECTRICALLY AMPLIFIED SHEAR WAVES IN THE 50-GHz RANGE

X-ray diffraction from piezoelectrically amplified acoustic shear waves in GaAs is reported. The spectrum of amplified acoustic flux is obtained in the microscopic limit, where the electron mean free path is much greater than the acoustic wavelength. The peak acoustic intensity occurs at 50 GHz, which corresponds to the frequency of maximum net gain according to the linear theory. The spectrum of piezoelectrically amplified acoustic waves is observed at frequencies an order of magnitude larger than may be studied by the previously reported Brillouin scattering technique.

Acoustoelectric Effects in Indium Antimonide

The acoustoelectric interaction in InSb is developed and investigated on the basis of a hydrodynamical theory. Comparison of numerical results obtained from this theory with the corresponding numerical results from more detailed microscopic theories reveals that the essential features of the microscopic theories are also present in the simpler hydrodynamical theory. In particular, the hydrodynamical theory accounts for the existence of two distinct modes of acoustic domain formation and for the reduction of peak acoustic gain at low values of magnetic field. Valuable insight into the physical basis of the acoustoelectric effect is obtained and it is shown that in the limit of large electron drift velocities and small transverse magnetic field strengths, the Mode I-type acoustoelectric interaction arises from a drift-enhanced quenching of electron diffusion effects. Moreover it is found that the frequency of maximum acoustoelectric gain, as given by the hydrodynamical theory of the present paper, does not occur at the fixed frequency f0 = (ωRωD)1/2/2π, but rather, it is dependent upon the exact values of drift velocity and magnetic field strength. Several computer-generated plots are presented and discussed in order to fully illustrate the results of this investigation.

Pressure Enhancement of the Net Acoustic Gain in Piezoelectric Semiconductors

Hydrostatic pressures of up to 16 kbar are shown to increase the net acoustoelectric gain in semiconducting CdS and CdSe. Decreasing conductivity with pressure in CdS is attributed to a decrease in both mobility and carrier concentration whereas no significant changes were observed in CdSe. The frequency of maximum gain, as calculated from linear theory, decreases with pressure in CdS.

Large-signal characteristics of acoustoelectric gain

In a previous paper, Gay and Hartnagel, large-signal expressions for gain and current saturation were derived. The numerical evaluation of these expressions for shear acoustic waves in CdS is presented in this paper. Generally the results compare well with those obtained by Tien in 1968, but in addition we show that at very high fields large-signal gains may exceed the small-signal gain, and that the maximum gain frequency is not equal to (ωcωD)1/2 under large-signal conditions.

Determination of parametric-amplifier nonresonant gain maximum

Formulas are derived for a parametric amplifier, permitting determination of the frequency shift and the gain increase in proceeding from the resonant frequency to the frequency of maximum gain. The validity of these formulas has been ascertained by comparison with the exact determination of frequency shift and gain increase from the frequency- response characteristics.

Frequency dependence of nonlinear acoustoelectric gain in piezoelectric semiconductors

The frequency dependence of acoustoelectric gain is calculated in the nonlinear regime for a sinusoidal electric potential. The frequency of maximum fundamental gain is found to reduce by a factor of 4 at a fundamental flux level of 6 kW/cm 2.

Acoustic amplification in piezoelectric semiconductors under large signal conditions

Extending the theory to third order, we find that the presence of waves of many frequencies causes μ E dc in the gain expression to be replaced by a quantity that approaches vd for large E dc, and shifts the frequency of maximum gain.

Effect of parasitic elements on parametric amplifier nonresonant gain maximum

A varactor diode having parasitic case capacitance and lead inductance, used in a parametric amplifier with resonant signal and idler circuits, gives a frequency of maximum gain which is slightly less than the resonant frequency, and is determined by the values of the parasitic elements and of the gain.

Optimum design of thin-layer GaAs amplifiers

A theoretical result shows that electron diffusion in thin-layer GaAs amplifiers produces a frequency of maximum gain which can be in the range of 1 to 100 GHz. This result is used to obtain a set of curves to aid in device design.

Theory of Laser Action Involving Free Excitons and LO-Phonon-Assisted Transitions

The laser system is described by the equations of motion for the creation operators (amplitude equations) of the excitons in the lowest band, the longitudinal optical phonons, and the photons in the laser mode. These equations include damping, pump, and fluctuation terms. By eliminating the `virtual excitons' with wavevector q=0 one finds the effective amplitude equations for the indirect transitions (A1-LO line). From these equations quantum mechanical rate equations are derived, whose fluctuation operators have shot-noise character. The mean stationary rate equations are treated in the limit of a short LO-phonon lifetime and of a fast relaxation of the excitons into the thermal distribution in the lowest band. For the example of CdS, we calculated the temperature dependence of (a) the maximum gain frequency at threshold, (b) the threshold pump rate Pth, (c) the spectrum of the gain function at threshold, and (d) the output power in the region 0.1≤P/Pth≤2.0, where P is the pump rate. Finally, the light intensities of the A1 line (direct transitions) and of the A1-LO line are calculated simultaneously in the same pump range. The calculated slopes of the intensity curves are in good agreement with those measured by Nikitine et al. in CdS.

FREQUENCY SHIFTS DURING GROWTH OF AMPLIFIED ACOUSTIC FLUX IN CdS

A simple experimental procedure based on measurements of the acoustoelectric after-current is described for estimating the frequency of maximum intensity of the amplified acoustic flux at various stages of its buildup. In CdS, the rapid buildup in flux leading to current saturation is followed by a slower growth which continues until the flux domain leaves the filament. The frequency of maximum intensity coincides initially with the frequency of maximum gain and decreases continuously as the domain propagates down the filament, reaching in a typical case a value ten times smaller.

Microwave Emission from Indium Antimonide Stimulated by Acoustic Wave Amplification

A small-signal theory is presented for the emission of microwave noise, stimulated by acoustic wave amplification, from n-type InSb at 77°K in a transverse magnetic field, for electric drift fields below 25 V/cm. The acoustic gain at frequencies different from ω0, the frequency of maximum acoustic gain, is greatest at drift fields exceeding that required for highest gain at ω0. At these fields the gain becomes an extremely broad band phenomenon with substantial amplification occurring at frequencies an order of magnitude greater than ω0. The presence of a transverse magnetic field has been shown to enhance the acoustic gain of a high mobility piezoelectric semiconductor, over a certain range of drift fields, by effectively reducing the rf mobility by the factor 1/[1+(μB)2]. Experimental results obtained from 700 MHz to 12 GHz have shown good agreement with the small-signal theory, which takes into account the electric field distribution within the crystal. In particular, the threshold curves obtained at X-band indicate that a constant value of acoustic gain is required for the production of the emission. Receivers of sensitivities around − 105 dBm were used and could detect emission only for magnetic fields exceeding 1kG, oriented close to the exactly transverse direction. Threshold fields as low as 1 V/cm were measured for the inch-long crystals used, for which μ=500 000 and n=1014 cm−3 at 77°K. The conclusions drawn are that this ``low field'' emission is acoustic in origin, requires the presence of a transverse magnetic field and is a one-carrier type phenomenon.