L. J. Challis

Phonon emission by a hot two-dimensional electron gas in a quantizing magnetic field

Abstract A detailed analysis is made of the acoustic phonon emission spectrum of a heated 2DEG in a (0 0 1) n-Si inversion layer, when a quantizing magnetic field B is applied perpendicular to the layer. Particular attention is given to the case of high magnetic fields when only a few Landau levels are occupied. The emitted power is then quasimonochromatic at the cyclotron frequency and the angular distribution shows a sharp maximum at a propagation angle ϑm to the field, given by sin ϑ m ∼ m ∗ v s /( 1 2 eB h ) 1 2 , where m∗ is the effective mass and vs the sound velocity. Both longitudinal and transverse modes are considered and the transition to zero field is discussed.

An investigation of the ground state of Cr2+ in MgO based on thermal conductivity measurements

Measurements of the thermal conductivity of MgO doped with chromium in the temperature range 0.4 to 300 K indicate the existence of resonant scattering by Cr2+ ions at 5.2 and 21 cm-1. These measurements confirm that the ion cannot be described by simple crystal field theory or by static Jahn-Teller theory, but they are consistent with the dynamic Jahn-Teller theory of Fletcher & Stevens (1969) with the parameters 8 (tunnelling frequency) = 16 cm-1 and D (spin-orbit splitting) = 4 cm-1. It is not possible to determine the sign of the anharmonic term, B, from the measurements. These parameters differ significantly from those determined by Fletcher & Stevens and those determined by Ham (1971) from acoustic paramagnetic resonance data for Cr2+ in MgO. The data also appear to confirm earlier indications that strong coupled mode effects are present. The scattering in a Ni-doped specimen was found to be largely due to the difference in mass between the Ni and Mg ions, whereas that in Fe-doped specimens was largely due to a process resonant at ca. 100 cm-1.

Phonon scattering studies of Ni and V centres in GaP and InP

Thermal conductivity measurements have been made from 50 mK to 100 K of GaP and InP samples doped with Ni or V. The GaP samples both show strong resonant phonon scattering at 500 and 380 GHz respectively which is attributed to the T1-T2 tunnelling splitting associated with a dynamic orthorhombic Jahn-Teller distortion of the T1 orbital ground state of Ni2+ and V2+. Low-frequency scattering in both systems is tentatively attributed to these same ions in complex with a defect. The assignment of the scattering to V2+ is supported by studies of photo-induced changes in the V2+ concentration. Uniaxial stress measurements on GaP:V suggest strong coupling to E modes but the strength of the coupling to T2 modes is less clear. The absence of resonance scattering in a n-type sample of InP:Ni suggests the Ni is all in the Ni+ state (2T2) as expected and the absence of scattering in n-type InP:V is consistent with the instability of V2+ in that system.

Phonon studies of Cr3+ in GaP and InP: evidence for orthorhombic Jahn-Teller systems

The thermal conductivity of GaP(Cr) and InP(Cr) has been found to be very sensitive to uniaxial stress. The strong phonon scattering attributable to Cr3+. The sensitivity observed to both E and T2 strains indicates that Cr3+ in GaP is an orthorhombic Jahn-Teller system. This may also be the case for InP but the evidence is less complete.

Phonon scattering by Cr ions in GaAs

Measurements of the thermal conductivity of 13 samples of Cr-doped GaAs within the range of 50 mK to 250K show the presence of strong resonant phonon scattering. Resonances at 21, 80, 150, 400 and 690 GHz which only occur in semi-insulating and p-type samples are attributed to substitutional Cr3+, which appears to be very strongly coupled to the lattice, and a possible level scheme is proposed. Scattering at <or approximately=5 GHz which only occurs in the semi-insulating and n-type samples is attributed to Cr2+. Since this could not occur in the static Jahn-Teller limit it provides support for a dynamic model and the data are in agreement with calculations by Abhvani et al. (1981) if the tunnelling parameter delta 1<or approximately=2 GHz. The thermal conductivity near 9K provides an effective method of determining the Cr3+ concentration in GaAs samples.

The effect of dispersion on the thermal conductivity of dielectrics containing resonant scattering centres

Abstract The effects of dispersion on the thermal conductivity of dielectrics containing randomly placed resonant scattering centres are considered. It is shown that the effects are negligible for small concentrations of strongly coupled ions such as Cr2+ ions in MgO but could still be of importance for concentrated (⪞ 1%) systems of weakly coupled ions.

Phonon scattering by 3d impurities in III-V semiconductors: evidence of a low-spin ground state for V2+ in GaAs?

Phonon scattering by 3d impurities in GaAs, GaP and InP has been investigated by measuring the thermal conductivity between 50 mK and 100 K. Seven of the systems studied conform to the expectation that orbital triplets should scatter more strongly than doublets. It seemed likely that this should also be the case for isolated V2+ in GaAs but in fact only weak scattering is observed at high frequencies ( nu 0>100 GHz). This is interpreted as evidence that V2+ in GaAs has a low-spin configuration leading to a doublet ground state, 2E. Two strong phonon resonances are observed at low frequencies, approximately=6 and approximately=20 GHz. These are sensitive to sub-band-gap illumination and are assigned to a centre previously seen by TDEPR and APR and attributed to a V2+ complex.

The role of surface phonon scattering in the growth and decay of frequency-crossing signals

Experiments, using the frequency-crossing technique, on phonon thermalisation in an Al2O3 bicrystal indicate that at 2 K and frequencies of around 200 GHz the process occurs predominantly at the surfaces. The high probability (about 1) of inelastic scattering at a fine-ground cylindrical surface is not reduced by annealing in argon at 1775 degrees C nor by a Syton polish followed by a hydrogen anneal at 1200 degrees C. Preliminary information is obtained on the spatial growth of holes in a phonon current as it travels through a resonantly scattering medium.

Phonon Thermalization at Al2O3 Surfaces

Studies of polished Al2O3 surfaces by techniques such as LEED show that vacuum annealing at temperatures above 1400°C and H2 annealing at 1200°C, a chemical etching process, are both effective in producing well ordered surfaces [1]. Further evidence for this is that phonon reflection at H2 annealed surfaces has recently been shown to be very largely specular [2]. In the present work we have investigated whether similar treatments reduce the probability of inelastic scattering at Al2O3 surfaces and studied the decay and growth of holes arising from it.

Phonon Spectroscopy of Iron Doped InP

Fe is the most common magnetic impurity in InP and we have examined its contribution to the phonon scattering as part of a programme of investigation of scattering by transition metal ions in the III–V’s. In InP, Fe substitutes for In and enters as Fe3+ which is expected to be a very weak scattering centre because of its orbital singlet ground state, 6A1. However InP normally contains ∿5 × 1016 cm-3 of shallow donors as impurities (1ppm = 2×1016 cm 2+ -3 ) and their electrons are trapped by any Fe3+ ions present to give Fe2+. So the concentration of Fe ions in InP is equal to that of [Fe] while [Fe] [D], The efficiency of Fe3+ as a trap is indicated by the room temperature resistivity of InP:Fe which can be ∿107 Ωcm (semi-insulating = SI) and the system has been widely studied in recent years [1]. Fe2+ has an orbital doublet 5E ground state and so should scatter phonons more strongly than Fe3+. Spin orbit interaction splits the 5E state to give the approximately equally spaced energy levels shown in fig. 1 with Δ known experimentally to be ∿450GHz [2] and the selection rule Γj × Γf = E indicates that resonant phonon scattering should occur predominantly at a frequency υ0 = 2Δ = 900GHz.