Crystal Gallium Research Articles

Longitudinal Magnetoresistance in Gallium at 20.3 °K

Measurements of magnetoresistance in single crystals of gallium at the temperature of liquid hydrogen are reported briefly and discussed.

Temperature dependence of the elastic constants of gallium antimonide

The adiabatic elastic stiffness constants of single crystal gallium antimonide were measured as a function of temperature from 4·2°K to 300°K by the ultrasonic pulse-echo technique. A pure ( p-type) and a doped ( n-type) sample were used. Both samples have carrier concentrations of the order of 10 17 cm −3. There was no significant difference between the elastic constants of these samples. The elastic constants of the pure sample at 4·2°K (in unit of 10 11 dyn-cm −2) are as follows: C 11=9·092, C 12=4·148, C 44=4·440 The Debye temperature was calculated using the values of elastic constants at 4·2°K. The result is 269 ± 3°K which agrees well with the 269·5°K from specific heat data.

Velocity of Sound and Acoustic Attenuation in Pure Gallium Single Crystals

The velocity of sound for both transverse and longitudinal waves has been measured in single crystals of pure gallium. These velocity data have been used to calculate a complete set of elastic constants for gallium at 273, 77, and 4.2 °K. A survey has also been made of the acoustic attenuation in gallium at approximately 5 MHz over the range 1.5–300 °K. The measurements were made using a transducerless method which utilizes the direct electromagnetic generation of acoustic waves at the surfaces of a metal to excite standing sound waves in a slab-shaped specimen. It is demonstrated that this technique is both convenient and sensitive: changes of 1:106 in the velocity of sound in gallium were found to be readily measurable over the range 1.5–300 °K.

Preparation of single phase gallium nitride from single crystal gallium arsenide

An analysis has been conducted on the final products obtained in attempts to prepare single phase gallium nitride from single crystal gallium arsenide. When the intermediate oxide phase was nitrided in pure ammonia it was found that (i) the lowest temperature at which rate of conversion ofβ-Ga2O3 to GaN became significant was in the range 600 to 700°C, (ii) over the temperature range 700 to 1000°C GaN was found to be the only crystalline phase present, (iii) above 1100°Cβ-Ga2O3 was the main constituent. In comparison, when the oxide phase was nitrided in a 50% NH3-50% N2 atmosphere it was found that (i) the lowest temperature at which conversion to GaN occurred lay between 700 and 750°C, (ii) there was only a narrow range of temperatures, 750 to 870°C, in which the final products were found to contain GaN as the only crystalline phase, (iii) samples nitrided above 870°C exhibited both GaN andβ-Ga2O3 phases, the proportion ofβ-Ga2O3 increasing with increasing temperature.

Gallium nitride formed by vapour deposition and by conversion from gallium arsenide

Attempts to prepare single crystal gallium nitride in thin films and bulk form are reported. The thin films were prepared by reacting GaCl3 and NH3 and depositing on to single crystal silicon carbide substrates. The bulk gallium nitride was prepared by the conversion of single crystals of gallium arsenide using an intermediate oxide phase.

X-ray determination of the orientation of gallium crystals

X-ray determination of the orientation of gallium crystals

Growth of gallium crystals over a wide range of growth rates

The kinetic growth of gallium crystals as a function of the temperature at the crystal-melt interface has been measured and reported. The experimental results have been compared with the results predicted by the Stranski-Kaishev, Burton-Cabrera-Frank, Borisov and Cahn-Hillig-Sears theories of crystal growth.

Zero Resistance in a Longitudinal Magnetic Field for Gallium Single Crystals at Liquid-Helium Temperatures

A zero resistance has been observed in three single crystals of gallium at liquid-helium temperatures for the case of magnetic field parallel to current parallel to $a$ axis, for fields greater than 2 kG. The onset of zero resistance is insensitive to impurity content as measured by the value of the residual resistance ratio, and to temperature in the range 2 to 4.2\ifmmode^\circ\else\textdegree\fi{}K. The most probable explanation of our results is in terms of magnetic breakdown. Calculation of energy gaps from our data range from 1.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}2}$ eV to 4.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ eV, dependent on the effective mass used.

Zinc Diffusion into Gallium Phosphide under High and Low Phosphorus Overpressure

The acceptor zinc has been diffused into n‐type single crystal gallium phosphide at temperatures between 700° and 1000°C from diffusion sources which lie in two different regions of the Ga‐P‐Zn phase diagram. One source (pure zinc) provides low phosphorus overpressure and leads to p‐n junctions which are distinctly nonplanar. The other (zinc plus excess phosphorus) provides high phosphorus overpressure and leads to smaller diffusion coefficients and considerably more planar p‐n junctions. These effects are consistent with the interstitial‐substitutional model for diffusion of zinc in . With either source, diffusion induced dislocations are formed throughout the diffused layer after an incubation time. The p‐n junction depth corresponding to the first appearance of the induced dislocations is found to be greater when the high phosphorus pressure source is used.

Electrical Properties of Zinc and Cadmium Ion Implanted Layers in Gallium Arsenide

Ion implantation has been used to dope high resistivity, single crystal gallium arsenide with cadmium and zinc. Implants were made with 20 kv ions into heated substrates held at 400°C. Electrical characteristics of the implanted layers have been studied as a function of isothermal and isochronal annealing cycles. The surface resistivity, average mobility, and carrier concentration in the layer have been determined by Hall measurements; it has been observed that these electrical properties are dependent on post‐implantation annealing and generally tend to improve significantly with annealing at relatively low temperatures for short times. For example, annealing of cadmium implanted samples at temperatures up to 800°C for less than 1 hr was sufficient to increase mobility from a value of 4 cm2/v sec to approximately 180 cm2/v sec, and to reduce sheet resistivity from approximately . Additional annealing for 20 min at 900°C further reduced sheet resistivity to 300 ohm/cm and increased surface carrier concentration to a maximum of . The increased carrier concentration eventually resulted in decreased mobility because of impurity scattering.

Luminescence measurement of doping levels in gallium arsenide

A simple ndt technique gives 100% testing of the concentration of donors or acceptors in gallium arsenide, which previous conventional destructive tests could not achieve. In production, this ndt technique has been used on gallium arsenide in the form of (a) slices taken from melt-grown crystals, (b) layers grown on sapphire and (c) layers grown on substrates. This novel method may be used for both polycrystalline and single crystal gallium arsenide.

Laser-excited phonon Raman spectrum of garnets

The laser excited low-temperature Raman spectra of single crystals of Yttrium Aluminum, Yttrium Gallium and Ytterbium Aluminum Garnet have been studied from 100–800 cm −1. Evidence has been found of factor group splitting. Although the crystallographic data indicate that only small differences exist between the crystallographic structures, marked differences occur in the Raman spectra of these crystals.

Size-Dependent Oscillatory Magnetoresistance Effect in Gallium

The nonmonotonic part of the magnetoresistance has been measured in five single crystals of gallium at 1.2\ifmmode^\circ\else\textdegree\fi{}K in the range 0 to 16 kOe using the audio-frequency field-modulation technique. The transverse coefficients were found to oscillate directly with the magnetic field with nondecreasing amplitude in the high-field region defined by ${\ensuremath{\omega}}_{c}\ensuremath{\tau}\ensuremath{\gg}1$. A large number of periods have been resolved by Fourier analysis of the data in the $\mathrm{ab}$ and $\mathrm{ac}$ planes, and a study has been made of the orientation and size dependence of the oscillation frequencies. Formulas are presented for the oscillatory frequencies and amplitudes giving their dependence on magnetic field strength and orientation, Fermi-surface parameters, and sample size. Theory suggests that the high-field amplitude growth may be correlated with the form of the conductivity tensor for a compensated metal and the diffusivity of the sample surface seen by electrons having extremal values of ${m}^{*}〈{v}_{z}〉$. Nearly-free-electron-model calculations show that electrons from the seventh and eighth band surfaces in gallium have these properties. Evidence for magnetic breakdown across the (100) face of the Brillouin zone is presented.

Doppler-Shifted Acoustic Cyclotron Resonance in Gallium

The absorption of 260-MHz longitudinal sound waves in single crystals of gallium has been measured at 1.2\ifmmode^\circ\else\textdegree\fi{} K for propagation along the [100] axis. With the magnetic field in the (001) and (010) planes, sharp resonant peaks in the attenuation are observed over a large angular range centered on the propagation axis. Two series of absorption maxima, degenerate in the (010) plane, are attributed to a magnetoacoustic density-of-states resonance of seventh-band electron orbits for which the differential area $\frac{\mathrm{dA}}{d{k}_{z}}$ is an extremum. The average drift velocity and cyclotron effective mass obtained from the Doppler splitting are compared with corresponding parameters in the nearly free-electron approximation. Other resonances near the [100] axis are identified with seventh- and eighth-band orbits and are correlated with dc size-effect measurements. A Doppler-shifted open-orbit resonance for H\ifmmode\cdot\else\textperiodcentered\fi{}[010] associated with the sixth-band hole surface which permits open orbits in the [001] direction is described. The carrier drift along the sound propagation is obtained from the separation of corresponding subharmonic peaks for $\ifmmode\pm\else\textpm\fi{}n$.

Calibration and Differential Field Measurement of High Magnetic Fields by Means of a Periodic Size Effect in Gallium

The periodic size effect in pure single crystal gallium plates is applied to high field calibration and particularly to accurate differential measurements of high magnetic fields. A simple rf probe is described which is used to measure the characteristics of the size effect and to demonstrate the applicability of the method to such measurements up to about 100 kG to an accuracy of at least 1%. By combining aluminum powder and Mylar tape as markers in the rf probe, NMR calibration of the unit can be made during a single field sweep. The rf probe is small and readily adapted to a wide variety of field geometries. In addition to a brief description of the probe, the characteristics of the periodic size effect in gallium are summarized and the rf and dc dependence of the oscillatory amplitude of the periodic size effect are also discussed.

Formation of Dislocation Networks in Gallium Single Crystals

The development of dislocation networks in gallium crystals, initially free of detectable dislocations, has been studied at room temperature by an x-ray diffraction topographic technique. The condition required for the development of these networks is the existence of spatial periodic fluctuations in impurity content. The networks develop, in the absence of an external stress, from individual loops which are first detected 3 to 10 days after the crystal has been grown. These loops grow for days at a uniform rate of 10−8 cm/sec and reach a size of a few hundred microns. No specific nucleation mechanism for these loops has been identified. It it is assumed that the loops expand by climb (by the addition of vacancies), their rate of growth and observed densities are consistent with a formation energy for vacancies Uf in the range 0.2 to 0.3 eV and a migration energy for vacancies Um in the range 0.4 to 0.7 eV. No values of Uf, Um, or Uf+Um determined from other experiments have been reported and a comparison is not possible at the present time. The change of initially straight dislocation lines into jagged lines has been observed and is interpreted as the climb of screw dislocations into irregular helical dislocations. A marked anisotropy in the growth of the loops and helices was observed and is attributed to an anisotropic coefficient of self-diffusion.

Slip and twinning in gallium

The plastic deformation of single crystals of gallium has been studied between room temperature and liquid nitrogen temperature. Gallium deforms by slip on (011) and (01̄1) planes in the [01̄1] and [011] directions respectively, and on the (100) and (001) planes in the [010] direction. It is concluded that slip on non-crystallographic planes in the 〈010〉 zone is composite in character, consisting of alternate slip on (001) and (100) planes. The variation of critical resolved shear stress with temperature and the nature of the slip bands is reported. Twinning occurs readily in gallium when the applied stress acts in such a way that the a and b axes of the orthorhombic lattice tend to become equal. The twins are basically mechanical in nature, with (110) and (11̄0) composition planes, and [11̄0] and [110] twinning directions respectively. Since the rotation of molecules plays a major part in the formation of the twin, they are compared with the Dauphiné twins of α-quartz. Work hardening of gallium has been investigated as a function of orientation and temperature, and is found to be extremely low under all conditions. At low temperatures gallium becomes extremely brittle, and fractures by cleavage on a number of crystallographic planes, invariably in the region of the grips. Twinning is closely associated with cleavage fracture on (110) planes.

Mean Free Path of Electrons and Magnetomorphic Effects in Small Single Crystals of Gallium. II

The variation of the electrical resistivity of pure gallium has been investigated as a function of specimen size in oriented single crystals for current flow along the $A$ and $B$ axes. An analysis of the data, based on the free-electron model and assuming diffuse scattering at the boundaries, gives ${({\ensuremath{\rho}}_{b}{l}_{b})}_{A\mathrm{axis}}=2.30\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ \ensuremath{\Omega} ${\mathrm{cm}}^{2}$, and ${({\ensuremath{\rho}}_{b}{l}_{b})}_{B\mathrm{axis}}=8.17\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ \ensuremath{\Omega} ${\mathrm{cm}}^{2}$. The longitudinal magnetoresistance was measured for fields up to 1400 G and was found to be dependent upon the dimensions of the wires. The resistivity of the wires was also found to be a function of measuring current, and this variation is attributed to the perturbation of carrier trajectories by the magnetic field of the current.

Single crystal gallium phosphide solar cells

Solar cells have been fabricated from epitaxially deposited single crystal gallium phosphide. Two types of cells have been found: (1) Those having their major spectral response at about 0·75 μ and referred. to as extrinsic, and (2) those which have their main response at 0·45 μ and are referred to as intrinsic cells. For the extrinsic cells, at 23°C in sunlight, an open circuit voltage ( V oc ) of about 0·6 V with a short circuit current density, J sc , of 4 mA/cm 2 has been found. Conversion efficiencies somewhat above 1 per cent have been noted. Correspondingly, for the 0·45 μ cells a V oc at 23°C of 1·35 V and a J sc of 1·4 mA/cm 2 have been obtained with a conversion efficiency, measured in sunlight, up to 1 per cent. Cell areas have ranged from 0·2 cm 2 to 0·5 cm 2. With increasing temperature, the V oc of both types of cells decreases with a temperature coefficient, β of about 3 mV/deg. The J sc of the 0·45 μ cell increases with temperature and the temperature variation can be expressed as ▪ with ΔE≈ ·05 eV. The extrinsic cell, on the other hand, shows no change in J sc to 200°C, after which it decreases rapidly. The p-n junctions of these cells appear to be graded as evidenced by the capacity-voltage ( c- v) relation which suggests a 1/c 3 variation with voltage. From measurement of the minority carrier diffusion length using the technique of Logan and Chynoweth [1] the minority carrier lifetime in these cells is found to vary between 10 −10 and 10 −12 sec.

Mean Free Path of Electrons and Magnetomorphic Effects in Small Single Crystals of Gallium

The variation of electrical resistivity of 99.9999%-pure gallium has been investigated as a function of size in oriented single crystals for current flow along the $C$ axis. The crystals were in the form of wires of square cross section and their dimensions varied from 1 to 0.1 mm. Analysis of the data based on the free-electron model, assuming diffuse scattering at the boundaries, yields a value of 8.11\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}11}$ \ensuremath{\Omega}-${\mathrm{cm}}^{2}$ for ${({\ensuremath{\rho}}_{b}{l}_{b})}_{\mathrm{Caxis}}$ and indicates that at 0\ifmmode^\circ\else\textdegree\fi{}K the mean free path of the charge carriers in the bulk metal is considerably in excess of 1 cm. The temperature dependence of the size effect seems to be in fair agreement with a theory due to Blatt and Satz. Within the accuracy of our measurements the ideal bulk resistivity at low temperatures varies as ${T}^{2}$, indicating that the electron-electron collisions may be contributing to the resistive processes. For low values of a longitudinal magnetic field, all the crystals showed a large decrease in resistance followed by an increase due to bulk magnetoresistance, both at 4.2\ifmmode^\circ\else\textdegree\fi{} and at 1.2\ifmmode^\circ\else\textdegree\fi{}K. For the same two temperatures these crystals also displayed a rather large magnetoresistance in transverse magnetic fields. Magnetomorphic effects for transverse fields were evidenced by the fact that the field dependence of magnetoresistance was less than quadratic for all crystals until the cyclotron radius of the charge carriers acquired a value much smaller than the cross-sectional dimensions of the specimens. The resistance of all the crystals was found to be a complicated function of the measuring current. Calculations based on certain simplifying assumptions show that for thin wires in which boundary scattering is predominant, the resistance decreases monotonically as a function of the current and is due to the trapping of the charge carriers in the magnetic field generated by the current. The details of the experimental curves can be reproduced reasonably well if the fall in resistance due to the trapped particles is superimposed on the magnetoresistance caused by the self field.