Donors In Ge Research Articles

On the Concentration Dependence of Far-IR Absorption by Sb-Doped Ge

Nisida and Horii have made detailed measurements of the concentration dependence of the far infrared absorption by Sb donors in Ge. A qualitative explanation of these observations is proposed, in which the strain produced by the donors themselves is able to account for the linewidths and asymmetry of the absorption lines in the low concentration range.

Valley-Orbit Interaction in Semiconductors

We consider the hypothesis that the valley-orbit interaction provides a sizable contribution to the observed splittings of the donor ground state in many-valley semiconductors. The effects of this interaction on the ground state of group-V donors in Si and Ge are estimated within the effective-mass theory and compared to central-cell corrections. It is shown that intervalley scattering effects are comparable in magnitude to central-cell corrections for donors in Si, whereas the latter are much more important for donors in Ge.

Interaction of Microwave Phonons with Donor Electrons in Ge and Si

It has been found that small concentrations of shallow donors in Ge and Si produce relatively large amounts of attenuation of microwave phonons at low temperatures (about 1 part per million produces about 10 dB/cm attenuation at 9 GHz). A theory is given which explains the various observed temperature, polarization, and frequency dependences of the attenuation in terms of ultrasonically induced relaxation of electrons bound to the donors. It is pointed out that such measurements can give information on the energy-level seperations, symmetries, and relaxation times of bound electrons.

Magnetic Field Dependence of the Ultrasonic Attenuation by Neutral Donors in Germanium

Magnetic field dependence has been calculated in detail for the attenuation of microwave phonons by neutral donors in Ge. Magnetic fields give rise to a considerable change in the attenuation. The aspect of the change depends on whether the product of the phonon angular frequency (ω q t ) and the relaxation time (τ) is larger or smaller than 1: roughly speaking, the attenuation increases with magnetic fields when ω q t τ≫1, while it decreases when \(\omega_{qt}\tau{\lesssim}1\). The magnitude of the change depends on the strength and the direction of magnetic fields and also on the level width of triplet states when \(\omega_{qt}\tau{\lesssim}1\). Besides the ultrasonic spin resonance, a resonant absorption of phonons in the triplet states can occur when the energy splitting of triplet states becomes equal to the phonon energy and the splitting becomes larger than the level width of triplet states.

Radiative Recombination in Melt-Grown n-Type, Ge-Doped GaAs

Photoluminescence measurements were made of closely compensated, n-type GaAs grown by the horizontal Bridgman method. The ratio of Ge donors to Ge acceptors is estimated to be ∼1.25. At 77°K (n≅3× 1017 cm−3) emission bands are observed at 1.51, 1.49, and 1.22 eV. The second band is nearly comparable in intensity to the first in these materials and is ascribed to a recombination process involving a shallow Ge acceptor level. These data suggest that this level is located 0.02–0.03 eV above the valence band. The band at 1.22 eV is considerably more intense than the other bands. Evidence is presented suggesting that this band is due to a shallow donor to deep acceptor radiative transition. The shallow donor is probably Ge. The deep acceptor level is approximately 0.2 eV above the valence band and may involve a lattice defect particularly prominent in melt-grown GaAs. The low-energy emission band has been correlated with an absorption peak. On the basis of the absorption data, the deep acceptor concentration is roughly estimated to be of the order of 1016 cm−3.

Electron Spin Resonance and Relaxation Effects on Donors in Stressed Ge

Various effects of uniaxial compressive stress on the electron spin resonance lines and related relaxation properties on phosphorus and antimony donors in Ge were investigated at liquid helium temperatures and at X-band. Besides general agreement with Wilson's data several new results were obtained: (1) The “one-valley” g -shifts were measured with stress applied along the [001] direction in a sample containing phosphorus of 1×10 17 /cm 3 . Two constants of the strain-induced spin Hamiltonian were determined experimentally by the aid of Nakayama's theory. (2) The spin-lattice relaxation times T s were measured on the resolved hyperfine lines of phosphorus of 2×10 15 /cm 3 , and a substantial change of T 1 with a large [111] stress was observed. Its magnitude was T 1 =1.1×10 -2 sec for the stress of 6×10 8 dyne·cm -2 in agreement with Nakayama-Hasegawa's estimation. (3) The line width was measured as a function of the magnitude of stress, the donor concentration, temperatures, and the orientation of magnetic field. The results are discussed from a point of view of the impurity conduction phenomena.

Cascade Capture of Electrons by Ionized Impurities

An improved theory of cascade capture by ionized impurities in semiconductors has been developed which retains the basic features of Lax's "giant trap" theory, but which uses a distribution function rather than a trajectory description. Assuming infrequent acoustic-phonon transitions, the classical Boltzmann equation describing the capture process near a single ionized impurity is converted into an integral equation for the distribution function in terms of total energy alone. This equation, which treats transitions between free and bound states identically to transitions between two bound states, is then transformed into a closely related integral equation for the "sticking probability." Numerical solution of the latter yields cross sections which are substantially larger than those previously found and which are in good agreement with recent experimental values for the shallow donors in Ge.

Thermal Conductivity of Solids IV: Resonance Fluorescence Scattering of Phonons by Donor Electrons in Germanium

The scattering of phonons from donor electrons in germanium is computed and applied to the problem of heat conduction below the low-temperature maximum. The effective-mass approximation is used for the electronic wave function. The calculation is analogous to that of the dispersive scattering of light by atoms. Since the ground state is split into a singlet and a triplet with a separation of energy within the thermal phonon distribution, anomalous effects due to resonance scattering occur. Apart from these, our results are similar to previous work by Keyes. Taking into account the boundary and isotopic scattering as well as the electron-phonon interaction, excellent quantitative agreement with thermal conductivity data is obtained, with no adjustable parameters, for Sb and As donors in Ge. Certain discrepancies at higher temperatures can be traced to the inadequacy of the effective-mass approximation. In addition, anomalies in the "phonon drag" thermoelectric power can be understood on the basis of our theory. A by-product of our calculation is the lifetime broadening of the triplet state. The slightly different case of $n$-type Si is worked out while a more qualitative treatment of our resonant scattering mechanism is given for $p$-type semiconductors and samples under uniaxial strain.

Corrections to the ground state energies of shallow donors in silicon and germanium

The correct potential in the effective mass equation should be the difference of the potential of a donor in the solid and that of an atom of the semiconductor host crystal. In the present paper such a difference potential is constructed for the central-cell region (defined by a sphere of radius of half the nearest neighbor distance), by making use of the Thomas-Fermi statistical theory, and considered as a perturbation to the potential (a simple Coulomb potential shielded by the static dielectric constant of the semiconductor) of the uncorrected theory. Using first-order perturbation theory the energy corrections are computed and the ground state energies of P, As, Sb and Bi in Si and Ge are found to be (the minus signs are not denoted) 31, 35, 39,45 meV and 8·9, 9·3, 9·6, 10.0 meV, respectively, representing a definite improvement over the values of 29 meV and 9.2 meV which were predicted for all donors in Si and Ge, respectively, by the uncorrected theory. The possible sources of the still remaining discrepancies between theoretical and experimental values are discussed and attributed partly to effects outside of the central-cell region and partly to approximations involved in the present treatment that resulted in obtaining a lower limit for the size of the corrections.

Relaxation Effects on Donor Spins in Silicon and Germanium

Two problems concerning strain effects on isolated donor states in Si and Ge are treated. One is a modulation of the hyperfine coupling between the donor electronic and nuclear spins which gives rise to a cross relaxation rate T x -1 ( Δ m s =±1, \(\varDelta m_{I}{=}{\mp}1\)). For Raman process (double-phonon process) T x -1 is shown to depend on the temperature as T -7 . For P-donor in Si the calculated value of T x is approximately 1.5×10 4 second at T =2.16°K, which is in good agreement with the experiments of Honig and Stupp. For single-phonon process the calculation shows that T x is sensitive to static strains in the crystal, which has been confirmed in the experiments of Wilson and Feher. The other problem treated is the effects of strong external stresses on Ge donor spin-resonance lines. The electronic g -tensor, the single-phonon relaxation rates T s -1 and T x -1 , and an inhomogenous broadening effect are derived for several orientations of the stress and the magnetic field. It is shown that b...

Ground State Energies of Donors in Ge and Si

Ground State Energies of Donors in Ge and Si

Kinetics of donor reactions in oxygen-doped germanium

The kinetics of the reactions leading to the formation of donors in oxygen-doped Ge have been investigated by means of resistivity and Hall effect measurements. Reaction rates have been measured for oxygen concentrations ranging from 0.9 to 12.0×10 17 cm −3 oxygen over the temperature range, 300–550°C. The apparent order of reaction is shown to increase with both temperature and oxygen concentration and to approach a limiting value of four. Although the reactions are complex in the kinetic sense, and consist of series as well as parallel reactions, both the forward and reverse reactions are shown to follow approximate first order rates over limited temperature ranges. The reaction of oxygen in the presence of copper is shown to result in the production of a neutral or paired conformation of the Cu and O atoms. The activation energy for donor generation in Cu-doped Ge is 47 kcal (2.0 eV) in excellent agreement with the activation energy for oxygen diffusion.