Hopping Transitions Research Articles

Indications for Diamagnetic Shift in the Ground State of Boron in Silicon

Indications for the observation of the diamagnetic shrinkage of the boron acceptor wave function (WF) in Si are reported. Uniaxial stress (X) was used to split the ground state (GS) of the boron acceptor into two energy 1evels with spatially complementary WF. The magnetic field selectively induces a shrinking of one of the two WF, depending on whether it is applied parallel or perpendicular to the X axis. As a result, the hopping transitions between lower and higher energy 1evels are redistributed, leading to significant changes in the activation energy e3. This effect was borne out by experiment.

Different effects of nickel and cobalt additions on the electronic conduction of copper tellurite glasses

Measurements of the d.c. electrical conductivity were made on 65TeO2-(35-x)CuO-x(MO) (mol %) glasses wherex=0, 0.5, 1, 2, 3, 4 and M represents nickel or cobalt. A variation in the conductivity and activation energy of the glasses is observed as CuO is replaced by NiO and by CoO. It is found that withx=0.5 to 3 mol % of NiO, the conductivity increases and the activation energy decreases due to the decrease in effective electron hopping distance between the transition metal (TM) ions. The conductivity is found to decrease with the substitution of 4 mol % of NiO and 0.5 to 4 mol % of CoO and this is attributed to the decrease in relative concentration of hopping centres because of the decrease in the hopping transitions between ions of the same element (e.g. Cu+ and Cu2+ ions) and between the ions of different TM elements (e.g. Cu+ and Ni2+, Cu+ and Co2+). This decrease in conductivity has also been described due to the formation of Ni-O-Ni, Cu-O-Ni and Co-O-Co, Cu-O-Co bridge bonds in NiO-and CoO-doped glasses respectively. The CoO-doped glasses have been found to be of a more insulating nature.

Far-infrared absorption of neutron-transmutation-doped germanium.

An investigation of the far-infrared absorption of compensated p-type Ge at a temperature of 3 K is presented. The absorption mechanism which is of interest is due to photon-induced hopping transitions of charge carriers between impurity centers. The samples were prepared by neutron transmutation doping. Samples with carrier concentrations (${\mathit{N}}_{\mathit{a}}$-${\mathit{N}}_{\mathit{d}}$) ranging from 2.3\ifmmode\times\else\texttimes\fi{}${10}^{15}$ to 2.6\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ show a broad maximum peaked at frequency between 10 and 24 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The absorption and the frequency of its maximum increase asymptotically with respect to time due to the evolution of the Ga-impurity concentration. It is found that at low frequencies the absorption coefficient is proportional to frequency. The overall behavior of the absorption spectra is found to be consistent with a theory based on the localized-pair model, but a theoretically predicted sharp peak at 20.4 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ on the absorption curve has not been observed in the experimental absorption spectra.

Theory of the absorption of electromagnetic radiation by hopping in p-type Hg1-xMnxTe in strong magnetic fields.

Absorption of polarized electromagnetic waves at 0 K in the wavelength region from 1.4 to 5 mm in p-type narrow-gap ${\mathrm{Hg}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te has been investigated in a magnetic field within the quantum-limit regime. The model of photon-induced hopping transitions of electrons between the ground states of the acceptors was used. An integral formula for the absorption coefficient is derived. In addition to this, numerical results for electromagnetic waves with the electric vector perpendicular and parallel to the applied magnetic field are presented. The range of validity of our results is discussed. We obtain an absorption coefficient of the order of 10 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for a range of concentration of acceptors up to 1\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ and compensation ratios up to 0.2.

Electrical conduction in copper phosphate glasses containing nickel or cobalt

A variation in d.c. conductivity and activation energy of 35 mol%CuO-65mol%P2O5 glasses is observed as CuO is gradually replaced by NiO or CoO. These results are believed to be due to the change in the redox ratio of the two transition metal oxide glasses, which causes an increase and then a decrease of polaron hopping transitions between the ions of the same element and between the ions of the different transition metal elements.

The Relation between Electrical Conductivity Mechanisms and Magnetic After-Effects in Single Crystal Magnetite

Measurements of electric conductivity and magnetic after-effect have been performed on single crystalline magnetite in order to obtain more information on the conductivity mechanisms below the Verwey temperature T v ≈124 K. Depending on the stoichiometry of the material, two or three temperature ranges were detected which are characterized by different magnetic relaxation processes and within which the conductivity follows Mott's T 1/2 -law as derived for the case of multi-range electron hopping. By combined measurements of the electrical conductivity and of the magnetic after-effects the activation energies for intra-atomic electronic excitations and inter-atomic hopping transitions of electrons were determined.

Optical-phonon—assisted hydrogen diffusion in metal hydrides

The quantum theory of diffusion for light interstitials in model nonstoichiometric systems is developed. The dispersive optical phonons are used to obtain an analytical expression for total transition probability ${W}_{p{p}^{\ensuremath{'}}}$. In the low-temperature limit, ${W}_{p{p}^{\ensuremath{'}}}$ is found to be temperature independent, while in the high-temperature limit the preexponential and exponential factors are temperature dependent. An explicit expression for migration energy is obtained and it is compared with other theoretical results. The dispersive phonons increase the migration energy. The effect of configurational interaction on ${W}_{p{p}^{\ensuremath{'}}}$ is also studied. It is found that at low temperature the tunneling transitions dominate and that at higher temperature the hopping transitions dominate. The impurity-excited states are accounted for in evaluating the diffusion constant for model nonstoichiometric metal hydrides. The diffusion coefficient for $\mathrm{Pd}{\mathrm{D}}_{x}$ is found lower than that for $\mathrm{Pd}{\mathrm{H}}_{x}$. The calculated values of preexponential factor and migration energy are found to agree reasonably well with the experimental data wherever available. The hydrogen is found diffusing faster than the deuterium at all temperatures in $\mathrm{Pd}{(\mathrm{H},\mathrm{D})}_{x}$. Similar calculations are carried out for $\mathrm{Nb}{(\mathrm{H},\mathrm{D})}_{x}$. The diffusion constant for $\mathrm{Nb}{\mathrm{D}}_{x}$ is found to be lower than that for $\mathrm{Nb}{\mathrm{H}}_{x}$. At low temperature the migration energy for D is found to be lower than that for H, while at high temperature the trend reverses. The calculated migration energy is found to be lower than the experimental values for which the possible reasons are discussed.

Graphic representation of the ground state wavefunctions of the shallow acceptor in germanium

Surfaces representing the loci of points of which psi *(r) psi (r) = psi *(O) psi (O)exp(-2r/a), where psi (r) are the wavefunctions of the components of the acceptor ground state in Ge, and a is the average Bohr radius of the acceptor ground state, are presented for several values of the uniaxial stress applied in the (001) orientation. The value of r/a was selected to be equal to 5 and consequently the surfaces give the location in space of points where the tunnelling probability to the point at the origin is equal and sufficiently small to represent the phonon-assisted hopping transitions. The authors demonstrate that the surface of constant tunnelling probability are deformed by the stress in a manner consistent with the assumptions involved in the model of piezoresistance of hopping conduction in p-type germanium formerly proposed by Chroboczek et al. (1981).

Phonon-induced hopping transitions in germanium and silicon : A. Myszkowski, J. Phys. Chem. Solids.31 (1970), p. 2453

Phonon-induced hopping transitions in germanium and silicon : A. Myszkowski, J. Phys. Chem. Solids.31 (1970), p. 2453

Phonon-induced hopping transitions in germanium and silicon

The probability of the phonon-induced electron transitions is basic for the theories of the hopping phenomena in Ge and Si at very low temperatures. Myszkowski and Rogala obtained the probability of the two-donor transitions using the adiabatic approximation and the approximation of the weak electron-lattice interaction. Both donor centers were assumed to be on substitutional sites in the same sublattice of the diamond-type crystal. Here the theory is extended to the ease of the donor centers on arbitrary substitutional sites and, also, the previous approximations are discussed. The transition probability is a rapidly-oscillating function of the donor positions. The performed average over small regions around each of the actual positions of the donor centers does not have the oscillating behaviour and will be convenient in practical applications, i.e. in the theories of the macroscopic phenomena, e.g. hopping conductivity.

Magnetic Field Dependence of the Hopping Transitions in Germanium and Silicon

The influence of magnetic field on the phonon-induced hopping transitions leads to some galvanomagnetic effects in germanium and silicon crystals, e.g., magnetoresistivity in the impurity conduction. Here the probability of the hopping transitions between two donor centers in the presence of a weak magnetic field is calculated on the basis of the previous results of Myszkowski and Rogala. Only the adiabatic processes accompanied by emission or absorption of one phonon are considered. The exact form of the deformation potential is used, and both LA and TA phonons are taken into account. The theory is valid for donor centers situated on arbitrary substitutional sites in the crystal.

Phonon-induced hopping transitions in germanium and silicon

Phonon-induced hopping transitions in germanium and silicon

Optical absorption of small polarons in semiconducting NiO and CoO in the near and far infra-red

The optical absorption associated with charge carriers in NiO and CoO has been obtained from transmission measurements on pure and Li-doped crystals in the wavelength region 05 to 700 μm, at temperatures between 100 and 500°K. The absorption increases smoothly with frequency to a maximum near 1 ev and then shows a further increase extending to 2 ev and higher. In the region from 05 to about 4 μm the absorption increases slowly with temperature and correlates with the Li concentration. In the far infra-red the absorption σFI is independent of frequency and, for T σdc. The activation energy associated with σFI is smaller than the d.c. value. The behaviour between 1 and 700 μm is very similar to that predicted by the theories of Klinger, Reik et al. and Bogomolov et al. for non-diagonal (hopping) transitions by small polarons. Similar absorption in TiO2 and other 3d oxides between 1 and 10 μm has been attributed to a hopping component in the free-carrier mobility. In NiO and CoO, however, we conclude that the absorption is primarily due to small-radius polarons hopping around Li centres with high-temperature activation energies Ea of 02-025 ev and 03-04 ev respectively. Above 400°K in NiO, σFI -> σdc and electrical studies indicate that about 20-30% of the carriers are ionized. No new features appear in the absorption but the above Ea values give an upper limit for the hopping energy of any non-diagonal component in the d.c. mobility. We infer a relaxation time of less than 10-13s for the diagonal component implying a bandwidth of at least 5 mev. Recent d.c. mobility data support a band picture, but a closer analysis indicates that an activated mobility with Ea less, similar 02 ev cannot be excluded.