DC conductivity of amorphous germanium

A critical review of the phonon-assisted hopping theory of the dc conductivity σ is given. It is argued that the current theories either contain uncontrollable approximations, or they yield the result of the same order of magnitude as the approximations used or they may also lead to temperature dependence of σ other than that described by the Mott law. For the simplest usually accepted model of amorphous Ge (a-Ge), the low-temperature asymptote of σ is obtained in the form of a power law. In the experimental part of the work, careful measurements from 300 down to 8 K are reported, both for the pure and the gold-doped a-Ge films. Since the results of such measurements yield a straight line in a wide interval of temperature both in the log σ versus $\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}$ and log σ versus log T scale, the power law appears to be equally well justified as the Mott law, both from the point of view of theory and that of experiment.     

Electrical and optical properties of amorphous boron and amorphous concept for ß-rhombohedral boron

Measurements of the conductivity (σ), thermoelectric power (S) and thermal conductivity (κ) of amorphous boron are made over wide temperature ranges (T = 77–850 K for σ, T = 300–850 K for S and T = 80–1100 K for κ). The room temperature spectral dependencies of the reflection (R) and absorption (α) coefficients are determined for the wavelength intervals 2–25 μm and 1.3–25 μm respectively. The I–V characteristics are also studied and shown to be consistent with the Poole-Frenkel law.The value obtained for the thermal energy gap of amorphous boron (1.3 eV) is slightly smaller than that of crystal ß-rhombohedral boron (1.4 eV). The temperature dependence of the electrical conductivity can be satisfactorily described by the Mott law $\text{ln}\text{σ ≈ ?(T}{}_0\text{/T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$, where $\text{T}{}_0\text{? 10}{}^8\text{K}$. This gives an estimate, N ≈ 10¹⁸ cm^?3, for the concentration of trapping levels responsible for the hopping conduction. The value $\text{?}{}_0\text{? 9}$ is found from the spectral dependence of R while α has Urbach-like character $\text{? α ≈}\text{exp}\text{(}\text{h}\text{?}\text{ω/Δ)}$, where $\text{Δ ? 0.19}\text{eV}$.A comparison is made between amorphous boron and crystalline ß-rhombohedral boron. Because of the very complex crystal structure and the large dimensions of the unit cell of ß-boron, some of its physical properties could be qualitatively described on the basis of the so-called ‘amorphous concept’.     

Small polaron conduction in V2O5P2O5 glasses

Dc conductivity measurements have been made between 90 and 520 K on three bulk samples of V₂O₅P₂O₅ glass. Heat treatment is found to result in a reduction of the activation energy at a given temperature and this is most noticeable at low temperatures. The behaviour at low temperatures can be described using Mott's variable range hopping arguments, and at high temperatures by non-adiabatic small polaron hopping between nearest neighbours. At intermediate temperatures a simple model is used in which excitations by optical and acoustic phonons are considered to make independent contributions to the jump frequency. Mott's theory is extended to the polaron case for $\text{T>}\text{1}\text{4}\text{?}$ and is shown to be in good agreement with results. Values for $\text{r}{}_{\mathrm{<mtext>p</mtext>}}\text{(～2.8}\text{A}\text{?}\text{)}$ the polaron radius and $\text{α(～3.5}\text{A}\text{?}{}^{\mathrm{?1}}\text{)}$ the electron decay constant are shown to be consistent with the model for small polarons. A method is suggested for obtaining α and N(E_F) from the ac conductivity and the slope of 1nσ versus $\text{1}\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ at low temperatures. Values of N(E) are obtained which correlate with those obtained by the previous analysis. This implies that the disorder energy separating adjacent sites Δ₀ is large (～0.4 eV) in these materials.     

Effects of pressure on the electrical conductivity of chalcogenide glasses

The effects of hydrostatic pressure (to ～2.4 GPa) on the electrical conductivity of AsTe, AsTeI and AsTeGe bulk semiconducting glasses have been determined. The electrical conductivity σ increases nearly exponentially with increasing pressure P. The Δ 1n σ/ΔP values are dependent upon composition and pressure, and vary from about 2 to 6 GPa^?1. This is a narrow range of values considering that the initial conductivies vary over five orders of magnitude for the compositions studied. Many of the glasses exhibited time-dependent conductivity changes both at high pressure and after cycling to high pressure. At high pressure the conductivity drifted to higher values over a period of several hours, initially following a logarithmic time dependence. Generally, the drifts were observed for P ? 0.8 GPa and for $\text{σ ? 10}{}^{\mathrm{t-1}}\text{(Ω-}\text{m}\text{)}{}^{\mathrm{?1}}$. Following the high-pressure experiment, the conductivity (and also the density) of some glasses were above that for the as-prepared material. These same samples had a slightly different conductivity temperature dependence. The conductivity slowly relaxed (over many months) toward the original conductivity state, again initially following a logarithmic time dependence. Much of our data can be interpreted consistently if we assumed that the conductivity changes depend primarily on “expected” volume changes. The kinds of behavior reported here are similar to those observed for a wide variety of glass systems. Any models developed for describing electrical transport under pressure must account for time-dependent as well as pressure-dependent effects.     

Prediction of glass-forming ability for metallic systems

The relative glass-forming ability (GFA) of metallic alloys is considered in terms of a parameter $\text{ΔT}{}^1\text{= (T}{}_{\mathrm{<mtext>liq</mtext>}}{}^{\mathrm{<mtext>mix</mtext>}}\text{? T}{}_{\mathrm{<mtext>liq</mtext>}}\text{)/T}{}_{\mathrm{<mtext>liq</mtext>}}{}^{\mathrm{mix}}$, which represents the departure of the alloy liquids temperature, T_liq, from that of the simple rule of mixtures liquids temperature, T_liq^mix. For values of $\text{ΔT}{}^1\text{> 0.20}$ a metallic system is likely to form a glass by melt-quenching in useful thicknesses (i.e. > 20 μm) at a cooling rate of 10⁵?10⁷ K s^?1. Hence, a rapid assessment of the GFA of novel compositions may in general be obtained simply from a knowledge of the melting points of the pure components and the liquidust emperatures of the alloys.     

Nucleation kinetics of sodium disilicate

The kinetics of crystal nucleation in Na₂O · 2SiO₂ have been determined over the range of undercoolings between 173 and 373°C. The plot of log(I_v?) versus $\text{1}\text{ΔT}{}^2{}_{\mathrm{r}}\text{T}{}^3{}_{\mathrm{r}}$ is a straight line of negative slope over some 13 orders of magnitude in I_v. The slope of this relation indicates a nucleation barrier of about 45 kT at ΔT_r = 0.2, and the intercept at $\text{1}\text{ΔT}{}^2{}_{\mathrm{r}}\text{T}{}^3{}_{\mathrm{r}}\text{= 0}$ is 10²⁶ cm^-3 sec^-1. poise. The results are in good agreement with predictions of the theory of homogeneous nucleation, even in the pre-exponential factor.     

Electrical,structural and optical properties of amorphous carbon

The planar and transverse electrical resistivity of amorphous carbon (a-C) films getter-sputtered at low temperature (77–95 K) is well-fitted by the expression $\text{? = ?}{}_0\text{exp}\text{(T}{}_0\text{/T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ The exponent T₀ being approximately the same in both cases (≈ 7 × 10⁷ K) suggests that the amorphous films are isotropic. Films thinner than 600 Å display a two-dimensional hopping conductivity from which one deduces a density of states N(E_F) at the Fermi level of 10¹⁸ eV^?1 cm^?3 and a radius of the localized wave functions (a) of 12 Å. Tunneling experiments and optical absorption measurements are consistent with a pseudogap of approximately 0.8 eV. Electron diffraction experiments indicate that a-C films consist of a mixture of diamond and graphite bonds; this fact taken in the light of the other experiments would suggest that the graphite bonds act as the localized conduction states.     

The electrical conductivity and Hall effect of glassy carbon

The electrical conductivity and Hall effect of glassy carbon heat treated for three hours between 1200 and 2700°C was measured at temperatures from 3 to 300 K in magnetic fields up to 5 tesla.The electrical conductivity, of the order of 200 (ohm cm)^?1 at room temperature, can be empirically written $\text{σ = A + B}\text{exp}\text{(?CT}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}\text{)-DT}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, where the first term is a strongly scattering metallic component, the second term is attributed to variable range hopping, and the third and new term is negative correction to the metallic conductivity associated with one-dimensionality. All of the constants A, B and C were insensitive to heat-treatment temperature; the constant D decreased with increasing temperature until it disappeared at about 2200°C.The Hall coefficient was independent of magnetic field, insensitive to temperature, but was a strong function of heat-treatment temperature, crossing over from negative to positive at about 1700°C and ranging from ?0.048 to 0.126 cm³/coul.The idea of one-dimensional filaments in glassy carbon suggested by the electrical conductivity is compatible with the present consensus view of the microstructure constructed through such means as lattice imaging in transmission electron microscopy, and X-ray diffraction and small angle scattering.     

Properties of amorphous silicon films— Dependence on deposition conditions

We report measurements on the electrical conductivity, optical absorption, electron spin resonance, Raman spectrum and electron diffraction of a set of a-Si films vaccum deposited at room temperature. As revealed by absorption at about 10 μm some of the films grown at deposition rates of about 0.4 Å/sec contain considerable amounts of oxygen. All the properties, except Raman spectra and electron diffraction, are found to vary strongly with the deposition rate and the background pressure during evaporation. Qualitatively, these variations show significant correlations. For instance, if the electrical conductivity is higher so is the spin density, the optical absorption and the low-frequency refractive index. Also, increasing oxygen content leads to lower conductivity. In addition, we have tried to establish a rough quantitative relation between the shift in the optical gap and the change in the spin density by connecting each of these changes to the variation in the low-frequency refractive index. The temperature dependence of the electrical conductivity was also measured and it was found that below about 150 K the data are consistent with recent theoretical predictions, i.e., log σ exhibits a ($\text{1/T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ dependence.     

Effect of thermal history on conductivity and electrical relaxation in alkali silicate glasses

Electrical conductivity σ₀ and electric field relaxation measurements have been carried out as a function of thermal history for two alkali silicate glasses, Na₂O3SiO₂ and K₂O3SiO₂. Specimens of each glass with three different thermal histories, two of the anneal-and-quench type and one of the rate-cool type, were studied. The average structural or fictive temperature T_f of each of the specimens was characterized by measuring their indices of refraction. Effects of thermal history on σ₀ and its activation enthalpy $\text{H}{}_{\mathrm{\sigma }}{}^1$ were in accord with results of previous investigators. That is, for a given type of thermal history σ₀ was lower and $\text{H}{}_{\mathrm{\sigma }}{}^1$ higher the lower T_f. In addition it was found that for two specimens with the same T_f or index of refraction but different thermal histories the rate-cooled specimen exhibited a lower conductivity than the annealed-and-quenched specimen, in accord with the results of Ritland. The distribution of relaxation times τ_σ for decay of the electric field due to ionic migration was found to be due primarily to a distribution in the pre-exponential term ln $\text{τ}{}_{\mathrm{\sigma }}{}^1$ in the equation $\text{ln}\text{τ}{}_{\mathrm{\sigma }}\text{=}\text{ln}\text{τ}{}_{\mathrm{\sigma }}{}^1\text{+ H}{}^1\text{/RT}$; the distribution in $\text{H}{}^1$ was extremely narrow. Differences in thermal history caused small differences in the distribution of τ_σ, but no difference in the average activation enthalpy $\text{〈H}{}^1\text{〉}$ for τ_σ. From this result it appeared that the dependence of the conductivity activation enthalpy $\text{H}{}_{\mathrm{\sigma }}{}^1$ on thermal history was due to the effect of thermal history on the temperature dependence of the distribution in τ_σ.     

Frequency dependence of conduction and polarization in conductive polymers

We report the results of the measurement and analysis of the complex conductivities of two high polymers over the frequency range 10²–10⁶ Hz, and temperature range 70–300 K. Giant polarization of the nomadic type is observed, with dielectric constants ranging from about 50 to 6000 in these aromatic hydrocarbon polymers. The complex conductivities resemble power law behavior, σ_ac = Aω^s (with s in the range 0.7–1.0) in some temperature ranges, and deviates from this in others. The dc conductivity and the real part of the ac conductivity at various frequencies follow a $\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}$ law. The dielectric constant varies as expected for nomadic polarization in long-chain molecules. An attempt is made to develop an understanding of the observed dependences of the complex conduction or polarization on temperature and frequency in terms of interchain and intrachain transport processes.     

Nonlinear ultrasonic attenuation in glasses

Measurements of the attenuation of longitudinal sound waves of frequencies between 730 MHz and 1400 MHz were made on a borosilicate glass at temperatures from 0.4 K to 2 K. For high acoustic intensity J the absorption decreases with decreasing temperature. At low temperatures the attenuation is strongly dependent on the acoustic input power and was found to be proportional to $\text{J}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ indicating a saturation of the absorption. For low acoustic intensities (J ? 2 × 10^?7 W/cm²) an increase of the attenuation with decreasing temperature below T < 0.6 K was observed. The experimental results are compared with recent data in vitreous silica and can qualitatively be described by current theories based on a tunneling model.     

Electrical conductivity and photoconductivity of As2S3PbS glasses

Measurements of dc electrical conductivity and photoconductivity of various glassy compositions (x = 0.1?0.625) in (As₂S₃)_1?x(PbS)_x have been made. Experimental results of the temperature dependence of dc conductivity from room temperature to 200°C (which includes the glass transition temperature) are reported. All the compositions exhibit intrinsic conduction in the measured temperature range. Thermal activation energy, glass transition temperature and σ₀ for the compositions studied, were determined from the experimental data. The low value of $\text{σ}{}_0\text{(10?10}{}^{\mathrm{?2}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}$) in these semiconducting glasses is attributed to the greater participation of localized states in the conduction process.In the measurements of photoconductivity, the variation of photocurrent with temperature, photon energy, light intensity and electric field is observed. The recombination model has been involved to explain the results of photoconductivity. Both electrical and photoconductivity data support the presence of higher density of localized states in the x = 0.1 composition than in others.     

Pressure-volume-temperature relations in liquid and glassy selenium

The PVT properties of amorphous selenium are studied experimentally and theoretically in the temperature range 0–70°C and for pressures up to 200 MPa. PVT surfaces are determined for the metastable liquid and for a glass formed by a pressurization and cooling procedure. Its liquid—glass intersection line $\text{T}{}_{\mathrm{<mtext>g</mtext>}}{}^2\text{(P)}$ is compared with the glass transition line T_g (P), here obtained by pressurizing the liquid isothermally at a rate of 2 MPa/min. Analytical expressions based on the PVT data are compared with the predictions of the Simha-Somcynsky hole theory originally formulated for open chainmolecular fluids. The agreement for the liquid, although satisfactory, is not as good as for amorphous organic polymers thus far studied, possibly because selenium contains both open-chain and Se₈ ring molecules. The theoretical scaling parameters for the best fit to experiment are compared with those obtained for polymers. A very high characteristic pressure and thus cohesive energy density are noted. The theoretical hole fraction is found to be nearly constant along the $\text{T}{}_{\mathrm{<mtext>g</mtext>}}{}^2\text{(P)}$ line for low pressures. For the glass, a theoretical equation of state obtained from that for the liquid by freezing the hole fraction, compares favorably with experiment. The Prigogine-Defray ratio ΔκΔC_p/TV(Δα)² at atmospheric pressure, calculated using literature values of ΔC_p, is found to be about 2.0.     

AC conductivity in amorphous germanium

The ac conductivity in evaporated amorphous germanium films has been measured as a function of annealing and has been found to obey the ω^0.8 law, in accordance with the hopping model. The dc conductivity measurements on the same samples show a $\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ law behaviour. The densities of localized states near the Fermi level g(E_F), obtained from both experiments are in reasonable agreement with each other. Both the measurements show a reduction by about a factor of 2 in g(E_F) when a freshly prepared film is fully annealed. High-temperature substrate films also show the ω^0.8 behaviour. This suggests that the frequency dependence of the ac conductivity is not caused by voids alone. Other possible explanations of our results are also discussed.     

The effects of oxygen,hydrogen and fluorine on the conductivity of high purity evaporated amorphous silicon films

Electron bombardment evaporation was used to deposit amorphous silicon (α-Si) films in an evaporator with a base pressure of 2 × 10^?10 Torr. Rutherford backscattering analysis was used to establish the conditions necessary for deposition of pure films.The DC conductivity was measured as a function of temperature (? 150°C to + 140°C). Pure films, which were deposited between room temperature and 400°C, were found to have a room temperature conductivity (σ_RT) in the region of 10^?3μ^?1cm^?1 and a log $\text{σα}\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ dependence. The value of σ_RT could be reduced by annealing reaching a minimum of 2 × 10^?7μ^?1 cm^?1 for an anneal temperature (T_A) of 520°C, but activated conduction was not observed.The implantation of hydrogen or fluorine (or contamination with oxygen) had the effect of reducing σ_RT, with a minimum value of less than 10^?8μ^?1cm^?1 (T_A = 400°C) for fluorine implantation to a dose of ≈ 10¹⁶ cm² (≈ 0.4 at% concentration). These films had high temperature (50°C) activation energies typical of activated conduction in extended states on the edge of the mobility gap. Implantation of fluorine to a dose of 1.5 × 10¹⁷ resulted in a rise of σ_RT (T_A = 400°C) to nearly 10⁴μ^?1 cm^?1 and log $\text{σα}\text{T}{}^{\mathrm{<mtext>?1</mtext><mtext>4</mtext>}}$ behaviour.X-ray analysis revealed that some crystallization occurred in films annealed at 600°C. This is correlated with a rise in σ_RT of the pure films and the disappearance of the effects of the introduced impurities.     

The Mott T−14 law from the rate equation formalism

The Mott $\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}$ law for the dc hopping conductivity for amorphous semiconductors is derived from the rate equation formalism by using the methodology of Butcher and Hayden. This formula is then fitted to the experimental data for a-Si, a-Ge, partially compensated heavily doped n-type Ge and polymer PPIB at 640 atmospheric pressures. It is found that the “simplified Butcher formula” approximately fits the experimental data for a-Si and a-Ge. The values of the density of states at the Fermi level calculated from the expression for the prefactor of this formula are much more reasonable values than those obtained from the original Mott formula. The origin of this significant improvement is found to lie not in improved approximations but in the choice of the values of the characteristics frequency R₀.     

Properties of heavily doped GDSi with low resistivity

Significant decrease in resistivity has been observed in glow-discharge-produced silicon (GDSi) containing 10¹⁹?10²¹ cm^?3 phosphorous atoms. At the highest doping level a resistivity of 0.01 ω cm at room temperature was obtained. The temperature dependence of the resistivity follows the form, $\text{? = ?}{}_0\text{exp}\text{(T}{}_0\text{/T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$, over a temperature range from 80–400 K. Optical absorption, which increased with wavelength and was roughly proportional to the conductivity, was observed in the longer wavelength side of the intrinsic absorption edge and it was ascribed to mobile charge carriers. Hall effect measurements have shown that μ_H of phosphorus doped GDSi is about 1 cm² V^?1s^?1 and has a normal (negative) sign.     

Pressure and heating rate dependence of the crystallization temperature for amorphous (Fe65Ni35)75P16B6Al3 and Ti50Be40Zr10

The crystallization temperature, T_x, was determined at constant heating rate, $\text{R =}\text{T}\text{?}\text{? 7}\text{K min}{}^{\mathrm{?1}}$, by monitoring the electrical resistance. Such experiments were carried out under pressures up to 2.5 GPa, and the resulting dT_x/dP was 15.9 K GPa^?1 for (Fe₆₅Ni₃₅)₇₅P₁₆B₆Al₃ and 8.7 K GPa^?1, 8.1 K GPa^?1 for the two crystallization processes in Ti₅₀Be₄₀Zr₁₀. The activation energies of crystallization under atmospheric pressure were obtained from measurements of T_x at rates from 0.05 K min^?1 ?55 K min^?1, analysed by plotting ln(T_x²R^?1) versus T_x^?1.