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.     

Temperature dependence of hopping transport in polymeric semiconductors

We report the results of measurement and analysis of the electrical conductivity of two synthetic highly purified copolymers of the polyacene quinone radical (PAQR) type. The dc conductivity was examined as a function of temperature and pressure. The conductivity-pressure relation is observed to go as log σ versus $\text{P}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The conductivities under moderate pressure (400–5000 atm) show linear relationships on log σ versus $\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}$ plots in the temperature range 70 K < T < 300 K. The possible interpretations as variable range hopping or as nearest neighbour hopping with distributions of activation energies are discussed.     

Study of amorphous Ge–SiO2–P+Si tunnel junctions

A new method to determine ac conductivity of amorphous Ge using Al-amorphous Ge–SiO₂–P⁺Si tunnel junctions is presented. Frequency dependence of ac conductivity is found to satisfy the power law in the frequency range between 1 and 50 kHz and the density of localized states at the Fermi level is estimated to be ～ 1.7 × 10²⁰ cm^?3 eV^?1 which decreases to ～ 4.5 × 10¹⁹ cm^?3 eV^?1 after annealing at 175°C.Temperature dependence of tunneling conductance of Al-amorphous Ge–SiO₂–P⁺Si junctions is appreciable only near zero bias. Zero bias conductance of the junctions obeys the $\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}$ law of Mott; the density of localized states obtained from the $\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}$ law is one order of magnitude smaller than that obtained by ac conductivity measurements, being insensitive to annealing. This behavior of the tunnel junctions differes in many respects from those of Al–Al₂O₃-amorphous Ge tunnel juntions.     

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’.     

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.     

ESR,Seebeck and Hall measurements on an amorphous system with hopping conduction

To get further information about the conduction mechanism, ESR, Seebeck and Hall measurements were performed on thermally degraded phenol-formaldehyde resins whose dc conductivity had proved to be proportional to exp $\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$. The Hall experiments yield no direct result. Although a sensitive double-frequency test set-up was used, no Hall voltage could be detected. As to the ESR and thermoelectric power measurements it was not difficult to get reliable results but rather difficult to interpret them. Most significant in this respect is the change in the sign of the Seebeck coefficient from minus to plus with rising thermal degradation. An estimation of the number of carriers from the thermo-emf leads to results compatible with those evaluated from the ESR signal.     

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.     

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.     

Radiative and non-radiative transition probabilities and quantum yields for excited states of Er3+ in germanate and tellurite glasses

Absorption and fluorescence spectra of Er³⁺ in germanate and tellurite glasses were obtained. Spontaneous transition probabilities of the ${}^4\text{S}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and ${}^4\text{F}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ to all terminal levels of Er³⁺ were calculated using the Judd-Ofelt theory and intensity parameters obtained from measured intergrated absorption coefficients. Quantum efficiencies of the ${}^4\text{S}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and ${}^4\text{F}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ fluorescences were measured by the comparative method and by the use of measured decay times. Multiphonon relaxation rates for ${}^4\text{S}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{→}{}^4\text{F}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ and ${}^4\text{F}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{→}{}^4\text{I}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ were calculated using the experimental data. The average rate for ${}^4\text{S}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{→}{}^4\text{F}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ in germanate is 1.16 × 10⁵ sec^?1 and in tellurite is 1.60 × 10⁴ sec^?1, and the rate for ${}^4\text{F}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{→}{}^4\text{I}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{is}\text{2.85 × 10}{}^5\text{sec}{}^{\mathrm{?1}}$ in germanate and 2.33 × 10⁵ sec^?1 in tellurite. The higher rates in germanate glasses are explained by the stronger interaction of the glass phonons with the electronic states of Er³⁺ in germanate than in tellurite glasses. This also explains the higher quantum yield of the visible fluorescence of Er³⁺ in tellurite glasses compared to other glasses.     

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.     

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.     

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.     

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.     

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.     

Alloying effect on the viscous flow in metallic glasses

The temperature dependence of viscosities near the glass transition is measured from the rates of thermal transformation for metallic glasses PtNiP, PdNiP, NiPBA1 and (Fe, Co)PBA1. Alloying among metallic elements which lowers the glass transition temperature T_g lowers the ideal glass transition temperature T₀, but raises the residual configurational entropy S_g and the activation energies for “diffusive” rearrangement, $\text{Δμ}{}^1$, of the alloying glasses, while compositional ordering associated with the addition of metalloids raises the T_g and T₀ and lowers the S_g and $\text{Δμ}{}^1$. Results are correlated to the atomic ordering and stability of the glasses. The extracted free volume and the critical diffusive volume are much smaller, by a factor of 4, for metallic glasses than for many other glasses.     

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.     

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.     

A new method of stirring for LPE growth

This paper describes a method of stirring a liquid during crystal growth in which each point on the growth face moves round a circle of radius b. If the face has a radius a and completes n revolutions per second, then the stirring is roughly equivalent to rotating the disc about a single axis at a rate $\text{2πc}{}^2\text{b}{}^2\text{n}\text{a}{}^2$ where c is a constant (c ∽ 2) but the system behaves as if only the liquid up to a distance $\text{(}\text{2v}\text{n}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ from the face is stirred. Uniform stirring occurs over the whole face except for an annulus of width 2b at the periphery. The necessary design criteria are discussed and a simple dynamically balanced apparatus and the results obtained with it whilst growing iron garnet films are described.     

Optical and lasing properties of fluorophosphate glass

Neodymium-doped fluorophosphate glass is a laser material newly-developed for use in high power laser fusion systems. The low refractive index (n_d ～ 1.45) and low dispersion (Abbe number ～90) of fluorophosphate glasses give them the properties of low nonlinear refractive indices and long Nd³⁺ fluorescence lifetimes, which are desirable for the high power laser applications. We have measured the intensity gain of 1.052 and 1.064 nm laser light produced by flashlamp-pumped fluorophosphate glass amplifiers, varying in size from 4–34 clear aperture. The measured gains are compared with those measured in other laser glass types and with those predicted from the spectroscopic properties of Nd³⁺. We estimate that the peak cross section for the ${}^4\text{F}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{→}{}^4\text{I}{}_{\mathrm{<mtext>11</mtext><mtext>12</mtext>}}$ transition in commercial fluorophosphate laser glasses is ～2.2 × 10^?20 cm².