Conductivity In Amorphous Semiconductors Research Articles

Modelling charge carrier transport with anomalous diffusion and heat conduction in amorphous semiconductors using fractional calculus

An ordered semiconductor has a crystalline lattice in which charge carriers move around by the Gaussian process of normal diffusion. The mean square displacement (MSD) of these charge carriers is proportional to time. On the contrary, the movement of carriers in a material with a non-crystalline structure such as amorphous semiconductors is considered to be non-Gaussian in nature. In this case, MSD is proportional to some power of time. Diffusion in this type of transport mechanism is classified as anomalous diffusion. The usual drift-diffusion equation (DDE) cannot adequately describe this process because it has non-Gaussian and dispersive transport mechanisms. Fractional calculus has been used to generalize the standard DDE to a time fractional equation in order to include the hereditary effects of the carrier transport. For power devices, the distribution and conduction of heat is the primary criteria considered when making a device. Therefore, an equation for heat conduction is added to the model for inclusion of variable temperature. The coupled system is solved using a Numerical scheme wherein Finite Difference method has been employed to discretize the Riemann - Liouville time derivative of order α and the space variable. The effects of different physical factors such as light intensity, heat and applied electric field are discussed with the help of graphical illustrations.

Honoring S. R. Elliott

Honoring S. R. Elliott

AN ADIABATIC HOPPING OF dc ELECTRICAL CONDUCTIVITY STUDIES ON NiO SUBSTITUTED LEAD VANADATE GLASSES

Glasses of the system x ( NiO ) (50 – x) PbO : 50V 2 O 5 were prepared by melt quenching in the range x = 0 mol % to 15 mol%. Measurements are reported for dc electrical conductivity for the above compositions in the temperature range 300 K–500 K. The experimental results are analyzed with reference to various theoretical models proposed for dc electrical conduction in amorphous semiconductors. The analysis shows that at high temperatures the temperature dependence of dc conductivity is consistent with Mott's model of phonon-assisted hopping conduction, variable range hopping mechanism and Schnakenberg's model mechanism. The hopping in this system is adiabatic in nature.

DC Ionization Conductivity of Amorphous Semiconductors for Radiation Detection Applications

DC ionization conductivity measurements were used to characterize the electrical response of amorphous semiconductors to ionizing radiation. Two different glass systems were examined: a chalcopyrite glass ( CdGexAs2; for x = 0.45-1.0) with a tetrahedrally coordinated structure and a chalcogenide glass ( As40Se(60-x)Tex; where x = 0-12 ), with a layered or three dimensionally networked structure, depending on Te content. Changes in DC ionization current were measured as a function of the type of radiation (alpha or gamma ), dose rate, applied field, specimen thickness and temperature. The greatest DC ionization response was measured with CdGe0.85As2 at -40degC from an alpha source (which is the first reported result for radiation response from an amorphous chalcopyrite semiconductor). Avalanche gain was observed in As40Se60 with exposure to alpha radiation at fields ges 7times103 V/cm. These results demonstrate the potential of these materials for radiation detection applications.

Pre-exponential factor for the crystallization of glassy Se80Te20 and Se75Te20M5 alloys: applicability of Meyer–Neldel rule

The Meyer–Neldel rule or MN rule (also known as compensation effect) is an empirical law known since 1937. This rule is observed in wide range of phenomena in physics, chemistry, biology and electronics. Many activated phenomena, including solid state diffusion in crystals and polymers, dielectric relaxation, conduction and thermally stimulated processes in polymers, and electronic conduction in amorphous semiconductors obey the MN rule. In the present article, we report the MN rule in the non-isothermal crystallization in glassy Se80Te20 and Se75Te20M5 (M = Ag, Cd, In, Sb) alloys. We have observed MN rule between pre-exponential factor K o and activation energy of crystallization E c in the present case for thermally activated non-isothermal crystallization.

Observation of compensation effect for isothermal crystallization in glassy Se80−x Ge20Inx and Se78−x Ge22Bix alloys

Many activated phenomena, including solid state diffusion in crystals and polymers, dielectric relaxation, conduction and thermally stimulated processes in polymers, and electronic conduction in amorphous semiconductors obey the compensation law or Meyer-Neldel rule. In the present paper, we discuss the results of investigation into the compensation effect observed under isothermal crystallization in glassy Se70Te30−xSbx alloys. It is found that the relation between the pre-exponential factor Ko and activation energy of crystallization Ec follows the Meyer-Neldel rule for the alloys studied.

Pre-exponential factor of Arrhenius equation for the isothermal crystallization of some Se–Ge, Se–In and Se–Te chalcogenide glasses

Compensation law or Meyer–Neldel rule is observed in many activated phenomena, including solid state diffusion in crystals and polymers, dielectric relaxation, conduction and thermally stimulated processes in polymers, and electronic conduction in amorphous semiconductors. In the present paper, we have reported the compensation effect for the isothermal crystallization of some Se–Ge, Se–In and Se–Te chalcogenide glasses. We have observed Meyer–Neldel rule between pre-exponential factor K0 and activation energy of crystallization Ec in the present case.

Observation of compensation effect for isothermal crystallization in glassy Se80−xGe20Inx and Se78−xGe22Bix alloys

Many activated phenomena, including solid state diffusion in crystals and polymers, dielectric relaxation, conduction and thermally stimulated processes in polymers, and electronic conduction in amorphous semiconductors, obey the compensation law or Meyer–Neldel rule. In the present paper, we report the compensation effect in the isothermal crystallization of glassy Se80−xGe20Inx (0 ⩽ x ⩽ 20) and Se78−xGe22Bix (0 ⩽ x ⩽ 10) alloys. We have observed the Meyer–Neldel rule between the preexponential factor K0 and the activation energy of crystallization Ec in the present case.

DC ELECTRICAL PROPERTIES OF CuO SUBSTITUTED LEAD VANADATE GLASS SYSTEM

Glasses of the system x( CuO )(50-x) PbO :50 V 2 O 5 were prepared by melt quenching in the range x=0 mol % to 15 mol%. Measurements are reported for DC electrical conductivity for the above compositions in the temperature range 300–500 K. The experimental results are analyzed with reference to various theoretical models proposed for DC electrical conduction in amorphous semiconductors. The analysis shows that at high temperatures the temperature dependence of DC conductivity is consistent with Mott's model of phonon-assisted hopping conduction, variable range hopping mechanism and Schnakenberg's model mechanism. The high-temperature thermoelectric power was satisfactorily explained by Heikes' relation and the data also showed evidence of small polaron formation in these glasses.

DC electrical conductivity, thermoelectric power measurements of TiO 2-substituted lead vanadate glasses

Glasses of the system x(TiO 2)(50− x)PbO:50V 2O 5 were prepared by melt-quench process in the range x=0–15 mole%. Measurements are reported for DC electrical conductivity as well as thermoelectrical power for the above compositions in the temperature range 27–227 °C. The experimental results are analyzed with reference to various theoretical models proposed for DC electrical conduction in amorphous semiconductors. The analysis shows that at high temperatures, the temperature dependence of DC conductivity is consistent with Mott's model of phonon-assisted hopping conduction, variable range hopping mechanism and Schnakenberg's model mechanism. The high-temperature thermoelectric power (TEP) was satisfactorily explained by Heikes’ relation and the data also showed evidence of small polaron formation in these glasses. Thermo EMF measurements indicate that all the glass samples including unsubstituted lead metavanadate are n-type at room temperature. As temperature is increased TiO 2-substituted samples change from n-type to p-type. When Heike's formula is applied to all the systems at room temperature, the amount of disorder was found to be the same in all the systems. When Emin's formula is used for the estimation of W D, the activation energy due to disorder, in TiO 2-substituted samples, unusually large values of W D (∼0.6 eV) are obtained. The present results indicate that the Emin's formula cannot be directly used to estimate the disorder energy in TiO 2-substituted lead vanadates. The temperature-dependent change of sign of the TEP S, in these systems may arise due to change in V 4+/V 5+ ratio with the change of temperature or due to the onset of band type of conduction as in MnO or other extrinsic compensated semi-conductors.

Applicability of Meyer–Neldel rule for isothermal crystallization in glassy Se 70Te 30− xSb x alloys

Many activated phenomena, including solid state diffusion in crystals and polymers, dielectric relaxation, conduction and thermally stimulated processes in polymers, and electronic conduction in amorphous semiconductors obey the compensation law or Meyer–Neldel rule. In the present paper, we report the compensation effect in the isothermal crystallization in glassy Se 70Te 30− x Sb x alloys. We have observed Meyer–Neldel rule between pre-exponential factor K o and activation energy of crystallization E c in the present case.

Investigation of compensation effect for isothermal crystallization in glassy Se80−xTe20Mx (M = Cd, Ge, Sb) alloys

The compensation effect (also known as the Meyer–Neldel (MN) rule) is observed in many activated phenomena, including solid-state diffusion in crystals and polymers, dielectric relaxation, conduction and thermally stimulated processes in polymers and electronic conduction in amorphous semiconductors. In the present paper, we have investigated the compensation effect for isothermal crystallization in glassy Se80−xTe20Mx (M = Cd, Ge, Sb) alloys. The extent of crystallization was estimated from the dc conductivity measurements for the present chalcogenide glasses. We have observed the MN rule relating the pre-exponential factor K0 and the activation energy of crystallization Ec for all three glassy systems.

Transport properties of ZnO substituted lead vanadate glass system at eutectic composition

Glasses of the system x(ZnO)(50 − x)PbO:50V 2O 5 were prepared by melt-quench process in the range x = 0–15 mol%. Measurements are reported for dc electrical conductivity as well as thermoelectrical power for the above compositions in the temperature range 27–227 °C. The experimental results are analyzed with reference to various theoretical models proposed for dc electrical conduction in amorphous semi-conductors. The analysis shows that at high-temperatures the temperature dependence of dc conductivity is consistent with Mott's model of phonon-assisted hopping conduction, variable range hopping mechanism and Schnakenberg's model mechanism. The high-temperature thermoelectric power (TEP) was satisfactorily explained by Heikes’ relation and the data also showed evidence of small polaron formation in these glasses. Thermo EMF measurements indicate that all the glass samples including unsubstituted lead metavanadate are n-type at room temperature. As temperature is increased ZnO substituted samples change from n-type to p-type. When Heikes’ formula is applied to all the systems at room temperature the amount of disorder was found to be the same in all the systems. When Emin's formula is used for the estimation of W D, the activation energy due to disorder, in ZnO substituted samples, unusually large values of W D (∼0.6 eV) are obtained. The present results indicate that the Emin's formula cannot be directly used to estimate the disorder energy in ZnO substituted lead vanadates. The temperature dependent change of sign of the thermoelectric power S, in these systems may arise due to change in V 4+/V 5+ ratio with the change of temperature or due to the onset of band type of conduction as in MnO or other extrinsic compensated semi-conductors.

Electron transport in heavily doped amorphous SnO 2 near metal–insulator transition

The metal–insulator transition (MIT) in amorphous SiO x thin films driven by heavily doping with native oxygen vacancies has been investigated. We have found that an amorphous semiconductor may be doped during growth process up to the level where continuous MIT occurs. The temperature dependence of the resistivity of the films is defined by the deposition conditions. In metallic samples the resistivity is temperature independent, while in the critical region of the metal–insulator transition (MIT) it obeys the power-law with experimental value of 0.96 for the critical exponent. In the insulating side of the transition electrical conductivity has an exponential temperature dependence. A possible mechanism is proposed to explain the temperature dependence of conductivity in amorphous semiconductors on the insulating side of the MIT.

Changes in the electrical conductivity of amorphous semiconductors

The changes in the electrical conductivity occurring in chalcogenide amorphous semiconductors, from the system GeSeTe, have been studied. This study includes the determination of I-V characteristics, the electrical conductivity and its relationship with temperature, and, finally, the ageing of samples started by annealing and by thermal switching due to Joule self-heating. To complete the analysis, the possible structural modifications which could have been produced during the experiments have been verified by means of X-ray diffraction.

Simulation of occupation function for thermally stimulated conductivity in amorphous semiconductors

The occupation functions for the general condition f(E, T), for the high field approximation (HTSC) fH(E, T) and for the steady state photoconductivity (SSPC) fP(E, T) in the thermally stimulated conductivity (TSC) of amorphous semiconductors have been investigated. It was found that the occupation function f(E, T) in TSC is in excellent agreement with the occupation function in SSPC fP(E, T) under the condition of σTSC(T) = σP(T). There is a large difference between fP(E, T) and fH(E, T), which can be much reduced by introducing an effective attempt to escape frequency νeff in the calculation of fH(E, T). The results show that the mobility-lifetime product (μτ) in TSC obtained from SSPC measurements under the above condition is valid. For high field approximation TSC, the simulated νeff is found to be temperature dependent.

Magnetic susceptibility of hopping electrons in a strong electric field.

We analyze here the magnetic susceptibility of hopping electrons in an amorphous semiconductor in the presence of a large electric field. We find that the susceptibility should be Curie-like and scale as 1/E in the large electric field, low-temperature limit. The pure Pauli susceptibility is shown to be unchanged by the application of an electric field. Our approach is based on the effective temperature treatment of hopping conduction in amorphous semiconductors by Marianer and Shklovskii. Experimental realizations of this effect are discussed.

Transport properties of vanadium germanate glassy semiconductors.

Measurements are reported for the dc as well as frequency-dependent (ac) conductivities (real and imaginary parts) for various compositions of the vanadium germanate glassy semiconductors in the temperature range 80--450 K. The experimental results are analyzed with reference to various theoretical models proposed for electrical conduction in amorphous semiconductors. The analysis shows that at high temperatures the temperature dependence of the dc conductivity is consistent with Mott's model of phonon-assisted polaronic hopping conduction in the adiabatic approximation, while the variable-range-hopping mechanism dominates at lower temperatures. Schnakenberg's model predicts the temperature dependence of the observed activation energy in the intermediate temperature range. The temperature dependence of the ac conductivity is consistent with the simple quantum-mechanical tunneling model at lower temperatures, although this model cannot predict the observed temperature dependence of the frequency exponent. The overlapping-large-polaron tunneling model can explain the temperature dependence of the frequency exponent at low temperature; however, this model predicts a temperature dependence of the ac conductivity much higher than the observed data show. On the other hand, the correlated-barrier-hopping model is consistent with the temperature dependence of both the ac conductivity and its frequency exponent over the entire temperature range of measurements.

Rapid thermal annealing of Al(0.8% Si)/Ti10W90/a-Si contacts

The effect of rapid thermal annealing on the composition, structure, and I-V characteristics of Al(0.8% Si)/Ti:W/a-Si contacts was studied. It was established that heat treatments in temperatures ranging between 300 and 500 °C for a time span of 10 s led to grain boundary diffusion of Si and Al through the Ti10W90 layer. Subsequently, Si diffused into the Al film while Al penetrated into the amorphous Si. No silicides or intermetallic compounds were observed to form as a result of the rapid heat treatments. The electrical measurements showed that the I-V curve in the forward bias is identical to that of the reversed bias. The electrical resistance of the contacts increased as a result of a rise in the heat treatment temperature. A model of electrical conductivity in amorphous semiconductors was applied to explain the electrical behavior of the contacts.

Mesoscopic effects in the conductivity of amorphous semiconductors

Results of the scaling theory of localisation are discussed with respect to transport near the mobility edge in amorphous semiconductors. It is shown how the statistical properties of the conductance strongly influence the activated temperature dependence of the conductivity. The range of validity of the approach is estimated.