Field-dependent electrical conductivity in disordered Ge1−xAux alloys. Cooper, J., R., Beyermann, W., P., Cheong, S., W., Grüner, G., & Von Molnar, S. Physical Review B, 36(14):7748-7750, 1987.
Field-dependent electrical conductivity in disordered Ge1−xAux alloys [link]Website  abstract   bibtex   
The electric-fieM-dependent conductivity was studied on Ge& — " Au " alloys near the metal-insulator transition. We have been able to rule out trivial heating eA'ects, and our experiments are described in terms of electron heating. Our findings are in good agreement with theories which discuss electron-phonon relaxation time eAects. While many interesting localization eff'ects have been explored recently in a variety of solid-state systems, ' much less is known about the dynamics of localized states. Near the metal-insulator transition, the conductivity o is expected to be frequency (co) dependent and possibly also electric field (E) dependent because of the small energy scales involved. Complementary studies of o (co) and cr(E) have proved to be very useful in investigating the dynamics of charge-density waves. As part of a similar study of disordered systems, we report here measurements of cr(E) for vapor-deposited GeAu films. In principle, trivial sample heating (i.e. , the heating of both electrons and phonons) may occur, especially for large applied dc voltages. This can be checked and some-times ruled out experimentally. The electric field can also lead to a heating of the electron gas alone (with the pho-non system remaining at the bath temperature), as was suggested as the most likely explanation of the nonlinear conductivity observed in thin metal wires. Finally, it is also possible that in some materials electric-field-induced delocalization can occur. We have performed electric-field-dependent conductivi-ty studies of the model system Ge& — Au " , which under-goes a metal-insulator transition as x is varied around a critical concentration x =12%. By performing experi-ments using pulsed fields, and on samples with various thicknesses, we can rule out trivial heating eff'ects. Also, by using a simple model of electron heating we can repro-duce all our findings concerning cr(T, E) over a broad temperature and field range. We argue that electron heating is the dominant mechanism for nonlinear effects in Ge~ " Au alloys. Ge~ " Au " alloys were prepared by fIash evaporating premelted ingots of the appropriate concentrations. The qualitative features of o(T,x) were similar to those of earlier studies, but more work is required to clarify which law best describes the temperature dependence below 1 K. Both dc and pulsed-field methods were used. In later experiments, the instrumental dead time for the pulse measurements was reduced to 400 ns, and pulses as short as 1 ps could be employed. Samples were directly im-mersed in liquid He or liquid He in order to cover the temperature range 4.2-0.4 K. Examples of the experi-mental results obtained using 2 ps pulses are shown in Fig. 2. Trivial sample heating was ruled out by initial experi-ments which showed that (a) the relevant thermal resis-tance was perpendicular to the plane of the film (since identical results were obtained for 2-lead and 4-lead mea-surements) and (b) two films with the same nominal con-centration and similar o (T) dependences, but different thicknesses (1100 and 3000 A), gave the same o(E) be-havior. In other words, the effect of trivial heating (heat-ing electrons and phonons together) could be separated from the other two possible eAects since it depends on the power dissipated per unit area rather than the power per unit volume or the electric field strength E. Thus, the nonlinearities observed could be due either to electron heating or to field-induced delocalization. In an electron-heating model, for small differences between the electron temperature (T,) and the phonon temperature crE R, — ph = (T, — Tph) =AT— = Aa'/(do'/dT) where R, — ~h is the electron-phonon thermal resistance at a temperature T, (or T~h) and der is the initial increase in conductivity which is proportional to E (Acr =o" (0)E /2). By measuring o "(0) and plotting cr" (0)/[2o(0)do/dT] vs T~h (or equivalently (dcr/ dV)/[o(0)do/dT]) R, zh can be determined at every base temperature T. This is shown in Fig. 1, where the various symbols represent data for 2-and 30-ps pulses and dc measurements. The full line shows T depen-dence. It can be seen that the exponent p=4 gives an adequate fit to the data, although one can hardly distin-guish between p =4 and p =5. We note that the large un-certainty in p arises from the fact that the E term in cr(E) is quickly overshadowed by higher-order terms, and is thus dificult to measure by pulse techniques. A simple model was used to calculate g, the rate of en-ergy transfer from electrons to phonons for arbitrary values of T, and T~h. For T, =T~h it gives R, ~h — T, in agreement with the above results. For general tempera-tures 7748 1987 The American Physical Society
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 title = {Field-dependent electrical conductivity in disordered Ge1−xAux alloys},
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 year = {1987},
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 pages = {7748-7750},
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 abstract = {The electric-fieM-dependent conductivity was studied on Ge& — " Au " alloys near the metal-insulator transition. We have been able to rule out trivial heating eA'ects, and our experiments are described in terms of electron heating. Our findings are in good agreement with theories which discuss electron-phonon relaxation time eAects. While many interesting localization eff'ects have been explored recently in a variety of solid-state systems, ' much less is known about the dynamics of localized states. Near the metal-insulator transition, the conductivity o is expected to be frequency (co) dependent and possibly also electric field (E) dependent because of the small energy scales involved. Complementary studies of o (co) and cr(E) have proved to be very useful in investigating the dynamics of charge-density waves. As part of a similar study of disordered systems, we report here measurements of cr(E) for vapor-deposited GeAu films. In principle, trivial sample heating (i.e. , the heating of both electrons and phonons) may occur, especially for large applied dc voltages. This can be checked and some-times ruled out experimentally. The electric field can also lead to a heating of the electron gas alone (with the pho-non system remaining at the bath temperature), as was suggested as the most likely explanation of the nonlinear conductivity observed in thin metal wires. Finally, it is also possible that in some materials electric-field-induced delocalization can occur. We have performed electric-field-dependent conductivi-ty studies of the model system Ge& — Au " , which under-goes a metal-insulator transition as x is varied around a critical concentration x =12%. By performing experi-ments using pulsed fields, and on samples with various thicknesses, we can rule out trivial heating eff'ects. Also, by using a simple model of electron heating we can repro-duce all our findings concerning cr(T, E) over a broad temperature and field range. We argue that electron heating is the dominant mechanism for nonlinear effects in Ge~ " Au alloys. Ge~ " Au " alloys were prepared by fIash evaporating premelted ingots of the appropriate concentrations. The qualitative features of o(T,x) were similar to those of earlier studies, but more work is required to clarify which law best describes the temperature dependence below 1 K. Both dc and pulsed-field methods were used. In later experiments, the instrumental dead time for the pulse measurements was reduced to 400 ns, and pulses as short as 1 ps could be employed. Samples were directly im-mersed in liquid He or liquid He in order to cover the temperature range 4.2-0.4 K. Examples of the experi-mental results obtained using 2 ps pulses are shown in Fig. 2. Trivial sample heating was ruled out by initial experi-ments which showed that (a) the relevant thermal resis-tance was perpendicular to the plane of the film (since identical results were obtained for 2-lead and 4-lead mea-surements) and (b) two films with the same nominal con-centration and similar o (T) dependences, but different thicknesses (1100 and 3000 A), gave the same o(E) be-havior. In other words, the effect of trivial heating (heat-ing electrons and phonons together) could be separated from the other two possible eAects since it depends on the power dissipated per unit area rather than the power per unit volume or the electric field strength E. Thus, the nonlinearities observed could be due either to electron heating or to field-induced delocalization. In an electron-heating model, for small differences between the electron temperature (T,) and the phonon temperature crE R, — ph = (T, — Tph) =AT— = Aa'/(do'/dT) where R, — ~h is the electron-phonon thermal resistance at a temperature T, (or T~h) and der is the initial increase in conductivity which is proportional to E (Acr =o" (0)E /2). By measuring o "(0) and plotting cr" (0)/[2o(0)do/dT] vs T~h (or equivalently (dcr/ dV)/[o(0)do/dT]) R, zh can be determined at every base temperature T. This is shown in Fig. 1, where the various symbols represent data for 2-and 30-ps pulses and dc measurements. The full line shows T depen-dence. It can be seen that the exponent p=4 gives an adequate fit to the data, although one can hardly distin-guish between p =4 and p =5. We note that the large un-certainty in p arises from the fact that the E term in cr(E) is quickly overshadowed by higher-order terms, and is thus dificult to measure by pulse techniques. A simple model was used to calculate g, the rate of en-ergy transfer from electrons to phonons for arbitrary values of T, and T~h. For T, =T~h it gives R, ~h — T, in agreement with the above results. For general tempera-tures 7748 1987 The American Physical Society},
 bibtype = {article},
 author = {Cooper, J. R. and Beyermann, W P and Cheong, S W and Grüner, G. and Von Molnar, S},
 journal = {Physical Review B},
 number = {14}
}
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