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­­­Theory of transport of charge carriers and radiation conductivity of polymers

Priority areas of development: engineering science
2015
The project has been carried out as part of the HSE Program of Fundamental Studies.

The purpose of research is creation of the theory of nonstationary transport of charge carriers in polymers, including generation of the geminal pairs, their separation into free charges and their subsequent drift and diffusion in non-stationary mode with applied electric field before entering on the pulling electrode including the development of semi-empirical model of transport of charges in molecular-doped polymers based on the quasi zonal model of a solid and methodology of the definition of the model parameters of the polymer on the results of laboratory experiments using advanced radiation-induced time-of-flight techniques, as well as the expansion of the database on radiation conductivity of technical polymers by determining of parameters of semiempirical models of the Rose-Fowler-Weisberg.

Methodology:

  • the modern physical-mathematical methods of modeling the transport of charge carriers in disordered solids;
  • radiation-induced time-of-flight method in application to the field of the ultrahigh fields, which are close to the electric strength of the molecular-doped polymers;
  • original (protected by several patents), the world's only method for studying of the electronic transport and electrification of polymer films on the basis of electron-beam ELA unit-50/5, established and based in Academic research laboratories functional safety of space vehicles and systems MIEM HSE;
  • method of the structural electrophysical simulation, based on the calculation of the pattern of the spreading currents through the elements of the carcasses of the spacecrafts (SC) during electrostatic discharge and subsequent determination of the level of electromagnetic interference in the fragments of the onboard cable network of the SC laid on the outer surface.

Empirical base of the research:

  • experimental studies on the dependence of the mobility of charge carriers in molecular-doped polymers from the applied electric field using an improved methodology based on radiation-induced variant time-of-flight technique;
  • carrying out numerical calculations on the basis of our developed  programm for the numerical analysis of non-equilibrium transport of charge carriers, using for this purpose a multiple trapping with Gaussian distribution of traps in energy.

Results of research:

The considered radiation conductivity of polymers on the alternating current. Observed in a number of polymeric materials the coordinated changes in conductance on alternating current and the effective dielectric constant can be explained from the laws of the hopping transport as a result of relatively small variations of the characteristic length of the tunnel hopping of charge carriers.

A theoretical analysis of the specifics of the nonlinear field dependence of radiation-pulse conductivity of polystyrene in strong electric fields. The explanation of previously misunderstood phenomenon of sharp increase of radiation conductivity in electric fields in excess of 5·107 V/m. This behavior cannot be explained on the basis of the Onsager theory for thermo-field generation of the free charges from the generated geminal pairs.

The general aspects of the transferal of excess charge carriers in polymers are considered.

The parameters of the transferal for the several polymers are given and the drift offset of the main charge carriers in them are calculated for several periods of time. The reasons of the unique photovoltaic properties of polyvinylcarbazole are discussed.

Model of transport of charge carriers, based on quasi zonal theory of multiple trapping with Gaussian distribution of traps in energy, is used for the theoretical analysis of the temperature-field dependence of hole mobility in a typical molecularly doped polymer. It is demonstrated that the accounting of the prescribed field dependence of the frequency factor by the Poole-Frenkel law in conditions of nonequilibrium transport allow to explain the observed decreasing of the effective disorder energy with increasing of the electric field, while maintaining unchanged the initial energetical distribution of the hopping centers.

Level of implementation,  recommendations on implementation or outcomes of the implementation of the results:

The results of the research work

Observed in a number of polymeric materials the coordinated changes in conductance on alternating current and the effective dielectric constant can be explained from the laws of the hopping transport as a result of relatively small variations of the characteristic length of the tunnel hopping of charge carriers. A deeper rationale of the proposed in this chapter approach requires a comparison with the results of more detailed experimental studies (for example, of the frequency dependence and of the absolute values of RC in different materials, the dependence of RC on temperature and on concentration of the hopping centers, etc.).

The nature of the response of polymers (curve shape of the current transient) in their photo- or radio- ionization in some cases strongly depends on the method of generation of charge carriers, i.e. whether it is subsurface or volumetric. This fact explains the qualitatively different results obtained by the two most common methods of studying the mobility of charge carriers – time-of-flight and nonstationary radiation conductivity. The most unique interpretation of the data, obtained using the latter method, as the least burdened with potentially important methodological factors and these data are compared with the results of the existing theoretical models. In a method time-of-flight the role of the subsurface layer, which definitely has a significant impact on the registered transition process in a certain time interval (the role of this factor in the method of non-stationary radiation conductivity is minimized) is not fully understood.

The complex of existing experimental data on radiation conductivity indicates that the transport of charge carriers in polymers, including model polyvinylcarbazole and molecularly doped polymers, is variance, not a Gaussian and is well described in the framework of the multiple trapping model with an exponential distribution of traps in energy. However, unlike quasi zonal model applied to polymers the physical essence of its main parameters is undergoing significant changes. The model of Gaussian disorder is definitely not applicable to the description of transport processes in polymers.

Existing theoretical models proposed for the interpretation of field, temperature and concentration dependence of mobility of charge carriers, measured at the moment of the end of the plateau on time-of-flight curve should be regarded as purely phenomenological, aimed at describing the plot of the curve of the transient current in the region of plateau in the near-surface nature of charge carrier generation, which is of great practical importance to understand the characteristics of photoreceptors in electrophotographic devices and light-emitting diodes operating on the principle of injection (including photoinjection) of charge carriers from the electrodes or lasing layers.

There is an urgent need to study the possible mechanisms of influence of surface layer of polymer on the features of the transient current at the surface way to generate excess charge carriers as in connection with needs of practice and to enhance the information content and reliability of the classical time-of-flight technique in application to disordered materials, including polymers.

Recommendations for the implementation of the results

The results obtained are recommended for use in the designing of the rocket and space technology and onboard radioelectronic devices of spacecrafts for its protection from the effects of the electrostatic discharge.

Publications:


Жаднов В. В. Методики расчета показателей ремонтопригодности автоматизированных систем управления и связи // В кн.: XXXIV Всероссийская научно-техническая конференция «Проблемы эффективности и безопасности функционирования сложных технических и информационных систем». Часть 5 Ч. 5: Проблемы повышения эффективности и безопасности функционирования автоматизированных систем управления и связи (информационных систем). Серпухов : Военная академия РВСН имени Петра Великого, 2015. С. 44-48.
Борисов Н. И., Востриков А. В., Жадов А. Д., Колтунова В. Э. Программирование методов расчета картины растекания токов по поверхности космических аппаратов // В кн.: Новые информационные технологии в автоматизированных системах: материалы восемнадцатого научно-технического семинара / Науч. ред.: В. А. Галактионов, С. Р. Тумковский. М. : Институт прикладной математики им. М.В. Келдыша РАН, 2015. С. 317-324.
Абрамешин А. Е., Жаднов В. В. Оценка интенсивности отказов интегральных схем бортовой космической аппаратуры при воздействии электростатических разрядов // В кн.: Инновации на основе информационных и коммуникационных технологий: Материалы международной научно-практической конференции (2015) / Отв. ред.: И. А. Иванов; под общ. ред.: С. У. Увайсов; науч. ред.: А. Н. Тихонов. М. : НИУ ВШЭ, 2015. С. 377-379.
A.P. Tyutnev, B.L. Linetskiy, A.V. Nikerov, V.S. Saenko. Pulsed RadiationInduced Conductivity of Polymers in Strong Electric Fields // Russian Journal of Physical Chemistry B. 2015. Vol. 9. No. 4. P. 648-657. doi
V.S. Saenko, A.P. Tyutnev, Nikolski E. V., Bakutov A. E. Protection of the Spectr-R Spacecraft Against ESD Effects Using Satellite-MIEM Computer Code // IEEE Transactions on Plasma Science. 2015. Vol. 43. No. 9. P. 2828 -2831.
Костенников С. И., Тумковский С. Р. Верификация скорости нарастания выходного напряжения макромодели операционного усилителя // В кн.: Новые информационные технологии в автоматизированных системах: материалы восемнадцатого научно-технического семинара / Науч. ред.: В. А. Галактионов, С. Р. Тумковский. М. : Институт прикладной математики им. М.В. Келдыша РАН, 2015. С. 339-344.
Жаднов В. В. Анализ методик расчетной оценки показателей ремонтопригодности радиоэлектронной аппаратуры // В кн.: Инновации на основе информационных и коммуникационных технологий: Материалы международной научно-практической конференции (2015) / Отв. ред.: И. А. Иванов; под общ. ред.: С. У. Увайсов; науч. ред.: А. Н. Тихонов. М. : НИУ ВШЭ, 2015. С. 380-382.