The main trend in the development of hardware components for digital and analog electronic equipment is to reduce the size of the active regions of diode and transistor structures. This can be achieved by improving the performance characteristics of micro- and nanoelectronics devices (increasing their speed and memory, increasing operating frequencies and power, noise reduction, etc.) while keeping production costs at the same level or even reducing them. Similar processes (with a certain time lag) also take place in the development of specialized hardware elements designed for use in space systems.

The ionizing radiation in outer space adversely affects electronic devices, resulting in reduced service life and sudden failures or malfunctions. Mathematical modeling of the response of such elements to the effects of ionizing radiation from outer space reduces the amount of testing, which eventually reduces the time and overall cost of developing micro- and nanoelectronics devices. However, analytical and simple numerical models based on linear superposition of radiation effects often fail in case of modern microwave semiconductor devices with submicron active regions, where the dynamics of physical processes is complex and non-linear.

The motion of charge carriers—electrons and holes—in semiconductor devices manufactured according to outdated topological standards with specifications for hundreds of nanometers (for comparison, the topological standards of modern processors are 10 nm) is a diffusion-drift process, that is, a slow displacement under the action of an electric field against chaotic scattering on various inhomogeneities. In this case, the system is in a locally equilibrium state, and its description is possible from the standpoint of classical statistical physics and thermodynamics.

On the contrary, particle transport in submicron semiconductor devices is quasiballistic, i.e. their motion is mostly directional, and the increase in the velocity of particles in the electric field is interrupted by sparse scattering. In this case, the system is in a deep nonequilibrium state and its thermodynamic parameters (such as the temperature of the electron-hole plasma) remain, strictly speaking, undetermined.

Traditional models of charge carrier transport are based on local-equilibrium diffusion-drift or quasi-hydrodynamic approximations formulated more than half a century ago. However, when the size of the active region of modern semiconductor structures is reduced to the energy and momentum relaxation length of the electron-hole plasma (20 ... 50 nm for Si and GaAs under normal conditions) and the flight time through the active region is reduced to duration of the order of the energy and momentum relaxation time of electron-hole plasma (0.1 ... 0.2 ps for Si and GaAs under normal conditions), the condition of locality is violated, which leads to an increase in the error when calculating the characteristics of the elements.

Analysis of the submicron structures' response to the effects of ionizing radiation from outer space additionally requires taking into account the heterogeneity of ionization and defect formation, as well as the stochastic nature of the interaction of radiation and particles with matter. As a result, the model of gradual degradation of the macroscopic characteristics of a semiconductor becomes inapplicable. Therefore, for submicron structures, the probabilistic model of sudden radiation failures becomes preferable.

According to Alexander Puzanov, Associate Professor at the UNN Department of Quantum Radiophysics and Electronics, researchers from Lobachevsky University together with their colleagues from the Institute of Physics of Microstructures of the Russian Academy of Sciences have proposed a diffusion-drift model in a locally non-equilibrium approximation for analyzing the excitation relaxation in an electron-hole plasma under the influence of heavy charged particles from outer space or of laser radiation that imitates them.

"It was shown that the locally nonequilibrium model has a wider application range for describing fast relaxation processes, in particular, it accurately takes into account the ballistic velocity of charge carriers, which is necessary to calculate the current flowing in semiconductor structures when they are exposed to heavy charged particles from outer space. It can also be used to determine the probability of failure and malfunction of micro- and nanoelectronics devices," notes Alexander Puzanov.

Currently, work is underway to develop the locally nonequilibrium model of carrier transport in the following areas:

- formulation of a locally nonequilibrium quasi-hydrodynamic model;
- calculation of the characteristics of submillimeter frequency multipliers based on Schottky diodes;
- verification of the model by comparing simulation results with experimental data.

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**More information:**
A. S. Puzanov et al, Application of the Locally Nonequilibrium Diffusion-Drift Cattaneo–Vernotte Model to the Calculation of Photocurrent Relaxation in Diode Structures under Subpicosecond Pulses of Ionizing Radiation, *Semiconductors* (2018). DOI: 10.1134/S1063782618110209

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