^{1}

^{*}

^{2}

^{1}

^{3}

Theoretical investigation of generation-recombination processes in silicon, which has a lifetime of charge carriers 10
^{-3} s and capture cross sections of 10
^{-16} sm
^{2}. For the study uses a method of phase portraits, which are widely used in the theory of vibrations. It is shown that the form of phase portraits strongly depends on the frequency of exposure to the external variable deformation.

For the analysis of all possible movements (natural vibrations) is “phase plane”. In mechanics, statistical physics and introduction of the concept of “phase space”, in the one case, it degenerates into a plane space. Analysis of the oscillating system using phase portraits has the advantage of clarity, and is a powerful tool for the study of oscillatory processes [

Variable external influence on the semiconductor structure may cause the alternation of the generation and recombination processes. This process of generation and recombination in nature is similar to the oscillatory process. Study of generation-recombination processes using phase portraits can give a fairly complete picture of the processes in semiconductors. In [

In this paper, by using the phase portraits the effect of variable frequency strain on the semiconductor film is investigated.

Under the effect of the deformation occurs changes the band structure leads to changes in the concentration of charge carriers, and a redistribution of charge carriers between energy valleys [

where

The solution of Equation (2) in the case where the deformation of e is a random function of time, is given by [

Equation (3) can be used to determine the magnitude of the concentration of non-equilibrium reacts to changing deformation. Assume that the deformation varies sinusoidally

Then, the band gap varies according to the same law

here

Then, from the expression (3) and (6) we have

By specifying an explicit form of time-dependent strain ε(t) can be obtained from the time dependence of the concentration n_{e}(t) from time to time. Equation (7) in a fairly wide range of deformation function e(t_{0}) allows to describe the change of the carrier density.

To demonstrate the method of preparation according n_{e}-ε, we consider a weak deformation, i.e.

the expression (7) can be written as

Let the sample is applied a sinusoidal deformation half-period

After the end of the deformation in the formula (8), the upper limit of the integral is to be p/w

Changing the frequency of external influence is making a tangible contribution to the concentration vs. time. Since the change in the external effects of low frequencies in the non-equilibrium charge carrier concentration will increase and decrease gradually. That is, there will be some period of time between generation and recombination of charge carriers from zone to zone. And when the frequency reaches the maximum values decrease and increase of charge carriers becomes imperceptible. In other words, the generation-recombination processes do not have time to react to changes in the band spectrum of the semiconductor and the concentration of charge carriers takes a steady average.

Consider the case where a variable deformation influences with increasing frequency in the semiconductor structure. Assume that the initial generation and charge carrier lifetime is respectively g_{0} = 10^{18} and τ = 10^{−}^{3} [_{0} = 3 Hz to ω = 210 Hz (see _{0} = 3 Hz change in the concentration range was n ≈ 0 - 2 × 10^{15} cm^{−}^{3}, then the frequency ω_{0} = 210 Hz range was the change in concentration n ≈ (5 × 10^{12}) - (1.9 × 10^{1}^{5}) cm^{−}^{3}. When the frequency of the alternating deformation reaches ω = 900 Hz (see ^{13}) - (7.5 × 10^{1}^{4}) cm^{−}^{3}.

With increasing frequency of the alternating deformation range of the concentration of charge carriers takes some average. As can be seen in ^{15} cm^{−}^{3} to increase the frequency up to 54 kHz. This suggests that the concentration of nonequilibrium charge carriers acquired its steady average.

Apparently by prolonged exposure of the periodic pattern deformation in semiconductor recombination centers may occur in crystal lattices. As a result, the development of the processes of generation and recombination can take a different turn, and accordingly the concentration of charge carriers may have a deviation from the established mean.

The case where the frequency itself changes periodically variable deformation, ranges from 0 to 20 kHz is shown in ^{−}^{3}. When the frequency of the variable deformation reaches a minimum value, a range of changes in the concentration ranges from 0 - 2 × 10^{15} cm^{−}^{3}. This is repeated for two seconds to 8 times.

To obtain the phase portrait is usually considered the dependence of some parameter x of its derivative

the deformation by changing the energy spectrum affects the generation-recombination processes, to obtain the phase portrait of such processes must be obtained from the dependence of the concentration n of its derivative

Consider the case of silicon, which has a lifetime of charge carriers 10^{−}^{3} seconds capture cross 10^{−}^{16} cm^{2} [

The phase portrait is the largest area when the frequency of the alternating deformation is 1000 Hz (see

Three-dimensional phase portrait is shown in ^{−}^{2} s, and capture cross sections of 10^{−}^{16} cm^{2}.

Thus, the shape of the phase portraits allows us to determine how to respond to the frequency change of the semi- conductor strain. Namely, with increasing frequency variable strain rate and the product carrier lifetime become

This work was supported by government grants of Uzbekistan F2-OT-O-15494 “Improving the efficiency of the radiators, solar cells and other optoelectronic devices based on quantum dot research and hetero nanostructure exciton and bipolaron transport phenomena”, F2-FA-0-97004 “Dynamics of solitons in ultracold quantum gases, and optical systems and synergistic processes in multicomponent semiconductors” and F2-21 “Mathematical modelling of the determination of the density of surface states at the semiconductor-insulator”.

GafurGulyamov,A. G.Gulyamov,A. Q.Ergashev,B. T.Abdulazizov, (2015) The Use of Phase Portraits for the Study of the Generation-Recombination Processes in Semiconductor. Journal of Modern Physics,06,1921-1926. doi: 10.4236/jmp.2015.613197