^{1}

^{2}

^{*}

^{2}

It is shown that the nonideality coefficient m actually depends on the electron temperature
*T*
_{e}, and the hole temperature
*T*
_{h}. We get more general expression for the nonideality coefficient, taking into account the concentration of electrons and holes, as well as their temperature, coefficient and diffusion length, the temperature of the phonons, the applied voltage, and the height of the potential barrier.

The development occupies an important place in microelectronics, semiconductor devices; therefore it requires a deep study of the physical fundamentals of semiconductor devices based on p-n-junction and the impact of external and internal factors on the characteristics of these devices. The main characteristic of a semiconductor diode based on p-n junction is a voltage-current characteristic. The theory of an ideal p-n junction was developed by Shockley [

In the works of S. P. Ashmontas [

The nonideality coefficient of CVC silicon p-n-junction in a microwave field was studied in the works of A. I. Veynger and others [

However, the above-mentioned work is not considered dependence of the nonideality coefficient of the simultaneous heating of electrons and holes.

The aim of this work is to study the effect of heating of electrons and holes by a nonideality coefficient of CVC p-n-junction.

The resulting expression of your total current passing through the diode consists of electron and hole currents and is defined as follows [

where,_{0}: height of the potential barrier in the absence of an electromagnetic wave;

AC voltage of the incident wave created by the barrier diode; T is the temperature of the lattice; k: Boltzmann constant; T_{e} and T_{h}: the temperatures of electrons and holes; E_{b}―electric field of the wave; e is the charge of an electron; D_{e} and D_{h}―diffusion coefficients of electrons and holes, L_{e} and L_{h}―their diffusion length; n_{p} and p_{n}―the concentration of minority carriers.

Using the mean value theorem [

we received for the considered case

of formula (1) we have to CVC p-n-junction following expression:

At low wave power (_{B} ≠ 0), when there is only outrage the potential barrier height, using the formula (2) obtain the CVC p-n-junction:

to take a logarithm of the expression (3), while taking into account the perturbation of the potential barrier height for the nonideality coefficient of current-voltage characteristics for p-n-junctions find the following formula:

High power microwave energy heated electrons and holes have different temperatures. In the works of A. I. Vengera and other experiments were conducted in a highly asymmetrical p-n-junction, where

Hence, for the nonideality coefficient we obtain the following expression:

It is seen that the nonideality coefficient is mainly dependent on the temperature of the holes.

If

This expression depends mainly on electron temperature.

According to the analysis of the results shows that in the special case when_{B} = 0 from (1) to obtain an expression for the nonideality coefficient of current-voltage characteristics of p-n-junction where the charge carriers are not warmed up.

We get more general expression for the nonideality coefficient, which takes into account the asymmetry of concentration, temperature, diffusion coefficients, diffusion length for electrons and holes, the temperature of the phonons, and the applied voltage, the height of the potential barrier. Analyses show that the nonideality coefficient strongly influenced by the concentration of charge carriers and the temperature perturbation potential barrier height, which are consistent with experimental results. In addition to the analytical expressions ((4), (6), (7)) on the basis of formula (1) can be transcendental equation coefficient imperfection independent simultaneous heating of electrons and holes. In addition to the analytical expressions ((4), (6), (7)) on the basis of formula (1) we received a transcendental equation for the nonideality coefficient, which depends on the simultaneous heating of electrons and holes.

Using this formula, for different values of m we can construct CVC p-n-junction (Figures 1-3).

The graphs show that the nonideality coefficient is more sensitive to the microwave field and the current- voltage characteristics of p-n-junction is shifted to higher direct voltage with an increase in the nonideality coefficient.

The results show that the nonideality coefficient m really depends on the electron temperature and the temperature of the holes.

With

We get more general expression for the nonideality coefficient, taking into account the concentration of electrons and holes, as well as their temperature, diffusion coefficient and diffusion length, temperature phonons, applied voltage and indignation potential barrier height.

GafurGulyamov,Muhammadjon Gulomkodirovich ,Dadamirzaev,Hasan YusupovichMavlyanov, (2015) The Nonideality Coefficient of Current-Voltage Characteristics for Asymmetric p-n-Junctions in a Microwave Field. Journal of Applied Mathematics and Physics,03,1679-1683. doi: 10.4236/jamp.2015.312193