Nanoscale Physics

	Modelling of the field effect in porous silicon

Monastyrskii L.S., Sokolovskii B.S., Boyko Ya.V., Alekseichyk M.P.
Faculty of Electronics and Computer Technologies, 
Ivan Franko National University of Lviv,
Dragomanov Str., 50 , Lviv-79005, Ukraine. 
E-mail: liu_mon@yahoo.com

This paper presents the results of theoretical  investigation of the  field effect in porous silicon with spherical geometry of pores. Knowledge of features of the field effect in porous silicon is  important  at  developing  gas sensors based on this material. Adsorption of gas molecules on the pore surfaces causes formation of the surface charge, which determines redistribution of charge carriers inside the material. As a result, local and integral conductivities of the semiconductor undergo changes what can be used for registration of an adsorbed gas.
For establishing the peculiarities of the field effect in porous silicon it is necessary to know spatial distribution of the electrostatic potential which can be found from the Poisson’s equation complemented with two appropriate boundary conditions. For the case of spherical symmetry of the problem it has been obtained and analyzed analytical expression for coordinate dependences of the electrostatic potential in porous silicon for different values of radii of pores and distances between them. Coordinate dependences of the electrostatic potential can be expressed through the effective screening length of charge carriers. It has been shown that this length in porous silicon depends not only on the physical parameters of the semiconductor but also on the curvature of pore surface.  It turns out that the screening length decreases with increasing the surface curvature and this decrease can be quite significant.
On the basis of coordinate dependences of electrostatic potential we have calculated the conductivity of porous silicon as a function of concentration of adsorbed atoms. The total conductivity depends on both the radius of pores and the distance between them. The relative change in electrical conductivity monotonically increases with an increase in the radius of the pores and decreases with increasing the distance between the pores. The largest changes are achieved when the distance between the walls of pores is as small as possible. 
    The established features of the field effect in porous silicon can be used for forecasting the parameters of gas sensors of a conductive type.