The influence of isovalent impurity of germanium upon the electrophysical properties of silicon

The developing of modern engineering demands the investigation of new semiconductor materials. Crystals of solid solutions Si are of great interest in this respect. Solid solutions of Si with the concentration of additional component of about 1% are regarded as semiconductors doped with isovalent impurities [1]. When doping the crystals of silicon with atoms of germanium inner local stresses arise as a result of difference between the covalent radii of Si (1.17 ) and isovalent impurity of Ge (1.22 ), deforming the crystal lattice, changing its constant and thus influencing upon electrophysical properties of the crystal.

The paper presents the results of the investigation of electrophysical parameters and piezoresistanse effects in the crystals Si of n-type with a concentration of germanium NGe=2101921020cm-3 by measuring temperature dependencies of conductivity, Hall coefficient, piezoresistance and piezo-Hall-effect. The object of the investigation were the crystals grown by Chokhralsky method with content of oxygen of (68)1017cm-3. The measurements of control samples without isovalent impurity of germanium (IIGe) were performed for comparison.

Figure 1 shows the temperature dependences of electron mobility  on the temperature in pure n-silicon (curve 1) and in n-silicon with different concentration of IIGe (dependences 2,3). Numbers of curves in Figure 1 correspond to the numbers of samples in Table 1.

Table 1

N

cmN10-13

cm-3NGe10-19

cm-3N010-17

cm-3300K

cm2/Vs77K

cm2/Vs

11303.1-7150023000

2815.126150021000

3656.246150019500

450976.5145018500

5984206148016400

Detailed experimental and theoretical investigations of electron mobility in n-silicon [2] showed that in the region of mainly phonon scattering it is determined both by in-valley and inter-valley scattering. Theoretical calculations, performed with account of scattering on long wave acoustic phonons and inter-valley pulse scattering at interaction of electrons and the phonons of corresponding averaged temperatures 1=190 K and 2=630 K, show the sufficiently detailed coincidence with the experiment in a wide temperature range 77450 K. It is confirmed by plot 1, Fig.1, which also shows the contributions of different scattering mechanisms according to [2]. Plot 1 has a distinctive bending in 100K range. Such behavior of the curve and the deviation from the dotted line which determines the temperature dependency of electron mobility in pure n-silicon at scattering on acoustic oscillations of the lattice may be explained by the increasing contribution of inter-valley scattering at T100 K. As it is seen in Fig.1, the slope of the dependency lg()=lg(T) changes from 1.5 to 2.3. The change of power exponent in dependency T-m in the region of phonon scattering for n-silicon is revealed in paper [3], in which the authors assume that the abrupt decrease of  at NGe1020cm-3 testifies to the change of phonon spectrum and to the elastic stress relaxation via formation of modular structure of crystals. As it is seen in Fig. 1, the identity of all the curves slopes in practically important temperature range of 220450K with the major contribution of inter-valley scattering testifies to the principal role of inter-valley scattering.

The decrease of electron mobility at temperatures T<200 K is a characteristic peculiarity of dependences lg()=lg(T) for crystals Si in comparison with pure n-Si. A like decrease of mobility is observed with the increase of the concentration of ionized impurities [4], however, in crystals 1, 2, 3, 5 (Table 1) the impurities concentration is practically equal. Hence, the contribution in electron scattering is that of IIGe. Therefore, at T<200 K and minority component concentrations NGe=2101021020cm-3 scattering on isovalent impurity adds to the existing scattering mechanisms.

As it is known, two interband electron junctions with absorption or emission of phonons are possible in silicon: g–junctions between the disposed along one axis valleys (of [100] type) and f - junctions between the valleys on interperpendicular axes. The application of strong uniaxial elastic deformations (P || [100]) makes it possible to obtain two-valley conduction band.The values of electron mobility obtained at uniaxial strain [100] || P=9000 kg/cm2 for n-silicon crystals with different IIGe concentrations at temperature range 77350 K fall with sufficient accuracy on a straight line on coordinates lg ()=lg (T) with a slope m=1.6. It is illustrated by dependence 4 in Fig.1. A considerable change of the slope of this dependence from 2.3 to 1.6 at T>100 K, absence of a kink as well as the approximation of index in to magnitude 1.5, which is characteristic of inter-value scattering on acoustic phonons, testify to the defining contribution of f – junctions into inter-valley scattering of electrons both in pure n-silicon and in solid solutions of Si at NGe21020cm-3.

Crystals n-Si manifest maximal piezosensitivity in case when current J and stress P are directed along [100], that is P || J || [100]. The general feature of the dependences is the decrease of piezoresistance with the increase of IIGe concentration [5]. As tensoeffect is caused by anisotropy of the crystal, the presented results testify to the fact that doping the crystal with isovalent impurity changes the corresponding anisotropy parameters. For the parameter of anisotropy of mobility K we have [6]:

,(1)

At deformations, affording the complete migration of the carriers into energy minima, we may write down

,(2)

where n is concentration of carriers, || is current carriers mobility along the leading axis of ellipsoid.

As it is known, the parameter of anisotropy of mobility is:

,(3)

where  is the mobility of current carriers in direction perpendicular to the leading axis of ellipsoid.

Let us plot a dependence lg()=(NGe), determining the parameter of anisotropy of mobility K from experimental data [5] according to (1) and using the expression (3). It is shown in Fig. 2.

It is seen from Fig. 2 that  sufficiently depends on the IIGe content in n-Si. Magnitude || characterizes the mobility along the leading axis of isoenergetic ellipsoid. The analysis of the obtained results shows that || practically does not depend (accurate up to 4%) on the concentration of isovalent impurity. There are grounds to consider to be the sensitive parameter introduetion of additional mechanism of scattering in semiconductors.

Let us write the parameter of anisotropy of relaxation times as:

,(4)

where , .

Values of K and K for n-Si crystals without IIGe agree with paper data [7]. Fig.3 shows the dependence to the IIGe concentration. One can see that parameter K tends to 1 with the increase

Using experimental data [5] we may determine the constant of deformation potential u for n-Si crystals with different concentration of IIGe. For temperature T=77K we have [6]:

,(5)

where =exp(E/kT), P is expressed in kg/cm2.

Thus, in the case of the dominating contribution of the mechanism of inter-valley redistribution of electrons to the piezoresistance we obtain a linear dependence lg (C104)=f(P). We find the constant of deformation potential from the slopes of dependencies. For pure n-Si and for crystals with IIGe up to NGe=71019cm-3 u=9.3eV. The decrease of deformation potential constant down to u=9.0eV is observed for concentration NGe=21020cm-3. The obtained data testify to the fact that band and elastic characteristics of solid solutions Si do not practically change at concentrations NGe21020cm-3.