The influence of isovalent impurity of germanium upon the electrophysical
properties of silicon
), 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 ntype with a concentration of germanium NGe=2(1019(2(1020cm3 by measuring temperature dependencies of conductivity, Hall coefficient, piezoresistance and piezoHalleffect. The object of the investigation were the crystals grown by Chokhralsky method with content of oxygen of (6(8)(1017cm3. 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 nsilicon (curve 1) and in nsilicon 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 (
((cm N(1013
cm3 NGe(1019
cm3 N0(1017
cm3 (300K
cm2/V(s (77K
cm2/V(s
1 130 3.1  7 1500 23000
2 81 5.1 2 6 1500 21000
3 65 6.2 4 6 1500 19500
4 50 9 7 6.5 1450 18500
5 98 4 20 6 1480 16400
Detailed experimental and theoretical investigations of electron mobility in nsilicon [2] showed that in the region of mainly phonon scattering it is determined both by invalley and intervalley scattering. Theoretical calculations, performed with account of scattering on long wave acoustic phonons and intervalley 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 nsilicon at scattering on acoustic oscillations of the lattice may be explained by the increasing contribution of intervalley 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 ((Tm in the region of phonon scattering for nsilicon is revealed in paper [3], in which the authors assume that the abrupt decrease of ( at NGe(1020cm3 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 intervalley scattering testifies to the principal role of intervalley 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 nSi. 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(1020cm3 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 twovalley conduction band.
The values of electron mobility obtained at uniaxial strain [100]  P=9000 kg/cm2 for nsilicon 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 intervalue scattering on acoustic phonons, testify to the defining contribution of f – junctions into intervalley scattering of electrons both in pure nsilicon and in solid solutions of Si at NGe(2(1020cm3.
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)
