Piezoresistance and Magnetopiezoresistance of n‐Ge in the [110] Direction

Abstract

I. V. DAKROVSKII (b), and V. V. KOLOMOETS (a) The piezoresistance and magnetopiezoresistance were investigated in n-Ge (I&, = 1.48 x ~1 0~~c m -~) for Xllfll HI1 [110] at T = 77 OK ( 0 5 1 x 1 5 6 0 0 0 k p~m -~; 0 5 I H I 5 100 kOe). It is shown that in the range of magnetic saturation the longitudinal magnetoresistance is approximately increased by 10 times when X 11 [llO] is altered from zero up to 6 X los kp On the basis of anisotropic scattering theory the dependences ex = f ( X ) , (Aeh/Aeo)x = f ( H ) , (A&/eo)H = f ( X ) were calculated, using the constants of deformation potentials Eu = 16.4 eV, E d = -6.4 eV and assuming that the uniaxial deformation results only in the redistribution of the current carriers between relatively shifted energy minima and does not change the shape of the equal-energy surfaces in n-Ge. Grundlage einer anisotropen Streutheorie wurden die Abhiingigkeiten ex = f ( X ) , (A&/eo)x= = f ( H ) , ( Aea/eo)R = f ( X ) berechnet, wobei die Konstanten des Deformationspotentials Eu = 16,4 eV und & = -6,4 eV benutzt wurden und angenommen wurde, daB die uniaxiale Deformation eine Umverteilung der Stromtriiger nur zwischen den relativ zueinander verschobenen Energieminima ergibt und die Form der Fliichen gleicher Energie in n-leitendem Ge nicht iindert. Die Ergebnisse der ausgefiihrten Experimente stimmen mit den theoretischen Berechnungen nicht nur qualitativ, sondern auch quantitativ iiberein. Die Benutzung einiger der in der modernen Literatur meist benutzten Konstanten Eu "d (anstatt der oben angegebenen) fur die theoretische Berechnung der Abhiingigkeit (Ae&/eo)R=50koe = f ( X ) fiihrt zu groBen Diskrepanzen zwischen den berechneten Kurven und den experimentellen Werten bei 1 x 1 > 3000 kp IntroductionThe dependence of resistivity and magnetopiezoresistance on uniaxial elastic deformation X l l j I( H 11 [111] was investigated in n-Ge (n, = 6 . 6~ 10ls a t 77 O K in [l]. It was shown later TheoryAssuming that the uniaxial deformation of n-Ge influences the population of different energy minima only and does not change the general concentration n,, the electron-phonon relaxation times, and the phonon spectrum, it can be shown on the basis of work No is the concentration of electrons in one minimum in the absence of deformation; Nl and N , are concentrations of electrons in lowering and raising energy minima respectively in the uniaxially stressed crystal. I n the case of compressive stress (X < 0) a Boltzmann transition of current carriers (because of the relative displacement of energy minima a t deformation) will result in the increase of their concentration in those ellipsoids in which the longitudinal axes form a small angle with the deformation axis. I n the limiting case (at sufficiently great X and not too high T), the electrons will transit completely from two ellipsoids characterized by index 2 t o minima of index 1 . Therefore complete saturation of ex = f ( X ) will be reached under the condition 2 Nl = 4 No = n, only, where ne is the total concentration of current...

Influence of γ-irradiation (60Со) on the concentration and mobility of carriers in Ge and Si single crystals of n-type

“…In the initial crystals the measured values of the mobility are in a good agreement with the values of the mobility, calculated within the framework of the theory of anisotropic scattering [9,10]. The averaged (by the data for 5 samples) results of carried out experiments for two different temperatures (300 and 77 K) in the range of non-monotonic change in parameters with growth of irradiation doses are summarized in Table 1.…”

“…The straightforward substantiation of this interpretation is given by the numerical values of mobility which were calculated in the framework of the theory of anisotropic scattering [9][10][11] (see Appendix) for the summarized values of N i = N a + N d ; they appeared to be much smaller than the experimental ones (dashed curve 2 in Fig. 2).…”

Interface model of low temperature plasticity in high uniaxially strained monocrystalline semiconductors

“…High pressure tensoresistivity (TR) data for n-Si(P) and n-Ge(Sb) crystals are shown in Figs 1(a) and 1(b), respectively. In order to identify the deviation from the TR mechanism caused by the electrons redistribution between the D 1 -minima in n-Si and the L 1 -minima in n-Ge, an approach of deformation potential constant Ξ u determination was used [7]. For nondegenerate distribution [8], the ratio of electron concentration in the upper valley (n 2 ) to the one in the lower valley (n 1 ) can be given by the relationship:…”

On methodology of measuring parameters with the increased sensitivity to residual or irradiation induced inhomogeneities in semiconductors

“…To realize the proposed technique let us use equation, which was determined in [3] for the pressure piezoresistance (3) and the strain piezoresistance…”