A generalization of the theory of the anisotropic scattering of current carriers is proposed for the case of a phonon-drag effect. For two selected versions of phonon-phonon scattering theory it is possible to determine the nonequilibrium partition-function of the phonons. Calculations are made of the longitudinal and t.ransverse Nernst-Et.t.inghausen effects in n-Ge on t,he basis of anisot.ropic scattering and a phonon-drag effect.. The resu1t.s nre compared with experimental data [I], and it is found t,hat the present theory agrces well with experiment.Eine Verallgemeinerung der Theorie der anisotropen Streuung von Strorntragern wird fiir den Fall eines Phonondrag-Effekts vorgeschlagen. Fur zwei ausgewahlte Darstellungen der Phonon-Phonon-Streuungstheorie ist es moglich, die Kichtgleichgewichtsverteililngsfiinktion der Phononen zu bestimmen. Berechnungen des longitudinalen und transversalen Nernst-Ettinghauseneffektes in n-leitendem Ge werden auf der Basis einer anisotropen Streuung und eines Phonondrag-Effektes durchgefiihrt. Die Ergebnisse werden mit experirnentellen Daten [l] verglichen; es wird gefunden, dal3 die dargelegte Theorie gut mit dem Experiment iibereinstimrnt.

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...

P. I. BARANSKII e t al. : Galvanothermomagnetic Effects in Anisotropic Media phys. stat. sol. r:b) 67, 291 (1975) Subject classification: 14.3 and 15; 22 c eaHHOfi TOZIKH 3peHHR @eHOMeHOJIOrWIeCKH paCCMOTpeIIb1 B03MOlfEHbIe 1IOIIepe.I-IlLIe (no OTHOIIIeHHIo K d HJIH V T ) H rtpO~OJIbHbIe (COBIIaAaIoUHe IIO HaIIpaBJIeHHIo C J HJIH V T) raJIbBaH0-H TePMOMX' HHTHbIe 3@@eKTbI, BO3HHHaIoUHe B aHH30TpOII-HbIX CpenaX. npenCTaBJIFlR TeH3opa $ II 2 B BHne CYMM CHMMeTPHqHbIX H aHTB-CHMMeTPHqHbIX qaCTe$I, YAaJIOCL IIpe&JIOlfEHTb ynO6HyIo HJlR IIpOBeAeHHR 3KCIIepII-MeHTaJILHbIX HCCJIeEOBaHHfi KJIaCC€f@HKaIJHIo IIpOAOJIbHbIX (II IIOIIepeqHbIX) , YeT-HbIX ( H HeqeTHbIX) IIO MarHHTHOMY IIOJIH) KiJIbBaHO-H TepMOMarHHTHbIX 3@@eIiTOB, B03HHKaIOWHX B aHH30TPOIIHbIX CpenaX. OCHOBaHHaH Ha @H3HqeCKHX COO6pa-XeHHRX KJIaCCH@HKaIJHR raJIbBaHOMarHHTHbIX H TePMOMarHHTHbIX B@@KTOB IIO-Ka3bIBaeT, q T 0 HapRay C yXe H3BeCTHbIMH RBJIeHHRMH, B aHB30TPOIIHbIX CpemX JIOjrmHbI BO3HHKaTb 3#@eHTbI, KOTOPbIe paHee He II3YqaJIHCb. I' a3BHTbIe B pa60l.e (PeHOMeHOJIOI' H9eCKHe IIpenCTaBJIeHIIR IJpHMeHHMbI AJIR JIIo6HbIX aHH30TpOIIHbIX Cpea. QeTaJIbHbIe qHCJIeHHbIe PaCYeTbI KHHeTHqeCKMX K03@@HIJHeHTOB9 HoToPbIMH OIIHCbIBaIoTCR paCCMOTpeHHbIe B pa6o~l: 3@@eHTbI, 'MOrYT 6bITb BbIIIOJIHeHbI ( W R TaIEHX KpHCTaJIJIOB KBK I' epMaHHB, KPeMHHfi H np.) Ha OCHOBe TeOpHH aHH30TPO-Horn paccemm.

The magnetic field dependences of the coefficient R̃ determining the even Hall effect are theoretically calculated and experimentally measured in n‐Ge at j ∥︁ [111] and H ∥︁ [110] in the magnetic field interval 0 ≦ H ≦ 35 kOe and in the range of dominant phonon scattering (at 77.4 °K). The results of the calculations are in quantitative agreement with experimental data. For the conditions of dominant phonon scattering it is shown theoretically and experimentally that the relation G = Ū(H)/UU = f(H) (where Ū(H) is the voltage of the even Hall effect and UH⟂ is the voltage determining the specific resistance of an investigated crystal in a transverse magnetic field of the same strength) is completely saturated in magnetic fields ≧ 15 kOe. This saturation is directly connected with the anisotropy parameter K. The saturation magnetic fields have considerably lower values than those (approximately 50 to 100 kOe) which are necessary for the saturation of the function M = ϱH∥︁H→∞(H). This fact advantageously distinguishes the proposed method of measurement of K from a formely known one, where M is used for this purpose.

The magnetic field dependence of the Hall coefficient, RH = ‖(H), has been investigated theoretically and experimentally in n‐Ge at 77°K on samples with different orientations (H ‖ [100] and H ‖ [110], I ‖ [110] in both cases) within wide interval of concentration. Calculations of the RH = f(H) dependence were carried out on the basis of the anisotropic scattering theory up to H = 106 Oe and measurements were made in the whole interval of magnetic fields (H ≦ 105 Oe) up to quantizing. Attention is attracted to a necessity of refusal from formal application of H → ∞ for the analysis of the field dependence RH = f(H), since the Boltzmann equation validity has an upper limit of H‐values, corresponding to quantizing effects set up. Taking into account this circumstance in the concrete case of n‐Ge both the results of calculations and the experimental data lead to conclusions that a) throughout the interval of classically strong H (up to 105 Oe at 77°K) the Hall coefficient remains anisotropic; b) when the impurity scattering contribution increases, then beginning with some values of this contribution, the saturation of RH = f(H) throughout the whole classically strong field range cannot be achieved.