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Submitted on 1 Jan 1978
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NONLINEAR PROPERTIES OF BISMUTH UNDER SOUND GENERATION CONDITIONS
Yu. Bogod, R. Valeev
To cite this version:
Yu. Bogod, R. Valeev. NONLINEAR PROPERTIES OF BISMUTH UNDER SOUND GEN- ERATION CONDITIONS. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-1117-C6-1118.
�10.1051/jphyscol:19786495�. �jpa-00217978�
JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 8, Tome 39, aoCC 1978, page ( 3 - 1 117
NONLINEAR PROPERTIES OF B I S M U T H UNDER SOUND GENERATION C O N D I T I O N S
Yu.A. Bogod and R.G. Valeev
Physicoqechnical I n s t i t u t e o f Low Temperature, UkrSSR, Academy o f Sciences, 47, Lenin Prospect Kharkov, 310164, USSR.
RBsum6.- Nous prBsentons des resultats sur les propriLt6s Blectriques non linBaires de monocristaux de Bi en rLgime de gBnLration de phonons, les champs magngtiques et Qlec- triques Btant crois6s. Nous Btudions les particularitBs des caractsristiques station- naires courant-tension (en particulier l'effet de non-r6ciprocit6), la stabilisation des phonons hors de llLquilibre, et l'excitation des instabilitss. Nous avons obtenu pour la premiPre fois sur ce corps qui n'est pas un semi-conducteur, une partie prG- sentant une conductivitB differentielle nBgative sur la caractgristique courant-tension stationnaire.
Abstract.- Nonlinear properties of massive single crystals of Bi are investigated under phonon generation in the course of superimposition of crossed electric and magnetic fields. Specific stationary I-V characteristics (the non-reciprocity effect, in parti- cular), nonequilibrium phonon stabilization, instability excitation are studied. For the first time on the stationary current-voltage characteristic (CVC) of the abject, which is not a semiconductor, the portion of negative differential conductivity (NDC) has been obtained
.
If a crystal is supplied even no acoustic power, the supersonic charge drift induced by ex- ternal fields brings about spontaneous phonon emission, which, in particular, will cause a kink in CVC. Esaki / I / was the first to observe this type of nonlinear effect in bismuth. According to
/ l / the transverse magnetoconductivity increases
sharply if CE/HS~I, where cE/H is the drift velo- city of a charge in the. direction[$x87, E and H are the strengths of electric and magnetic fields, S is the sound velocity.
We report'here the results of the studies of nonlinear electric properties of bismuth in strong external fields, the stationary strength of the electric field being 200 V/cm.
1. Oscillations of the transverse nonlinear magne- toresistance were observed, whose extrema were in the vicinity of the Shubnikov-de Haas oscillation extrema /2/. Under the conditions of sound gene- ration the oscillation amplitude increases with transition from helium to hydrogen temperatures.
The anomalous temperature behaviour of the oscil- lation amplitude can be accounted for by the simple theory, wh,ich is developed assuming the possibility of describing the interaction between electrons and nonequilibrium phonons in terms of acoustic E.M.F. Comparing the dkrived fokula /2/ with the experimentally measured CVC gave for the first time information on the temperature and magnetic
field dependence of the coefficient of nonequili- brium phonon generation. Oscillations of the coef- ficient of nonequilibrium phonons-generation as a function of' the magnetic field (Figure 1) and the Fermi surface anisotropy taken into account permit the understanding of physical reasons and explana- tion of new peculiar features of the nonreciproci- ty effect which consists,in nonreproducibility of the nonlinear portion of CVC under the magnetic field inversion.
Fig. 1 : Generation coefficient as a function of magnetic field at T=4.2 K, E P = cE/HS = 0.825 (so- lid curve, left-hand scale) and T=20.4 K, Ef=1.4
(broken curve).
New features are the equivalency of the magnetic and electric fields inversion; the nonmo- notonic field dependence of the difference between the strengths of the electric field in the sample AE (H) = E (H)-E(-H) for a given value of current;
r
fs6 4 8
r
e
0 50 to0 H , K O ~
4-h-L
I .L/ I /- I)--
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786495
the change of AE sign at certain H; the possibili- ty of suppressing or exciting instability through reversing the direction of the drift velocity of charge carriers.
The numeric calculation of the electron drift velocities in the approximation of the ellip- soidal Fermi surface taking into account the transverse (with respect to the current density vector) electric fields appearing in limited sam-, ples accounted for the transition experimentally observed/2/ in Bi to the regime of phonon genera- tion at cE/H<S.
2. Under the conditions of preset current the por- tion of NDC is obtained on the stationary CVC (fi- gure 2)/2/. This is the first observation of NDC in the object which is not a semiconductor. The exis- tence of NDC is related to the electron gas cooling due to the energy withdrawal from the electron sys- tem by nonequilibrium phonons.
Fig.
3.3.
tlon
2 : Stationary CVC of Bi at H=138 kOe, T=4.2K C3 = 8'. Ek is the electric field of transi- to regime of phonon generation.
3. The lifetime of rlonequilibrium phonons is found to depend nonmonotonically on the magnetic field, being insensitive to the variation of the electric field strength. Thus
,
it follows that the phonon- electron interaction is of predominant significan- ce in stabilization of nonequilibrium phonons du- ring their transition to a new state of current.The most probable range of frequencies
(%lo7
Hz)generated by "supersonic" electrons at ~ ~Oe is 1 0 ~ shown.
pal signal) on the drif; velocity appears to repeat the shape of the typical curve for the sound am- plification coefficient. It is found that instabi- lities are not related to the excitation of the second sound in Bi. The period of current oscilla- tions for the sample of a given size is shown to be dependent on the direction of the drift veloci- ty, which, in turn, is dictated by the magnetic field orientation with respect to the crystal axes, by the magnetic field magnitude and the re- lationship between the mobility tensor components.
References
/l/ Esaki, L., Phys. Rev. Lett.
8
(1962) 4./ 2 / Bogod, Yu.A., Valeev, R.G., Fiz. Nizk. Temp.
2 (1976) 897; 3 (1977) 874; 4 (1978) 481.
- - -
4 . An attempt has been made to find the regulari-
ties of excitation of current oscillations in the nonlinear regime. The dependence of the oscilla- tion amplitude (it amounts to 40 % of the princi-
