Investigation of static skin effect on atomic pure (100) and (110) faces of tungsten single crystal

Solid State Communications,Vol. 15, pp. 1793—1796, 1974

Printed in Great Britain

Pergamon Press.

INVESTIGATIONOF STATIC SKIN EFFECT ON ATOMIC PURE (100) AND (110) FACES OF TUNGSTEN SINGLE CRYSTAL A.A. Kharlamov, O.A. Panchenko and Yu.G. Ptushinskii Institute of Physics, Ukrainian SSR, Academy of Sciences, Kiev, USSR

(Received 27 June 1974 by E.A. Kaner)

When a Bloch wave is specularly reflected from the metal boundary, several states may appear on different isoenergetic surface sheets. Depending on the shape, Gauss curvature sign and arrangement of separate sheets of the isoenergetic surface as well as orientation of the crystal physical boundary, such reflections may cause to reverse the tangential components of the electron group velocity after the “mirror” reflection. In W crystals such reflections are realized on the faces (100) and (111) and cannot occur on the (110) face. A comparative investigation of the character of the conduction electron reflection from the atomic pure and oxidized faces (100) and (110) of the tungsten single crystal has been made. The method of static skin effect is used.

INVESTIGATIONS of the basic faces of refractory metal single crystals, cleaned by high-temperature heating from the oxides and carbides and kept in ultra-high vacuum, suggest that there are reasons to believe the upper atomic layers to be fairly ordered structures and to arrange nearly in the same order as in the metal bulk.1’2 Such atomic smooth and clean surfaces make up peculiar two-dimensional diffraction lattices causing a specular reflection of the conduction electrons.~It is noteworthy, however, that the specular reflection of the Bloch wave does not always correspond to a conservation of the tangential cornponent of the group electron velocity. Indeed, in metals with a multi sheeted Fermi surface, the incident

pattern of the surface scattering processes in the crystals of tungsten and molybdenum. Let us assume that two closed isoenergetic surfaces, e.g. spheres of equal size but different Gauss curvative signs are oriented in the directions (100>, alternating with the reciprocal lattice constant. Staggered, these surfaces occupy the whole reciprocal space (Fig. 1). Using the laws of conservation of energy and quasimomentum tangential component, we determine possible states of reflected electrons. In the case of reflection from the face (100) these states are on all the isoenergetic surfaces at the points of their intersection with the straight lines k 1 = const., parallel to the axis of (100> (e.g. at B, C and D, if A is an initial state, in symmetric cases it is possible to limit relative our consideration to W the states B and C realized with probabilities 1 and 14’2). It should be stressed that with A -÷ B type transitions, v11 remains invariable, whereas the A C type transitions, accompanied by a conversion between an electron and a hole, cause a change of the sign of v~.

Bloch wave can give rise to several reflected waves depending on the shape or arrangement of individual sheets of the isoenergetic surface 7and orientation Due to these of the physical boudary of a crystal. features of reflection the tangential components of the electron velocity before and after “mirror” reflections appear opposite for some directions.

-+

Let us consider a similar situation using a simple model, suitable nevertheless for ifiustrating a qualitative

For reflections from the face (110), the straight 1793

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ATOMIC PURE (100) AND (110) FACES OF TUNGSTEN

~

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~O’Q+0

FIG. 1. Topology of Fermi surface in tungsten; (a) idealized model, (b) model built following the data of reference 9.

The electron surfaces are hatched for explicity. lines k11

= const. are oriented along the axis of (110> and intersect only the electron surfaces or only the hole surfaces, for this reason the conversion between particles does not occur on this face.

Let us analyze what are the consequencies of the interband scattering considered for the static 8 For “good” metals here it is the normal skin-effect. practice that the inter- and intravalley relaxation times are the same order values (r 1 r2); therefore, we take that W1 W2 0.5. In the presence of a high magnetic field (1 ~‘ y, where y = r/1, r is the Larmor radius and 1 the mean free path), direct parallel to the surface of a thin plate H I n, (where n is the normal to the surface and H Ij, where j is the current direction), the surface conductivity is determined by electrons travelling in a thin, of the scale r, layer near the interface and colliding with the surface. In the case of the specular reflection (p = provides I), a correlation of incident and reflected electrons optimal conditions for the drift of carriers along the surface, Their drift length is limited only by 1. When p = 0, the mean free path is considerably smaller and equals to the distance between two successive collisions with the surface, i.e. to r. When the interband transitions on the mirror surface occur, the character of the carriers’ drift on the interface changes essentially depending on the transition type (A C or A B) realized in each particular collison event, the carrier can return to the site of a preceding start or advance one “step” forward. With W 1 = W2, the “steps” back and forthdrifting are equally probable, motion electron near the surfaceand must obey of theanlaws of Brownian movement. In this case the mean free path is r and p = 0. -~

-~

When H II n, the electrons diffusely reflected from the surface, are most mobile. With each collision of this kind, the axes of spiral trajectories of the electrons in the magnetic field are shifted in the plate plane by the value of the order of r. A collision with the mirror surface does not change the position of the current-tube, the surface does not affect the conductivity.

When the interband transitions on the surface are involved, the position of the current tube in the space does not change also, only the direction of the carrier rotation in the magnetic field is changed. The surface in this case remains effectively specular. The experimental investigation of similar interactions was made at temperature 4.2°Kon the samples cleaned in high vacuum3 (10h1 torr). The rectangular plates, samples were 6 X 2 X 0.08 mm cut from a high cleanlinessingot with the residual resistance ~ = 20 X 1 o~. The plate surfaces coincided with the faces (100) and (110), the current was passed in the direction (100>. The sample preparation and measurement methods are given in references 5 and 6. The measurement results of the resistance angular dependence in the constant magnetic field H

=

8.9 kOe

are shown in Fig. 2. The concentration of the2surface oxygen impurity is the parameter of varying from to 1015 cm” the curve. The0 magnetoresistance of the bulk crystals measured for the magnetic field oriented along (100> and (110> is respectively pr~,= 8.2 X iO~and

ATOMIC PURE (100) AND(l 10) FACES OF TUNGSTEN

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______

______ ___

___ _____

(Na)

___

___

_

__

—a --

—

______ ___

(fto)

10’

LAf

ia

p.

1000

____

__

~

_____ __—— _______

1795

__

__

__

__

____

__

____

MUM °

~

w

FIG. 2. Magnetoresistance angular dependences PH. s.

9koe(cb) for tungsten plates directed parallel to the faces. (a) (100); (b) (110); 0— oxidized surface; • atomic pure surface. —

FIG. 3. Relative changes of magnetoresistance in thin (d = 0.1 mm) tungsten crystals in the constant rnagnetic field 8.9 kOe (H In) as a function of the oxygen deposition time. 1

—

face (110); 2

—

face (100).

—

—

1.1 X 10-6 ~2cm. From Fig. 2 it is seen that: (1) for all the orientations p ~ (2) evaporation of an oxygen film leads to an increase of the magnetoresistance for H II n by 20 per cent and to its decrease for H In. Relative changes of ~Pii/Pii are essentially different in the crystals oriented in the (100) and (110) faces: in the first case this change is found to be 19 per cent and in the second case 450 per cent. The dynamics of time variation of P11 during adsorption of oxygen in the constant flux is shown in Fig. 3. Measurements were performed for H I fl on the two equally thick (d = 0.1 mm) crystals oriented in the faces (100) and (110) and mounted in the same experimental apparatus. The oxygen adsorption is seen to cause the magnetoresistance increase ~piu/puu(100) by 3—4 per cent and ~ii/p~i (110) by 100 per cent. By cleaning the surface the magnetoresistance is returned to initial values. Thus, an oxidation (or cleaning) of the surface for H In yields only small changes of ~p11/p~in a

.

thin plate oriented m the face (100). This fact can be explained by assuming the atomic pure face (100) to scatter the conduction electrons almost diffusely (it is postulated, of course, that the surface oxidation results in a full or almost full diffusivity arising from disturbance of the periodical potential relief of the surface). Using the data shown in Fig. 2 and assuming that on the oxidized surface p = 0, one can estimate p for the atomic pure surface (100) for HI n and H II n. For the face (110) such estimates were made earlier in references 5 and 6 and it was found that Pu = Pi = 0.8. Using the same method of interpretation of the results as in references 5 and 6, the following values for the face (100) are obtained: ~ = 0.2 and p1 = 0.8. It is important to stress that p measured on different faces of one particular crystal were found essentially different. The difference can be explained by the interband transitions realized on the face (100) with high probability near 0.5. In the perpendicular magnetic field p are the same for different faces which supports nontriviality of the results obtained in the parallel field for the face (100).

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REFERENCES I. 2.

STERN R.M.,AppL Phys. Lett. 5, 218 (1964). ESTRUP P.J.,and MCRAE E.G., Surf Sci. 25, 1(1972).

3.

ANDREEVA.F.,Usp.Fiz.Nauk. 105, 113(1971).

4.

GREEN R.F., Solid State Surface Science, Vol. 1, New York (1969).

5.

LUTSISHIN P.P., PANCHENKO O.A. and K1-IARLAMOV A.A.,Zh. Eksp. i Teor. Fiz. 64,2148(1973).

6.

PANCHENKO O.A., LUTSISHIN P.P. and PTUSHINSKII Yu.G., Zh. Eksp. i Teor. Fiz. 66, 2191(1974).

7. 8.

MORE R.M., Phys. Rev. B 9, 392 (1974). PESCHANSKY V.G. and A~BELM.Ya., Zh. Eksp.

9.

SPARLIN D.M. and MARCUS J.A.,Phys. Rev. 144,484(1966).

L

Teor. Fiz. 55, 1980 (1968).

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