On the Positron Work Function for a Metal with a ... - Springer Link

0 downloads 0 Views 129KB Size Report
The positron annihilation method is one of the sensitive tools for diagnostics of the bulk and surface of massive bodies, ultradispersed media, and nanostruc.
ISSN 10637842, Technical Physics, 2011, Vol. 56, No. 11, pp. 1689–1690. © Pleiades Publishing, Ltd., 2011. Original Russian Text © V.V. Pogosov, A.V. Babich, P.V. Vakula, A.G. Kravtsova, 2011, published in Zhurnal Tekhnicheskoi Fiziki, 2011, Vol. 81, No. 11, pp. 150–151.

SHORT COMMUNICATIONS

On the Positron Work Function for a Metal with a Dielectric Coating V. V. Pogosov*, A. V. Babich, P. V. Vakula, and A. G. Kravtsova Zaporozh’e National Technical University, ul. Zhukovskogo 64, Zaporozh’e, 69063 Ukraine *email: [email protected] Received March 1, 2011

Abstract—It is shown that a dielectric coating on the metal surface may change the sign of the positron work func tion. Calculations are performed using the Kohn–Sham method for polycrystals and faces of Al, Cu, and Zn. DOI: 10.1134/S1063784211110181

The positron annihilation method is one of the sensitive tools for diagnostics of the bulk and surface of massive bodies, ultradispersed media, and nanostruc tures (see [1–3] and the literature cited therein). After the formation of a lowenergy beam, positrons are injected into a medium. Analysis of the annihilation spectra shows that positrons in metals are thermalized even at helium temperatures. The positron annihilation rate in a medium depends on the concentration of electrons in the surroundings. The main characteristics of the positron are its work func tion Wp (or the binding energy) and the lifetime in the medium. Electron work function We for a metal is always positive (the metal is a potential well for electrons). The positron work function is positive for some metals and negative for a number of other metals [1, 2]. This corresponds to the experimentally observed reverse emission of injected positrons. Metals with negative values of Wp include, for example, Al, Cu, Fe, Mo, Ni, Cr, and Ti. For these metals, the values of Wp < 0 were obtained in [4, 5] from analysis of the energy spectrum of reverse emission (relative to the vacuum level); such a metal is a potential barrier for the injected positrons. One of the channels for detecting reverse emission of positrons is the recording of “emission” of positro nium atoms. The Ps atoms are formed at the tail of the spatial electron distribution behind the metal surface. Work function WPs can be calculated using the Born cycle. To “extract” a positronium atom from a metal, an electron and a positron should be extracted sepa rately and then “combined” into an atom: W Ps = W e + W p – Ry , 2

(1)

Ry = 13.6 eV. The work functions of the electron and positron are determined by their bulk components and by the sur face dipole barrier D:

bulk

+ eD,

(2)

bulk

– eD,

(3)

We = We

Wp = Wp

bulk

where e is the elementary positive charge and W p p–e – E corr

p–e E corr

=

– E0. The contributions and E0 corre spond to positron–electron correlations in a homoge neous electron gas and to the positron–ion interaction bulk in the unit cell. The values of W p = 3.97, 2.82, and 3.80 eV for Al, Cu, and Zn, respectively, were calcu lated earlier (see [6] and the literature cited therein). Assuming that the electric potential at a large dis tance from the surface is zero, the electrostatic barrier is D = – φ , where φ < 0 is the electrostatic potential in the bulk of the metal [7]. Since D > 0, the competition of the terms in Eq. (3) leads to values of Wp of different signs. The value of the dipole barrier at the metal sur face depends on the crystallographic indices of the face and is very sensitive to the computational method. An approach that makes it possible to calculate the characteristics of a metal surface coated with an insu lator was proposed in [7]. The calculations were based on the Kohn–Sham method using the stable jelly model. Since the D(ε) dependence was found to be strong (ε is the permittivity of the coating), we can state that the sign of the positron work function for the same metal (or for the same indices of the face) may change upon a variation in ε. In accordance with Eqs. (1)–(3), the positronium work function is com pletely determined by the bulk properties of the metal and is independent of surface barrier D(ε). The results of computations for Al and Cu demon strating the effect of sign reversal of the positron work function are shown in the figure. The D(ε) depen dence for polycrystalline Zn/Zn (0001) face does not lead to significant changes: Wp = +0.61/–2.59 and +2.01/–1.23 eV for ε = 1 and 80, respectively. Analogous conclusions can be drawn for faces

1689

1690

POGOSOV et al.

Wp, eV Al

1

Cu

0

REFERENCES

−1

(poly) (111) ~ ~

−2

tion for anticopper, for example, would be equal to the electron work function for copper. These results can be used for surface diagnostics of metals, nanomaterials, and probably in nanotechnol ogies.

0

3

5

7

9

11 79 ε 81

Positron work functions of Al and Cu vs. their permittivi ties.

Al(110)/(100) (Wp = –4.86/–2.23 and –3.39/–0.55 eV) and Cu(110)/(100) (Wp = –4.52/–2.64 and –3.02/–0.95 eV) for ε = 1 and 80, respectively. It should be noted that in antimatter (antimetal), conduction antielectrons should exhibit the same manyparticle effects as the conduction electrons in conventional metals in accordance with the Pauli principle. As a consequence, the positron work func

1. P. J. Schultz and K. G. Lynn, Rev. Mod. Phys. 60, 3 (1988). 2. V. V. Pogosov and I. T. Yakubov, Fiz. Tverd. Tela (St. Petersburg) 36, 2343 (1994) [Phys. Solid State 38, 1274 (1994)]. 3. V. I. Grafutin, O. V. Ilyukhina, G. G. Myasishcheva, E. P. Prokop’ev, S. P. Timoshenko, Yu. V. Funtikov, and Yu. A. Chaplygin, Nanostr. Mat. Fiz. Model. 2, 15 (2010). 4. M. Jibaly, A. Weiss, A. R. Koymen, D. Mehl, L. Sti borek, and C. Lei, Phys. Rev. B 44, 12166 (1991). 5. M. Jibaly, A. R. Koymen, L. Chun, D. Mehl, and A. Weiss, in Proceedings of the 9th International Confer ence on Positron Annihilation, 1992, Vol. 105–110, p. 1399. 6. R. M. Nieminen and J. Oliva, Phys. Rev. B 22, 2226 (1980). 7. V. V. Pogosov and A. V. Babich, Zh. Tekh. Fiz. 78 (8), 116 (2008) [Tech. Phys. 53, 1074 (2008)].

Translated by N. Wadhwa

TECHNICAL PHYSICS

Vol. 56

No. 11

2011