Publicaciones y obras de creación

V. E´ . Bukharov and A. G. Rokakh N. G. Chernyshevski State University, Saratov

共Submitted February 16, 1999兲

Pis’ma Zh. Tekh. Fiz. 25, 55–60共December 26, 1999兲

It is shown that the well-known fact that the radiation resistance of CdS improves considerably when PbS is added关A. G. Rokakh, E. V. Elagina, L. P. Matasova, and N. A. Novikova, Composition to Fabricate Film Photoresistors, Author’s Certificate No. 1110351, publ.

March 17, 1983兴 accompanied by the formation of the heterogeneous photoconductor CdS–PbS may be attributed to the gettering of radiation defects by narrow-gap phase inclusions.

This gettering occurs because the radiation-stimulated diffusion is considerably more pronounced in the wide-gap CdS–PbS component compared with the narrow-gap component. A model is proposed to explain the radiation resistance of a CdS–PbS system and this is used to determine the steady-state defect concentration profile. © 1999 American Institute of Physics.

关S1063-7850共99兲02512-4兴

As we are well aware, degradation of the photoelectric and luminescence properties of II–VI compounds is caused by the formation of defects which lead to additional doping of the sample2 and/or the establishment of new effective re- combination channels.3 It has been shown that the radiation resistance of CdS may be improved considerably by adding lead salts to the photoconductor, particularly PbS.1As a re- sult of the limited mutual solubility of CdS and PbS, a het- erogeneous material forms, conventionally designated CdS– PbS, which consists of a wide-gap matrix comprising a solid solution of PbS in CdS 共PbxCd1⫺xS兲 and narrow-gap, low- resistivity CdyPb1_⫺yS inclusions. The presence of these in- clusions is evidenced by a plasma resonance analysis of a CdS–PbS system.1兲Since these narrow-band inclusions have low resistivity, the wide-gap matrix connected in series with the narrow-gap phase is the working material from the pho- toconductivity point of view.

Explanations for the radiation resistance of CdS–PbS have been forward using the idea that the recombination ac- tivity is extracted from the wide-gap to the narrow-gap phase.4The aim of the present study is to construct a model of the resistance of a CdS–PbS system from a slightly dif- ferent point of view, based on the assumption that the diffu- sion of radiation defects is intensified by radiation to differ- ent degrees in the narrow-gap and wide-gap components.

The main mechanisms for radiation-stimulated diffusion were examined in Refs. 5–7. When applying these studies to CdS–PbS, we must take into account the characteristics of the material and the diffusants.

Mak7 considered diffusion stimulated by recombination charge transfer between centers. However, formula 共2兲 pro- posed by Mak only holds if each charge transfer event leads to a diffusion jump, i.e., after charge transfer the center is in an unstable position. In fact, charge transfer generally only reduces the energy barrier U for defect migration by ⌬U

⬇0.5–1 eV 共Ref. 8兲 so that in formula 共2兲 from Ref. 7 we

introduced the factor exp关⫺U⫺⌬U/kT兴, where k is the Bolt- zmann constant and T is the temperature.

Stepanov5 considered a mechanism for radiation- stimulated diffusion based on the transfer of energy to dif- fusing atoms as a result of particles in the radiation flux being scattered at these atoms. Since we are considering dif- fusion of recombination centers rather than the diffusion of atoms of the dominant material, in formula共17兲 from Ref. 5 we introduced the probability factor P that a center will par- ticipate in a diffusion jump, which may be expressed as P⫽N/Na, where N is the concentration of centers and Na is

the atomic concentration.

VinetskiŽ and ChaŽka6examined the diffusion of recom- bination centers stimulated when the energy of free carriers is transferred to them as a result of recombination. Numerical calculations based on our own experimental data and the data given in Refs. 8–12 showed that this last mechanism of radiation-stimulated diffusion plays a dominant role in the wide-gap phase of CdS–PbS, and the coefficient of radiation-stimulated diffusion calculated for this mechanism under electron beam irradiation of 1013cm⫺2s⫺1 共current density 10⫺6A/cm2, dose rate 106rad/s兲 is D*⫽2

⫻10⫺9_cm2_{/s. This value seems fairly realistic since the ex-} perimentally determined coefficient of radiation-stimulated diffusion of the radiolysis products for x-ray irradiation of CdS at a dose rate of 250 rad/s was D*⫽10⫺12–10⫺11cm2/s

共Ref. 13兲 and our radiation power was three orders of mag-

nitude higher.

In the narrow-gap phase of CdS–PbS, none of these mechanisms gives any significant stimulation of diffusion. For instance, the recombination mechanism is ineffective here because of the low recombination energy which cannot exceed the band gap. This means that the field of the diffu- sion coefficient D(r) in CdS–PbS can be considered to un- dergo a jump at the phase boundary.

TECHNICAL PHYSICS LETTERS VOLUME 25, NUMBER 12 DECEMBER 1999

994

As our model problem we analyzed the generation, an- nihilation共recombination兲, and one-dimensional diffusion of defects in an infinite region where D varies periodically as given by

D⫽

再

D1, ⫺l⫹共2l⫹2r兲k⬍x⬍l⫹共2l⫹2r兲, D2, l⫹共2l⫹2r兲⬍x⬍r⫹2l⫹共2l⫹2r兲,

共1兲

where k is an integer and 2l and 2r are the thicknesses of regions 1 and 2 with the diffusion coefficients D1 and D2 (D1⬎D2). This corresponds to the CdxPb1⫺xS–PbyCd1⫺yS periodic superlattice under irradiation. Although strict peri- odicity is not always satisfied experimentally, this apprecia- bly simplifies the analysis since on account of the symmetry we only need to analyze the region 0⭐x⭐l⫹r, and the boundary conditions are simplified.

We analyzed the equation of continuity for the defects ⳵N

⳵t ⫽D

⳵2_N

⳵x2⫺R⫹G, 共2兲

where N is the defect concentration, G and R are their rates of generation and annihilation, which are given by11

G⫽␩n, R⫽␬N2, 共3兲

where␩ and␬ are proportionality factors, and n is the con- centration of free electrons. The last expression in Eq. 共3兲 implies that the concentrations of vacancies and interstitial atoms are equal.

The symmetry of D(x) yields the boundary conditions ⳵N1/⳵x兩x⫽0⫽0, ⳵N2/⳵x兩x⫽l⫹r⫽0, 共4兲

where the subscripts 1 and 2 refer to the corresponding regions.

In order to obtain ‘‘matching’’ conditions for the solu- tions at the boundary of the regions we shall analyze the defect fluxes J1 and J2 from the appropriate regions. By

analogy with the kinetic theory of gases, we can obtain J_i

⫽Ni(l)vi/6, where the rates of displacement of the defects in

the crystal are vi⫽ai/␶i (aiis the lattice constant and ␶i is

the average residence time of a defect in one of the equilib- rium positions兲. Expressing ␯_i in terms of D_i 关see formula

共III, 6兲 from Ref. 8兴, we obtain Ji⫽DiNi(l)/ai. The result-

ant flux ⫺D1(⳵N1/⳵x)兩x⫽l, passing across the boundary of

the regions is determined by the difference between J1 and J2: ⫺D1 ⳵N1 ⳵x

冏x

⫽l ⫽D2 ⳵N2 ⳵x

冏x

⫽l ⫽D1 a₁N1共l兲⫺ D2 a₂N2共l兲. 共5兲

If N1(l)⬇N2(l), a1⬇a2, and D1ⰇD2, the right-hand side of Eq. 共5兲 is positive and a flux of defects appears from region 1 to region 2, i.e., they are gettered by a narrow-gap inclu- sion. For a more accurate analysis we need to allow for the surface annihilation of defects which modifies condition共5兲. Figure 1 gives the dependences N(x) (N1 and N2) ob- tained by solving the problem 共2兲–共5兲 numerically for vari- ous values of D2. It can be seen that the defect concentration in the working region共region 1兲 is 1.5–2.5 orders of magni- tude lower than that in the gettering region and the higher the ratio D1/D2, the lower the steady-state defect concentrations in the working region, i.e., the more effective the gettering.

Thus, the radiation resistance of the heterogeneous pho- toconductor CdS–PbS may be attributed to the gettering of radiation defects which function as fast recombination cen- ters, by narrow-gap, low-resistivity inclusions. This gettering occurs because the diffusion of defects in the narrow-gap and wide-gap phases of CdS–PbS is intensified by irradiation to different degrees.

FIG. 1. Calculated profile of the steady-state concentration N of defects in the heterogeneous photoconductor CdS–PbS for various rates of diffusion in the narrow-gap phase: G⫽4⫻1012_cm⫺3_•s⫺1_{, ␬⫽2⫻10}⫺20_cm3_•s⫺1_{, l⫽3⫻10}⫺3_{cm, r⫽3⫻10}⫺5_{cm, D}

1⫽10⫺9cm2/s. 1 — D2⫽10⫺11cm2/s; 2 — D2 ⫽10⫺12_cm2_{/s; 3 — D}

2⫽10⫺13cm2/s; 4 — D2⫽10⫺14cm2/s; 5 — D2⫽10⫺15cm2/s; and 6 — D2⫽10⫺18cm2/s.

995

1兲_{The authors are grateful to N. B. Trofimova for supplying this data.}

1

A. G. Rokakh, E. V. Elagina, L. P. Matasova, and N. A. Novikova,Com-

position to Fabricate Film Photoresistors关in Russian兴, Author’s Certifi-

cate No. 1110351, published March 17, 1983.

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G. E. Davidyuk, N. S. Bogdanyuk, A. P. Shavarova, and A. A. Fedonyuk, Fiz. Tekh. Poluprovodn. 31, 1013 共1997兲 关Semiconductors 31, 866

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Translated by R. M. Durham

Superhardness of cast iron induced by copper under laser treatment

In document Unión Europea. Libro de estilo interinstitucional (página 178-183)