Trapping of photoelectrons around dislocation lines in alkali halides

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possible number of dislocations, one finds for the 4” samples a relative separation, S, of 56 A and for the 6” samples a reIative separation of 35 A. Underlying this model one can relate the value

.--__l__

T&e

161

DISLOCATIONS

This relation yields for the capture diameter, d, the values given in Table 1. For comparison, values for the capture diameter determined with random dislocations(*) and with dislocation arrays of wider separation(a) are given in Table 2.

1

Table

Misfit angle

Number of samples

Capture rate of boundary, y

4” 6” 25”

3 2 2

0.16, 0.18, 0.22 0.33, 0.25 0.61, 0.56

Capture diameter d (A)

2

I

I-

6.5

56, 6.4, 7.8 7.0, 5.6

d ( MCKELVY@~)

d (WERTuEIMf4))

d (Average)

5.6

6.8 I

I REFERENCES

of y with the capture diameter, d, of the individual dislocations :

n-d (17)

Y==z

J. Phys. Chem. Solids

1. MUELLER R. K. To be published. 2. MUELLER R. K., Report on 18th Amual Conference an Physical Electronics, MIT, p. 29 (1958). 3. TWEET A. G., Phys. Rev., 99, 1182 (1955). 4. WERTHEIM G. K. and PEARSONG. L., Phys. Rev. 107, 694 (1957). 5. MCKELW T. P., Plzys. Rev. 106, 910 (1957).

Pergamon Press 1959. Vol. 8. pp. 161-165.

Printed in Great Britain

TRAPPING OF PHOTOELECTRONS DISLOCATION LINES IN ALKALI

F.6

HAZIMU Department

KAWAMURA

THE effect of mechanical working upon the photocurrents in colored KC1 and KBr single crystals was investigated in the temperature range from -200 up to 0°C. The irradiation was performed by chopping the light from a tungsten incandescent lamp at 30 c/s, the photocurrent being lock-in detected. An a.c. field of 1000 c/s was applied to the crystal so that the space charges were eliminated. Although it is to be expected that the range of a photoelectron is shortened as the result of the trapping by a dislocation line or by its jog, the effect is complicated by the formation of complex centers such as M- or R-centers, which accompany mechanical working or irradiation with M

and

HIBOSHI

of Physics, Osaka City University,

AROUND HALIDES

OKURA Osaka, Japan

F-light. Fig. la shows how rapidly the complex centers are formed in the deformed crystal upon irradiation with F-light. However, when the crystal was purified by recrystallization from the melt, these complex centers did not appear even with much longer irradiation, as shown in Fig. lb. Thus, by employing such a pure crystal, we were assured of freedom from parasitic effects due to complex centers. The recrystallized pure single crystals of KC1 and KBr were additively colored by heating at 420 - 560°C in sodium or potassium vapor. The densities of F-centers were 101s - 1017 cm--a as shown in Table 1. The crystal was cleaved into several pieces, which were then mechanically

162

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DISLOCATIONS

worked to varying degrees. Each specimen was pulse-annealed at 400°C for 1 min. The mechanical working consisted of linear compression by a weight tester, and the degree of deformation was measured by the fractional thickness reduction. Typical results are shown in Figs. 2a and 2b, in which the solid line relates to the undeformed crystal and the dotted line to the deformed one. Each specimen was obtained from the same piece of colored crystal. These curves may be interpreted in terms of the shortening of the range of the photoelectron due to shallow trapping centers produced by mechanical working, which become

ineffective above -120°C. If Tp is the mean lifetime of a photoelectron due to the trapping b!F-centers and TD that arising from shallow traps, the net mean lifetime T for the deformed crystal is given by the relation l/T = l/Tp+l/T~. Since the photocurrent for the undeformed sample is proportional to TF and that for the deformed one proportional to T, we have ~/TD= ~/T--I/TFN~/I-~/I~,

where

TFITD = IO/I- 1;

(2)

I,, and I are the photoconductances

for

TEMP. ‘C

@I

(4

(1)

and

FIG. 1. Absorption coefficients of colored KBr as functions of photon energies. (a) Usual crystal which underwent 13 per cent deformation; - before irradiation and - - - after 10 min irradiation. (b) Recrystallized specimen which underwent 19 per cent deformation; - before irradiation and - - - 30 min irradiation with F-light.

TEMP. SC

FIG. 2. Photoconductance for KBr and KC1 as thr functions of temperature. (a) KBr; undeformed crystal and - - - crystal 9 per cent deformed. (b) KCl; undeformed, - - - crystal 19 per cent deformed, - - - * * quantum efficiency for F-F’ transition, and - *the photoconductance according to PoHL.@)

Table 1 N.+crne3)

_-

KBr

KC1

le.5 x 10’6 1.5 x 101s 4.3 x 10’6 4.0 x 101s 3.8 x 101s 7.7 x 101s 1.3 x 101’ Mean

4.0 x 101s 4.0 x 10’6 1.6 x 10’7 1.6 x 10” Mean

Degree of deformation (per cent)

T

-iT*(T)

--

NDwINF~

--

-168

-16.5 -150 -150 -153 -155

16 25 19 21

-

ND(cmM2)

w(cm)

xl09 7.6 9.6 4.5 4.6 5.8 4.6 8.4

x10-8 2.6 3.4 7.1 8.5 22 14 9.3 9.3

_-

_-170 -167 -170 -167. -167 -167

16 21 8 9 11 9 18

NDW(CKI-1)

1.4 2.3 a.7 1.0 3.3 0.9 0.6

xl02 2.0 3.3 3.2 3.9 12.5 6.6 7.8

3.8 7.6 2.2 3.4

xl03 1.5 3.0 3.5 5.5

--

_-

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undeformed and deformed crystals, respectively. Making use of the relation (l), we can obtain the temperature-dependence of ~/TD from the experimental curves as shown in Fig. 3. The temperature at which the derivative of this curve becomes a maximum can be used to give an order-of-magnitude estimate of the trap depth. It is about - 170°C for KCI. If the trap depth for KBr and -155°C is E, the releasing frequency may be expressed as Y = vs exp(-E/kT), where v. is of the order of 1010 see-1. Since it would be reasonable to assume that v becomes of the order 1 set-1 at the above characteristic temperature, we can estimate the trap depth E to be 0.21 and 0.24 eV for KBr and KCl, respectively.

FIG. 3. The reciprocal of the mean lifetime of a photoelectron due to trapping by dislocation line as a function

of temperature and its derivative curve.

Since, as shown later, the cross-section becomes much too large if only the jog of a dislocation line is responsible for trapping, we shall assume that the dislocation line itself traps a photoelectron. TF/TD can be obtained by analyzing the experimental data with the aid of equation (2). It becomes constant at low temperature where release from the trap is negligible. If No is the number of dislocation lines per cm2 and w is the effective width of the dislocation line for trapping, ~/TD is proportional to Now. On the other hand, ~/TF is proportional to NFCT,where NF is the density of F-centers and o is the effective cross-section for electron trapping. Hence we have NDW/NFO= TF/TD = lo/I-

1,

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DISLOCATIONS

(3)

from which we get Now, assuming o to be lo-14 ems. The values obtained are shown in the fourth

and fifth columns of Table 1. In a separate experiment we estimated the density of dislocations in deformed crystals of KBr by the use of nuclear magnetic resonance. Results are shown in the sixth column. Using these values, we obtain the effective width w as shown in the last column. If this effect is attributed only to the jogs of the dislocation lines, their cross-section must be as large as lo-13 ems, even if they were spaced every ten atomic distances along the dislocation line. The potential field around dislocation line is estimated by making use of the deformation potential. It can trap an electron at either the compressed or dilated side, according to the sign of the deformation potential. Although an electron may be trapped as a moving polaron along a dislocation line or self-trapped by polarizing the medium, the latter state is little more stable than the former according to a rough estimate. The energy of the self-trapped state was estimated by a variational method. Employing the value of 5.4 eV as the deformation potential for KCl, which we have obtained by the use of the cellular method, we found that the energy required to release the electron from the self-trapped state to the bottom of the conduction band is 0.27 eV, which is to be compared with the experimental value of 0.24 eV. The temperature range where trapping is effective just overlaps the range where the optically excited F-electrons can escape thermally into the conduction band. In this range the quantum efficiency r) for the production of photoelectrons is less than unity and is temperature-dependent. In Fig. 2b, 7 obtained by experiment(z) on the F-F’ transition is shown together with the photocurrent for KC1 due to PoHL.@) It seems likely that POHL’S specimen was considerably strained, since the trend of the photoconductivity curve should be similar to that of the 7 curve, if the temperature variation of electron mobility is neglected. The photoconductivity curve may thus fall further when electron trapping becomes effective at low temperature. REFERENCES 1. OTSUKAE. and KAWAMURAH., J. Phys. Sot. Japan

12, 1071 (1957). 2. PICK H., Ann. Phys., Lzg. 31, 365 (1938). 3. POHLR. W., PYOC.Phys. Sot. 49, 13 (1937).