Photoconductivity of CdS under high pressure

Volume 135, number 4,s

PHOTOCONDUCTIVITY

CHEMICAL PHYSICS LETTERS

10 April 1987

OF CJS UNDER HIGH PRESSURE

Pavle SAVIC Serbian Academy of Sciences and Arts, 11000 Belgrade, Yugoslavia

and Vladeta UROSEVIC Institute ofphysics, P.O. Box 57, 11001 Belgrade, Yugoslavia Received 23 December 1986; in final form 27 January 1987

The photoconductivity of the high-pressure (rocksalt) phase of Cd.5 has been investigated over the 30-l 20 kbar pressure range. A decrease of the photo-threshold from 1.60 eV (at 30 kbar) to 1.49 eV (at 120 kbar) indicates an indirect gap semiconductor. The values obtained have been compared with the SaviC-KaSanin theory.

1. Introduction High-pressure studies on cadmium sulfide (CdS) were first carried out by Edwards and Drickamer [ 1] and Samara and Drickamer [ 21 who found an abrupt change in the optical-absorption edge and resistivity at x 27 kbar, as well as the stability of the new phase after reversal to lower pressure. Owen et al. [ 31 showed by X-ray diffraction studies that the new phase had a rocksalt structure. Brown, Homan and MacCrone [ 41 renewed the interest in high-pressure investigations of this material by reporting the observation of a large diamagnetism, approaching 100% flux exclusion, and possible superconductivity in pressure-quenched CdS at 77 K. Batlogg et al. [ 51 showed that the energy gap was direct in the wurtzite phase (2.4 eV at atmospheric pressure) and indirect in the high-pressure phase ( < 1.7 eV). In this paper we present some preliminary results of photoconductivity measurements on pure CdS under high pressure ( 30- 120 kbar). Under the common action of pressure and absorbed photons electrons can be transferred from the valence to the conduction band if hv 3 Eg, where Eg is the band gap at a given pressure. The minimum photon energy hvo causing a photocurrent corresponds to E, and should

in principle be the same as the Eg value obtained by optical absorption measurements. The results have been compared with a simple theory [6,7] which predicts the interaction energy atoms under pressure to vary as e21Ar,where Ar is the change in the “effective radius” of an atom in a high-pressure field.

2. Experimental The high pressure was generated in a diamond anvil cell of NBS type [ 81. A preindented stainless steel gasket was prepared by drilling a hole (300 pm in diameter) at the center of indentation and by cutting the disc into two symmetrical parts which were cemented between two mica supports with central holes greater than the anvil diameter. A small CdS platelet *was pressed into the gasket hole and the gap between the two gasket segments filled with fine alumina powder and cemented with epoxy resin. This configuration (fig. 1) was able to sustain pressures up to 120-l 30 kbar. A flat ruby ship was inserted into the front side of the CdS sample and the pressure was measured in the backscattering geometry.

0 009-2614/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

* The cadmium sulfide samples have been prepared using the method proposed by Yoshimatsu et al. [ 91.

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3 *.A

-3 9

JO-

DIAflOMD

HV

AUWL

‘EM

Fig. 1.Top vtew of sample and electric circuit. Anvil diameter 1 mm, sample diameter 0.5 mm, distance between gasket segments x0.3 mm. HV-stabilized dc voltage supply, EM-sensitive electrometer. >

5w

The electrical contacts between gasket halves, which serve as electrodes, and the CdS sample were obtained by applying the highest (120 kbar) pressure to the sample. For illumination of the sample we used a xenon arc lamp, a double optical monochromator and a branched light guide for simultaneous measurement of the incident radiation flux at each wavelength used. The electric circuit, shown in fig. 1, consisted of a stabilized dc voltage source and a sensitive electrometer.

3. Results and discussion Fig. 2 shows the dependence of the photocurrent (divided by the photon flux) on the wavelength of the incident radiation, the parameter being the applied pressure. The minimum photon energy hve causing a photocurrent at a given pressure (the photocurrent threshold), which should equal the band gap Eg at this pressure, can be obtained by numerical determination (least-squares fit) of the zero Ail@ value. From a set of such curves we obtained the dependence of the photocurrent threshold (hv,) on the pressure shown in fig. 3. In the pressure range investigated there is a decrease in hv, with increasing pressure from 1.60 eV (at 30 kbar) to 1.49 eV (at 394

550

600

650

700

750

BOO

8M

A id

Fig. 2. The dependence of photocurrent divided by photon flux (relative units) on the wavelength of incident radiation at PI = 30 kbar (&=774+ 12 nm) andP,=70 kbar (&=804+ 15 nm).

120 kbar) . This confirms the findings of Batlogg et al. [ 51 that the high-pressure phase of CdS is an indirect gap semiconductor. The slope of the curve is A( hv,,)lApz 1 meV, which agrees with AE,IAp= 0.7 meV [ 1,5] within experimental error. The rather small difference in AE,/Ap and the absolute Eg values between the present and earlier work, where optical absorption measurements were used, can be explained by the absence of truly hydrostatic conditions in our work and perhaps also by the difference in the two measuring methods.

4. A simple theoretical model In order to avoid the difficulties connected with exact quantum mechanical calculations, many attempts have been made to find some simple formula for an approximative estimation of the behaviour of materials under high pressure. The most successful has been the Herzfeld formula [ 91 for the calculation of metallization pressures for closed shell systems. In the early 1960s one of the authors of the present work developed a simple semiclassical the-

Volume 135, number 4,s

&50

CHEMICAL PHYSICS LETTERS

10 April 1987

t

t

t

lfa

* 10

20

30

40

50

Ml

70

80

90

100

10

fza

P (kbor)

Fig. 3. The dependence of the photo-threshold hvO(eV) on the applied pressure P (kbar). The slope obtained in the 30- 120 kbar range is AhvdAPc 1 mevtkbar.

[6,7] based on the assumption that the “effective radius” of atoms in compressed material continually changes over some pressure range corresponding to a given phase i, abruptly changing its value when the phase transition i+i+ 1 occurs. The theory included both crystallographic transitions and pressure excitation and ionization of atoms. At the end of the ith phase the effective radius r: is given by

ory

r*=2-“3rz I

mI

(1)

where rz=0.8539x

lo-”

P”3 m

(2)

and P is the molar volume at P=O and T= 0. The corresponding quantity at the beginning of the same phase is 0 r, = c~"~rk

m ,

(3)

where a = 615 for odd i,and 5/3 for even sure at the end of the ith phase is: P:=O.96x

10-29j?1(r:)-4

Pa

i.The

pres(4)

and at the beginning of the same phase: PP=0.96x10-29y,(rp)-4

where

Pa,

(5)

/3,= 1.39 for even i , =I.13 yi ~0.885 = 0.704

foroddi, for even i , for odd

i.

The energy of an outer atomic electron is simply taken as: E= &$J=

14*4xrlo-‘o

eV,

(6)

where e is the electron charge. These relationships are directly applicable only to simple monatomic substances at T= 0, but with some modification they can also be used for more complex materials and for T> 0. For CdS at room temperature, instead of c we shall use the molar volume fi which corresponds to the beginning of the second phase: yo= g = 144464~10~~ 6.10x103 2 Pi!

=23683x

10e6 m3 ,

where the value p? = 6.10 x 10 3 kg/m3 is taken from Owen’s three X-ray diffractometric measurements at 40 kbar. Starting from this value for @ and the formulae given in ref. [ 71, we can obtain the following quantities (Vin lOW’m,pin 103k~m3andrin lo-”

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PHYSICS

10 April 1987

LETTERS

and

m):

meV/kbar .

Vy=34.104,

py~4.236,

r:=1.92,

ALYhp~0.7

V:=28.419,

~7~5.083,

r:=

E=23.683,

&=6.10,

rS= 1.70,

Vt=

p:= 10.167,

r:=

This is identical with the AEgfAPvalue obtained from optical absorption measurements [ 1,5] ( x 0.7 meV/kbar) and is also consistent with our A( hvo)lAP data ( x 1 meV/kbar) within experimental error. In general, the agreement between the calculated and experimental data is encouraging taking into account that: (i) the theory is developed for T=O while the experimental results have been obtained at room temperature, and (ii) the calculations are based on a value for p: which corresponds to P=40 kbar and not to P= 27 kbar.

14.209,

1.807,

1.434,

where the lower indices correspond to the phase number (i= 1 or 2), while the upper denote the beginning (0) or the end ( * ) of the phase. Using the above quantities we can compare some calculated and measured values: (i) The applied pressure needed for the phase transition l-2,

5. Conclusions =5.2x

lo9 Pa=52

kbar ,

while the experimental value is PI -r2 = 27 kbar [ 11. (ii) The volume change during the phase transition l-+2, v-V-4

~

vt

lOO=

28.419-23.683 28.419

loo=

l6 7% , .

The experimental value given by Owen et al. [ 31 is 21%. (iii) The change in electron energy during the phase transition 1+2, 1 T - $

AE=14.4x10-10 (

12

=0.5 eV >

and the experimental value is 0.7 eV [ 1,5]. (iv) The change in electron energy with pressure in the second phase (i= 2). Owen et al. [ 31 obtained by X-ray diffractometry mean a, values of 5.42x lo-” m at 40 kbar and 5.20x lo-” m at 200 kbar. These quantities should be proportional to the “effective radii” used in the SaviC-KaSanin theory. Using relation (6) we can calculate the change in electron energy with pressure in the second phase

An experimental method for examination of photoconductivity at pressures up to 120 kbar has been developed and used for investigating the high-pressure phase of pure CdS. A decrease of the photothreshold from 1.60 eV (at 30 kbar) to 1.49 eV (at 120 kbar) has been found in satisfactory agreement with the AE,/AP value obtained by optical absorption studies. It is shown that a simple theoretical model ( SaviC-KaSanin theory) can be successfully used for realistic estimation of the behaviour of material under pressure even for non-monatomic substances and at T> 0. It will be interesting to compare this model with recent low temperature experimental results and with other materials.

Acknowledgement We are grateful to Dr. J.M. Besson and his staff for very useful discussions concerning the construction of our first diamond anvil cell and to our colleagues M. Kaplarevic, B. Petrovic, Lj. Zekovic, V. Celebonovic, B. JovaniC and B. Antic for help with the experiment.

(i=2): Al?= 14.4x lo-‘0

X

396

1 a,( 200 kbar)

References 1 co.11 - ao( 40 kbar) >

eV

[ I] A.L. Edwards and H.G. Drickamer, 1149.

Phys. Rev. 122 (1961)

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CHEMICAL

[2] G.A. Samara and H.G. Drickamer, J. Phys. Chem. Solids 23 (1962) 457. [3] N.B.Owen,P.L. Smith, J.E. MartinandA.J. Wright, J. Phys. Chem. Solids24 (1963) 1519. [ 41 E. Brown, C.G. Homan and R.K. MacCrone, Phys. Rev. Letters 45 (1980) 478. [ 51 B. Batlogg, A. Jayaraman, J.E. van Clere and R.G. Maines, Phys. Rev. B27 (1983) 3920. [ 61 P. SaviC, Bull. Sci. Math. Natur. Acad. Serbe Sci. Arts No. 8,26 (1961) 107.

PHYSICS

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10 April 1987

[ 71 P. Savic and R. KaSanin, The behaviour

of materials under high pressures, Vols. l-4 (Serbian Academy of Sciences and Arts, Belgrade, 1962-65). [S] G.J. Piermarini and S. Block. Rev. Sci. Instr. 46 (1975) 973. [9] Ref. [ 1371 in: R.H. Bube, Photoconductivity of solids (Wiley, New York, 1960). [ lo] K.F. Herzfeld, Phys. Rev. 29 (1927) 701.

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