- Email: [email protected]
Stress-induced anisotropy in chalcogenide glasses
Journal of Non-Crystalline Solids 119 (1990) 243-253 North-Holland
243
STRESS-INDUCED ANISOTROPY IN CHALCOGENIDE GLASSES
I. Optical studies Keiji T A N A K A Department of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo 060, Japan Received 28 July 1989 Revised manuscript received 16 January 1990
The optical properties of amorphous materials subjected to uniaxial compression up to 100 kbar have been studied. As2S3 glass undergoes elastic deformation, this results in photoelastic anisotropy at pressures below 5 kbar. At higher pressure, the material is fractured, but the cracked powders are squeezed into a transparent flake. Further compression induces substantial red-shifts of the optical absorption edge in Se, As2S3 and GeS2. The glassy flakes released from the squeezed states to 1 arm exhibit quasi-stable isotropic and anisotropic properties, which can be relaxed by light illumination and annealing. The mechanisms of these optical changes are discussed.
1. Introduction A m o r p h o u s materials are inherently isotropic, and by contrast crystals show anisotropic properties as evinced by cleavage. It m a y be interesting, therefore, to examine anisotropic a m o r p h o u s materials, since the study m a y fill the gap between crystalline and a m o r p h o u s physics, the latter being still lacking in convincing structural knowledge [1]. I n d u c e d anisotropies m a y a c c o m p a n y oriented atomic structures, which can be utilized to shed light on the origin of the a m o r p h o u s properties governed by r a n d o m l y oriented atomic units. Investigations of the problems of how and what kinds of anisotropies can be induced in non-crystalline solids m a y uncover novel phenomena. In applications, the study m a y lead to the development of new devices such as birefringent optical fibers [2]. U p to now, there has been m u c h work d o n e on anisotropic liquids, i.e. liquid crystals, whereas anisotropic glasses have hardly been examined. Techniques for producing anisotropic amorp h o u s materials m a y be classified into two groups as shown in table 1. The first group includes the preparation procedures of bulk glasses [3], fibers [4] and thin films [5]. A l t h o u g h heterogeneous structures are involved. The multilayer films [6]
currently studied extensively m a y also give rise to anisotropic properties. A m o r p h o u s substances having frozen-in anisotropies can be obtained using these procedures. T e m p o r a r y anisotropies can be induced by applications of stress [7-10], electric [7,11] and magnetic [7,12] fields. W h e n these forces are removed, the materials recover to initial isotropic states. In addition to these unstable anisotropies, chalcogenide and oxide glasses are k n o w n to exhibit quasi-stable optical and electronic anisotropies when illuminated by linearly polarized light [13,14]. The anisotropy, which ap-
Table 1 Methods for producing anisotropic chalcogenide and oxide
glasses Method
Technique cooling in [ temperature ~ gradient
Preparation [ extrusion / oblique deposition [ (multilayer) photoeffect squeezing Treatment elastic deformation electric field magnetic field
0022-3093/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
Property
quasi-stable
temporary
Ref. [3]
[4l [51 [6] [13,14] [19] [7-10] [7,111 [7,12]
244
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
pears to be induced by electric field of light, is stable after cessation of illumination. Anisotropies in chalcogenide and oxide glasses generated by uniaxial compression are investigated in the present work. Extensive studies have been performed for amorphous semiconductors under hydrostatic pressure [15-18], and accordingly we will try to understand the hydrostatic and uniaxial features in a coherent way. Upon applications of intense uniaxial stress, glassy samples exhibit stress-induced squeezing behaviors which accompany frozen-in anisotropies [19]. We will examine the details here, specifically optical properties, and the following paper [20] will deal with structural properties.
A C support
< B
<
/-
~diamond I ~ I
~Ffl
pLe
Fig. 1. A cross-sectional view of a sample compressed between a pair of diamond anvils. Three optical paths A, B and C are plotted by solid lines with arrows.
2. Experimentalprocedures The material studied was As2S 3 glass prepared by conventional melt-quenching procedures [1]. Ingots were polished to cubic shapes with side lengths of 0.1-0.5 ram, and subsequently annealed in argon atmosphere at 180°C for 1 h to release residual strain. Other materials including orthorhombic S, glassy Se, glassy GeS 2, glassy GeO 2 were examined for squeezing characteristics. Uniaxial compression experiments were conducted employing a pair of 0.12 carat diamondanvils [21] with culet faces of 0,8 mm in diameter as shown in fig. 1. The generated pressure was calibrated as follows. When a sample was deformed elastically, the pressure P was evaluated from the fractional change e in sample thickness using P = re,
(1)
where Y was Young's modulus, 162 kbar [22-24]. The change in thickness e was calculated from peak wavelengths of multiple-interference fringes of light reflected at the culet faces (optical path C in fig. 1). The pressure in the squeezed state was determined using the ruby R 1 method [21], the details of which are described in the following section. The optical transmittance of glassy samples and the ruby photoluminescence were measured using a spectral system combined with microscope
optics [25]. For detecting the transmitted light intensity a cooled PbS and a photomultiplier were employed, and for probing anisotropies in transmittance spectra a polaroid plate was placed in front of an incandescent light source. In addition, the optical birefringence of squeezed glasses was inspected using a conventional polarization microscope attached with a Berek's compensator.
3. Results 3.1. Overall feature
It seems helpful to describe first the gross features of a typical compression sequence of polished glassy As2S 3. (A series of color photographs is informative here, and the reader is referred to fig. 1 in ref. [19].) We visualize a cubic sample in the pressure cell at 1 atm. The specimen appears clear yellow in accordance with the optical band-gap energy of 2.4 eV [1]. Upon uniaxial compression up to 5 kbar, the sample color changes to a darker orange shade. Deformation in this pressure range is elastic so that the sample recovers to the initial state when released to 1 atm even after being stored at 5 kbar for 1 day. Under pressures higher than 5-10 kbar, the sample is inevitably fractured with cracking. This proceeds with a decrease in the gap separation between the anvils, and as a
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
consequence the sample becomes fragmented. Here, strain is mostly released through the fragmentation process, and hence the assembly of As2S 3 chips appears as a blurred yellow. Startlingly, an anomalous phenomenon is observed following further compression. If we pressurize the assembly to 20 kbar, the fragments at the culet center coalesce into a transparent orange flake, in which the dimension increases with pressure. At 100 kbar the flake is circular, typically 0.5 mm in diameter and 20 ~tm in thickness. The sample color is black at the center, gradually changing to orange in the outer region, which is surrounded by powdered As2S 3 appearing opaque yellow. It should be noted here that the dimension and the color distribution of the flake are governed by the compressing strength, and are almost independent of time intervals after application of pressure. If we store the sample at 100 kbar for 1 day, the pressure at the central part decreases by about 5 kbar, probably reflecting viscous a n d / o r plastic flow, whereas the appearance of the sample hardly changes. Glassy powders which have been crushed in mortars show the same behavior. We tentatively refer to the phenomenon whereby pulverized samples merge into transparent disks under intense uniaxial compression as 'squeezing' [19]. In paper II [20] it is shown that the mechanism of the squeezing process is ascribed to plastic deformation, differing from diffusion-controlled sintering and hot-pressing processes [26]. If we depressurize the squeezed sample to 1 atm, the color becomes lighter, but the transparency is retained. With a decrease in pressure, some cracks in radial directions appear, which have been argued to be manifestations of concentric pressure distributions at the squeezed states [19]. The released sample shows optically and thermally induced relaxations afterwards. Pressure in squeezed samples was estimated from the R 1 photoluminescence of a ruby chip [21] about 10 Fm in diameter, which was put on the fractured assembly. In the squeezed states, the ruby might be packed in the disk, being located at the sample surface. The R 1 peak of the ~ruby excited by focused light from an argon laser [25] was broader than ___5 .~ in wavelength, indicating non-hydrostatic pressure distributions [21]. How-
10C
.
.
*
i
.
245 .
.
.
.
.
E 50
0
I
i
I
5
|
I
strain (%)
1
I
10
Fig. 2. The red-shift AE of the optical absorption edge in elastically compressed As2S3. 570 strain corresponds to 8 kbar stress.
ever, the generated pressure around the ruby chip could be known within an accuracy of + 10 kbar, unless the ruby was directly stressed by the anvil pair.
3.2. Elastic change When subjected to small uniaxial compression, As2S3 is elastically deformed and the optical absorption edge shifts to lower photon energies. Figure 2 shows the change AE in the position of the optical absorption edge evaluated with the photon energy at (x = 200 cm-1, where a is the absorption coefficient. Probe light is propagated in a direction parallel to the compressive stress (A in fig. 1). In the elastic region, the optical absorption edge shifts in parallel without changing its shape and, thus, the red shift may be a good measure of a decrease in the optical band-gap energy Eg. (This approximation is applied throughout the present work.) The anisotropy of the optical absorption coefficient, i.e. the dichroism, was induced by the uniaxial compression. In order to measure the anisotropy, linearly polarized probe light was propagated perpendicular to the compression direction (B in fig. 1), and the polarization direction was varied. The anisotropy defined as E a = E (11)-
246
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
E ( ± ) increases linearly with strain as shown in fig. 3, where E(II) and E ( ± ) are the absorption edges measured with the light in which the electric field runs parallel and perpendicular to the stress direction. Birefringence n a = n ( I I ) - n ( ± ) also appeared with the magnitude of 0.008 when the strain was 4% (stress was 6 kbar), where n is the refractive index in visible wavelengths. By using these values we obtain the stress birefringence coefficient r , fl = n a//O ,
(2)
of - 0.0013 k b a r - 1, where o is the stress which is assumed negative for compression. The magnitude is quantitatively consistent with the result reported by Galkiewicz and Tauc [9], -0.0009 kbar -1, measured under uniaxial tension. Note that the signs of both E a and n a are positive, in harmony with the Kramers-Kronig relations [27]. These optical anisotropies disappear when the sample is released to 1 atm.
3.3. Squeezing behavior In the squeezed state, a pressure increase redshifts the optical absorption edge with a decrease of the slope of the Urbach tail [1]. However, the
IG
laJ
i
0
i
i
|
2 strain(*/.)
Fig. 3. Stress-induced dichroism E a = E(II) ± E( .L ) in As2S3, where E denotes the position of the absorption edge, measured by linearly polarized light having electric field vectors parallel (11) and perpendicular ( 1 ) to the stress direction.
slope change is not substantial, and we will concentrate on the red shift. In Se and orthorhombic S, the spectral changes induced by the squeezing were nearly the same as those observed upon hydrostatic compression [18,28]. Thus, it may be assumed that for soft materials the two compression modes induce similar changes in fundamental electronic properties. As shown in fig. 4, however, there exist some quantitative differences between hydrostatic and squeezing compressions in A S E S 3 and GeS 2. In s q u e e z e d A s 2 S 3 , the absorption edge red-shifts more substantially at around 30 kbar, and with further increases in pressure the difference is reduced. GeS 2 exhibits a more marked discrepancy. At all pressures the absorption edge under squeezing appears to be more red-shifted by - 0 . 4 eV than the hydrostatic values [18]. The difference may become more noticeable, if the absorption edges are evaluated as a function of the volume change. Note that in fig. 4 the hysteresis of the absorption edge is larger in GeS2, and the squeezed samples show more prominent hysteresis than that in hydrostatically compressed glasses [29]. In Se released from squeezing compressions up to 100 kbar, no hysteresis was observed, as well as the samples freed from hydrostatic compression [29]. (Squeezed Se transformed to the hexagonal Se at 110 kbar, as was demonstrated by Fuhs etal. [20].) The behavior can be attributed to the low glasstransition temperature of about 30 ° C at 1 atm [1], at which thermal relaxation can take place immediately. The characteristics in As2S 3 appear to be intermediate between these two behaviors. Although hysteresis exists, the squeezed and isotropically pressurized glasses show similar features. It may be appropriate here to describe briefly the experimental details for the result shown in fig. 4. The absorption coefficient a is related to the transmittance T under neglection of multiple reflection as T = (1 - R ) 2 e x p ( - a W ) ,
(3)
where R is the reflection coefficient and W is the sample thickness. R was calculated using the Fresnel formula, being given as a function of the
247
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I i
i
i
i
!
i
!",, £. \ 3£ ". ;. \ \ ~" \
2.5
.
.
.
.
.
.
(a)
.
.
.
.
2.5 ~ \
i
i
i
|
i
i
'
'
(b)
i,.
.
i
\
\:'
\
..\ ".\
\
\
~".,.
2.C
\ \
•.
"-" tu2.C
"-.
>
\
IV
\ X
hi
~
\.,> \
\ \
\
1.5
I
0
i
i
i
i
i
50 p r e s s u r e (kbar)
i
i
i
i
i
i
100
0
'
'
'
'
'
'
'1
o'
'
150
pressure (kbar)
Fig. 4. Pressure dependence of the optical absorption edge in (a) As2S3 and (b) GeS2. Solid and dashed lines show the results of squeezed and hydrostatic compressions, and dotted lines show hypothetical routes from 1 atm to squeezed states. Hysteresis effects are shown by lines with arrows, which fix only the starting and released points. In (a), the arrow indicates the hysteresis in the samples released from hydrostatic and squeezed pressures of 100 kbar.
refractive indices of the diamond, 2.4, which was nearly independent of pressure, and of the sample. For the sample indices, the magnitudes may be assumed to be the same as the hydrostatic values [18]. However, the thickness W was difficult to measure. Only the value at the highest pressure could be estimated through measuring the thickness of the released samples, if the expansion along the release was calibrated. The calibration could be done using the pressure-volume data under hydrostatic compression [18]. Thus, the resuits shown in fig. 4 were obtained from many squeezing runs up to different pressures. 3.4. Relaxation and anisotropy in released samples The samples released from squeezing procedures exhibited relaxation behavior, which was enhanced by light illumination and thermal annealing. Figure 5 shows the change of the location
of the absorption edge in As2S 3, which is depressurized from 100 kbar. The sample undergoes the relaxation immediately after the release, and it becomes undetectable after being stored for 10 h at room temperature. However, light illumination of about 20 m W / c m 2 in intensity provided from an ultrahigh-pressure mercury lamp induces a further change, which terminates within 30 rain. A complete recovery to the initial state can be obtained through an annealing treatment for 1 h at 180°C, just below the glass-transition temperature [1]. If the annealed sample is illuminated again by the band-gap light, the so-called reversible photodarkening [31] appears with the red shift 50 meV of the absorption edge. Note that these relaxation characteristics are qualitatively the same as those observed in the samples released from hydrostatic compression [29]. The samples released from the squeezing exhibit quasi-stable birefringence. Figure 6 shows -
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses 1
248
2.4
=
=
"7
2.3 l-
t-
w
!
2.2
0
S
iluminateiluminate
(h)
lb% 3'0 (min) time
gence n a for successive treatments of releasing, illumination and annealing. (Here, the accuracy of n a is + 20%, because the measurements were carried out for cross-sections of cracked fragments.) Figure 6 shows some different characteristics between in As2S 3 and GeS 2. Changes in n W with annealing are opposite. By contrast, it is a comm o n feature for these materials that the anisotropy na disappears only with annealing. G e O 2 glass showed a similar relaxation of n a = 0.002, whereas its absorption edge could not be measured because of the high energy of 6 eV [32]. The following discussion therefore will be focused on the chalcogenide glasses.
3'0 g0 (rain)
Fig. 5. Relaxation and photoinduced changes in the position of the optical absorption edge E in As2S3 released from 100 kbar squeeze.
variations in A s 2 S 3 and GeS 2 absorption-edge position E, the optical path length n W measured along the compression direction, and the birefrin-
4. Discussion
4.1. Elastic red-shift and photo-elastic effect The result shown in fig. 2 obtained in the elastic region indicates that d E g / d P u = - 6 . 5 m e V / k b a r , in contrast to the coefficient d Eg/d Ph ,
i
i
,
3.(3 25
(a)/
A
>
2£
60.-.
I.tJ
~-/o.,. /o 36~=.
ta1.5 1.0
(b)F~
2.5 2.0
50 ~
34
i ,° , i°I g "U
"U
~
c"
1.5
~0
o
~
I
I
,
N
~
"0
•
m •
= ~
"" ¢ll ._c
E
--r
]0.02c~ b--J0 --
rll •¢ - .
~-
.--
Fig. 6. Variations of the optical absorption edge E, the optical path length n W and the birefringence na in (a) A%S 3 and (b) GeS 2, which are squeezed to 100 kbar, released, illuminated and annealed.
K. Tanaka / Stress-inducedanisotropy in chalcogenideglasses I
249
=-12 m e V / k b a r evaluated at a low-pressure region [33], where the subscripts u and h denote uniaxial and hydrostatic. We see a difference in the magnitudes of a factor two. In uniaxial compression experiments, however, the sample expands in directions normal to the stress, and naturally hydrostatic compression induces an isotropic contraction. Thus, a comparison of volume coefficients may be more appropriate. Using some elastic equations [26], we obtain
The intrinsic birefringence in homogeneous media may be treated in two ways, using ideas based on bond models assuming polarizable units [8] and on band models. In the latter treatments, some workers [9,10] have followed the single oscillator model proposed by Wemple and DiDomenico [36], in which the refractive-index dispersion n(hto) is approximated as
(4)
where hto is the photon energy, and F and E 0 are constants denoting oscillator strength and energy. In typical chalcogenide glasses such as ASES3, it has been demonstrated that the changes in F are comparatively larger than those in E 0 [9,10,18]. This means that in chalcogenide glasses the photoelasticity is governed by volume changes and hence Pll 2 P12 [9], where p is the photoelastic constant. Since the stress coefficient fl is connected with the photoelastic and the elastic constant c as [9]
Vd E J d V . = 3K d E , / d Pu,
and V d E g / d V h = K d E g / d P h,
(5)
where K is the bulk modulus. The volume coefficients are then calculated as V d E g / d V , = (2.5 + 0.3) eV and V d E g / d V h = (1.5 _+ 0.3) eV, in which the uncertainties arise mainly from variations 103-139 kbar of the bulk modulus [22-24,34]. In this evaluation, the uniaxial coefficient is larger than the hydrostatic value. Several possibilities are evoked for the difference in the coefficients, and we cannot assert at present whether it is intrinsic or extrinsic to the material. An extrinsic reason may be non-ideal pressure distribution in the compression device. Since frictional forces exist at the boundaries between the sample and the diamond anvils, the generated pressure is not purely uniaxial. Hence the above calculation assuming uniaxial elastic deformation should be modified. In addition, the sample surface could not be polished completely parallel. A geometrical calculation shows that a fractional deviation of 1% in thickness can cause an overestimation of 30% in the uniaxial pressure value. As for intrinsic origins, structural modifications such as dangling bonds plausibly generated by the shear component in uniaxial pressure may have an influence on the optical properties. The photoelasticity originates from homogeneous or inhomogeneous microscopic structures. When a material has heterogeneous structures consisting of optically isotropic parts birefringence may appear [35]. Nonetheless, in most samples of chalcogenide bulk glasses, no traces of phase separation are detected, and thus the photoelasticity originates from homogeneous structures.
n ( h t o ) 2 = 1 + F / [ E 2 - (hw)2] ,
fl
=
-n3(pl, -Pa2)/(c,1 - q2),
(6)
(7)
the induced anisotropy n a defined by eq. (2) is relatively small. 4.2. Squeezing-induced red-shift
Under some assumptions, which may be satisfied here, the pressure distribution in thin squeezed flakes is given as [26,37] P ( r ) o: e x p [ 2 T ( a - r ) / W ] ,
(8)
where r is the shear strength of the disk sample with a radius a and r is the radial distance. We may assume here that the pressure has qualities between hydrostatic and uniaxial features, depending on some factors, e.g., r and r. For softer materials the pressure appears to be more isotropic. It seems reasonable therefore that the hydrostatic and squeezed results are almost the same for Se and S. For As2S 3 and GeS 2, shear components included in the squeezing forces can induce three effects, which are mostly absent from hydrostatic compression. First, it is plausible that the shear forces are responsible for breaking the covalent bonds, effectively producing dangling bonds. As a result, the absorption edge can be red-shifted more
K Tanaka / Stress-inducedanisotropyin chalcogenideglassesI
250
Table 2 Fractional changes in the optical path length A(nW)/nW, the refractive index An/n and the thickness AW/W in As2S3 and Ge,gz induced by illumination and annealing. All the quantities are expressed in % Glass
As2S3 GeS2
Change Illumination
ACnW)/(nW) -55:1 -55:2
Annealing
An/n -3 -5
AW/W -2 0
remarkably by the squeezing procedure than the hydrostatic compression. The other possibilities are related to glassy structures. It has been demonstrated that chalcogenide glasses are composed of low-dimensional molecular clusters held together with weak intermolecular forces mostly consisting of van der Waals type [1]. Therefore, it can be speculated that these molecules are oriented when the glasses are subjected to the squeezing compression. For instance, layer molecules possibly contained in A s 2 S 3 and GeS: may tend to be stacked parallel to the sample surfaces, as is suggested in part II [20]. In that case, the optical spectra which were measured by light having electric polarization parallel to the sample surfaces are governed by intralayer properties. This anisotropic effect may result in more dramatic red-shifts in squeezed glasses. As for the last possibility, the stacking of the layer molecules may become irregular, since the assembly is sheared. The disordered stacking could also give rise to the enhanced red-shifts [38]. However, at ultra-high pressures the atomic coordination number may be increased by the hydrostatic component [33], and thus the difference between squeezed and hydrostatic compression will be reduced. In short, the shear and hydrostatic forces can be considered to cause the difference and the similarity between the optical properties in the two types of compressions.
4.3. Origin of the quasi-stable birefringence A key point in the examination of the relaxation behaviors shown in fig. 6 may lie in resolving the changes in n 14/ into modifications in the refractive index n and the sample thickness W. The
aCnW)/CnW) +55:1 -105:1
an /n -1 -16
AW/W +6 +6
analysis can be performed using an empirical relationship obtained from hydrostatic pressure experiments. Figure 7, which is replotted from the results shown in ref. [18], gives the coefficient ~, in the Moss rule [27]
nVEg = constant,
(9)
to be 2 for As2S 3 and 1.2 for GeS 2. Under the approximation E g = E (fig. 6), the fractional change A n / n induced by illumination and annealing can be evaluated. Since
A(nW)/(nW)
= An/n + AW/W,
(10)
the changes in n W shown in fig. 6 gives A W l W. These results are summarized in table 2. Table 2 shows that the photoinduced change is mostly electronic. That is, the fact A (n W ) / n W = A n / n suggests that A W / W can be neglected here.
h
,,,,
3
3
'-
Se
''''
"'-
'i''
Eg(eV) Fig. 7. Relationships between the refractive index n and the optical band-gap energy Eg in Se, As2S3 and GeS2 subjected to hydrostatic compression. Open circles indicate the states at 1 atm, with increasing pressure by arrows. Dotted curves axe the best fits of the Moss rule (see the text).
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
Mechanisms of the photoinduced changes can be related to local structural changes. It has been argued that local stresses contained in chalcogenide glasses can be released by illumination [29,33]. It is plausible that such relaxations in localized structures have an effect on the absorption-edge position and the refractive index. Since photoinduced effects were not detected in the birefringence, it is assumed that the defects have no dipole moments a n d / o r the defects are not oriented. The defect density is estimated to be comparable to that for the photodarkening, 1020 cm -1 [25,31], because the shifts of the absorption edge induced by the two photoinduced changes are similar. The modifications induced by annealing seem to be more complicated. As shown in table 2, values of A(nW)/(nW) and An/n are substantially different for this case, and we must assume a thickness expansion of AW/W= 6%. (The same magnitudes for the two glasses may be coincidental.) The geometrical change is dominant in As2S 3, but in GeS 2 the electronic change still governs the decrease in the optical path length. This thickness expansion can be considered as a relaxation process, since annealing at the glasstransition temperature brings glasses to the lowest energy state [1]. The annealed sample must have identical properties to the unloaded glass in all respects. In contrast, as demonstrated above, the thickness of the released and illuminated samples are nearly the same, and these are 6% thinner than the annealed flake. Therefore, it can be assumed that the released and the illuminated samples are plastically strained. The annealing effect can be understood as resulting from structural relaxations extending over wider regions. The relaxation is induced by thermal viscous flow [1] which accompanies the volume relaxation. For GeS 2 the annealing induces relatively larger effects, because the illumination cannot relax the defective strained structures effectively. The disappearences of the isotropic optical changes and the birefringence can be connected with the volume change as discussed below. The thermally induced strain release can accompany the blue-shift of the absorption edge. Taking the results [18] obtained under hydrostatic
251
pressure into account, we can estimate that the uniaxial volume expansion of 6%, which may be regarded as equivalent to the isotropic linear expansion of 2%, gives a blue shift of 0.1 eV in As2S 3 and 50 meV in GeS 2. The magnitude in As2S 3 is quantitatively comparable with the experimental result shown in fig. 6(a), but for GeS2 the shift is a tenth of the observations. The residual shift in GeS 2 may be ascribed to electronic effects. The frozen-in strain of 6% is also considered to be a cause of the quasi-stable birefringence. Under the assumption that the strain-birefringent coefficient, or the photo-plastic constant [39], is the same as the photo-elastic constant, the 6% strain gives n a = +0.014 for As2S 3 through the photoelastic equation (2). This value is consistent with the experimental result shown in fig. 6(a), i.e. + 0.01, both in sign and magnitude. As mentioned in section 3.2., the elastic effect is mostly attributable to volume effects, and thereby this agreement may suggest that the frozen-in strain has a similar character. For GeS 2, no photo-elastic data seem available, and the analysis cannot be performed. The above assumption concerning the similarity between the photo-elastic and the photo-plastic constants may be reinforced by comparing the observed changes induced by the 6% plastic strain and by the elastic strain normalized with the same magnitude. We see in table 3 that the measured quantities are comparable to each other. This suggests that elastically and plastically deformed As2S 3 glasses exhibit nearly the same behavior in optical properties. Table 3 M e c h a n i c a l l y a n d p h o t o - i n d u c e d c h a n g e s in the o p t i c a l abs o r p t i o n edge A E , the d i c h r o i s m E a = E ( I I ) - E ( ± ) a n d the b i r e f r i n g e n c e n a = n ( II)- n( .L ) in A s 2 S 3. A E is m e a s u r e d w i t h reference to the value in the a n n e a l e d sample, a n d the directional n o t a t i o n s assign that the p r o b e electric-field v e c t o r parallel (II) a n d p e r p e n d i c u l a r ( .1. ) to the m e c h a n i c a l stress or the i n d u c e d light field
Elastic Plastic Photoinduced
Strain(%)
AE(meV)
Ea(meV )
na
- 6 - 6 ?
- 60 - 50 - 50
+ 10 ? - 5
+ 0.01 + 0.009 - 0.002
252
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
It is noted that the anisotropic structures are not noticeable in the birefringence. In part II [20] we see that the squeezed glass is partially oriented, and thus the glasses released from squeezing may h.ave remnants of the anisotropic structures. Here, we may assume that released As2S 3 has layer structures analogous to that included in the crystal, in which the layer plane is defined by the fi and directions [40]. Detailed optical studies [40-43] for crystalline As2S 3 and As2Se 3, which is homoeomorphous to the sulfide, have demonstrated that n(~ II '~) > n(c II ~) > n(c II t'), where c denotes the electric field vector. Accordingly, since n(I[) and n ( ± ) may approximate the interlayer and intralayer dispersions, these results predict that the quasi-stable birefringence n~ is negative, in disagreement with the experimental result. (Further, the observed anisotropy 0.01 in As2S3 glass is much smaller than that, 0.5, in orpiment [40].) Hence, the structural analogy is not acceptable. Otherwise, the speculation may need more refined models. Finally, it may be valuable to discuss from the present context the origin of the optically induced anisotropy effect in chalcogenide glasses [13]. As summarized in table 1, the anisotropies produced by squeezing and by the illumination of linearly polarized light are similar in character. Both can be induced by physical treatments after preparation and are quasi-stable. However, the origins cannot be understood in a unified way. Table 3 also lists the magnitudes of the photoinduced anisotropy,in which the II and ± notations defining E~ and n~ refer to the directions of the electric fields of probed and excited light. For this normalization, we see that the signs of E a and n~ of the photoinduced effect are opposite to those induced mechanically. Thus, if the mechanism of the photoinduced change were the same as those of the strain-induced anisotropies, we must expect an expansion of the sample dimension along the electric field vector of the excitation light. Such a possibility, however, is difficult to assume, since the photoinduced effect is observed in evaporated films attached to substrates. The electric field vector lies in the film plane, so that the substrates suppress the geometrical change.
The photoinduced anisotropy in chalcogenide glasses cannot be attributed to dangling bonds. Selective generation of paramagnetic defects oriented by light illumination has been experimentally demonstrated in SiO 2 glass [14]. However, no paramagnetic defects are created in ms2S 3 which is illuminated at room temperature [1]. Studies on other mechanisms are needed.
4. Summary Optical properties of glassy Se, As2S 3 and GeS 2 subjected to uniaxial compression up to 100 kbar have been studied, with less extensive investigation for orthorhombic S and glassy GeO 2. Characteristics observed in samples under elastic deformations and squeezed states, and those after being released to 1 atm can be summarized as follows. It has been demonstrated that elastically deformed As2S 3 shows photo-elastic birefringence and dichroism, and a monotonic red-shift of the optical absorption edge with pressure. A large part of the changes can be accounted for by volume contraction. Under intense uniaxial compression, the sampies are squeezed, showing several unique properties. First, the red-shifts of the absorption edge are comparable to or more prominent than those induced by hydrostatic compression. Second, the released samples from the squeezing accompany the frozen-in birefringence and some isotropic optical modifications, which can be relaxed by illumination and annealing. The effects induced by illumination and annealing may be a result of local structural changes and volume expansion induced by viscous flow, respectively. The author would like to thank Dr S. Tadano for useful discussions and Mr T. Matsuda for assisting in the elastic dichroism experiment. The work was partially supported by Nippon Sheet Glass Foundation.
References [1] S.R. Elliott, Physics of Amorphous Materials (Longman, 1983, London).
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
[2] V. Ramaswamy, R.H. Stolen, M.D. Divino and W. Pleikel, Appl. Opt. 18 (1979) 4080. [3] V.N. Patel and J.T. Edmond, J. Opt. SOc. Am. 72 (1982) 644. [4] R. Bruckner, J. Non-Cryst. Solids 95&96 (1987) 961. [5] S. Rajagopalan, K.S. Harshavardhan, L.K. Malhotra and K.L. Chopra, J. Non-Cryst. Solids 50 (1982) 29. [6] E. Maruyama, Jpn. J. Appl. Phys. 21 (1982) 213. [7] J. Tauc, Amorphous and Liquid Semiconductors (Plenum, London, 1974) p. 212. [8] P.Y. Yu and M. Cardona, Phys. Status Solidi B47 (1971) 251. [9] R.K. Galkiewicz and J. Tauc, Solid State Commun. 10 (1972) 1261. [10] S. Fukuda, T. Shiosaki and A. Kawabata, Jpn. J. Appl. Phys. 19 (1980) 2075. [11] G. Weiser, U. Dersch and P. Thomas, Philos. Mag. B57 (1988) 721. [12] B. Vanhuyse, P. Van den Keybus and W. Grevendonk, J. Phys. C4 42 (1981) 923. [13] J.M. ~ and M.A. Paesler, J. Non-Cryst. Solids 97&98 (1987) 1235. [14] J.H. Stathis, Phys. Rev. Lett. 58 (1987) 1448. [15] B.A. Weinstein, R. Zallen and M.L. Slade, Phys. Rev. B24 (1981) 4652. [16] S. Minomura, in: Semiconductors and Semimetals 21A (Academic Press, Orlando, FL, 1984) p. 273. [17] G. Parthasarathy and E.S.R. Gopal, Bull. Mater. Sci. 7 (1985) 271. [18] K. Tanaka, in: Disordered Systems and New Materials, ed. M. Borissov (World Scientific, Singapore, 1989) p. 270. [19] K. Tanaka, Jpn. J. Appi. Phys. 28 (1989) L679. [20] K. Tanaka, J. Non-Cryst. Solids, this issue, 254. [21] A. Jayaraman, Rev. Sei. Instr. 57 (1986) 1013. [22] Servofrax Data Sheet: Servofrax Corporation. [23] F.W. Glaze, D.H. Blackburn, J.S. Osmalov, D. Hubbard and M.H. Black, J. Res. Nat. Bur. Stand. 59 (1957) 83.
253
[24] T.N. Claytor and R.J. Sladek, Phys. Rev. B18 (1978) 5842. [25] K. Tanaka, Jpn. J. Appl. Phys. 25 (1986) 779. [26] A.H. Cottrell, The Mechanical Properties of Matter (Wiley, New York, 1964). [27] J.1. Pankove, Optical Processes in Semiconductors (Dover, New York, 1971). [28] T.E. Slykhouse and H.G. Drickamer, J. Phys. Chem. Solids 7 (1958) 275. [29] K. Tanaka, J. Non-Cryst. Solids 97&98 (1987) 391. [30] W. Fuhs, P. Schlotter and J. Stake, Phys. Status Solidi B57 (1973) 587. [31] K. Tanaka, in: Fundamental Physics of Amorphous Semiconductors, ed. F. Yonezawa (Springer, Berlin, 1981) p. 104. [32] N.M. Ravindra, R.A. Weeks and D.L. Kinser, Phys. Rev. B36 (1987) 6132. [33] K. Tanaka, Phys. Rev. B30 (1984) 4549. [34] K. Tanaka, Solid State Commun. 60 (1986) 295. [35] R. Bruckner, J. Non-Cryst. Solids 73 (1985) 421. [36] S.H. Wemple and M. DiDomenico Jr., Phys. Rev. B1 (1970) 193. [37] M. Wakatsuki, K. Ichinose and T. Aoki, Jpn. J. Appl. Phys. 11 (1972) 578. [38] Y. Watanabe, H. Kawazoe and M. Yamane, Phys. Rev. B38 (1988) 5677. [39] J. Javornicky, Photoplasticity (Elsevier, Amsterdam, 1974). [40] R. Zallen and D.F. Blossey, in: Physics and Chemistry of Materials with Layered Structures, ed. E. Mooser (Reidel, Dordrecht, 1976) p. 231. [41] J. Perrin, J. Cazaux and P. Soukiassian, Phys. Status Solidi B62 (1974) 343. [42] H.L. Althaus, G. Weiser and S. Nagel, Phys. Status Solidi B87 (1978) 117. [43] E. Tarnow, A. Antonelli and J.D. Joannopoulos, Phys. Rev. B34 (1986) 8718.
243
STRESS-INDUCED ANISOTROPY IN CHALCOGENIDE GLASSES
I. Optical studies Keiji T A N A K A Department of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo 060, Japan Received 28 July 1989 Revised manuscript received 16 January 1990
The optical properties of amorphous materials subjected to uniaxial compression up to 100 kbar have been studied. As2S3 glass undergoes elastic deformation, this results in photoelastic anisotropy at pressures below 5 kbar. At higher pressure, the material is fractured, but the cracked powders are squeezed into a transparent flake. Further compression induces substantial red-shifts of the optical absorption edge in Se, As2S3 and GeS2. The glassy flakes released from the squeezed states to 1 arm exhibit quasi-stable isotropic and anisotropic properties, which can be relaxed by light illumination and annealing. The mechanisms of these optical changes are discussed.
1. Introduction A m o r p h o u s materials are inherently isotropic, and by contrast crystals show anisotropic properties as evinced by cleavage. It m a y be interesting, therefore, to examine anisotropic a m o r p h o u s materials, since the study m a y fill the gap between crystalline and a m o r p h o u s physics, the latter being still lacking in convincing structural knowledge [1]. I n d u c e d anisotropies m a y a c c o m p a n y oriented atomic structures, which can be utilized to shed light on the origin of the a m o r p h o u s properties governed by r a n d o m l y oriented atomic units. Investigations of the problems of how and what kinds of anisotropies can be induced in non-crystalline solids m a y uncover novel phenomena. In applications, the study m a y lead to the development of new devices such as birefringent optical fibers [2]. U p to now, there has been m u c h work d o n e on anisotropic liquids, i.e. liquid crystals, whereas anisotropic glasses have hardly been examined. Techniques for producing anisotropic amorp h o u s materials m a y be classified into two groups as shown in table 1. The first group includes the preparation procedures of bulk glasses [3], fibers [4] and thin films [5]. A l t h o u g h heterogeneous structures are involved. The multilayer films [6]
currently studied extensively m a y also give rise to anisotropic properties. A m o r p h o u s substances having frozen-in anisotropies can be obtained using these procedures. T e m p o r a r y anisotropies can be induced by applications of stress [7-10], electric [7,11] and magnetic [7,12] fields. W h e n these forces are removed, the materials recover to initial isotropic states. In addition to these unstable anisotropies, chalcogenide and oxide glasses are k n o w n to exhibit quasi-stable optical and electronic anisotropies when illuminated by linearly polarized light [13,14]. The anisotropy, which ap-
Table 1 Methods for producing anisotropic chalcogenide and oxide
glasses Method
Technique cooling in [ temperature ~ gradient
Preparation [ extrusion / oblique deposition [ (multilayer) photoeffect squeezing Treatment elastic deformation electric field magnetic field
0022-3093/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
Property
quasi-stable
temporary
Ref. [3]
[4l [51 [6] [13,14] [19] [7-10] [7,111 [7,12]
244
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
pears to be induced by electric field of light, is stable after cessation of illumination. Anisotropies in chalcogenide and oxide glasses generated by uniaxial compression are investigated in the present work. Extensive studies have been performed for amorphous semiconductors under hydrostatic pressure [15-18], and accordingly we will try to understand the hydrostatic and uniaxial features in a coherent way. Upon applications of intense uniaxial stress, glassy samples exhibit stress-induced squeezing behaviors which accompany frozen-in anisotropies [19]. We will examine the details here, specifically optical properties, and the following paper [20] will deal with structural properties.
A C support
< B
<
/-
~diamond I ~ I
~Ffl
pLe
Fig. 1. A cross-sectional view of a sample compressed between a pair of diamond anvils. Three optical paths A, B and C are plotted by solid lines with arrows.
2. Experimentalprocedures The material studied was As2S 3 glass prepared by conventional melt-quenching procedures [1]. Ingots were polished to cubic shapes with side lengths of 0.1-0.5 ram, and subsequently annealed in argon atmosphere at 180°C for 1 h to release residual strain. Other materials including orthorhombic S, glassy Se, glassy GeS 2, glassy GeO 2 were examined for squeezing characteristics. Uniaxial compression experiments were conducted employing a pair of 0.12 carat diamondanvils [21] with culet faces of 0,8 mm in diameter as shown in fig. 1. The generated pressure was calibrated as follows. When a sample was deformed elastically, the pressure P was evaluated from the fractional change e in sample thickness using P = re,
(1)
where Y was Young's modulus, 162 kbar [22-24]. The change in thickness e was calculated from peak wavelengths of multiple-interference fringes of light reflected at the culet faces (optical path C in fig. 1). The pressure in the squeezed state was determined using the ruby R 1 method [21], the details of which are described in the following section. The optical transmittance of glassy samples and the ruby photoluminescence were measured using a spectral system combined with microscope
optics [25]. For detecting the transmitted light intensity a cooled PbS and a photomultiplier were employed, and for probing anisotropies in transmittance spectra a polaroid plate was placed in front of an incandescent light source. In addition, the optical birefringence of squeezed glasses was inspected using a conventional polarization microscope attached with a Berek's compensator.
3. Results 3.1. Overall feature
It seems helpful to describe first the gross features of a typical compression sequence of polished glassy As2S 3. (A series of color photographs is informative here, and the reader is referred to fig. 1 in ref. [19].) We visualize a cubic sample in the pressure cell at 1 atm. The specimen appears clear yellow in accordance with the optical band-gap energy of 2.4 eV [1]. Upon uniaxial compression up to 5 kbar, the sample color changes to a darker orange shade. Deformation in this pressure range is elastic so that the sample recovers to the initial state when released to 1 atm even after being stored at 5 kbar for 1 day. Under pressures higher than 5-10 kbar, the sample is inevitably fractured with cracking. This proceeds with a decrease in the gap separation between the anvils, and as a
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
consequence the sample becomes fragmented. Here, strain is mostly released through the fragmentation process, and hence the assembly of As2S 3 chips appears as a blurred yellow. Startlingly, an anomalous phenomenon is observed following further compression. If we pressurize the assembly to 20 kbar, the fragments at the culet center coalesce into a transparent orange flake, in which the dimension increases with pressure. At 100 kbar the flake is circular, typically 0.5 mm in diameter and 20 ~tm in thickness. The sample color is black at the center, gradually changing to orange in the outer region, which is surrounded by powdered As2S 3 appearing opaque yellow. It should be noted here that the dimension and the color distribution of the flake are governed by the compressing strength, and are almost independent of time intervals after application of pressure. If we store the sample at 100 kbar for 1 day, the pressure at the central part decreases by about 5 kbar, probably reflecting viscous a n d / o r plastic flow, whereas the appearance of the sample hardly changes. Glassy powders which have been crushed in mortars show the same behavior. We tentatively refer to the phenomenon whereby pulverized samples merge into transparent disks under intense uniaxial compression as 'squeezing' [19]. In paper II [20] it is shown that the mechanism of the squeezing process is ascribed to plastic deformation, differing from diffusion-controlled sintering and hot-pressing processes [26]. If we depressurize the squeezed sample to 1 atm, the color becomes lighter, but the transparency is retained. With a decrease in pressure, some cracks in radial directions appear, which have been argued to be manifestations of concentric pressure distributions at the squeezed states [19]. The released sample shows optically and thermally induced relaxations afterwards. Pressure in squeezed samples was estimated from the R 1 photoluminescence of a ruby chip [21] about 10 Fm in diameter, which was put on the fractured assembly. In the squeezed states, the ruby might be packed in the disk, being located at the sample surface. The R 1 peak of the ~ruby excited by focused light from an argon laser [25] was broader than ___5 .~ in wavelength, indicating non-hydrostatic pressure distributions [21]. How-
10C
.
.
*
i
.
245 .
.
.
.
.
E 50
0
I
i
I
5
|
I
strain (%)
1
I
10
Fig. 2. The red-shift AE of the optical absorption edge in elastically compressed As2S3. 570 strain corresponds to 8 kbar stress.
ever, the generated pressure around the ruby chip could be known within an accuracy of + 10 kbar, unless the ruby was directly stressed by the anvil pair.
3.2. Elastic change When subjected to small uniaxial compression, As2S3 is elastically deformed and the optical absorption edge shifts to lower photon energies. Figure 2 shows the change AE in the position of the optical absorption edge evaluated with the photon energy at (x = 200 cm-1, where a is the absorption coefficient. Probe light is propagated in a direction parallel to the compressive stress (A in fig. 1). In the elastic region, the optical absorption edge shifts in parallel without changing its shape and, thus, the red shift may be a good measure of a decrease in the optical band-gap energy Eg. (This approximation is applied throughout the present work.) The anisotropy of the optical absorption coefficient, i.e. the dichroism, was induced by the uniaxial compression. In order to measure the anisotropy, linearly polarized probe light was propagated perpendicular to the compression direction (B in fig. 1), and the polarization direction was varied. The anisotropy defined as E a = E (11)-
246
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
E ( ± ) increases linearly with strain as shown in fig. 3, where E(II) and E ( ± ) are the absorption edges measured with the light in which the electric field runs parallel and perpendicular to the stress direction. Birefringence n a = n ( I I ) - n ( ± ) also appeared with the magnitude of 0.008 when the strain was 4% (stress was 6 kbar), where n is the refractive index in visible wavelengths. By using these values we obtain the stress birefringence coefficient r , fl = n a//O ,
(2)
of - 0.0013 k b a r - 1, where o is the stress which is assumed negative for compression. The magnitude is quantitatively consistent with the result reported by Galkiewicz and Tauc [9], -0.0009 kbar -1, measured under uniaxial tension. Note that the signs of both E a and n a are positive, in harmony with the Kramers-Kronig relations [27]. These optical anisotropies disappear when the sample is released to 1 atm.
3.3. Squeezing behavior In the squeezed state, a pressure increase redshifts the optical absorption edge with a decrease of the slope of the Urbach tail [1]. However, the
IG
laJ
i
0
i
i
|
2 strain(*/.)
Fig. 3. Stress-induced dichroism E a = E(II) ± E( .L ) in As2S3, where E denotes the position of the absorption edge, measured by linearly polarized light having electric field vectors parallel (11) and perpendicular ( 1 ) to the stress direction.
slope change is not substantial, and we will concentrate on the red shift. In Se and orthorhombic S, the spectral changes induced by the squeezing were nearly the same as those observed upon hydrostatic compression [18,28]. Thus, it may be assumed that for soft materials the two compression modes induce similar changes in fundamental electronic properties. As shown in fig. 4, however, there exist some quantitative differences between hydrostatic and squeezing compressions in A S E S 3 and GeS 2. In s q u e e z e d A s 2 S 3 , the absorption edge red-shifts more substantially at around 30 kbar, and with further increases in pressure the difference is reduced. GeS 2 exhibits a more marked discrepancy. At all pressures the absorption edge under squeezing appears to be more red-shifted by - 0 . 4 eV than the hydrostatic values [18]. The difference may become more noticeable, if the absorption edges are evaluated as a function of the volume change. Note that in fig. 4 the hysteresis of the absorption edge is larger in GeS2, and the squeezed samples show more prominent hysteresis than that in hydrostatically compressed glasses [29]. In Se released from squeezing compressions up to 100 kbar, no hysteresis was observed, as well as the samples freed from hydrostatic compression [29]. (Squeezed Se transformed to the hexagonal Se at 110 kbar, as was demonstrated by Fuhs etal. [20].) The behavior can be attributed to the low glasstransition temperature of about 30 ° C at 1 atm [1], at which thermal relaxation can take place immediately. The characteristics in As2S 3 appear to be intermediate between these two behaviors. Although hysteresis exists, the squeezed and isotropically pressurized glasses show similar features. It may be appropriate here to describe briefly the experimental details for the result shown in fig. 4. The absorption coefficient a is related to the transmittance T under neglection of multiple reflection as T = (1 - R ) 2 e x p ( - a W ) ,
(3)
where R is the reflection coefficient and W is the sample thickness. R was calculated using the Fresnel formula, being given as a function of the
247
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I i
i
i
i
!
i
!",, £. \ 3£ ". ;. \ \ ~" \
2.5
.
.
.
.
.
.
(a)
.
.
.
.
2.5 ~ \
i
i
i
|
i
i
'
'
(b)
i,.
.
i
\
\:'
\
..\ ".\
\
\
~".,.
2.C
\ \
•.
"-" tu2.C
"-.
>
\
IV
\ X
hi
~
\.,> \
\ \
\
1.5
I
0
i
i
i
i
i
50 p r e s s u r e (kbar)
i
i
i
i
i
i
100
0
'
'
'
'
'
'
'1
o'
'
150
pressure (kbar)
Fig. 4. Pressure dependence of the optical absorption edge in (a) As2S3 and (b) GeS2. Solid and dashed lines show the results of squeezed and hydrostatic compressions, and dotted lines show hypothetical routes from 1 atm to squeezed states. Hysteresis effects are shown by lines with arrows, which fix only the starting and released points. In (a), the arrow indicates the hysteresis in the samples released from hydrostatic and squeezed pressures of 100 kbar.
refractive indices of the diamond, 2.4, which was nearly independent of pressure, and of the sample. For the sample indices, the magnitudes may be assumed to be the same as the hydrostatic values [18]. However, the thickness W was difficult to measure. Only the value at the highest pressure could be estimated through measuring the thickness of the released samples, if the expansion along the release was calibrated. The calibration could be done using the pressure-volume data under hydrostatic compression [18]. Thus, the resuits shown in fig. 4 were obtained from many squeezing runs up to different pressures. 3.4. Relaxation and anisotropy in released samples The samples released from squeezing procedures exhibited relaxation behavior, which was enhanced by light illumination and thermal annealing. Figure 5 shows the change of the location
of the absorption edge in As2S 3, which is depressurized from 100 kbar. The sample undergoes the relaxation immediately after the release, and it becomes undetectable after being stored for 10 h at room temperature. However, light illumination of about 20 m W / c m 2 in intensity provided from an ultrahigh-pressure mercury lamp induces a further change, which terminates within 30 rain. A complete recovery to the initial state can be obtained through an annealing treatment for 1 h at 180°C, just below the glass-transition temperature [1]. If the annealed sample is illuminated again by the band-gap light, the so-called reversible photodarkening [31] appears with the red shift 50 meV of the absorption edge. Note that these relaxation characteristics are qualitatively the same as those observed in the samples released from hydrostatic compression [29]. The samples released from the squeezing exhibit quasi-stable birefringence. Figure 6 shows -
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses 1
248
2.4
=
=
"7
2.3 l-
t-
w
!
2.2
0
S
iluminateiluminate
(h)
lb% 3'0 (min) time
gence n a for successive treatments of releasing, illumination and annealing. (Here, the accuracy of n a is + 20%, because the measurements were carried out for cross-sections of cracked fragments.) Figure 6 shows some different characteristics between in As2S 3 and GeS 2. Changes in n W with annealing are opposite. By contrast, it is a comm o n feature for these materials that the anisotropy na disappears only with annealing. G e O 2 glass showed a similar relaxation of n a = 0.002, whereas its absorption edge could not be measured because of the high energy of 6 eV [32]. The following discussion therefore will be focused on the chalcogenide glasses.
3'0 g0 (rain)
Fig. 5. Relaxation and photoinduced changes in the position of the optical absorption edge E in As2S3 released from 100 kbar squeeze.
variations in A s 2 S 3 and GeS 2 absorption-edge position E, the optical path length n W measured along the compression direction, and the birefrin-
4. Discussion
4.1. Elastic red-shift and photo-elastic effect The result shown in fig. 2 obtained in the elastic region indicates that d E g / d P u = - 6 . 5 m e V / k b a r , in contrast to the coefficient d Eg/d Ph ,
i
i
,
3.(3 25
(a)/
A
>
2£
60.-.
I.tJ
~-/o.,. /o 36~=.
ta1.5 1.0
(b)F~
2.5 2.0
50 ~
34
i ,° , i°I g "U
"U
~
c"
1.5
~0
o
~
I
I
,
N
~
"0
•
m •
= ~
"" ¢ll ._c
E
--r
]0.02c~ b--J0 --
rll •¢ - .
~-
.--
Fig. 6. Variations of the optical absorption edge E, the optical path length n W and the birefringence na in (a) A%S 3 and (b) GeS 2, which are squeezed to 100 kbar, released, illuminated and annealed.
K. Tanaka / Stress-inducedanisotropy in chalcogenideglasses I
249
=-12 m e V / k b a r evaluated at a low-pressure region [33], where the subscripts u and h denote uniaxial and hydrostatic. We see a difference in the magnitudes of a factor two. In uniaxial compression experiments, however, the sample expands in directions normal to the stress, and naturally hydrostatic compression induces an isotropic contraction. Thus, a comparison of volume coefficients may be more appropriate. Using some elastic equations [26], we obtain
The intrinsic birefringence in homogeneous media may be treated in two ways, using ideas based on bond models assuming polarizable units [8] and on band models. In the latter treatments, some workers [9,10] have followed the single oscillator model proposed by Wemple and DiDomenico [36], in which the refractive-index dispersion n(hto) is approximated as
(4)
where hto is the photon energy, and F and E 0 are constants denoting oscillator strength and energy. In typical chalcogenide glasses such as ASES3, it has been demonstrated that the changes in F are comparatively larger than those in E 0 [9,10,18]. This means that in chalcogenide glasses the photoelasticity is governed by volume changes and hence Pll 2 P12 [9], where p is the photoelastic constant. Since the stress coefficient fl is connected with the photoelastic and the elastic constant c as [9]
Vd E J d V . = 3K d E , / d Pu,
and V d E g / d V h = K d E g / d P h,
(5)
where K is the bulk modulus. The volume coefficients are then calculated as V d E g / d V , = (2.5 + 0.3) eV and V d E g / d V h = (1.5 _+ 0.3) eV, in which the uncertainties arise mainly from variations 103-139 kbar of the bulk modulus [22-24,34]. In this evaluation, the uniaxial coefficient is larger than the hydrostatic value. Several possibilities are evoked for the difference in the coefficients, and we cannot assert at present whether it is intrinsic or extrinsic to the material. An extrinsic reason may be non-ideal pressure distribution in the compression device. Since frictional forces exist at the boundaries between the sample and the diamond anvils, the generated pressure is not purely uniaxial. Hence the above calculation assuming uniaxial elastic deformation should be modified. In addition, the sample surface could not be polished completely parallel. A geometrical calculation shows that a fractional deviation of 1% in thickness can cause an overestimation of 30% in the uniaxial pressure value. As for intrinsic origins, structural modifications such as dangling bonds plausibly generated by the shear component in uniaxial pressure may have an influence on the optical properties. The photoelasticity originates from homogeneous or inhomogeneous microscopic structures. When a material has heterogeneous structures consisting of optically isotropic parts birefringence may appear [35]. Nonetheless, in most samples of chalcogenide bulk glasses, no traces of phase separation are detected, and thus the photoelasticity originates from homogeneous structures.
n ( h t o ) 2 = 1 + F / [ E 2 - (hw)2] ,
fl
=
-n3(pl, -Pa2)/(c,1 - q2),
(6)
(7)
the induced anisotropy n a defined by eq. (2) is relatively small. 4.2. Squeezing-induced red-shift
Under some assumptions, which may be satisfied here, the pressure distribution in thin squeezed flakes is given as [26,37] P ( r ) o: e x p [ 2 T ( a - r ) / W ] ,
(8)
where r is the shear strength of the disk sample with a radius a and r is the radial distance. We may assume here that the pressure has qualities between hydrostatic and uniaxial features, depending on some factors, e.g., r and r. For softer materials the pressure appears to be more isotropic. It seems reasonable therefore that the hydrostatic and squeezed results are almost the same for Se and S. For As2S 3 and GeS 2, shear components included in the squeezing forces can induce three effects, which are mostly absent from hydrostatic compression. First, it is plausible that the shear forces are responsible for breaking the covalent bonds, effectively producing dangling bonds. As a result, the absorption edge can be red-shifted more
K Tanaka / Stress-inducedanisotropyin chalcogenideglassesI
250
Table 2 Fractional changes in the optical path length A(nW)/nW, the refractive index An/n and the thickness AW/W in As2S3 and Ge,gz induced by illumination and annealing. All the quantities are expressed in % Glass
As2S3 GeS2
Change Illumination
ACnW)/(nW) -55:1 -55:2
Annealing
An/n -3 -5
AW/W -2 0
remarkably by the squeezing procedure than the hydrostatic compression. The other possibilities are related to glassy structures. It has been demonstrated that chalcogenide glasses are composed of low-dimensional molecular clusters held together with weak intermolecular forces mostly consisting of van der Waals type [1]. Therefore, it can be speculated that these molecules are oriented when the glasses are subjected to the squeezing compression. For instance, layer molecules possibly contained in A s 2 S 3 and GeS: may tend to be stacked parallel to the sample surfaces, as is suggested in part II [20]. In that case, the optical spectra which were measured by light having electric polarization parallel to the sample surfaces are governed by intralayer properties. This anisotropic effect may result in more dramatic red-shifts in squeezed glasses. As for the last possibility, the stacking of the layer molecules may become irregular, since the assembly is sheared. The disordered stacking could also give rise to the enhanced red-shifts [38]. However, at ultra-high pressures the atomic coordination number may be increased by the hydrostatic component [33], and thus the difference between squeezed and hydrostatic compression will be reduced. In short, the shear and hydrostatic forces can be considered to cause the difference and the similarity between the optical properties in the two types of compressions.
4.3. Origin of the quasi-stable birefringence A key point in the examination of the relaxation behaviors shown in fig. 6 may lie in resolving the changes in n 14/ into modifications in the refractive index n and the sample thickness W. The
aCnW)/CnW) +55:1 -105:1
an /n -1 -16
AW/W +6 +6
analysis can be performed using an empirical relationship obtained from hydrostatic pressure experiments. Figure 7, which is replotted from the results shown in ref. [18], gives the coefficient ~, in the Moss rule [27]
nVEg = constant,
(9)
to be 2 for As2S 3 and 1.2 for GeS 2. Under the approximation E g = E (fig. 6), the fractional change A n / n induced by illumination and annealing can be evaluated. Since
A(nW)/(nW)
= An/n + AW/W,
(10)
the changes in n W shown in fig. 6 gives A W l W. These results are summarized in table 2. Table 2 shows that the photoinduced change is mostly electronic. That is, the fact A (n W ) / n W = A n / n suggests that A W / W can be neglected here.
h
,,,,
3
3
'-
Se
''''
"'-
'i''
Eg(eV) Fig. 7. Relationships between the refractive index n and the optical band-gap energy Eg in Se, As2S3 and GeS2 subjected to hydrostatic compression. Open circles indicate the states at 1 atm, with increasing pressure by arrows. Dotted curves axe the best fits of the Moss rule (see the text).
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
Mechanisms of the photoinduced changes can be related to local structural changes. It has been argued that local stresses contained in chalcogenide glasses can be released by illumination [29,33]. It is plausible that such relaxations in localized structures have an effect on the absorption-edge position and the refractive index. Since photoinduced effects were not detected in the birefringence, it is assumed that the defects have no dipole moments a n d / o r the defects are not oriented. The defect density is estimated to be comparable to that for the photodarkening, 1020 cm -1 [25,31], because the shifts of the absorption edge induced by the two photoinduced changes are similar. The modifications induced by annealing seem to be more complicated. As shown in table 2, values of A(nW)/(nW) and An/n are substantially different for this case, and we must assume a thickness expansion of AW/W= 6%. (The same magnitudes for the two glasses may be coincidental.) The geometrical change is dominant in As2S 3, but in GeS 2 the electronic change still governs the decrease in the optical path length. This thickness expansion can be considered as a relaxation process, since annealing at the glasstransition temperature brings glasses to the lowest energy state [1]. The annealed sample must have identical properties to the unloaded glass in all respects. In contrast, as demonstrated above, the thickness of the released and illuminated samples are nearly the same, and these are 6% thinner than the annealed flake. Therefore, it can be assumed that the released and the illuminated samples are plastically strained. The annealing effect can be understood as resulting from structural relaxations extending over wider regions. The relaxation is induced by thermal viscous flow [1] which accompanies the volume relaxation. For GeS 2 the annealing induces relatively larger effects, because the illumination cannot relax the defective strained structures effectively. The disappearences of the isotropic optical changes and the birefringence can be connected with the volume change as discussed below. The thermally induced strain release can accompany the blue-shift of the absorption edge. Taking the results [18] obtained under hydrostatic
251
pressure into account, we can estimate that the uniaxial volume expansion of 6%, which may be regarded as equivalent to the isotropic linear expansion of 2%, gives a blue shift of 0.1 eV in As2S 3 and 50 meV in GeS 2. The magnitude in As2S 3 is quantitatively comparable with the experimental result shown in fig. 6(a), but for GeS2 the shift is a tenth of the observations. The residual shift in GeS 2 may be ascribed to electronic effects. The frozen-in strain of 6% is also considered to be a cause of the quasi-stable birefringence. Under the assumption that the strain-birefringent coefficient, or the photo-plastic constant [39], is the same as the photo-elastic constant, the 6% strain gives n a = +0.014 for As2S 3 through the photoelastic equation (2). This value is consistent with the experimental result shown in fig. 6(a), i.e. + 0.01, both in sign and magnitude. As mentioned in section 3.2., the elastic effect is mostly attributable to volume effects, and thereby this agreement may suggest that the frozen-in strain has a similar character. For GeS 2, no photo-elastic data seem available, and the analysis cannot be performed. The above assumption concerning the similarity between the photo-elastic and the photo-plastic constants may be reinforced by comparing the observed changes induced by the 6% plastic strain and by the elastic strain normalized with the same magnitude. We see in table 3 that the measured quantities are comparable to each other. This suggests that elastically and plastically deformed As2S 3 glasses exhibit nearly the same behavior in optical properties. Table 3 M e c h a n i c a l l y a n d p h o t o - i n d u c e d c h a n g e s in the o p t i c a l abs o r p t i o n edge A E , the d i c h r o i s m E a = E ( I I ) - E ( ± ) a n d the b i r e f r i n g e n c e n a = n ( II)- n( .L ) in A s 2 S 3. A E is m e a s u r e d w i t h reference to the value in the a n n e a l e d sample, a n d the directional n o t a t i o n s assign that the p r o b e electric-field v e c t o r parallel (II) a n d p e r p e n d i c u l a r ( .1. ) to the m e c h a n i c a l stress or the i n d u c e d light field
Elastic Plastic Photoinduced
Strain(%)
AE(meV)
Ea(meV )
na
- 6 - 6 ?
- 60 - 50 - 50
+ 10 ? - 5
+ 0.01 + 0.009 - 0.002
252
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
It is noted that the anisotropic structures are not noticeable in the birefringence. In part II [20] we see that the squeezed glass is partially oriented, and thus the glasses released from squeezing may h.ave remnants of the anisotropic structures. Here, we may assume that released As2S 3 has layer structures analogous to that included in the crystal, in which the layer plane is defined by the fi and directions [40]. Detailed optical studies [40-43] for crystalline As2S 3 and As2Se 3, which is homoeomorphous to the sulfide, have demonstrated that n(~ II '~) > n(c II ~) > n(c II t'), where c denotes the electric field vector. Accordingly, since n(I[) and n ( ± ) may approximate the interlayer and intralayer dispersions, these results predict that the quasi-stable birefringence n~ is negative, in disagreement with the experimental result. (Further, the observed anisotropy 0.01 in As2S3 glass is much smaller than that, 0.5, in orpiment [40].) Hence, the structural analogy is not acceptable. Otherwise, the speculation may need more refined models. Finally, it may be valuable to discuss from the present context the origin of the optically induced anisotropy effect in chalcogenide glasses [13]. As summarized in table 1, the anisotropies produced by squeezing and by the illumination of linearly polarized light are similar in character. Both can be induced by physical treatments after preparation and are quasi-stable. However, the origins cannot be understood in a unified way. Table 3 also lists the magnitudes of the photoinduced anisotropy,in which the II and ± notations defining E~ and n~ refer to the directions of the electric fields of probed and excited light. For this normalization, we see that the signs of E a and n~ of the photoinduced effect are opposite to those induced mechanically. Thus, if the mechanism of the photoinduced change were the same as those of the strain-induced anisotropies, we must expect an expansion of the sample dimension along the electric field vector of the excitation light. Such a possibility, however, is difficult to assume, since the photoinduced effect is observed in evaporated films attached to substrates. The electric field vector lies in the film plane, so that the substrates suppress the geometrical change.
The photoinduced anisotropy in chalcogenide glasses cannot be attributed to dangling bonds. Selective generation of paramagnetic defects oriented by light illumination has been experimentally demonstrated in SiO 2 glass [14]. However, no paramagnetic defects are created in ms2S 3 which is illuminated at room temperature [1]. Studies on other mechanisms are needed.
4. Summary Optical properties of glassy Se, As2S 3 and GeS 2 subjected to uniaxial compression up to 100 kbar have been studied, with less extensive investigation for orthorhombic S and glassy GeO 2. Characteristics observed in samples under elastic deformations and squeezed states, and those after being released to 1 atm can be summarized as follows. It has been demonstrated that elastically deformed As2S 3 shows photo-elastic birefringence and dichroism, and a monotonic red-shift of the optical absorption edge with pressure. A large part of the changes can be accounted for by volume contraction. Under intense uniaxial compression, the sampies are squeezed, showing several unique properties. First, the red-shifts of the absorption edge are comparable to or more prominent than those induced by hydrostatic compression. Second, the released samples from the squeezing accompany the frozen-in birefringence and some isotropic optical modifications, which can be relaxed by illumination and annealing. The effects induced by illumination and annealing may be a result of local structural changes and volume expansion induced by viscous flow, respectively. The author would like to thank Dr S. Tadano for useful discussions and Mr T. Matsuda for assisting in the elastic dichroism experiment. The work was partially supported by Nippon Sheet Glass Foundation.
References [1] S.R. Elliott, Physics of Amorphous Materials (Longman, 1983, London).
K. Tanaka / Stress-induced anisotropy in chalcogenide glasses I
[2] V. Ramaswamy, R.H. Stolen, M.D. Divino and W. Pleikel, Appl. Opt. 18 (1979) 4080. [3] V.N. Patel and J.T. Edmond, J. Opt. SOc. Am. 72 (1982) 644. [4] R. Bruckner, J. Non-Cryst. Solids 95&96 (1987) 961. [5] S. Rajagopalan, K.S. Harshavardhan, L.K. Malhotra and K.L. Chopra, J. Non-Cryst. Solids 50 (1982) 29. [6] E. Maruyama, Jpn. J. Appl. Phys. 21 (1982) 213. [7] J. Tauc, Amorphous and Liquid Semiconductors (Plenum, London, 1974) p. 212. [8] P.Y. Yu and M. Cardona, Phys. Status Solidi B47 (1971) 251. [9] R.K. Galkiewicz and J. Tauc, Solid State Commun. 10 (1972) 1261. [10] S. Fukuda, T. Shiosaki and A. Kawabata, Jpn. J. Appl. Phys. 19 (1980) 2075. [11] G. Weiser, U. Dersch and P. Thomas, Philos. Mag. B57 (1988) 721. [12] B. Vanhuyse, P. Van den Keybus and W. Grevendonk, J. Phys. C4 42 (1981) 923. [13] J.M. ~ and M.A. Paesler, J. Non-Cryst. Solids 97&98 (1987) 1235. [14] J.H. Stathis, Phys. Rev. Lett. 58 (1987) 1448. [15] B.A. Weinstein, R. Zallen and M.L. Slade, Phys. Rev. B24 (1981) 4652. [16] S. Minomura, in: Semiconductors and Semimetals 21A (Academic Press, Orlando, FL, 1984) p. 273. [17] G. Parthasarathy and E.S.R. Gopal, Bull. Mater. Sci. 7 (1985) 271. [18] K. Tanaka, in: Disordered Systems and New Materials, ed. M. Borissov (World Scientific, Singapore, 1989) p. 270. [19] K. Tanaka, Jpn. J. Appi. Phys. 28 (1989) L679. [20] K. Tanaka, J. Non-Cryst. Solids, this issue, 254. [21] A. Jayaraman, Rev. Sei. Instr. 57 (1986) 1013. [22] Servofrax Data Sheet: Servofrax Corporation. [23] F.W. Glaze, D.H. Blackburn, J.S. Osmalov, D. Hubbard and M.H. Black, J. Res. Nat. Bur. Stand. 59 (1957) 83.
253
[24] T.N. Claytor and R.J. Sladek, Phys. Rev. B18 (1978) 5842. [25] K. Tanaka, Jpn. J. Appl. Phys. 25 (1986) 779. [26] A.H. Cottrell, The Mechanical Properties of Matter (Wiley, New York, 1964). [27] J.1. Pankove, Optical Processes in Semiconductors (Dover, New York, 1971). [28] T.E. Slykhouse and H.G. Drickamer, J. Phys. Chem. Solids 7 (1958) 275. [29] K. Tanaka, J. Non-Cryst. Solids 97&98 (1987) 391. [30] W. Fuhs, P. Schlotter and J. Stake, Phys. Status Solidi B57 (1973) 587. [31] K. Tanaka, in: Fundamental Physics of Amorphous Semiconductors, ed. F. Yonezawa (Springer, Berlin, 1981) p. 104. [32] N.M. Ravindra, R.A. Weeks and D.L. Kinser, Phys. Rev. B36 (1987) 6132. [33] K. Tanaka, Phys. Rev. B30 (1984) 4549. [34] K. Tanaka, Solid State Commun. 60 (1986) 295. [35] R. Bruckner, J. Non-Cryst. Solids 73 (1985) 421. [36] S.H. Wemple and M. DiDomenico Jr., Phys. Rev. B1 (1970) 193. [37] M. Wakatsuki, K. Ichinose and T. Aoki, Jpn. J. Appl. Phys. 11 (1972) 578. [38] Y. Watanabe, H. Kawazoe and M. Yamane, Phys. Rev. B38 (1988) 5677. [39] J. Javornicky, Photoplasticity (Elsevier, Amsterdam, 1974). [40] R. Zallen and D.F. Blossey, in: Physics and Chemistry of Materials with Layered Structures, ed. E. Mooser (Reidel, Dordrecht, 1976) p. 231. [41] J. Perrin, J. Cazaux and P. Soukiassian, Phys. Status Solidi B62 (1974) 343. [42] H.L. Althaus, G. Weiser and S. Nagel, Phys. Status Solidi B87 (1978) 117. [43] E. Tarnow, A. Antonelli and J.D. Joannopoulos, Phys. Rev. B34 (1986) 8718.