Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.issp.ac.ru/lhpp/PapersAntonov/140.pdf Äàòà èçìåíåíèÿ: Fri Feb 10 18:35:21 2012 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 06:33:38 2012 Êîäèðîâêà:

INS

TITUTE OF

P

HYSICS

P

UBLISHING

J

OURNAL OF

P

HYSICS:

CONDENS

ED

MATTER

J. Phys.: Condens. Matter 14 (2002) 11227­11232

PII: S0953-8984(02)39343-3

Transport properties of the pressure-induced amorphous semiconductor state of Al32 Ge68
V E Antonov , O I Barkalov , A F Gurov , A I Harkunov and A I Kolyubakin
Institute of Solid State Physics, RAS, 142432 Chernogolovka, Moscow District, Russia

Received 1 June 2002 Published 25 October 2002 Online at stacks.iop.org/JPhysCM/14/11227 Abstract The temperature dependences of the dc conductivity and thermopower of the bulk amorphous alloy Al32 Ge68 were investigated at 6­420 K and at 80­ 370 K, respectively. The samples were prepared by solid-state amorphization of a quenched crystalline high-pressure phase while heating from 77 to 400 K at ambient pressure. Amorphous Al32 Ge68 was found to be a p-type semiconductor with an unusual combination of transport properties. The behaviour of the properties was described semi-quantitatively in terms of a modified Mott­Davis model assuming that theFermi level lies inside the valence band tail.

1. Introduction Spontaneous amorphization of quenched high-pressure phases during their heating at ambient pressure allows production of bulk homogeneous amorphous samples. At the present time, the electric properties have been studied for only two amorphous (a-) semiconductors prepared in this way, a-Zn41 Sb59 [1] and a-GaSb [2]. The a-Zn41 Sb59 alloy was found to be a typical amorphous semiconductor with an activated behaviour of the electrical conductivity (T ) and a linear increase in the thermopower S with increasing 1/ T . By contrast, the a-GaSb alloy showed a combination of (T ) and S (T ) dependences never observed in a-semiconductors and inconsistent with the conventional Mott­Davis model [3]. The present paper reports on the conductivity and thermopower of the bulk amorphous semiconductor Al32 Ge68 measured over wide temperature ranges. The samples were prepared by amorphization of a quenched crystalline high-pressure phase. The structure of the amorphous a-Al32 Ge68 phase was studied by neutron diffraction [4], transmission electron microscopy and x-ray diffraction [5]. 2. Experimental details At ambient pressure, the Al­Ge system has a eutectic at 424 C and about 30 at.% Ge [6]. The components form no intermediate equilibrium phases. At a pressure of 10 GPa, a new
0953-8984/02/4411227+06$30.00 © 2002 IOP Publishing Ltd Printed in the UK 11227


11228

VE Antonov et al

0 0 lg ( , cm )

5

10

15

20

-1

-2
2

-1

-4
2

1

-6 0

1

50

100

150

200
-1

1000/T, K

Figure 1. Temperature dependences of the dc conductivity for two samples of a-Al32 Ge68 drawn with two different T -scales. The dashed curves represent the sums of 1 ( T ) from equation (1) and 2 ( T ) from equation (3) with the corresponding fitting coefficients. The solid curves show the sums of 1 ( T ) + 2 ( T ) + 3 ( T ),where 3 ( T ) is given by equation (5).

crystalline metallic -phase with a simple hexagonal structure is formed within a narrow concentration range around 68 at.% Ge [7]. Pellets of -phase were obtained in a metastable state at ambient pressure by cooling to liquid nitrogen temperature at high pressure. The recovered pellets were transformed to the amorphous state by heating to 130 C [5]. The samples, 1 â 1 â 5mm3 in size, were cut out of different a-pellets. The dc conductivity, ,and the thermoelectric power, S ,were measured at temperatures from 6 to 420 K and from 80 to 370 K, respectively. 3. Results and discussion Representative temperature dependences of and S for two a-Al32 Ge68 samples are shown in figures 1 and 2. As seen from figure 1, the (T ) curves are of an approximately activated character at T > 150 K and exhibit rather large activation energies E act exceeding 0.1 eV. At lower temperatures, E act (T ) gradually decreases and at T < 40 K, the (T ) dependences obey well the formula 1 = B1 T -1/2 exp[-(T0 / T )1/4 ] typical of variable-range hopping conductivity [3]. The fitting parameters are B1 = 0.0029 and 0.054 -1 cm-1 K1/2 and T0 = 38 000 and 32 000 K for samples 1 and 2, respectively. As seen from figure 2, the thermopower is positive, which points to the p-type conductivity of a-Al32 Ge68 , which is characteristic of most amorphous semiconductors. However, the S (T ) dependences look rather unusual. At 300 > T > 150 K, S decreases approximately linearly with increasing 1/ T , Se/ k 5­0.05 [eV]/ kT , while at T < 150 K the dependence becomes much less steep and S remains positive and small, Se/ k 0.4 or less. According to the conventional Mott­Davis model, the Fermi level E F in amorphous semiconductors is pinned in the mobility gap at a relatively narrow peak of the density of states N ( E ) for charge carriers, usually near the middle of the gap; see figure 3(a). The low-temperature transport properties of amorphous semiconductors can be described in terms of variable-range hopping conductivity due to the states near the Fermi level. This


Transport properties of the pressure-induced amorphous semiconductor state of Al32 Ge68
400 250 200 150 125 100

11229

T, K

3

2 (e /k ) S

2 1

1
1

0

2

2

4

6

8

10

12
-1

1000/T, K

Figure 2. Temperature dependences of the thermopower S for the same two samples of a-Al32 Ge68 as in figure 1. The solid curve represents S ( T ) from equation (6).

Figure 3. Schematic density of states diagrams for amorphous semiconductors: (a) the conventional Mott­Davis model, (b) the modified Mott­Davis model with a narrow band positioned inside the valence band tail. E F is the Fermi energy; E a is the valence band tail edge; E v and E c are the mobility edges for the valence and the conduction band.

mechanism gives a small value of thermoelectric power | S1 e/ k | < 1 and usually leads to Mott's equation for conductivity [3, 8]: 1 = B1 T
-1/2

exp[-(T0 / T )

1/4

].

(1)

The behaviour of the experimental (T ) is described well with equation (1) at T < 40 K and their Se/ k values already fall below 1 at T < 150 K (figure 2). One can therefore conclude that the transport properties of a-Al32 Ge68 at T < 40 K are mainly determined by thevariable-range hopping mechanism.


11230

VE Antonov et al

In the framework of the Mott­Davis model, the transport properties of a-semiconductors at high temperatures are mostly due to hopping conductivity of carriers thermally excited into the band tails. The tails originate from the absence of long-range order in amorphous substances and are assumed not to overlap with the Fermi peak; see figure 3(a). The basic parameter of the model is E = E F - E a ,where E a is the tail edge energy. In p-type semiconductors this is the valence band tail and therefore E > 0. The density of states in the valence band tail can be approximated as N ( E ) ( E a - E )n [3, 8] which leads to conductivity of an almost activated type: T n exp[-( E + W )/ kT ], where W is the activation energy for hopping mobility in the band tail. approximation [3, 8], Se/ k E / kT + n +1. In the same

The thermopower is therefore non-degenerate, Se/ k > 1, and should increase with increasing 1/ T . As seen from figures 1 and 2, at T > 160 K a-Al32 Ge68 demonstrates an approximately activated character of conductivity and also Se/ k > 1. However, the S -value of a-Al32 Ge68 decreases steeply with 1/ T which is inconsistent with the predictions of the Mott­Davis model for conduction in band tails. At the same time, there must be the conduction in band tails as any mechanism of conduction in localized states near the Fermi energy gives Se/ k < 1 and 0.1 eV [3, 8]. small values of E act (T ) Anomalous behaviour of and S at high T similar to that found for a-Al32 Ge68 was observed for a-GaSb semiconductor [2]. The effects were explained assuming E < 0for the p-type amorphous materials. Negative E suggests that the Fermi level is positioned inside the tail of the valence band, as schematically shown in figure 3(b). The transport properties of p-type a-semiconductors are governed [8] by the holes located near the maximum of the N ( E ) f ( E )[1- f ( E )]function, where f ( E ) is the Fermi­Dirac function. At high temperatures f ( E )[1 - f ( E )] exp[( E - E F )/ kT ], and with the density of states N ( E ) ( E a - E )n in thevalence band tail [3, 8] the final product ( E a - E )n exp[( E - E F )/ kT ]has a maximum at E m = E a - nk T , (2) inside the band tail. The conventional model with E F > E a (figure 3(a)) imposes no additional limitations on the temperature region where equation (2) is valid. With E F < E a (figure 3(b)), this equation is true only in the non-degenerate case when ( E F - E m )/kT > 1, that is, at sufficiently high temperatures T > ( E a - E F )/(n - 1)k . According to[3, 8], eµkT N ( E m ) exp[( E m - E F )/kT ]and Se/ k ( E F - E m )/kT , where the mobility µ has a thermally activated character, µ T -1 exp(-W /kT ). Substituting E m from equation (2), one gets Se/ k ( E F - E a )/ kT + n and T n exp[-( E + W )/kT ]. More rigorous evaluation [8] gives Se/ k = E / kT + n +1. At high T (typically, at T > 100 K), E as well as the mobility gap E g usually vary approximately linearly with temperature: E (T )/ E 0 E g (T )/ E 0g 1 - T ,where E 0 and E 0g refer to T = 0 K [8]. Correspondingly, (T ) and S (T ) can be written as 2 AT n exp[-( E 0 + W )/ kT ], S2 e/ k E 0 / kT + n +1 - E0/ k . (3) (4)

The expressions obtained are formally identical to those of the standard Mott­Davis model, but they nevertheless differsignificantly in two aspects: (i) E is negative and (ii) the expressions are valid only at high T > | E |/(n - 1)k .


Transport properties of the pressure-induced amorphous semiconductor state of Al32 Ge68

11231

Equations (3) and (4) allow an estimation of the values of E 0 and n for a-Al32 Ge68 . A linear approximation of the S (1/ T ) dependences at T > 130 K (figure 2) yields C 5.0and E 0 -0.05 eV. Taking a value of = 10-4 K-1 typical of a-semiconductors [8], one gets E 0 / k < 0.1and, correspondingly, n C - 1 4. At T > 190 K, the (T ) dependences for samples 1 and 2 are well described by equation (3) with n = 4, A = 1.03 â 10-9 and 0.93 â 10-9 -1 cm-1 K-4 and with E 0 + W = 0.097 and 0.087 eV. With E 0 = -0.05 eV this gives W 0.14­0.15 eV for the activation energy of mobility in the band tail of a-Al32 Ge68 . With the values of E 0 and n thus determined, the condition T > ( E a - E F )/(n - 1)k of applicability of non-degenerate Boltzmann statistics used to obtain equation (2) for E m is valid at T > 200 K. All calculations above are therefore self-consistent in this temperature range. It is worth mentioning that the transport properties of a-semiconductors at high T will also be affected by conduction due to holes excited into the extended states below the mobility edge E v . One could suspect that thedeviation of the S (T -1 ) dependences for a-Al32 Ge68 from the straight line observed at T > 300 K (figure 2) might be due to the growing contribution from this very conduction mechanism. The dashed curves in figure 1 show the sum of 1 (T ) and 2 (T ) given by equations (1) and (3), respectively. These curves fit the experimental points at T > 150 K and T < 40 K. However, at 40 < T < 150 K the calculated curves differ significantly from the experimental ones. The difference might be due to the contribution from the third conduction mechanism: constant-range hopping conduction in localized states near the Fermi energy. In fact, the variable-range hopping regime dominating at low T should change to the constant-range regime with increasing T because the hopping distance will reach its minimum possible value when the carriers jump between the nearest-neighbour sites [3]. Constant-range hopping results for S < k /e and given by 3 B3 exp(-w3 / kT ), (5) where w3 is the energy of the order of the half-width of the peak at the Fermi energy [3]. In the case of a-Al32 Ge68 this contribution seems to be significant over a large temperature interval, which allows a rather reliable evaluation of the fitting parameters B3 = 1.1 â 10-4 and 8 â 10-4 -1 cm-1 for samples 1 and 2, respectively, and w3 0.02 eV for both samples. For the total value of the thermopower we therefore have S = ( S1 1 + S2 2 + S3 3 )/ where S1 e/ k S3 e/ k 0.2and S2 e/ k = 4. Conclusions Our results demonstrate that amorphous Al32 Ge68 is a p-type semiconductor showing three different conductivity mechanisms in different temperature ranges. At T < 40 K, the dominating mechanism is variable-range hopping conduction in localized states near the Fermi energy. At 40 < T < 150 K, constant-range hopping conduction in localized states near the Fermi energy significantly contributes to the transport properties. At T > 150 K, these properties are mainly governed by conduction in the valence band tail. In contrast to all other amorphous semiconductors except a-GaSb [2], amorphous Al32 Ge68 shows a combination of the (T ) and S (T ) dependences that cannot be explained in the framework of the conventional Mott­Davis model and requires the assumption that the Fermi energy is less than the edge energy of the valence band tail (see figure 3(b)). The Mott­Davis model changed in this way E 0 / kT + n +1. (6)


11232

VE Antonov et al
68

yields a self-consistent description of the transport properties of a-Al32 Ge temperature interval studied. Acknowledgments

over the entire

This work was supported by grant Nos 99-02-17007 and 01-02-06184 from the Russian Foundation for Basic Research. One of the authors(VEA) thanks the Organizing Committee of AIRAPT-18 for financial support for attending the conference. References
[1] [2] [3] [4] [5] [6] [7] [8] Antonov V E et al 1994 J. Non-Cryst. Solids 176 58 Antonov V E et al 1996 Phys. Status Solidi b 198 497 Mott N F and Davis E A 1979 Electron Process in Non-Crystalline Materials (Oxford: Clarendon) Kolesnikov A I et al 1999 Phys. Rev. B 60 12 681 Barkalov O I et al 1996 J. Non-Cryst. Solids 202 266 Hansen M 1958 Constitution of Binary Alloys (New York: McGraw-Hill) Ponyatovsky E G and Barkalov O I 1992 Mater. Sci. Rep. 8 147 Nagels P 1985 Amorphous Semiconductors (Springer Topics in Applied Physics) vol 37, ed M H Brodsky (New York: Springer)