High pressure superconductivity of silicon

Physica 135B (1985) 235-238 North-Holland, Amsterdam

HIGH PRESSURE SUPERCONDUCTIVITY OF SILICON

J.M. MIGNOT*, G. CHOUTEAU** and G. MARTINEZ* *Centre de Recherches sur les Tr~s Basses Tempdratures, CNRS, BP 166 X, 38042 Grenoble Cedex, France ~Service National des Champs Intenses, CNRS, BP 166 X, 38042 Grenoble Cedex, France

We report detailed investigations of the superconducting properties of silicon in its high-pressure fl-Sn and primitive hexagonal (ph) phases. Resistivity measurements have been performed on two single crystals of p-type silicon (.-~-1016cm -3, p(300) = 0.5 ~ cm) using an improved Bridgman-type device, with sintered-diamond anvils. In both phases, silicon is superconducting. In the /3-Sn modification (Si II), we find Tc = 6.3 K with a very small value of dTJdP, in good agreement with earlier results. In the hexagonal phase (Si V), To goes through a maximum at 8.2 K near the II/V phase boundary, then steadily decreases down to 3.6 K at 25 GPa. Comparison is made to the calculations of Chang et al. The theory correctly predicts the decrease of T c in the ph phase. A reasonable agreement is also found between the calculated superconducting parameters and those deduced from the experimental Tc's.

1. Introduction

When subjected to high pressures of the order of 10 GPa (100 kbar), silicon undergoes a structural transition from the usual diamond-type semiconducting (sc) phase to a new tetragonal metallic one [1, 2]. The latter structure, which corresponds to the so-called "/3-Sn" modification of tin, was also reported to occur in germanium at similar pressures, pointing to an interesting isomorphy among the elements of the 4th group in the periodic table [2]. The analogy was extended to the superconducting properties of these elements by the pioneering work of Wittig [3] on metallic Si and Ge. More recently, new experimental investigations of the high-pressure phase diagrams of these elements were stimulated by the results of ab initio calculations on the thermodynamic stability of several possible metallic phases [4, 5]. In the case of Si, X-ray diffraction studies by two different groups [6, 7] agree on the following sequence (increasing pressure): diamond (I) --~ fl-Sn ( I I ) - ~ primitive hexagonal (V), up to 25 GPa. The system ultimately reaches a compact hcp structure for pressures higher than 40 GPa [7]. The lower two transitions appear to initiate at about 11 and 13 GPa, respectively [6].

Considering the richness of this phase diagram, the question arises whether the new metallic phases will also become superconducting at low temperatures. This point is of particular interest in the case of silicon, since the most recent theoretical calculations [8] have become accurate enough to provide reliable estimates of the relevant electronic-structure and vibrational parameters, an unusually favourable situation indeed in superconductor physics. We have carried out detailed resistivity measurements on metallic silicon up to 25 GPa. In this paper, we will focus on the superconducting properties of phases II and V which can be obtained on increasing pressure. An additional, body centered cubic phase, labelled III, which normally appears on release of pressure and remains metastable to P = 0, could not be produced in the present experiments without unacceptably large pressure inhomogeneities within the cell.

2. Experiments

The experiments were carried out in an improved Bridgman-type device [9] using sintereddiamond anvils to increase the upper pressure

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J.M. Mignot et al. / High pressure superconductivity

limit. The pressure-cell consisted of a pyrophyllite gasket filled with a solid pressure-transmitting medium (steatite) chosen for its high flowing capability. The Si sample was embedded in the steatite, together with a Pb strip serving as a superconducting manometer. Two different specimens (L x l = 0.8 x 0.07mm), hereafter labelled A and B, were cut from p-type singlecrystalline material (p = 1016 c m = 3 ; p(300) 0.5 12cm), previously polished to 25 ixm thickness. The electrical contacts were performed by pressing annealed Pt leads (~b= 25 txm) onto metallized areas of the sample (Au-Ge evaporation). The resistance was measured by a conventional 4-terminal ac technique with nanovolt resolution using current densities lower than 60 m A / m m 2. The small size of the pressure cell and its plastic deformation under pressure precludes any accurate measurement of the sample geometrical factor I/s. However, a crude estimate (-+30%) of this parameter was used in the following whenever resistivity values were needed. It should be understood that only relative changes, not absolute values, are quantitatively significant. All the measurements were performed on increasing pressure. Each run consisted of (i) increasing the load at 300 K (ii) cooling down to liquid helium temperature (iii) measuring the superconducting transitions of lead and silicon and (iv) recording the R - T curve of silicon while warming up to room temperature. The superconducting transitions were measured by slowly sweeping the temperature across Tc while measuring R. The curves were systematically checked for reproducibility upon warming and cooling. The temperature was deduced from the resistance of a calibrated germanium sensor with a precision better than 50 mK, including the effect of thermal gradients. The pressure homogeneity within the pressure cell was estimated from the width of the lead transition.

3. Results

At room temperature, the pressure dependence of R is dominated by the dramatic decrease

of silicon

asociated with the sc-metal transition. In semiconductor compounds the resitance is known to be very sensitive to shear forces and lack of hydrostacitity. For this reason, and because of the very large contact resistances between the Pt leads and the sample before the metallization occurs, the results obtained in the low-pressure phase cannot be considered quantitative and were not reproduced here. The tail of the resistance discontinuity extends far into the /3-Sn phase, suggesting that an appreciable fraction of phase I is still present. This contribution obscures any possible abrupt resistance anomaly at the II --~ V transition. Above 15GPa, R decreases only weakly with pressure in the hexagonal phase. The R - T curves between 1 and 300K are characteristic of a metal, with relatively large resistivity ratios of about 20 for both specimens. The residual resistivity decreases steadily as P increases from 0.2951x~cm at 14.8GPa to 0.180 IXflcm at 25.0 GPa (sample B). Since both dimensional changes and cold working of the sample are expected to produce the opposite effect, this variation is most likely intrinsic. The superconducting transition curves for sample B are presented in fig. 1, and the corresponding Tc's are plotted in fig. 2 for both samples as a function of pressure. The poorer pressure homogeneity for sample B is probably due to the larger filling factor of the pressure cell that was

R/Ro

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.6

_So,4

j+ 5

6

7

8

T(K)

Fig. 1. Superconducting transition curves of metallic silicon under pressure (sample B).

J.M. Mignot et al. / High pressure superconductivity of silicon [

I

l

l

l

I

~F

I--

I

sl

3t:

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4. Discussion

- ~ '---,~-s-~II~ p.h (V)

~o~

l- . . . . . . . . . . . . . . . . . . . . . . I

10

I

14

both a depression of the higher T c and an increase of the lower one, as observed in these latter curves. At higher pressures, T c starts decreasing with d T c / d P = - 0 . 5 4 K / G P a . For pressures larger than 22 GPa, T c decreases more slowly. Furthermore, since the lead presure scale probably underestimates P in this region, owing to the crude linear extrapolation performed beyond the GaP fixed point [12], the deviations from a straight line in the T c - P curve of silicon could be even more pronounced than indicated in fig. 2.

,o.

- - - -.I

3

237

I

I

I

I

18 22 PRESSURE ( G P a )

I

I

26

Fig. 2. Pressure dependence of Tc in metallic phases of silicon; • sample A, C) sample B.

used in order to reach higher pressures. It can be noted, however, that this difference does not produce any appreciable inconsistency between the two sets of data. In the/3-Sn phase, superconductivity sets in at (6.28-+0.03) K for P = 1 2 G P a , a somewhat lower critical temperature than previously reported by Wittig (6.6 K in ref. 3). The temperature coefficient d T c / d P is small, as evidenced by the narrowness of the transition, and its sign could not be assessed in the present experiments (Wittig found it negative and II'ina and Itskevich [10] reported a weak maximum near 11 GPa). At the II ~ V transition ( 1 3 . 7 G P a ) , Tc increases by more than 1 K [11]. The corresponding curve (fig. 1) represents a situation where some parts of the sample are subjected to lower pressures and remain in the /3-Sn phase, whereas a large fraction has already transformed into the ph structure. Comparison of curves at 13.7 and 1 4 . 8 G P a also indicate that d T c / d P is initially positive in the latter phase and reaches a maximum value of 8.2 K at 15 GPa. It is not clear at the moment whether this variation is a genuine property of the ph phase, or a proximity effect in an intimate admixture of phases II and V causing

We will focus on the properties of the ph phase which is stable over a large range of pressure. The residual resistivity as a function of pressure decreases sharply between 15 and 2 0 G P a and then saturates. Since the density of states at the Fermi level does not vary significantly with pressure [8, 13], this abrupt decrease has to be related to a variation of the scattering mechanism, which may be due to the admixture of phases as already mentioned. We will therefore determine the superconducting parameters of this phase in the pressure range above 20 GPa. The Debye temperature can be evaluated by an analysis of the p vs T curves between 30 and 300 K. This is done assuming p obeys a general equation p(P) = po(P) + A(P)ck(T/OD). Although 4~ is not found to reduce to a simple B l o c h - G r u n e i s e n function, one can estimate a value for 0D of about 620 K at 20 GPa, increasing with pressure at a rate of +14 K / G P a . We will discuss the results using the BCS formula: T c = 1.130De~l./~*withh * = A/(1 + A) - / x * , rather than McMillan's [14] since a weak coupling regime is more likely to occur in a system well described by a nearly free electron model. If we assume that /x* can be deduced from Benneman and Garland's empirical formula [13, 15], a value of 0.06 for this parameter has to be taken. Then the values of h can be calculated with the known Tc's. For instance, at 20 GPa, we find h = 0.39 to be compared to the value h = 0.3 calculated in ref. 13 using only the zone-boundary

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J.M. Mignot et al. / High pressure superconductivity o f silicon

p h o n o n s . H o w e v e r a full z o n e c a l c u l a t i o n p e r f o r m e d at 1 4 G P a [13] suggests t h a t t h e p r e v i o u s approximation underestimates A by 20%. That w o u l d c o r r e s p o n d at 2 0 G P a to a t h e o r e t i c a l v a l u e A -- 0.375 q u i t e close to t h a t d e d u c e d f r o m the experiment. At higher pressures, the theory predicts the a p p e a r a n c e o f a soft p h o n o n m o d e n e a r t h e p h ~ hcp t r a n s i t i o n l e a d i n g to a m i n i m u m in T c a r o u n d 30 G P a a n d a s t r o n g i n c r e a s e in T c n e a r 40 G P a . A l t h o u g h o u r e x p e r i m e n t a l s e t u p has n o t a l l o w e d such high p r e s s u r e s up to n o w , the d e p a r t u r e f r o m l i n e a r i t y f o u n d in t h e Tc vs P c u r v e a b o v e 20 G P a m a y b e an i n d i c a t i o n o f this phenomenon.

5. Conclusion W e h a v e r e p o r t e d t h e first e x p e r i m e n t a l invest i g a t i o n o f t h e s u p e r c o n d u c t i n g p r o p e r t i e s of h e x a g o n a l silicon ( p h a s e V ) o v e r a l a r g e r a n g e o f p r e s s u r e s . T h e m a i n results a r e t h e m a x i m u m v a l u e o f T c = 8 . 2 K close to t h e I I - - * V p h a s e b o u n d a r y a n d its s t e a d y d e c r e a s e d o w n to 3.6 K at the highest pressure. O u r d a t a a r e in c l o s e a g r e e m e n t with t h e c a l c u l a t i o n s o f C h a n g a n d c o w o r k e r s u p to 25 G P a . F u r t h e r e x p e r i m e n t s a r e n o w in p r o g r e s s to e x t e n d t h e p r e s e n t results to h i g h e r p r e s s u r e s .

Acknowledgements W e a r e g r a t e f u l to P r o f e s s o r M . L . C o h e n for

suggesting Dacorogna sions. W e metallizing

t h e s e e x p e r i m e n t s , a n d to M . M . a n d O. B e t h o u x for useful discusa r e also i n d e b t e d to M. R e n a r d for the s a m p l e .

References [1] S. Minomura and H.G. Drickamer, J. Phys. Chem. Solids 23 (1962) 451. [2] F.P. Bundy, J. Chem. Phys. 41 (1964) 3809. [3] W. Buckel and J. Wittig, Phys. Lett. 17 (1965) 187. J. Wittig, Z. Phys. 195 (1966) 215. [4] M.T. Yin and M.L. Cohen, Phys. Rev. Lett. 45 (1980) 1004. [5] A.K. McMahan and J.A. Moriarty, Phys. Rev. B27 (1983) 3235. [6] J.Z. Hu and I.L. Spain, Solid State Commun. 51 (1984) 263. [7] H. Olijnyk, S.K. Sikka and W.B. Holzapfel, Phys. Lett. 103A (1984) 137. [8] K.J. Chang and M.L. Cohen, Phys. Rev. B30 (1984) 5376. [9] A. Eichler and J. Wittig, Z. Angew. Phys. 25 (1968) 319. [10] M.A. II'ina and E.S. Itskevich, Sov. Phys. Solid State 22 (1980) 1833. [11] This discontinuity in Tc was reported for the first time in ref. 10. However, the authors erroneously attributed the higher Tc to the /3-Sn phase. [12] J. Wittig, Z. Phys. B38 (1980) 11. B. Bireckoven, Diplomarbeit, University of Cologne (1984). [13] K.J. Chang, M.M. Dacorogna, M.L. Cohen, J.M. Mignot, G. Chouteau, G. Martinez, Phys. Rev. Lett. 54 (1985) 2375. [14] W.L. McMillan, Phys. Rev. 167 (1968) 331. [15] K.H. Benneman and J.W. Garland, in: Proc. of the Conf. on Superconductivity in d- and f-band Metals, Rochester 1971, D.H. Douglas, ed. (ALP, New York, 1972) p. 103.