phys. stat. sol. (b) 243, No. 4, 778–781 (2006) / DOI 10.1002/pssb.200564673

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Determination of the lattice constant of CrS

from Mn1–xCrxS MBE epitaxial layers

L. David* and K. A. Prior

David Brewster Building, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

Received 12 September 2005, revised 25 January 2006, accepted 26 January 2006 Published online 3 March 2006

PACS 61.10.Nz, 68.55.Nq, 68.65.Ac, 81.05.Dz, 81.15.Hi

A series of Mn1–x

CrxS epitaxial structures have been grown with the composition ZnSe/Mn

1–xCr

xS/ZnSe

with varying x. X-ray Interference measurements were used to determine the layer thicknesses and com-positions, and by varying the lattice parameter of CrS an improved fit was obtained. The lattice parameter of CrS was found to be 5.387 ± 0.025 Å.

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

In previous studies, we have shown that using ZnS as a sulphur source, both MgS [1] and MnS [2] can be grown epitaxially on GaAs substrates in the metastable zinc blende (ZB) structure. Thicknesses in excess of 130 nm have been produced before the conversion to the stable rocksalt (NaCl) structure. The growth technique used to produce these sulphides can potentially be applied to any sulphide com-pound containing a metal less volatile than zinc. The compound chosen to continue this work was CrS, which has been predicted to be ferromagnetic with a high Curie temperature even when undoped [3]. The stable crystal structure for this compound is based on NiAs with octahedral coordination of the Cr atoms. In this paper, we describe two problems which must be overcome before the successful growth of CrS can commence. The first problem is the purity of the source materials used in the MBE system, as a clean source of Cr could not be obtained commercially. However, a more important problem was with the choice of a suitable substrate for the growth of metastable ZB CrS which is dictated by the lattice parameter of the epitaxial layer to be grown. In order to lattice match an epitaxial layer to a substrate, the in-plane strain must be less than 1%. Preliminary calculations were carried out at Heriot–Watt using published atomic radii to calculate the lattice parameters of the first row transition metal sulphides and then taking into consideration the known lattice parameter of MnS. This indicated that the lattice param-eter could be as large as 5.806 Å [4]. However, ab initio calculations carried out by I. Galanakis et al. [5] have determined the lattice parameter of CrS to be 5.04 Å, while H. Shoren et al. [6] calculated it as 5.309 Å. As the possible range of values spans that of the available III–V substrates, from GaP to InP, a definitive value for the lattice parameter of ZB CrS was required before work to produce the material could begin.

2 Growth procedure

For the other compounds we normally grow, the purity of the source materials in the MBE system are all greater than 5N8. The Cr source used was 5N (Newmet Koch). The Cr source was cleaned by tempera-

* Corresponding author: e-mail: l.david@hw.ac.uk, Phone: +44 (0) 131 451 3030, Fax: +44 (0) 131 451 3136

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ture cycling of the Cr cell, before any growth commenced. In this process, the temperature of the Cr cell was repeatedly cycled between 700 and 1150 °C. While the cell is at the lower temperature, contami-nants segregate to the surface of the material. At higher temperatures these will alloy with the source material, however the sudden rise in temperature does not allow them to establish an equilibrium before they are evaporated from the surface of the source. The condition of the vacuum is monitored using a mass spectrometer during this process and the procedure is terminated when no change is observed in the molecular hydrogen peak over the course of one cycle. In order to determine the lattice parameter of ZB CrS, a series of samples containing Mn1–xCr

xS layers

were grown for X-Ray Interference (XRI) [7] measurements. The samples all had the same structure, GaAs (sub)/ZnSe/MnCrS/ZnSe. The thickness of the ZnSe layers was kept the same at a value of 48 nm, based on previous calibration runs, while the Mn1–xCr

xS layers were all grown for 60 seconds.

All the structures were grown in a Vacuum Generators V80H MBE system using 6N Zn and Se ele-mental sources, a 6N ZnS compound source, elemental sources of 5N8 Mn and 5N Cr. The samples were grown on GaAs(100) substrates, which had been etched in a 15:2:2 solution of H2SO4 :H2O2 :H2O, sub-sequently heated in the growth chamber to 600 °C to remove the surface oxide layer, and then cooled to the growth temperature (typically 240–270 °C) under a Zn flux [8]. Accurate flux measurements from the Cr cell were not possible, due to the high N2 background from the pBN crucible of the Cr cell. Accordingly, no flux measurements were routinely recorded but the cell temperatures were kept constant for all the sources except the Cr. Based on published values of the Cr vapour pressure as a function of temperature, an initial sample was grown with the temperature of the Cr cell, TCr, at 1100 °C. However, XRI scans of this sample did not show Pendellösung fringes, as is normally observed from identical structures containing MnS. There-fore, the temperature of the Cr cell was decreased in 20 °C intervals until the fringes were observed in the XRI scan. The three samples that were analysed in this study were grown with TCr at 1020, 1010 and 1000 °C which showed strong Pendellösung fringes. Analysis of the structure was done by comparing the experimental curve with a simulation produced by the Bede RADS Mercury simulation software. This requires a value for the lattice parameter of CrS, aCrS, in order to calculate the Cr mole fraction, x, in the Mn1–xCr

xS layers. Initially a value of 5.806 Å was

used for aCrS based on the previous estimates made at Heriot–Watt [4]. Figure 1 shows the 004 XRI and simulated data for the structure grown with TCr = 1010 °C (Sample 1). It can be seen that the fit to the data is not very good, with a standard error of 0.196, (where a value below 0.1 is regarded as good) therefore a modification of the lattice parameter of CrS was required. For all simulations a value of 0.4 was used for the Poisson’s ratio, ν . This value is reasonable for a metastable sulphide. Changing ν is equivalent to changing aCrS, however from simulations using a range of values we have determined that the effect is small. The main error arises from the spacing of the iteration steps which were 0.05 Å apart, giving us an error in aCrS of ±0.025 Å.

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780 L. David and K. A. Prior: Determination of the lattice constant of CrS

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-b.com

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Fig. 2 004 XRI experimental curve for the same sample as shown in Fig. 1 (a) and simulations using (b) aCrS

= 5.487 Å and (c) aCrS = 5.387 Å.

Since the Heriot–Watt calculated value for aCrS was over 0.4 Å greater than published ab initio values, the value was recalculated using atomic radii obtained from Ref. [9]. The lattice parameter was calcu-lated using different definitions of atomic radii, including the Empirical radii and Atom–Atom bond lengths. The values were then averaged to determine aCrS = 5.487 Å. Similar calculations for MnS and ZnS were carried out. The accepted values for these compounds are aMnS = 5.559 Å [10] and aZnS = 5.409 Å and the values calculated from the atomic radii were aMnS = 5.595 Å and aZnS = 5.39 Å. The calculated values for the lattice parameters are within 1% of the accepted values, therefore the result for aCrS can be considered to be accurate to within the same margin. The XRI experimental scan and a simulation calculated using aCrS = 5.487 Å from Sample 1 are com-pared in Fig. 2. The standard error of this simulation has been reduced to 0.131. Using aCrS = 5.487 Å as an initial value, the simulation was recalculated varying aCrS in steps of 0.05 Å while monitoring the change in the standard error. Figure 2 also shows the XRI experimental scan and corresponding simula-tion for the same sample using aCrS = 5.387 Å, which has the lowest standard error of 0.125. Using these lattice constant values, simulations were also obtained for the other samples in the series. The results from these simulations can be found in Table 1. Subsequently, thicker layers were produced for X-ray Diffraction (XRD) measurements. Figure 3 shows the XRD scan from a Mn1–xCr

xS layer which was grown for 12 minutes on a 30 nm buffer of ZnSe

with TCr of 1000 °C. The diffraction peak from the ZnSe layer can be seen to the left of the substrate peak, while the peak relating to the Mn1–xCr

xS layer can be found at approximately 11000 arcsecs to the

Table 1 Results from simulations of XRI scans using a

CrS = 5.387 Å.

TCr (°C) layer thickness (nm) material X

1020 49.9 13.8 45.0

ZnSe Mn1–xCr

xS

ZnSe

0.68

1010 49.9 5.9 45.0

ZnSe Mn1–xCr

xS

ZnSe

0.49

1000 47.5 5.1 45.4

ZnSe Mn1–xCr

xS

ZnSe

0.28

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right. Simulations were performed using the three different values of aCrS = 5.806, 5.487 and 5.387 Å. There was no possible composition of Mn1–xCr

xS able to fit the data using either aCrS = 5.806 Å or

5.487 Å using the simulation program. However it was possible to simulate the structure using aCrS = 5.387 Å, with x ~ 36%. Samples grown with the cell temperatures kept constant showed that x varied from 0.28 to 0.36, indicating a variation in the Cr flux of approximately 25%. This behaviour was found on all samples containing Cr and the poor run-to-run reproducibility could be due to the granular nature of this particular source material.

3 Conclusions

In order to determine the lattice parameter of ZB CrS, a series of MnCrS layers with varying Cr compo-sition have been produced for XRI analysis. Through iteration of the value of aCrS in the XRI simulation software, the lattice parameter of ZB CrS has been determined to be 5.387 ± 0.025 Å. This is in close agreement with previous theoretical values [5, 6]. Having determined this value, work has subsequently been able to commence on the growth of ZB CrS lattice matched to GaP (100) substrates (5.45 Å). Results from this work will be published else-where.

Acknowledgement We are grateful to EPSRC for funding this work.

References

[1] C. Bradford, C. B. O’Donnell, B. Urbaszek, C. Morhain, A. Balocchi, K. A. Prior, and B. C. Cavenett, Phys. Rev. B 64, 195309 (2001).

[2] L. David, X. Tang, G. Beamson, D. Wolverson, K. A. Prior, and B. C. Cavenett, phys. stat. sol. (b) 241, 471 (2004).

[3] T. Dietl and H. Ohno, Physica E 9, 185 (2001). [4] K. A. Prior, C. Bradford, L. David, X. Tang, and B. C. Cavenett, phys. stat. sol. (b) 241, 463 (2004). [5] I. Galanakis and P. Mavropoulos, Phys. Rev. B 67, 104417 (2003). [6] H. Shoren, F. Ikemoto, K. Yoshida, N. Tanaka, and K. Motizuki, Physica E 10, 242 (2001). [7] K. A. Prior, X. Tang, C. O’Donnell, C. Bradford, L. David, and B. C. Cavenett, J. Cryst. Growth 251, 565

(2003). [8] L. H. Kuo, K. Kimura, S. Miwa, C. G. Jin, K. Tanaka, and T. Yao, Appl. Phys. Lett. 68, 2413 (1996). [9] WebelementsTM http://www.webelements.com, accessed April 2005. [10] L. David, C. Bradford, X. Tang, T. C. M. Graham, K. A. Prior, and B. C. Cavenett, J. Cryst. Growth 214, 197

(2000).

Fig. 3 004 XRD experimental scan (a) and simulation using a

CrS = 5.387 Å (b) for a sample

with the structure ZnSe (30 nm)/Mn1–x

CrxS

(~45 nm). The quoted Mn1–x

CrxS thickness was

determined from the layer composition and the known MnS growth rate.