Pressure dependence of the band gaps in Si quantum wires

Pressure dependence of the band gaps in Si quantum wires Chin‐Yu Yeh, S. B. Zhang, and Alex Zunger Citation: Applied Physics Letters 64, 3545 (1994); doi: 10.1063/1.111219 View online: http://dx.doi.org/10.1063/1.111219 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/64/26?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Valence band spectroscopy in V‐grooved quantum wires Appl. Phys. Lett. 69, 2965 (1996); 10.1063/1.117745 Intersubband relaxation time in the valence band of Si/Si1−x Ge x quantum wells Appl. Phys. Lett. 69, 3069 (1996); 10.1063/1.116842 Impurity band conductance through oxygen vacancy donor states in bismuth iron molybdate J. Appl. Phys. 79, 7703 (1996); 10.1063/1.362435 Modal analysis of optical guides with two‐dimensional photonic band‐gap boundaries J. Appl. Phys. 79, 7483 (1996); 10.1063/1.362419 Energy gap of nanoscale Si rods J. Appl. Phys. 79, 3619 (1996); 10.1063/1.361416

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Pressure dependence

of the band gaps in Si quantum wires

Chin-Yu Veh, S. B. Zhang, and Alex Zunger Natiotml Renawabl~Energy Laboratory Golden, Colorado 80401 (Received 25 January 1994; accepted for publication 14 April 1994) The pressure coefticients II. of interband transitions in (001) silicon wires are calculated using a plane-wave basis and carefully fitted empirical pseudopotentials. We find purely red shifts (a) Si wires. a* are averaged arithmetically within each hand. ‘The unscaled EPM rz values are given in the parrntheses.

implies tilat the pressure coefficients of the wires are given by a sum o&r k” [Eq. @),I and ~1 of the hulk pressure coefficients $

+ rr

2 k*

l/yJ

Y!$.

We thus interpret the calculated red shift of (001)oriented wires with [110] surfaces as a manifestation of the. analogous bulk properties along the ‘2rr/n,,(0,l,Oj direction in the Brillouin zone. The value of k’“’ having the largest projection will be denoted k&. Analyzing our directly calculated wire wave functions, we find that as the wire size increased, k&, moves towards the value 2&~,(0,1).8S,c)) at which ha& Si has its CBM [Fig. t.(aj]. These values are indicated in Fig. 1(bj by solid circles and vertical arrows. We conclude the following: (ij The dczduttxl pressure coefficients for the larger wires approach the bulk value iz(A scj at the CBM (as expected by continuity arguments) since k$, approaches the CRM. !iij The band edge pressure coefticients of small wires are less negative than aO(AI,), since, by Eq. (33, the wire CRM represents a mixture of a few bulk states Irz.k”), most of which have n,~(k*)>a(Al,j [Fig. i(b)]. (iii) The fact that the c2~sen~d wire pressure coefficients !‘Tabte 1I are often most negative than the (observed) IziA,,) bulk value suggests either nonbutk (.i.e., surface) or nonidcality effects. (For example, the different compressibilities of Si and the empty pours could create an effective shear that will split the wire VNM, pushing statc.s further into the gap and increasing Ial.) (iv) For wires with different surfaces and different orientations, the pressure coefficients could have contributions off the bulk r-,X’ line. Examination of onr I’B&calculated pressure coefficients of bulk Si for off Y-X directions near A,,. shows that they are all negative and smaller in absolute w&.~c that1 a( A 1,:j. Thus if the emission is caused by intrinsic quantum confinement! we expect a small and negative pressure coefficient for porous Si regardless of

its orientation, shape, and size. iv) Since higher energy Gx? bands (/?,y!(r...) are constructed from correspondingly higher energy bulk bands, their pressure coefficients are less negative. In fact, the S band had a positive pressure coefficient [Fig. 3(aj] since it is composed of states near the bulk r2ti state [see Fig. l(b)]. Given the predicted off-r character of the wire CNM at ambient pressures,*‘)-” the analogy” draw by Ryan et ~1.” between porous Si and the direct gap GaAs under pressure clearly does not hold. The confusion arises, in part, because both Sanders and Chang’” and RuJa et ul. l1 have incorrectly used the term “direct” instead of “pseudodirect” to characterize their X-folded CBM. On the other hand, a molecular interpretation of fhe porous Si (e.g., siloxene) cannot explain a large positive b, either.‘,‘” It is possible”“73’” that the blue shift does not represent an intrinsic feature of Si wires but rather a pressure-induced size-reducing chemical reaction that takes place in the pressure cell: Sood et &,“*” noted that the conventional methanol-ethanol mixture used as a pressure-transmitting medium actually reacts with porous Si.17 Rtuc shifts were indeed seen only in experiments using alcohols as a pressure medium”24?h but not in experiments using inert fluids.““q18 We conclude that the predicted red shift is an intrinsic property of the Si wires, describable in terms of bulklike effects, but that the blue shifts is not explainable in these terms. We wish to thank V. P&ova-Koch for many helpful discussions. This work was supported by the Office of Energy Research (OER) [Division of Materials Science of the Office of Basic Energy Science @ES)], U. S. Department of Energy, under Contract No. DE-AC02-S3-CF-I10093, ‘J. Camassel, E. Massone, S. Lyapin, J. Allcgre, P. Vicente, A. Foucaran, A. Raymond, and J. 1.. Robert, in f’rixcc&rzgs oftkc 2.I.r~ Intrmaticmal Conference on fhc Physics of Scmicorzdnctor.s, edited by Ping Jiang and LouZhi Zhang (World Scientific, Singaporet lYY2j, p. ‘1463. ‘1% Zhou, H. Shen. J. F. Harvey, R. A. 1.11x,M. Dutta, E Lu, C. II. Perry, R. Tsu, N. M. Kalhhoran, and E Nawavar, Appl. Phys. Lctt. 61, 1435 ( 1992). ‘A. K. Sood, K. Jayaram, and D. V. S. Mathu, J. Appl. Phys. 72, 3963 (19923.

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This article copyrighted as indicated in the Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Yeh, Zhang, and ZungerDownloaded 3547 to IP: Appl.is Phys. Let, Vol. 64! No. 26, 27 article. June 1994 128.138.41.170 On: Tue, 14 Jul 2015 12:20:07