Breakdown of continuum elasticity theory in the limit of monatomic films

Abstract

We demonstrate that the predictions of continuum elasticity theory fail in the ultimate limit of monolayer films. We directly measure the lattice distortion of ultrathin InAs layers in GaAs by highresolution electron microscopy. For InAs films of 3 monolayer thickness, the observed tetragonal distortion agrees with the prediction of elasticity theory. For single InAs monolayers, however, the measured strain is much higher than expected. The InAs unit cell in this case is strained such as to conserve the bulk bond length at the interface PACS numbers: 62.20.Dc, 61.16.Di, 68.35.Gy The progress in crystal growth techniques has made it possible to synthesize artificial layered materials built up of structurally and chemically dissimilar constituents. The accurate control of the growth processes allows the thickness of the individual layers to be scaled down to the atomic regime. The successful synthesis of such structures led to the exciting opportunity to address a fundamental question of solid-state physics; namely, at which scale the bulk properties of the constituent materials are established and serve as an adequate description of the heterostructure, and, on the other hand, at which scale the properties of the structure are dominated by the local atomic configuration of the interface [1-3]. Much effort is hence currently devoted to the understanding of the formation and atomic configuration of semiconductor heterointerfaces [4-6].In this Letter, we demonstrate a novel method to determine the atomic configuration at the interface between crystalline materials. By analyzing high-resolution lattice images of coherently strained InAs films in GaAs, we directly measure the tetragonal distortion of the InAs unit cell. The distortion of 3 monolayers (ML) InAs agrees with continuum elasticity theory. In contrast, the elasticity theory fails for 1 ML InAs, where the lattice distortion is much larger than expected. In this case, the distortion of the unit cell is consistent with the conservation of the bond length at the interface. Our study thus demonstrates that the continuum case establishes rapidly, but significant deviations occur in the ultimate limit of a monatomic layer.The investigated structures consist of single InAs films buried in GaAs and are synthesized by solid-source molecular-beam epitaxy on semi-insulating (100) GaAs substrates. The nominal thicknesses of the InAs films are either 1 or 3 ML. A novel growth procedure has been developed to ensure the controlled buildup of both InAs/GaAs and Ga As/In As interfaces [7]. This technique allows us to synthesize atomically smooth InAs films of well-defined thickness even in the monolayer regime. For the high-resolution electron microscopy (HREM) experiments, cross-sectional samples along the (110) direction are prepared by conventional ion milling. The specimen thickness is then between 10 and 20 nm, as determined by image simulations. Lattice images are taken in a JEOL 4000FX electron microscope operating at 400 kV. Qualitative information about the interface...

A methodology development for the study of near surface stress gradients

“…In this paper, Streitz et al [20] had calculated the thickness-dependent biaxial modulus of thin metal films. It seems that a film of roughly few monolayers (0.5 -1 nm) can already be considered as an elastic continuum where bulk constants are valid as confirmed by [21,22]. In our present study the lower mean penetration depth is in the order of 100 nm.…”

Structural and Optical Studies of CdTe/ZnTe Superlattices with Ultrathin ZnTe Layers

“…Given the uncertainty on the amount of Zn atoms incorporated during growth, no breakdown of the continuum elasticity theory is necessary to explain our results unlike the conclusion reached by the workers of Ref. [5] for the strain state of one InAs ML embedded in GaAs. However, the local distortion analysis shows that, even though the lattice mismatch strain is mainly accomodated in the ZnTe planes (within 70%0), there is still some residual strain extending over 3 to 5 MLs after the last ZnTe plane location.…”

“…The results are reported in Fig. 3 and compared with the ones obtained for MnTe/CdTe [10] and InAs/GaAs [4,5]. The former system has a lattice mismatch of 6.2% similar to the ZnTe/CdTe one which allows to insert only a few MLs of InAs planes into GaAs without relaxation occurring.…”

“…For IIl-V lattice mismatched materials, this problem was addressed by measuring the local distortion of ultrathin InAs layers embedded in GaAs [4] and their photoluminescence properties [3]. It was proposed that the elasticity theory fails to account for the distortion of one InAs monolayer [5] and that a self-consistent pseudopotential method is necessary to calculate the energy gap in the monomolecular-plane system [6]. We report here on the II-VI CdTe/ZnTe lattice mismatched system where ultrathin ZnTe layers were grown into CdTe by molecular beam epitaxy (MBE).…”

Exciton dephasing and biexciton binding in CdSe/ZnSe islands

“…[1][2][3] The optical properties of such islands have been mainly studied by incoherent methods. [4][5][6][7] Driven by the search for blue-green-emitting semiconductor materials, the fabrication [8][9][10][11][12][13] and optical characterization [14][15][16][17][18] of self-assembled II-VI islands have recently been the subject of intensive research. Only little is known about the coherent properties of these structures, giving information about exciton scattering and biexciton formation.…”