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Using quantitative chemical mapping, we study the low-temperature interdiffusion of HgCdTe/CdTe multilayers, sampling volumes 14 orders of magnitude smaller than previously needed for such measurements. Our results shown interdiffusion to be strongly depth dependent and nonlinear, and allow the direct determination of thermodynamic parameters of interest at individual interfaces. The high spatial resolution of our technique establishes that the stability of a layer can depend sensitively on its depth from the surface. PACS numbers: 66.30.Hs, 68.35.FxThe advent of highly perfect epitaxial interfaces, across which only the composition changes precipitously, allows the investigation of two questions of fundamental and technological interest. The first concerns the chemical relaxation of inhomogeneous solids which are far from equilibrium, for example by nonlinear diffusion and mixing. The second regards the room-temperature stability of modern multilayered systems, which may well be governed by processes not observable at high temperatures. To study such effects, it is necessary to investigate extremely small interdiffusions on an atomic scale. Twenty years ago, Cook and Hilliard 1 introduced a method capable of measuring small interdiffusivities (-10 ~2 0 cm 2 /s), thus verifying the predicted importance of nonlinearity in the intermixing of the metallic Au/Ag system. 2 This method monitors the intensity of the x-ray satellites produced by the presence of a stack of alternating layers of different composition, and thus averages over a number of interfaces, sampling a volume typically ~~ 5 x 10 " 6 cm 3 .In this Letter, we apply the recently developed chemical mapping technique 3 to study local diffusion in the Hg/CdTe system. Our method samples a volume about 14 orders of magnitude smaller than that sampled by xray techniques, but is still capable of measuring interdiffusivities of -10~2 0 cm 2 /s. We thus study, quantitatively and with atomic-layer resolution, the initial stages of interdiffusion across individual HgCdTe/CdTe interfaces. Our results can be summarized as follows: (i) Interdiffusion is a sensitive function of the distance from the sample surface, varying by up to 2 orders of magnitude as the interface depth is changed from 100 to 7000 A. This establishes the vital importance of investigating interdiffusion at high spatial resolutions, and questions the general validity of techniques that average over a number of interfaces at different depths, (ii) Linear analysis of interdiffusion in terms of a concentration-independent diffusion coefficient yields a depth-dependent activation energy, (iii) Explicit consideration of the concentration dependence of the diffusion coefficient yields depth-independent free ener-

Quantitative information may be extracted from local areas of images that consist of one or more types of unit cell. Fourier-space analysis, real-space intensity analysis, and real-space vector pattern recognition are discussed. The pattern recognition approach efficiently exploits the available information by representing the intensity distribution within each unit cell of the image as a multidimensional vector. Thus, the amount and the effect of noise present are determined, statistically significant features are identified, and quantitative comparisons are made with model images. In the case of chemical lattice images, the position of a vector can be directly related to the atomic composition of the unit cell it represents, allowing quantitative chemical mapping of materials at near-atomic sensitivity and resolution. More generally, the vector approach allows the efficient and quantitative extraction of information from images, which consist of mosaics of unit cells.

We apply quantitative chemical mapping techniques to study thermal interdiffusion and ion-implantation induced intermixing at single heterointerfaces at the atomic level. Our results show thermal interdiffusion to be strongly depth dependent. This is related to the need for the presence of native point defects (interstitials and vacancies) to bring about interdiffusion. Since their initial concentration in the bulk is negligible, the point defects must be injected at the surface and transported to the interface for interdiffusion to occur. In the case of ion-implanted samples, we find the passage of a single energetic ion through a sample at 77 K causes significant intermixing, even when the sample receives no subsequent thermal treatment.