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  • 1
    Electronic Resource
    Electronic Resource
    The energy of finite systems of misfit dislocations in epitaxial strained layers (1992)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 72 (1992), S. 2242-2248 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Previous approaches to calculating the energy of a system of misfit dislocations in epitaxial strained layers have assumed that the system is infinite in the plane of the epitaxial interface and that the dislocations are uniformly spaced. Here a method is presented which is capable of dealing with finite systems of nonuniformly spaced dislocations of the type observed experimentally. The principle of the method is to explicitly account for the interactions between pairs of misfit dislocations. When the dislocations are infinite and uniformly spaced the present approach is shown to be equivalent to an earlier exact treatment. The present approach applied to finite systems of uniformly spaced dislocations shows that the energy per unit area converges to that of the infinite system very slowly; particularly when the spacing of the dislocations is less than the thickness of the epitaxial layer. Typically, systems must be larger than 30×30 dislocations for their energy per unit area to be within 10% of that of the infinite system. Similarly the infinite system will overestimate the energy of a 10×10 array by about 30%.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.351617
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  • 2
    Electronic Resource
    Electronic Resource
    Energy of arrays of nonperiodic interacting dislocations in semiconductor strained epilayers: Implications for strain relaxation (1993)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 73 (1993), S. 1773-1780 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The interaction energy EirrI of arrays of dislocations with nonperiodic (or irregular) distribution is calculated. The calculations have been made for uniform-random and Gaussian distributions of dislocations. The method used is, however, general and can also be applied to any arbitrary or an observed distribution of dislocations. The results for several values of average spacing p¯ and standard deviation σ are given and are compared with the energy EI of periodic arrays with spacing p=p¯. The total energy EirrT of strained layers containing nonperiodic dislocation arrays is also calculated. The results for both 90° and 60° dislocations are given. For sufficiently large numbers of dislocations, EirrI is always larger than EI. The difference between the energies EirrI and EI increases rapidly as the standard deviation σ of the nonperiodic distribution increases. The equilibrium strain relaxation in thick layers and the strain relaxation on annealing the metastable layers are usually calculated by modeling the nonperiodic array as an equivalent periodic array with p=p¯. It is found that this procedure for the calculation of the strain relaxation is not valid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.353213
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  • 3
    Electronic Resource
    Electronic Resource
    Edge-induced stress and strain in stripe films and substrates: A two-dimensional finite element calculation (1995)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 78 (1995), S. 1630-1637 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Finite element calculations of stresses and strains in substrates and stripe films of thickness h and width 2l are reported. Both variation of the stress in the vertical direction (away from the interface) in the film and distortion of the substrate are taken into account. The calculations show that both the horizontal and vertical lattice planes are curved in the film as well as in the substrate. If the thickness of the substrate is infinite, the curvature in the substrate is maximum near the interface and decays rapidly with depth. Furthermore, the edges near the top are over-relaxed, i.e., if the film is originally under compression, the stress becomes tensile because the free edge surfaces affect the relaxation. For a film with h/l=1 or greater, the stress is reversed throughout the top layer. The change from compression to tension takes place partly because of the Poisson effect and partly due to the bending of the lattice planes. The approximations made in the existing analytical models were examined and the conditions under which the models describe the stresses in the film or in the substrate were determined to a good approximation. Our finite element calculations agree with the available experimental data. Ours are the only theoretical results with which measured substrate stresses agree qualitatively. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.360257
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  • 4
    Electronic Resource
    Electronic Resource
    Energetics of dislocation dipoles in capped epitaxially strained layers (1994)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 76 (1994), S. 1598-1603 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Most device structures based on strained epitaxial layers are capped by a second, unstrained layer to increase the mechanical stability of the structure. In order to calculate the energies of these structures it is necessary to synthesize the total energy from the energies of the line defects they contain (interfacial dislocations and dislocation dipoles). The self energies and interaction energies of dislocations and dipoles are calculated and their behavior examined as a function of their spacing and the thicknesses of the strained and capping layers. The results confirm the observations that capped strained layers are more stable than uncapped ones (of the same strained layer thickness) and that capping layers do not need to be thicker than approximately three times the strained layer thickness. An expression is deduced for the total energy of finite, nonuniform arrays of dipoles in capped layers and, by analogy with a similar earlier expression for dislocations in uncapped layers, it is concluded that the effect of a nonuniformity in the dipole spacing will be to increase the energy of the system compared with that of a uniform array having the same average spacing. The results in this paper can be used to assess the stability of devices and their rate of degradation by strain relaxation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.357739
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  • 5
    Electronic Resource
    Electronic Resource
    Strain, dislocations, and critical dimensions of laterally small lattice-mismatched semiconductor layers (1995)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 77 (1995), S. 1907-1913 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A rectangular strained epilayer with its length much larger than its height h and width 2l is considered. The energy change on introducing a 60° dislocation either parallel to the long dimension (longitudinal) or parallel to the short dimension (transverse) into the epilayer is calculated. The effects of free surfaces on the mismatch stress and on the dislocation energy are taken into account approximately. For a given misfit, there is a critical height and critical width such that if the dimensions of the layer exceed their critical values, introduction of a longitudinal misfit dislocation is energetically favored. However we show that a transverse dislocation always sets in before a longitudinal one and as a result, the critical thickness is almost equal to that for a film of infinite extent even when the width is very small. The results are found to be different from an earlier calculation [S. Luryi and E. Suhir, Appl. Phys. Lett. 49, 140 (1986)] and show that the relaxation caused by the free surfaces cannot explain the lower densities of dislocations observed experimentally in such structures. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.358822
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