Schematic of the core/shell NW geometry with a core radius of rc , shell thickness of t, and length of L. The dashed loop represents an edge dislocation loop with Burger's vector along the NW growth direction.
Plot of the strain components as a function of radial distance from the center of the core. Solid lines and dashed lines correspond to wurtzite InAs/InP and InP/InAs core/shell NWs, respectively, with core radius of 20 nm and shell thickness of 10 nm. The vertical dotted line represents the core/shell interface.
(a) Plot of the change in the interfacial strain components (at r = rc ) and (b) elastic strain and dislocation energies per unit length as a function of shell thickness of wurtzite InAs/InP core/shell NWs with a fixed core radius of 20 nm.
(a) Plot of the change in the interfacial strain components (at r = rc ) and (b) elastic strain and dislocation energies per unit length as a function of shell thickness of InAs/InP core/shell NWs with fixed shell thickness of 14 nm.
Plot of the calculated critical shell thickness as a function of core radius for wurtzite InAs/InP (solid line) and zincblende GaAs/GaP (dashed line) core/shell NWs. The open and solid data points are the experimental results for NWs with and without dislocations detected, respectively. The squares are for InAs/InP core/shell NWs, while the circles are for GaAs/GaP NWs. The coherency is maintained for thicknesses below the curves.
Plot of the critical core radius as a function of lattice mismatch between core and shell materials with zincblende structure (left). The critical shell thicknesses of core/shell NWs with a particular core radius of 100 nm are plotted on the right.
(a) Bright field and dark field TEM images of an InAs/InP core/shell NW taken by (b) (0002) and (c) (2110) diffracted spots, (d) selected area diffraction pattern of the middle of the core/shell NW, and (e) a high resolution TEM image of the InAs/InP interface. The arrow in (e) shows the InAs/InP interface.
Examples of TEM investigations of strain relaxed wurtzite InAs/InP core/shell NWs (a) BF and (b) (0002) DF TEM images for a NW with a core radius of 30 nm and shell thickness of 25 nm with a corresponding SAD pattern in (c). (d) (2110) DF TEM image of another NW with a core radius of 37 nm and shell thickness of 22 nm with a corresponding SAD pattern in (e) and HRTEM in (f). (g) (0002) DF TEM image of a NW with a core radius of 15 nm and a shell thickness of 22 nm. The observed contrasts in (a), (b), and (d) are perhaps due to the formation of loop dislocations, while the contrast in (g) is due to the formation of stacking faults.
(a) BF TEM image and (b) corresponding SAD pattern of a GaAs/GaP core/shell NW with a core radius of 25 nm and shell thickness of 13 nm. (c) HRTEM image of the core/shell interface, indicating the presence of an edge dislocation inside the white circle.
Plot of the calculated critical shell thickness as a function of core radius for zincblende GaAs/GaSb (dashed-dotted curve), zincblende InAs/GaAs (dotted curve), and wurtzite InAs/GaAs (dashed curve) core/shell NWs. The open and solid data points are the experimental results for NWs with and without dislocations detected, respectively. The experimental results for InAs/GaAs core/shell NWs are from Ref. 3 .
Summary of reported values of the shear modulus, μ; the Poisson's ratio, ν; and the stiffness constants, cij for selected compound semiconductors with ZB structure and calculated cij for WZ structure.
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