Rough interfaces

Quantum well interface roughness Carrier or doping density Electron temperature Rotational relaxation times Viscosity Relative quantity Molecular weight Polymer conformation Radiative efficiency Surface damage Excited state lifetime Impurity or defect concentration... 

Fig. 8. X-ray reflection diagram of a thin polystyrene film on float glass [160]. The reflectivity R is plotted against the glancing angle . The film is spin coated from solution. A model fit (dashed line) to the reflectivity data is also shown where the following parameters are obtained film thickness = 59.1 0.1 nm, interface roughness glass-polymer = 0.4 0.1 nm, surface roughness polymer-air = 0.6+1 nm, mean polymer density = 1.05 + 0.01 g/cm-3. The X-ray wavelength is 0.154nm...

The oscillations in the reflectivity curves arise from interference between the X-rays reflected from the various interfaces. The frequency of the oscillations is proportional to layer thickness and the amplitude depends on the interface roughness. 

Figure 21 Friction coefficient for differently oriented Ni(100)/Ni(100) interfaces. Rough surfaces have a 0.8 A rms variation in roughness added to the atomically smooth surfaces. Reproduced with permission from Ref. 85.

A lateral variation of the anodization current will produce different growth rates and consequently an interface roughness for porous layers. Note that this is not the case for stable macro PS formation on n-type, because here the growth rate is independent of current density. An inhomogeneous current distribution at the O-ring seal of an anodization cell or at masked substrates produces PS layer thickness variations, as shown in Fig. 6.6. Inhomogeneities of the current distribution become more pronounced for low doped substrates, as shown in Figs. 6.3 b and 6.5 d [Kr3]. 

As a result of the crystal growth process Si wafers usually show striations, a variation in the bulk Si resistivity in a concentric ring pattern with a spacing in the order of millimeters. This variation of the bulk Si resistivity modulates the current density and thereby the porosity, which results in an interface roughness [Lel6]. Mesopore formation due to breakdown at the pore tips is very sensitive to striations and can be used for their delineation. 

A PS-bulk-interface roughness on the pm scale is found to develop for meso and micro PS layers with increasing PS thickness. This roughness especially impairs reflectivity measurements and the manufacture of optical superstructures... 

Interface roughness rough smooth smooth smooth smooth smooth... 

Figure 3.11. Prediction of interface roughness obtained by (a) Jackson [13] and (b) Temkin [14], [15]. (a) The horizontal axis shows the surface site occupancy ratio, and the vertical axis depicts the change in free energy. Numerals are a factors.

Figure 3.12. Changes in interface roughness as a result of changing a and A/n, taken from the results of a computer experiment [17]. (a)-(d) indicate changes in interface state for varying awhile keeping A/n/kT constant (e) shows a step created by a screw dislocation at equihbirum, A/ir/kT=0,and (f)-(h) show how it advances under A/ir/kT=1.5, with a constant.

Anisotropy in interface roughness and in a roughening transition. Anisotropic distribution of active centers for growth, such as lattice defects, which contribute to growth. 

Difference in the environmental phases. Since the interface roughness will be different for the same crystal species depending on whether the crystal was grown from the melt, solution, or vapor phases, different growth forms are expected for different environmental phases. This implies that the Tracht of the same crystal species will depend on the structure of the environmental phases, the degree of condensation, and the solute-solvent interaction. 

The growth temperature and driving force, which affect interface roughness. 

Since the one-dimensional roughness of the steps determines whether a spiral takes circular or polygonal form, these morphologies may be treated similarly to the roughening transition of an interface, as described in Chapter 3. It is possible to predict interface roughness either by Jackson s a factor or by Bennema-Gilmer s generalized factor (see Section 3.8). The coefficients which determine the a... 

Co/Ag Co(15 nm)/Ag(6.0 nm) electron-beam evaporation on top of a 5,0-nm Cr buffer layer on Si(l 11) substrates interface roughness important in understanding connection between GMR and antiferromagnetic coupling... 

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