Theoretical approach Figure 1 shows a schematic diagram of a regular sinusoidal ripple pattern with wave vector
aligned parallel to the projection of the incident ion flux of density J. Ion flux is incident in the xOz plane at an angle θ with respect to normal of the mean surface plane (the Oz axis) at any arbitrary point, O, on the surface. The gradient of the surface ∂h/∂x is given by tan , where α is the angle between the local surface normal and the Oz direction. Figure 1 Ion bombardment of a sinusoidal wave geometry. Ion flux density, J, incident at an angle θ with respect to mean surface plane is shown. Local surface gradient, tan . Sinusoidal wave is described by h = h 0 sin(2πx/λ), Alvelestat cell line where λ is the wavelength of the ripples, and h 0 is the amplitude. Following Carter, under the assumption of small local surface gradient everywhere, the fractional change in sputter erosion rate (with respect to a plane surface) can be expressed as follows: (1) where Y(θ) is the sputtering yield, and the coefficients a(θ), b(θ), and c(θ) are functions of cosθ, sinθ, and sputtering yield Y(θ) and its derivatives. Thus, fractional change in sputtering yield becomes a polynomial function of even powers of https://www.selleckchem.com/products/icg-001.html h 0/λ. As the h 0/λ ratio increases with continuous ion
bombardment, the local angle of incidence, (θ-α), along the ripple patterns will eventually become so large that the upstream part of the ripples will be shadowed from the incoming ion flux by the preceding peak. Thus, the limiting condition to avoid such shadowing of many incident beam is [26]: (2) According to this condition, if the ratio (h 0/λ) exceeds a threshold value, troughs of a sinusoid will not be eroded further but instead erosion will take place at the crests. This in turn may give rise to a sawtooth-like waveform. Methods The substrates
used in the experiments were cut from a Si(100) wafer. A UHV-compatible experimental chamber (PREVAC, Rogów, Poland) was used which is equipped with a five-axes sample manipulator and an electron cyclotron resonance-based broad beam, filamentless ion source (Tectra GmbH, Frankfurt, Germany). The chamber base pressure was below 5 × 10-9 mbar, and the working pressure was maintained at 2.5 × 10-4 mbar using a differential pumping unit. Silicon samples were fixed on a sample holder which was covered by a sacrificial silicon wafer of the same lot to ensure a low impurity environment. The beam diameter and the fixed ion flux (throughout this study) were measured to be 3 cm and 1.3 × 1014 ions cm-2 s-1, respectively. Corresponding to this flux value of 500 eV argon ions, the rise in sample temperature is nominal, and hence for all practical purposes, sample temperature should not be very high from room temperature.