Extended incident-angle dependence formula for physical sputtering

We extend a new semi-empirical formula for incident-angle dependence of normalized sputtering yield that includes the contribution from the direct knock-out process to the sputtering yield. This was not considered fully in the previous sputtering formula. Three parameters included in the new formula are estimated for data calculated with a Monte Carlo code ACAT for D+ ions incident obliquely on C, Fe and W materials in incident energy regions from several tens of eV to 10 keV. Then, the parameters are expressed as a function of incident energy. The extended formula with these functions well reproduces the calculated data of normalized sputtering yield in the whole energy ranges