depends on the relative energy resolution only, as well as the relative stopping power of incoming and outgoing ions. The detector resolution and energy broadening associated with the measuring geometry contribute to the energy spread, δE. The detector acceptance angle and the finite beam spot size define a scattering angle range δϕ causing a kinematic energy spread δEkin according to equation 6: (6) A detailed analysis of the different contributions to depth resolution shows that this kinematic effect is the predominant term near the surface, severely limiting the permitted detector acceptance angle, whereas energy straggling dominates the resolution at larger depth. For example, if one estimates δϕ for a scattering angle of 37.5° causing a kinematic energy shift comparable to typical detector energy resolutions of 1%, the angular spread δψ must be less than 0.4°. The angular spread can be maintained within this range by contributions from the beam spot size; however, the solid angle geometry of the detector is only 0.04 msr. Therefore, a detector system with large solid angle as well as high depth resolution may enable corrections for the kinematic energy shift. In an elastic scattering event, the kinematics requires that the target atom is recoiled with significant energy. Equation 7 models the recoil kinematical factor that occurs during the ion bombardment. (7) (8) (9) (10) Equation 7 gives a mathematical model of the collision event when the heavier ions in the beam strike the specimen. Ks is termed the kinematical factor for the scattered particle (Eq. 8) with a scattering angle of θ, and the recoiled particle (Eq. 9) with a recoil angle of Φ. The variable r is the ratio of mass of the incident nuclei to that of the mass of the target nuclei, (Eq. 10). To achieve this recoil of particles, the specimen needs to be very thin and the geometries need to be precisely optimized to obtain accurate recoil detection. Since ERD beam intensity can damage the specimen and there has been growing interest to invest in the development of low energy beams for reducing the damage of the specimen. The cathode is divided into two insulated halves, where particle entrance position is derived from charges induced on the left, l, and right, r, halves of the cathode. Using the following equation, x-coordinates of particle positions, as they enter the detector, can be calculated from charges l and r : (11) Furthermore,