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首页> 外文期刊>Physical review. B, Condensed Matter And Materals Physics >Trajectory reversal approach for electron backscattering from solid surfaces
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Trajectory reversal approach for electron backscattering from solid surfaces

机译：固体表面电子反向散射的轨迹反转方法

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The backscattering of medium energy electrons from solid surfaces is investigated by analysis of a linearized Boltzmann-type kinetic equation. A closed expression is derived for the Green's function in an infinite medium valid for a spherically symmetric potential describing the interaction with the ionic subsystem. The solution is expressed in terms of fluctuations of the energy loss and scattering angles and the collision statistics associated with them. Since the fluctuation part is independent of the boundary conditions of the considered problem, solution of the backscattering problem requires an appropriate treatment of the collision statistics. In this context, the exact solution for the Oswald-Kasper-Gaukler model is derived and its limitations are analyzed. An exact approach is presented and implemented in an efficient Monte Carlo scheme based on the trajectory reversal technique. The resulting procedure is faster than the conventional Monte Carlo algorithm by several orders of magnitude. Results for the angular distribution are compared with conventional Monte Carlo calculations and perfectly agree with the latter within their statistical uncertainty. A second approximate algorithm is also given. The approximation involved in this second procedure turns out to be very reasonable: deviations from direct Monte Carlo calculations remain below ～5% for energies exceeding 200 eV. The integral elastic-backscattering coefficient for normal incidence for a large number of materials in the energy range 50 eV-10 keV is found to approximately exhibit a universal dependence on the ratio of the inelastic and the transport mean free paths, the so-called scattering parameter.
机译：通过分析线性化的玻耳兹曼型动力学方程，研究了中能电子从固体表面的反向散射。对于在描述与离子子系统相互作用的球对称电势有效的无限介质中，格林函数导出了一个封闭表达式。解决方案用能量损失和散射角的波动以及与之相关的碰撞统计量表示。由于起伏部分独立于所考虑问题的边界条件，因此后向散射问题的解决方案需要对碰撞统计信息进行适当的处​​理。在这种情况下，导出了Oswald-Kasper-Gaukler模型的精确解，并分析了其局限性。在基于轨迹反转技术的高效蒙特卡洛方案中提出并实现了一种精确的方法。生成的过程比常规的蒙特卡洛算法快几个数量级。将角度分布的结果与常规的蒙特卡洛计算进行比较，并在统计上的不确定性内与后者完全吻合。还给出了第二种近似算法。事实证明，第二种方法的近似值是非常合理的：对于超过200 eV的能量，与直接蒙特卡洛计算法得出的偏差保持在〜5％以下。发现许多材料在50 eV-10 keV能量范围内对法向入射的积分弹性后向散射系数大致表现出对无弹性和传输平均自由程之比的普遍依赖性，即所谓的散射参数。

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