Resistivity scaling model for metals with conduction band anisotropy

Abstract

It is generally understood that the resistivity of metal thin films scales with film thickness mainly due to grain boundary and boundary surface scattering. Recently, several experiments and ab initio simulations have demonstrated the impact of crystal orientation on resistivity scaling. The crystal orientation cannot be captured by the commonly used resistivity scaling models and a qualitative understanding of its impact is currently lacking. In this work, we derive a resistivity scaling model that captures grain boundary and boundary surface scattering as well as the anisotropy of the band structure. The model is applied to Cu and Ru thin films, whose conduction bands are (quasi-) isotropic and anisotropic respectively. After calibrating the anisotropy with ab initio simulations, the resistivity scaling models are compared to experimental resistivity data and a renormalization of the fitted grain boundary reflection coefficient can be identified for textured Ru.

Ab initio screening of metallic MAX ceramics for advanced interconnect applications

“…𝜏 𝑛 (𝒌) = 𝜏. This assumption is preferred in cases when the resistivity is limited by phonon scattering [41]. By contrast, an assumption of isotropic  is more appropriate when the scattering is due to randomly distributed point defects.…”

First principles-based screening method for resistivity scaling of anisotropic metals

“…One approach is to describe the band structure anisotropy with an anisotropic effective mass tensor, for which a generalization of the Mayadas-Shatzkes model can be obtained analytically, as presented in Ref. [36]. Another approach is presented in Ref.…”

“…Therefore, the usefulness of the ρλ product as a figure-of-merit can be questioned, as it does not capture the anisotropy of the charge carriers in the conduction band(s). While there are strong indications that band structure anisotropy should not be neglected [33,34], the impact of band structure anisotropy on the resistivity scaling has received rather little attention so far [14,27,35,36].…”

Квантовый Транспорт В Полупроводниковом Нанослое С Учетом Поверхностного Рассеяния Носителей Заряда

“…Выведем из уравнения Лиувилля (3) уравнение, аналогичное кинетическому уравнению Больцмана. Если представить гамильтонианĤ как сумму собственного гамильтонианаĤ 0 и зависящего от времени потенциала V (t), индуцирующего переходы между собственными состояниями, то уравнение для матричных элементов оператора плотности ρ n ′ n принимает вид [23] i 10), запишем уравнение для диагональных элементов матрицы плотности f n = ρ nn :…”

“…В полупроводниковых пленках наблюдается резкое увеличение сопротивления при малых толщинах [4][5][6]. Имеется значительное количество теоретических работ, в которых для решения задач об электропроводности тонких пленок и проволок использовался стандартный кинетический метод [7][8][9][10][11][12][13]. Однако данный метод неприменим, когда толщина пленки или радиус проволоки сравнимы или меньше длины волны де Бройля носителя заряда.…”