Elsevier

Microelectronics Reliability

Volume 64, September 2016, Pages 225-229
Microelectronics Reliability

Numerical investigation of the effects of phosphorus on the mechanical responses of [1 1 0]-oriented silicon nano-wires

https://doi.org/10.1016/j.microrel.2016.07.070Get rights and content

Highlights

  • The tensile strength of P doped unnotched Si NWs decreases as the doping concentration increases.

  • Dopant P can strengthen Si NWs by raising the threshold of cracking and blocking the propagation of cracks.

  • The unnotched pure 2 nm and 3 nm Si NWs exhibit plastic behaviour under uniaxial tension, but partially become brittle.

Abstract

The mechanism that phosphorus (P) impurities, one of the most commonly used impurities in silicon (Si), affect the tensile mechanical responses of [1 1 0]-Si nano-wires (NWs) is investigated using molecular dynamics (MD) with a Modified Embedded Atom Method (MEAM) potential. Tensile tests at 300 K are carried out for unnotched and notched Si NWs. For unnotched cases, P impurities randomly replace Si atoms at specific concentrations. Two patterns are considered for notched models, one undoped and one with doped notch tip. Results show that evenly distributed P impurities introduce an overall decrement in fracture strength of unnotched Si NWs as the concentration increases. The failure manner is that the local defects come into being around P, then rapidly nucleate and propagate, finally lead to fracture. However, for notched models, P can evidently enhance the fracture strength by impeding the cracking and growth of pre-existing cracks. With regard to Si NWs with surface defects exposed to strain, fracture usually starts from surface owing to stress concentration, indicating that P functions more critically on surface, especially near crack tips. Hopefully, this finding can be applied in the reliability design of Si-based NW devices. Moreover, when doped with P or notched on surface, the transition of failure mode for 2 nm and 3 nm NWs can happen, namely from ductile to brittle.

Introduction

Si NWs are promisingly widely applied in nano-technology areas such as nano-scale transistors [1], power sources [2], sensing element [3], actuators [4], and battery nodes [5]. The mechanical properties of Si NWs are much different from macro Si structures owing to their extremely small size and high surface/volume ratio. As an important structure with great engineering significance, the fundamental understanding of Si NW properties is a critical issue for its application.

The mechanical properties of Si NWs have been tested by experiments [6], [7], [8], [9] in recent years, and exhibit orientation dependant features. For instance, [1 1 1] Si NWs are brittle [6] under uniaxial tensile stress while [1 1 0] Si NWs are ductile with diameters below 60 nm [7]. However, these experiments mainly focused on the effects of processing techniques, testing measurements, and size effect, from which one can hardly extract useful instructions of reliability design for Si NWs. Besides manufacturability and testability, the reliability of Si NWs is one of the most concerned issues.

During fabrication process, surface and intrinsic defects, and foreign elements in Si NWs are unavoidable, which are closely related to its reliability. This work only focuses on the influences of impurities. Many literatures have reported that impurities exert significant effects on the mechanical properties of bulk Si [10], [11], [12], [13]. Accordingly, it is worth finding out how impurities affect Si NWs. The electrical and photovoltaic properties of Si NWs are activated by foreign traces of elements such as P, one of the most widely used dopants in macro Si structures, which is also an important dopant in Si NWs [14]. In present work we take the representative [1 1 0]-oriented Si NWs as research subject, for [1 1 0] is the preferred growth direction when the diameter is below 10 nm [15], and they possess some particular properties such as plasticity under uniaxial stress as mentioned above.

Experiments provide the most reliable data and phenomena. However, it is time consuming and not economical compared with numerical simulations. A large number of numerical studies concerning NWs, including multi-scale [16] and MD simulations [8], [9], [17], [18], have been reported. Among the published MD calculations about Si NWs, only Zhan et al. [17] investigated the effects of stacking faults on the mechanical properties while the others only focused on defectless NWs.

In this study, large-scale MD simulations are employed to investigate how substitutional P impurities affect the tensile responses of [1 1 0] Si NWs, including two patterns of models, unnotched (including pure and doped models without notches) and notched Si NWs. We aim to clarify the underlying physical mechanisms so as to provide suggestions for reliability design of Si NWs based devices. Actually, interstitial [19] and phosphorus-vacancy pair [20] are also common sites for dopant P in crystal Si, which will be discussed in our future work.

Section snippets

Interatomic potential model

The reliability of MD results largely depends on interatomic potentials. A semi-empirical model Modified Embedded Atom Method (MEAM) is used in current work, which was constructed by Baskes et al. [21] Some other formalisms such as SW [22], Tersoff [23], EDIP [24] have been widely used to characterize Si but fail to maintain its brittle nature while MEAM does [9]. Besides, MEAM also takes the advantage in describing the surface properties of Si [9], [25], which is extremely important to

Tensile strength-doping concentration relationship in unnotched Si NWs

Fig. 1 plots the tensile strengths as a function of doping concentration for various diameters, where a typical stress-strain curve for brittle fracture is also presented. The typical ductile stress-strain curve is shown in Fig. 3. Modelling and tensile tests are repeated 10 times for each concentration. One can see the uncertainty of strength introduced by random distribution and the overall decreasing trend. The lattice distortion introduced by substitutional P atoms evolves into local

Summary

MD is employed to investigate how the electro-active impurity P affects the mechanical properties of [1 1 0]-Si NWs. Substitutional doping site is considered in present work. Some interesting results have been obtained and listed below, which are sufficiently compared with experiments to testify the reliability of MD simulations.

  • (1)

    The tensile strength of unnotched NWs decreases as the doping concentration increases.

  • (2)

    P can strengthen Si nano-wires by raising the threshold of cracking and blocking

Acknowledgements

This work is financially supported by National Natural Science Foundation of China [No. 51175503], Doctoral Innovation Foundation of NUDT [No. B140305] and China Scholarship Council [No. 201403170367].

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