A simplified predictive model for high-fluence ultra-short pulsed laser ablation of semiconductors and dielectrics Benxin Wu a, *, Yung C. Shin b a Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, 10W. 32nd Street, Engineering 1 Building, Chicago, IL 60616, United States b School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, United States 1. Introduction Ultra-short pulsed lasers have extremely high achievable radiation intensities, and can ablate almost any materials. They also have extremely short pulse durations, and therefore can realize precise material removal with very small heat affected zone. Therefore, ultra-short pulsed lasers have many competitive applications in micromachining of metals, semiconductors and dielectrics for the production of electronic, medical and optical devices [1]. Hydrodynamics [2–5] or molecular dynamics (MD) [6–14] models are powerful tools for the detailed study of the funda- mental physics in ultra-short laser-matter interactions. However, they are often very time-consuming, and not very easy to apply. On the other hand, some models (such as that in Ref. [15]), although very easy to use, involve free adjustable variables and hence are not really predictive. For micromachining and many other applications, where laser ablation depth is the major concern, a predictive model (without any free adjustable variables) that is easy to apply but at the same time can also provide reasonably accurate predictions of ablation depth is very desirable for process design and optimization. However, this kind of model has been rarely reported in literature. In the authors’ previous work [17], a simplified predictive model has been developed for high-fluence ultra-short laser ablation of metals, which is based on the so-called ‘‘separation temperature’’ concept as will be explained later. The model is computationally efficient and very easy to apply (only the two- temperature heat conduction equations need to be solved), and the predictions have shown good agreements with experimental measurements for high-fluence metal ablation with pulse dura- tions less than around 10 ps [17]. In this paper, following a similar concept, a simplified predictive model will be developed for high- fluence ultra-short pulsed laser ablation of dielectrics and semiconductors. It should be noted that the reported modeling work in this paper is significantly different from the authors’ previous work in Ref. [17] because of the big differences in the governing equations as will be shown later. Next, the ‘‘separation temperature’’ concept will be explained. Ultra-short laser ablation is a very complicated process, and several different physical mechanisms have been proposed in literature to explain the fundamental mechanisms for material removal, such as spallation, Coulomb explosion, phase explosion, critical point phase separation, fragmentation, etc. [3–14,16]. The dominant physical mechanism certainly depends on laser para- meters. The hydrodynamic simulations in Ref. [3] and the molecular dynamic simulations in Ref. [6] suggest that the critical point phase separation (CPPS) is the dominant physical mechanism for material removal during ultra-short laser ablation at high- fluences. Despite the many complex physical processes involved, there are some features of the high-fluence ultra-short laser- matter interactions that make the development of a simplified but reasonable model possible. It has been found in Ref. [3] that during the ultra-short laser ablation the thermodynamic trajectories of Applied Surface Science 255 (2009) 4996–5002 ARTICLE INFO Article history: Received 18 June 2008 Received in revised form 19 October 2008 Accepted 21 December 2008 Available online 27 December 2008 Keyword: Femtosecond laser ablation ABSTRACT Ultra-short pulsed laser ablation is a very complicated process and a predictive model is very desirable for process design and optimization in practical applications. However, the molecular dynamics or hydrodynamic models, although they are powerful and necessary tools for the study of the fundamental physics, are time-consuming and difficult to apply for practical applications. In this paper, a predictive, simplified and easy to apply model has been developed for high-fluence ultra-short laser ablation of semiconductors and dielectrics. Unlike many other simplified models, this model does not involve any free adjustable variables. The model predictions agree well with experimental measurements for femtosecond laser ablation, while the model is not very applicable for pulse durations more than 10 ps. ß 2009 Elsevier B.V. All rights reserved. * Corresponding author. Tel.: +1 312 567 3451; fax: +1 312 567 7230. E-mail address: bwu11@iit.edu (B. Wu). Contents lists available at ScienceDirect Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc 0169-4332/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2008.12.051