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Reaction-Diffusion Model

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Fundamentals of Bias Temperature Instability in MOS Transistors

Part of the book series: Springer Series in Advanced Microelectronics ((MICROELECTR.,volume 52))

Abstract

This chapter discusses different aspects of the Reaction-Diffusion (RD) model used to interpret dissociation and reformation of the Si−H bonds (in other words, creation and reverse-anneal of dangling Si-bonds or interface traps) present at the silicon/oxide interfaces of a CMOS transistor. The theory presented in this chapter is later combined with other features of NBTI to interpret measurements in Chap. 6. The reaction part of the R-D model interprets the chemical reactions like Si−H bond dissociation and reformation taking place at the interface, while the diffusion part interprets the transport of Hydrogen species in the oxide and the gate medium. In the NBTI stress phase with a particular stress bias, the Si−H bond dissociation initiates generation of interface traps over time, which later reaches quasi-equilibrium with the diffusive components. After that the diffusion of Hydrogen species defines the time evolution of interface trap generation with a power law. The power-law time exponent is a unique signature of the diffusing species and it shows no variation with the change in stress conditions (bias, temperature and frequency). In the NBTI relaxation phase, the diffusion of Hydrogen species also defines the time evolution of interface trap repassivation. This single dependence of the time evolution, in both stress and relaxation phases, only on the diffusing species leads to frequency independence of interface trap generation—a distinct feature of NBTI measured over a wide range of transistors.

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Notes

  1. 1.

    This solution is intriguing, as among many differential equations used to describe natural phenomena in this universe, RD is a unique one that gives a robust power-law time exponent for several decades in time, whose value depends only on nature of diffusion.

  2. 2.

    An alternate dissociation mechanism of Si−H via passivated dopants like phosphorous-Hydrogen (P–H) complex though have a lower dissociation energy and a exothermic reaction, P–H assisted dissociation of Si−H results n ~ 1/4 [12, 26] and E A,IT ~ 0.36 eV, which is not supported by recent NBTI measurements, see Chap. 3.

  3. 3.

    Similar calculation can also be performed using Sanderson’s scale [58] that leads to similar values.

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Acknowledgments

The authors acknowledge Narendra Parihar for his editorial support.

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Authors and Affiliations

  1. Materials and Manufacturing Directorate, Air Force Research Laboratory, Dayton, OH, 45433, USA

    Ahmad Ehteshamul Islam

  2. National Research Council, National Academy of Sciences, Washington DC, 20001, USA

    Ahmad Ehteshamul Islam

  3. Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India

    Nilesh Goel & Souvik Mahapatra

  4. Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47907, USA

    Muhammad Ashraful Alam

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  1. IIT Bombay, Mumbai, India

    Souvik Mahapatra

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Islam, A.E., Goel, N., Mahapatra, S., Alam, M.A. (2016). Reaction-Diffusion Model. In: Mahapatra, S. (eds) Fundamentals of Bias Temperature Instability in MOS Transistors. Springer Series in Advanced Microelectronics, vol 52. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2508-9_5

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  • DOI: https://doi.org/10.1007/978-81-322-2508-9_5

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