Invited paper
Comphy — A compact-physics framework for unified modeling of BTI

https://doi.org/10.1016/j.microrel.2018.04.002Get rights and content

Abstract

Metal-oxide-semiconductor (MOS) devices are affected by generation, transformation, and charging of oxide and interface defects. Despite 50 years of research, the defect structures and the generation mechanisms are not fully understood. Most light has been shed onto the charging mechanisms of pre-existing oxide defects by using the non-radiative multi-phonon theory. In this work we present how the gist of physical models for pre-existing oxide defects can be efficiently abstracted at a minimal loss of physical foundation and accuracy. Together with a semi-empirical model for the generation and transformation of defects we establish a reaction-limited framework for unified simulation of bias temperature instabilities (BTI). The applications of the framework we present here cover simulation of BTI for negative (NBTI) and positive (PBTI) gate voltages, life time extrapolation, AC stress with arbitrary signals and duty cycles, and gate stack engineering.

Introduction

The past 50 years of BTI research [1] and the numerous ongoing controversies [2] suggest that a) the underlying physical mechanisms are so diverse and complex that a rigorous description is barely feasible and b) the apparent phenomena are so peculiar that models without sound physical foundation can only cover a small range of observations. The controversies start with the role of dangling bonds at the oxide/channel interface: While it is commonly accepted that dangling bonds are created during stress, there are experimental studies which show that they do not dominate the degradation at BTI conditions [3, 4], opposed to what is typically assumed in reaction-diffusion (RD) models [5]. Attempts towards a rigorous description of charge trapping as an important contributor to BTI are based on the non-radiative multi-phonon (NMP) theory [[6], [7], [8]]. In particular, the 4-state NMP model [9] has been successfully applied to model various aspects of BTI [10, 11]. Hydrogen reactions were often linked to BTI and recently put into the context of NMP models [12]. However, given the complexity of this detailed physical model which tries to capture a number of peculiarities possibly not essential for life time prediction, many researchers employ simple power law descriptions which are used to fit the evolution of the threshold voltage shift ΔV th as a function of stress time ts, but have limited prediction accuracy and do not include recovery.

While there is certainly not a lack of BTI models in general, there still seems to be a gap between “detailed physical theory which is barely applicable for practical purposes” and “practical approximations which miss important aspects of oxide degradation”.

In this paper we present an abstraction of the most elaborate findings from recent NMP studies [[13], [14], [15]] together with a semi-empirical model for defect generation and transformation and put them into a fast and easy-to-use framework we call “Comphy”, short for “compact-physics”. The core of this effort is the abstraction of the more complex multistate NMP processes to an effective 2-state model [16]. While this abstraction inevitably implies a slight loss in accuracy, which affects the switching behavior of individual defects, it still provides accurate results for the mean degradation and has a very limited number of effective physical parameters. It will be shown that this 2-state NMP model describes charging of oxide defects with “90% accuracy at 10% complexity” and is applicable across technologies and stress polarities.

As a fundamental prerequisite to any physical reliability model, we show in Section 2 how the electrostatics of MOS structures are computed based on the material parameters of the channel and the gate stack and we give a summary of the defect models used in Comphy. In Section 3 we apply Comphy to a) a commercial 130 nm SiON technology to confirm the correctness of the model for NBTI degradation under DC and AC stress b) a commercial planar 28 nm high-κ technology to discuss the NBTI and PBTI life time predictions, corroborated by a stress experiment covering 12 decades in stress time and c) to an imec technology targeting DRAM periphery devices with thick oxides to investigate the impact of gate stack engineering on PBTI and NBTI. Across all technologies we find very similar defect properties which enable unified modeling of NBTI and PBTI.

Section snippets

Modeling

The simulation of the threshold voltage Vth for arbitrary time-dependent gate voltages VG and temperatures with Comphy is based on a description of the gate stack and channel properties as discussed in the first part of this section. It will be demonstrated that the mean degradation ΔVth under all BTI conditions can be accurately captured by a 2-state NMP model and a simple double-well (DW) model as outlined in the second and third part of this section. The 2-state NMP model accounts for

Application

Comphy 1.0 is used throughout this work and all simulations can be fully reproduced using the material and defect parameters given in Tables 6 and 7 (in the Appendix). The following assumptions are used throughout all simulations presented in this work.

  • The reduction of the electric field due to the charges in the oxide is considered, except for simulations using the dedicated fast AC simulation mode.

  • pMOS and nMOS devices of the same technology are simulated with the same set of defects.

  • For

Conclusions

Reliability phenomena increasingly dictate advances in the semiconductor industry. This led to intensive research which revealed fundamental oxide degradation mechanisms. Detailed models were proposed which try to capture the common root source of various reliability phenomena, making such universal physical models very attractive. However, adopting these models for standard reliability analyses is difficult because of their inherent complexity. The Comphy framework we have presented here

Acknowledgments

Stimulating discussions with Hans Reisinger, Gunnar Rott, Alexander Grill, Adrian Vaisman Chasin, Al-Moatasem El-Sayed, Lars-Åke Ragnarsson, Hiroaki Arimura, Franz Schanovsky, and Wolfgang Goes are gratefully acknowledged. The research leading to these results has received funding from the FFG project no 861022 and the Austrian Science Fund (FWF) project no i2606-N30. GTS (Global TCAD Solutions) is acknowledged for support.

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