Extraction of parameters and simulation of the hard breakdown I-V characteristics in ultrathin gate oxides

Abstract

Modeling of the post-breakdown current in MOS devices is receiving considerable attention in the last years because of the ever decreasing reliability margins of the gate insulators as a consequence of the ongoing miniaturization trends. In this work, we explore a compact representation for this current after a hard breakdown event suitable for circuit simulation environments. The model is based on a diode-like equation with series resistance. Accurate parameters extraction is accomplished by means of the Integral Difference Function (IDF) method using the exact expression for the current-voltage (I-V) characteristic. IntroductionAs it is well known, the application either of a high or prolonged electrical stress to a thin oxide layer in a MOS device leads inexorably to the formation of a low-resistance current path between gate and substrate. This localized current flow through the insulating layer is the signature of dielectric breakdown [1]. Several attempts have been made not only to enhance the understanding of the electron transport mechanism under such circumstance but also with the aim of finding a suitable mathematical representation of the phenomenon for circuit simulation purposes. Concerning the so-called final, catastrophic or hard breakdown (HBD) event, two approaches have been followed: firstly, we have those models which rely on numerical simulation schemes like the oxide thinning model [2] or the multiple quantum wire model [3], and secondly, those which provide a closedform expression for the I-V characteristic like the quantumpoint-contact model (QPC) for dielectric breakdown [4]. This latter model predicts that the breakdown path simply behaves as a resistor with conductance values in the order of the quantum conductance unit 2e 2 /h≈(12.9kΩ) -1 , e and h being the electron charge and the Planck's constant, respectively. Nevertheless, since the QPC model assumes metallic-like charge reservoirs at the two ends of the constriction, instead of semiconductor electrodes, the model is unable to account for properly the low voltage region. In this work, we explore an alternative approach to this problem which circumvents this deficiency. We propose that the combined system electrodes-breakdown path is well represented by a diode-type equation affected by a series resistance. Nevertheless, as important as having a good model is the adequacy of the parameter extraction process and this problem is addressed by means of the IDF [5]. The use of an integral method rather than a differential one makes this approach especially immune to measurements errors because of the low-pass filter nature of integration.

Logarithm Cofactor Difference Extrema Method of MOSFET's Post-Breakdown Current and Application to Parameter Extraction

“…[1][2][3][4][5][6][7][8][9] In order to model the breakdown current characteristics, several models have been reported. Among them, a simple model based on an ideal diode with a series resistance is proposed to describe the I-V characteristics.…”