Study of Time Dependent Dielectric Breakdown Distribution in Ultrathin Gate Oxide

Abstract

The computer simulations of the time dependent dielectric breakdown (TDDB) percolation path are performed for ultrathin gate oxides. With our new percolation model, an interesting and new behavior of TDDB distribution was found. Weibull slope decreases monotonously with decreasing oxide thickness, and has a gap at an oxide thickness of approximately the effective defect size. This behavior can be understood well if we consider that an overlap of two neighboring defects becomes necessary to cause a sudden breakdown when oxide thickness exceeds the effective defect size. This phenomenon is very important because Weibull slope has a large effect on device reliability.

Lifetime of high-k gate dielectrics and analogy with strength of quasibrittle structures

“…Various percolation models have been proposed to study gate dielectric breakdown numerically. 4,17,18 From optimum fitting of experimental observations, it has been inferred that the effective size of the defects is about 2 -3 nm, although the physical extent of the defect might be smaller. 4 Now imagine that each cell consists of n = t ox / l 0 subcells, where t ox = thickness of the oxide layer and l 0 = effective thickness of a subcell ͓Fig.…”

“…For gate dielectrics, some previous microscopic models have employed percolation theory to connect the electrontrapping defect density to the probability of breakdown via a spanning defect cluster in a finite system. 4,17,18 For very thin gate dielectrics, recent mathematical results could also be used to describe the smoothed percolation transition from nonspanning to spanning clusters in a small finite system. [23][24][25] A difficulty with this approach, however, is that it requires additional input to describe the dynamics of breakdown ͑d / dt͒ in response to the local applied voltage V a ͑t͒.…”

“…But we will see that only minimal, generic, assumptions about the microscopic physics are required. We start by considering percolation models for gate dielectrics, 4,17,18 which relate breakdown to the appearance of a spanning cluster of ͑uncorrelated͒ conducting defects. In this context, the simplest way to describe time evolution would be to postulate a differential equation for the mean defect density ͑t͒ in a potential breakdown cell.…”

“…Although our theory is based on general notions of parallel and series couplings of capacitors, which become resistors upon local breakdown, 13,14 in principle, its key assumptions can also be connected to microscopic statistical models, 15 such as the original dielectric breakdown model ͑DBM͒ of Niemeyer et al 16 as well as more recent percolation models developed for gate dielectrics. 4,17,18 In Sec. IV, we test predictions of the theory against the experimental data for the breakdown of high-k gate dielectrics.…”

Estimation of Breakdown Electric-Field Strength While Reflecting Local Structures of SiO2 Gate Dielectrics Using First-Principles Molecular Orbital Calculation Technique

“…The dielectric breakdown of a SiO 2 film with defects has been widely discussed in terms of percolation theory, [3][4][5] which is illustrated in Fig. 1.…”