Time-dependent Dielectric Breakdown Data Research Articles

A microscopic mechanism of dielectric breakdown in SiO2 films: An insight from multi-scale modeling

Despite extensive experimental and theoretical studies, the atomistic mechanisms responsible for dielectric breakdown (BD) in amorphous (a)-SiO2 are still poorly understood. A number of qualitative physical models and mathematical formulations have been proposed over the years to explain experimentally observable statistical trends. However, these models do not provide clear insight into the physical origins of the BD process. Here, we investigate the physical mechanisms responsible for dielectric breakdown in a-SiO2 using a multi-scale approach where the energetic parameters derived from a microscopic mechanism are used to predict the macroscopic degradation parameters of BD, i.e., time-dependent dielectric breakdown (TDDB) statistics, and its voltage dependence. Using this modeling framework, we demonstrate that trapping of two electrons at intrinsic structural precursors in a-SiO2 is responsible for a significant reduction of the activation energy for Si-O bond breaking. This results in a lower barrier for the formation of O vacancies and allows us to explain quantitatively the TDDB data reported in the literature for relatively thin (3–9 nm) a-SiO2 oxide films.

Temperature dependence of reliability characteristics for magnetic tunnel junctions with a thin MgO dielectric film

Temperature dependence of the reliability characteristics of magnetic tunnel junctions (MTJs) with a thin (∼1 nm thick) MgO dielectric film were investigated by numerical analyses based on the E-model, 1/E-model, and power-law voltage V-model, as well as by measuring time-dependent dielectric breakdown (TDDB) degradation. Although the tunneling process giving rise to TDDB is still under debate, the temperature dependence of TDDB was much weaker using the 1/E model than the E-model or power-law model. The TDDB data measured experimentally in CoFeB/MgO/CoFeB MTJ devices also showed rather weak temperature dependence, in good agreement with the numerical results obtained from the 1/E-model considering the self-heating effect in MTJ devices. Moreover, we confirmed by interval voltage stress tests that some degradation in the MgO dielectric layer occurred. Based on our findings, we suggest that to characterize the reliability of MTJs, combined temperature measurements of TDDB and 1/E-model analyses taking the self-heating effect into account should be performed.

Electrical Analysis of High Dielectric Constant Insulator and Metal Gate Metal Oxide Semiconductor Capacitors on Flexible Bulk Mono-Crystalline Silicon

We report on the electrical study of high dielectric constant insulator and metal gate metal oxide semiconductor capacitors (MOSCAPs) on a flexible ultra-thin $(25~\mu{\rm m})$ silicon fabric which is peeled off using a CMOS compatible process from a standard bulk mono-crystalline silicon substrate. A lifetime projection is extracted using statistical analysis of the ramping voltage $({\rm V}_{\rm ramp})$ breakdown and time dependent dielectric breakdown data. The obtained flexible MOSCAPs operational voltages satisfying the 10 years lifetime benchmark are compared to those of the control MOSCAPs, which are not peeled off from the silicon wafer.

Towards understanding intrinsic degradation and breakdown mechanisms in SiOCH low-k dielectrics

The degradation and breakdown mechanisms of a SiOCH low-k material with k = 2.3 (25% porosity) and thicknesses ranging from 90 nm to 20 nm were investigated. By combining the time dependent dielectric breakdown data at positive/negative bias stress with the thickness scaling results, dielectric failure is proven to be intrinsic and not influenced by copper drift or metal barrier deposition induced dielectric damage. It is shown that stress induced leakage current (SILC) can be used as a measure of dielectric degradation. Therefore, low field lifetimes can be safely estimated using SILC extrapolation. Based on our results, both the impact damage model and the power law model have a good accuracy for low field lifetime prediction. Recovery and anneal experiments are used to study the physical nature causing the observed negative flatband voltage shifts in our metal-insulator-semiconductor planar capacitor structures, where hydrogen induced unstable fast and slow donor type interface states are hypothesized to be the root cause of the observed shifts. We suggest that atomic hydrogen is released from the dielectric during electron injection and migrates to the interfacial region. Our model is further supported by an observed irreversible SILC change during the recovery and anneal studies. The degradation mechanism proposed in this work, supported by the low field lifetime data, provides a feasible explanation for intrinsic low-k dielectric failure.

Extreme-Value Statistics and Poisson Area Scaling With a Fatal-Area Ratio for Low- $k$ Dielectric TDDB Modeling

During the study of time-dependent dielectric breakdown (TDDB) of back-end-of-line low- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> dielectrics, accurate statistical and area-scaling models are important for the final reliability lifetime projection. The extrapolated product lifetime from high percentiles to low percentiles has strong dependence on the choice of a statistical model. Meanwhile, the lifetime of a product chip is obtained typically by extrapolating TDDB data from small test structures to large chip areas by an area-scaling law. In this paper, a thorough investigation of low- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> TDDB statistical distribution with large sample size and various metal areas was conducted to validate a physically relevant statistical model for low- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> TDDB modeling. In addition, we explored the various TDDB dependence on metal area and introduced a new fatal-area-ratio concept for low- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> TDDB area-scaling model in the event that the conventional Poisson area-scaling law failed based on the as-designed area ratio. A graphic shift-and-compare method was then developed to determine, experimentally, the fatal-metal-area ratio. The determination of the fatal-metal-area ratio should be critical for an accurate low- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> TDDB lifetime projection and process assessment.

Time-Dependent Dielectric Breakdown of 4H-SiC/$ \hbox{SiO}_{2}$ MOS Capacitors

Time-dependent dielectric breakdown (TDDB) is one of the major issues concerning long-range reliability of dielectric layers in SiC-based high-power devices. Despite the extensive research on TDDB of SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> layers on Si, there is a lack of high-quality statistical TDDB data of SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> layers on SiC. This paper presents comprehensive TDDB data of 4H-SiC capacitors with a SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gate insulator collected over a wide range of electric fields and temperatures. The results show that at low fields, the electric field acceleration parameter is between 2.07 and 3.22 cm/MV. At fields higher than 8.5 MV/cm, the electric field acceleration parameter is about 4.6 cm/MV, indicating a different failure mechanism under high electric field stress. Thus, lifetime extrapolation must be based on failure data collected below 8.5 MV/cm. Temperature acceleration follows the Arrhenius model with activation energy of about 1 eV, similar to thick SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> layers on Si. Based on these experimental data, we propose an accurate model for lifetime assessment of 4H-SiC MOS devices considering electric field and temperature acceleration, area, and failure rate percentile scaling. It is also demonstrated that temperatures as high as 365 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deg</sup> C can be used to accelerate TDDB of SiC devices at the wafer level.

Time-Dependent Dielectric Breakdown Studies of PECVD H:SiCN and H:SiC Thin Films for Copper Metallization

Time-dependent dielectric breakdown (TDDB) of hydrogenated silicon carbon nitride (H:SiCN) and silicon carbide (H:SiC) thin films and the impact of copper (Cu) ions has been investigated using metal-insulator-semiconductor (MIS) capacitors with Cu gate electrodes. These films were deposited using a plasma-enhanced chemical vapor deposition technique. Bias temperature stress tests of the MIS capacitors were done at up to 275°C using an electric field up to 3.0 MV/cm. With the introduction of an electric field-dependent factor, the first law of thermodynamics was found to describe the experimental TDDB data of these films very well. The time to breakdown was found to decrease exponentially with an increase in the electric field and temperature, agreeing with the thermochemical E model excellently. The presence of Cu ions in these films was found to significantly accelerate the breakdown. It is believed that the electric field enhancement in the dielectric films at the cathode region due to the accumulation of positive Cu ions causes the breakdown acceleration. The data in this work suggest that the quick initial leakage current decrease during the TDDB tests of Cu-gated capacitors is caused by electron trapping instead of the Cu ion accumulation in the dielectric films. © 2004 The Electrochemical Society. All rights reserved.

Determination of the nature of molecular bonding in silica from time-dependent dielectric breakdown data

An effective molecular dipole moment of 7–13 e Å is routinely observed during time-dependent dielectric breakdown testing of silica-based dielectrics. A Mie-Grüneisen analysis of the molecular bonding states indicates that the upper end of the effective dipole moment range (13 e Å) is associated with a stretched silicon-oxygen bond while the lower end (7 e Å) is consistent with a hole-captured silicon-oxygen bond.

Time-dependent dielectric breakdown of hydrogenated silicon carbon nitride thin films under the influence of copper ions

Time-dependent dielectric breakdown (TDDB) of hydrogenated silicon carbon nitride (H:SiCN) thin films deposited using a plasma-enhanced chemical vapor deposition has been studied using metal-insulator-semiconductor capacitors with Cu gate electrodes. The experimental TDDB data of these films agree excellently with the thermochemical E model where the time to breakdown decreases exponentially with an increase in the electric field and temperature. Breakdown of the H:SiCN films was found to be significantly accelerated by the presence of Cu ions in the films. The breakdown acceleration is believed to be caused by an electric field enhancement due to the accumulation of positively charged Cu ions.

Thermochemical description of dielectric breakdown in high dielectric constant materials

A thermochemical/molecular model is developed for breakdown in high dielectric constant materials and the model suggests that a fundamental relationship exists between dielectric breakdown strength (Ebd) and dielectric constant (k). The model indicates that Ebd should show an approximate (k)−1/2 dependence over a wide range of high dielectric constant materials. The model also predicts that the field-acceleration parameter (γ), from time-dependent dielectric breakdown (TDDB) testing, should increase with dielectric constant. TDDB and Ebd data are presented for model support. The thermochemical model suggests that the very high local electric field (Lorentz-relation/Mossotti-field) in high-k dielectrics tends to distort/weaken the polar molecular bonds making them more susceptible to bond breakage by standard Boltzmann processes and/or by hole capture and thus lowers the breakdown strength.

Characteristics of n+ polycrystalline-Si/Al2O3/Si metal–oxide– semiconductor structures prepared by atomic layer chemical vapor deposition using Al(CH3)3 and H2O vapor

We report interface and dielectric reliability characteristics of n+ polycrystalline-silicon (poly-Si)/Al2O3/Si metal–oxide–semiconductor (MOS) capacitors. Al2O3 films were prepared by atomic layer chemical vapor deposition using Al(CH3)3 and H2O vapor. Interface state density (Dit) and dielectric reliability properties of n+ poly-Si/Al2O3/Si MOS structures were examined by capacitance–voltage, conductance, current–voltage, and time-dependent dielectric breakdown measurements. The Dit of the n+ poly-Si/Al2O3/Si MOS system near the Si midgap is approximately 8×1010 eV−1 cm−2 as determined by the conductance method. Frequency dispersion as small as ∼20 mV and hysteresis of ∼15 mV were attained under the electric field of ±8 MV/cm. The gate leakage current of ∼36 Å effective thickness Al2O3 dielectric measured at the gate voltage of −2.5 V is ∼−5 nA/cm2, which is approximately three orders of magnitude lower than that of a controlled oxide (SiO2). Time-dependent dielectric breakdown data of Al2O3/Si MOS capacitors under the constant current/voltage stress reveal excellent charge-to-breakdown characteristics over controlled oxide. Reliable gate oxide integrity of Al2O3 gate dielectric is manifested by the excellent distribution of gate oxide breakdown voltage on 128 million MOS capacitors having isolation edges. Extracted time constant and capture cross section of the Al2O3/Si junction are discussed.

Time dependent breakdown of ultrathin gate oxide

Time dependent dielectric breakdown (TDDB) of ultrathin gate oxide (<40 /spl Aring/) was measured for a wide range of oxide fields (3.4<|E/sub ox/|<10.3 MV/cm) at various temperatures (100/spl les/T/spl les/342/spl deg/C). It was found that TDDB of ultrathin oxide follows the E model. It was also found that TDDB t/sub 50/ starts deviating from the 1/E model for fields below 7.2 MV/cm. Below 4.8 MV/cm, TDDB t/sub 50/ of intrinsic oxide increased above the value predicted by the E model obtained for fields >4.8 MV/cm. The TDDB activation energy for this type of gate oxide was found to have linear dependence on oxide field. In addition, we found that /spl gamma/ (the field acceleration parameter) decreases with increasing temperature. Furthermore, it was found that testing at high temperatures (up to 342/spl deg/C) and low electric field values did not introduce new gate oxide failure mechanism. It is also shown that TDDB data obtained at very high temperature (342/spl deg/C) and low fields can be used to generate TDDB model at lower temperatures and low fields. Our results (an enthalpy of activation of 1.98 eV and dipole moment of 12.3 e/spl Aring/) are in complete agreement with previous results by McPherson and Mogul. Additionally, it was found that TDDB is exponentially dependent on the gate voltage.

Monte Carlo Sphere Model for Effective Oxide Thinning Induced Extrinsic Breakdown

The Monte Carlo sphere model is extended to deal with the extrinsic time-dependent-dielectric-breakdown (TDDB) by incorporating the well-known “effective oxide thinning” concept. Percolation simulation, based on this model for the first time, evidences that the process defects induced extrinsic TDDB is also statistical in nature as is the intrinsic one, and is characterized by a probability function defining local oxide thinning. The experimental bimodal or even multimodal characteristics can be reproduced accordingly. Furthermore, the simulation results in the extrinsic regime are found to be sample-size (i.e., the total number of samples that span the breakdown statistics) dependent, suggesting that care should be taken when evaluating the extrinsic TDDB data in a real manufacturing process.

Underlying physics of the thermochemical E model in describing low-field time-dependent dielectric breakdown in SiO2 thin films

The underlying physics behind the success of the thermochemical E model in describing time-dependent dielectric breakdown (TDDB) in SiO2 thin films is presented. Weak bonding states can be broken by thermal means due to the strong dipolar coupling of intrinsic defect states with the local electric field in the dielectric. This dipole-field coupling serves to lower the activation energy required for thermal bond-breakage and accelerates the dielectric degradation process. A temperature-independent field acceleration parameter γ and a field-independent activation energy ΔH can result when different types of disturbed bonding states are mixed during TDDB testing of SiO2 thin films. While γ for each defect type alone has the expected 1/T dependence and ΔH shows a linear decrease with electric field, a nearly temperature-independent γ and a field-independent ΔH can result when two or more types of disturbed bonding states are mixed. The good agreement between long-term TDDB data and the thermochemical model suggest strongly that the oxygen vacancy is an important intrinsic defect for breakdown and that field, not current, is the primary cause of TDDB under low-field conditions.

On‐Chip Decoupling Capacitance with High Dielectric Constant and Strength Using SrTiO3 Thin Films Electron‐Cyclotron‐Resonance‐Sputtered at 400°C

It is shown that thin (100 nm) film electron‐cyclotron‐resonance‐sputtered at 400°C has a good time dependent dielectric breakdown (TDDB) characteristic, a high dielectric constant, and high dielectric strength. Extrapolation of TDDB data suggests that the lifetime of the films can be estimated to be 10 years at an electric field of 2 MV/cm. These electrical properties and process parameters imply the possibility of dielectrics of on‐chip decoupling capacitors. The deposition and annealing temperatures (both 400°C) of this film satisfy the temperature requirement of aluminum interconnect processing in the fabrication of standard complementary metal oxide silicon large‐scale integrated circuits.

Comparison of proportional hazards models and neural networks for reliability estimation

Because of increased manufacturing competitiveness, new methods for reliability estimation are being developed. Intelligent manufacturing relies upon accurate component and product reliability estimates for determining warranty costs, as well as optimal maintenance, inspection, and replacement schedules. Accelerated life testing is one approach that is used for shortening the life of products or components or hastening their performance degradation with the purpose of obtaining data that may be used to predict device life or performance under normal operating conditions. The proportional hazards (PH) model is a non-parametric multiple regression approach for reliability estimation, in which a baseline hazard function is modified multiplicatively by covariates (i.e. applied stresses). While the PH model is a distribution-free approach, specific assumptions need to be made about the time behavior of the hazard rates. A neural network (NN) is particularly useful in pattern recognition problems that involve capturing and learning complex underlying (but consistent) trends in the data. Neural networks are highly non-linear, and in some cases are capable of producing better approximations than multiple regression. This paper reports on the comparison of PH and NN models for the analysis of time-dependent dielectric breakdown data for a metal-oxide-semiconductor integrated circuit. In this case, the NN model results in a better fit to the data based upon minimizing the mean square error of the predictions when using failure data from an elevated temperature and voltage to predict reliability at a lower temperature and voltage.

Characterization of time-dependent dielectric breakdown in intrinsic thin SiO 2

Time-dependent dielectric breakdown data collected from 6.5-, 9-, 15-, 20- and 22.5-nm-thick SiO 2 films are presented. The failure distributions are of single mode with no apparent extrinsic population. The logarithm of the median-test-time-to failure, log( t 50), is described by a linear electric field dependence. Contrary to reports in earlier studies, the field acceleration parameter is observed to be insensitive to temperature and has a value of approximately 1.0 decade MV −1 cm −1 for the range of oxide thicknesses studied. Capacitance-voltage studies indicate that there is no strong correlation between oxide trapped charges and time to failure under constant voltage stress conditions.

Time-dependent dielectric breakdown measurements on RPECVD and thermal oxides

Time-dependent dielectric breakdown (TDDB) measurements have been made on 96, 121 and 147 Å oxides deposited by remote plasma enhanced chemical vapor deposition (RPECVD) upon 300°C Si( 100) device grade substrates. The oxides were used to form an array of 10 μm × 10 μm square capacitors. The oxides were then subjected to electron injection from the substrate at 0.1 A cm −2 constant stress current. Analysis of the forcing voltage during stress showed the RPECVD oxide to have an initial electron trap density of 1.7±0.2 × 10 18 cm −3. The stress voltage rose linearly with time, giving net electron trap filling rates of 3.1±0.2 × 10 16 cm −3 s −1. The TDDB data were analyzed to find breakdown occurring on average in localized areas of (69±9 Å) 2 containing 19±4 filled electron traps. A similarly fabricated 92 Å thermal oxide showed an initial electron trap density of 5.6±2 × 10 17 cm −3 and a net electron trap filling rate of 2.0±0.2 × 10 16 cm −3 s −1. For the 92 Å thermal and 96 Å RPECVD oxides, both ≈ 100 Å thick, an average localized breakdown area of (68±11 Å) 2, containing 18±3 filled electron traps was calculated. The breakdown area and electron trap numbers did not vary in a statistically significantly manner with deposition technique or oxide thickness. Analysis of the electric field showed that at breakdown for the thermal oxide 1/ E = 0.0702±0.0008 cm MV −1, while the RPECVD oxide had 1/ E=0.11±0.01 cm MV −1.

Electrical breakdown induced by silicon nitride roughness in thin oxide–nitride–oxide films

The time-dependent dielectric breakdown (TDDB) characteristics of thin oxide–nitride–oxide (ONO) films containing 4 nm of Si3N4 were found to be exclusively determined by statistical thickness fluctuations of the Si3N4 layer. A two-parameter statistical model describes this roughness and explains experimental TDDB data. A simple growth model combined with the statistical model reduces the number of parameters to one. It is consistent with TDDB data and is in quantitative agreement with transmission electron microscopy and x-ray photoelectron spectroscopy data and is able to explain the origin of the roughness. On an ONO with a 4 nm Si3N4 layer and an area of 8 cm2—corresponding to the total storage area of a 256 Mbit dynamic random access memory—the thinnest point in the Si3N4 can be expected to be below 10 Å. So eliminating the Si3N4 roughness would bring a drastic improvement in reliability.

Time Dependent Dielectric Breakdown Measurements on RPECVD and Thermal Oxides

Time dependent dielectric breakdown (TDDB) measurements have been made on a 96 Å oxide deposited by remote plasma enhanced chemical vapor deposition (RPECVD) upon a 300°C Si(100) device grade substrate. The oxide was used to form an array of square capacitors. The oxide was then subjected to electron injection from the substrate at 0.1 A/cm2 constant stress current. The charge‐to‐breakdown (QBD) was measured and found to be . A similarly fabricated 92 Å thermal oxide capacitor array showed a QBD value of . Analysis of the forcing voltage during stress showed the RPECVD oxide to have an initial trap density of , compared to for the thermal oxide. In both cases, at 0.1 A/cm2, the stress voltage across the oxide rose linearly with time. Trap generation rates of and were measured for the RPECVD and thermal oxides, respectively. The TDDB data were analyzed to find breakdown occurring in localized areas of containing filled electron traps.