Vincent M. Dwyer

Thermal failure in semiconductor devices

Abstract A first principles approach to the problem of thermal breakdown in semiconductor devices is developed using Greens function formalism. The problem of thermal runaway at a defect of arbitrary geometry, subject to an arbitrary power profile, is considered. A solution is presented for the specific case of a rectangular parallelepiped shaped defect, subject to constant input power. It is expected that this geometry will model the defect in many semiconductor devices more accurately than the defect geometries used in the past. Unlike previous work, this allows all three dimensions of the defect to take on the full range of values. The theory developed here provides a natural framework for the explanation of results previously reported in the literature. It is shown that there are four time domains and not three as previously thought, and these exist for all shapes of defect. Thus, it is wrong to conclude that a pulse power/time to failure dependence of the form P f α t f − 1 2 necessarily implies a roughly two-dimensional defect. Several relationships are found to exist within the model which allow estimates to be made of the defect dimensions and failure temperature. Experimental data drawn from the literature, produce Pf/tf profiles similar to those indicated by the theory.

The effects of elastic backscattering on the Auger or X-ray photoelectron spectra of solids

Simple attempts to understand the background on the low energy side of a spectral Auger or photoemission peak picture the electron as undergoing multiples of a typical loss according to a Poisson process with a mean distance λ. This model ignores elastic backscattering effects, and leads to the rather unrealistic situation in which the multiple loss peaks have the same intensity as the no loss peak. Here we have considered two related one-dimensional models which include backscattering and which allow exact solution. We find that, in general, losses follow a non-Poisson distribution governed by a characteristic distance Λ which includes both elastic and inelastic effects. However, contrary to the approximate results of Tougaard and Sigmund, the same value of Λ operates for electrons at all depths and so exponential attenuation is predicted. This modified (non-Poisson) distribution then leads to a background which decays with energy E from the peak as E−12 for large E and which varies approximately logarithmically closer to the peak, results which are in agreement with Tougaard and Sigmund and in support of the experimental work of Tougaard and Ignatiev.

Electrostatic discharge thermal failure in semiconductor devices

The problem of calculating for electrostatic discharge (ESD) thermal failure is considered by the thermal convolution integral technique. It is shown that the common assumption that threshold failure occurs after five time constants is unjustified and that the simple average power method for assessing threshold parameters is, consequently, invalid. New expressions for the threshold parameters are presented which retain the simplicity of the average power method, yet represent only a small sacrifice of the accuracy (typically 5%) of more complex methods. In addition, the relaxation of the constraints of a pure Wunsch-Bell damage profile and of an exponentially decaying current pulse is considered. >

A comparison of electron transport in AES/PES with neutron transport theory

Abstract The Boltzmann equation represents the standard theory for particle transport in random media. It is thus applicable to Auger/photo electrons in polycrystalline solids. In this paper we compare the convential Auger/PES theory, which neglects angular deflection of the emitted electrons, with two scattering models which have been found to be useful in Reactor physics. We find that the conventional Auguer yield formula φ em (θ) = ( Nλ i 4π )cos θ holds approximately qualitatively, but not quantitatively. We also find that, in keeping with Monte Carlo calculations, there is a substantial alteration to the mean depth of analysis relative to the no-scattering model.

An investigation of electromigration induced void nucleation time statistics in short copper interconnects

The stress evolution model (SEM) of Korhonenet al., is used to calculate the void nucleation time in a large number of short interconnects (lengths up to 50 μm). Finite element calculations show that the effect of the nonlinearity in the SEM model is small, and that a mesh size of the order of the grain size is quite adequate to give accurate simulation results. Via failure is the only mode considered in the current calculations, however the gain in simulation time over other solution methods means that more complex situations, possibly including void dynamics, may be modeled in future in this way. Using normal mass-lumping methods the analysis is isomorphic to the voltage development on a random RC chain, so standard methods from very large scale integrated static timing analysis may be used to obtain dominant time constants at each mesh point. This allows the distribution of nucleation times to be obtained as a function of the distributions of line parameters. Under the assumption of a lognormal grain s...

Electromigration failure in a finite conductor with a single blocking boundary

The (one‐dimensional) electromigration boundary‐value problem is considered for the case of a single blocking boundary with a constant vacancy supply at the other boundary. Using the drift/diffusion model expressed by the Fokker–Planck equation, we find that the saturation time (tsat) increases exponentially with current density (j) and not as j−2, as has been suggested. However, it is not the saturation time which determines the lifetime (tbd); it is the time to reach some critical vacancy concentration (c*). In agreement with experimental results and numerical calculations, we find that tbd∼j−2. We also find that tbd∼c*.

Modeling the electromigration failure time distribution in short copper interconnects

The electromigration (EM) lifetime in short copper interconnects is modeled using a previously developed means of generating realistic interconnect microstructures combined with the one-dimensional stress evolution equation of Korhonen et al. [J. Appl. Phys. 73, 3790 (1993)]. This initial analysis describes the void nucleation and subsequent growth in lines blocked at one end and terminated with a pad at the other. For short copper interconnects, the failure time is largely spent on void growth, and, for sufficiently short lines (≲50 mm), the growth is largely steady state. This allows for the development of a simple expression for the variation of the failure time with microstructure. Assuming that the diffusion activation energies are normally distributed, the permanence property of summed lognormals leads to a roughly lognormal distribution for EM failure times. Importantly for EM design rules, linear extrapolation on lognormal plot is found to slightly underestimate interconnect reliability.

Thermal breakdown in GaAs MES diodes

Abstract A thermal breakdown analysis of planar GaAs metal-semiconductor diodes is presented and three models relating failure power ( P f ) to corresponding failure times ( t f ) are compared. The standard Wunsch and Bell model, a modified form of the Tasca model, and a three-dimensional model (developed by the authors) are fitted to experimental data. The results indicate that, within given failure time domains, GaAs structures of this kind follow the same general patterns, P f αt f − q , as those previously reported for silicon semiconductor devices. There is one exception. In the time domain roughly between 1 and 20 μs, the failure power is given by P f α 1/ log e ( t f ). Analytic expressions are used to extract three “defect” dimensions from forward bias experimental data. These “defect” dimensions are discussed with reference to the device dimensions and the ambient temperature. Two distinct visible and electrical failure modes have been observed and these are linked to changes in the channel conductance subsequent to an applied pulse.

Electromigration behavior under a unidirectional time-dependent stress

The problem of current induced electromigration in VLSI interconnects, under an arbitrary time-dependent stress, is considered within the drift/diffusion model. It is shown that, by transforming into the convected frame and solving the resulting moving boundary problem, the vacancy build-up may be followed by solving two coupled integral equations. The important large-time behavior is obtained using standard asymptotic techniques. A series solution and an approximate small-time solution are also derived. It is found that, for a unidirectional periodic stress, the equivalent dc current, appropriate to EM reliability tests is the periodic average value. In addition a design rule for arbitrary time-dependent stress is suggested.

Latent damage and parametric drift in electrostatically damaged MOS transistors

Abstract The relationship between parametric drift and latent damage in ESD gate-stressed MOSFETs is studied. Sub-breakdown damage causes minor characteristic distortion, which may remain undetected until failure. However, such damage is only significant within a narrow stress-voltage window. Oxide breakdown may cause straightforward malfunction (i.e. catastrophic failure ) or degraded transistor action. Degraded devices can degenerate further under working voltages (0–10 V), providing a latent failure mechanism. Degradation phenomena are attributed to the intrusion of polysilicon gate-material into the oxide and channel regions. Catastrophically failed and degraded devices are modelled using the PSpice circuit simulation system. The effects of degradation upon CMOS logic operation are also examined.