Surface Diffusion Field Research Articles

Distinct Failure Modes of AlGaN/GaN HEMTs Under ESD Conditions

This article reports the distinct failure mechanisms and insights on device degradation of AlGaN/GaN high electron mobility transistors (HEMTs) under electrostatic discharge (ESD) stress conditions. The role of device surface, MESA isolation, and gate Schottky junction in defining the degradation type is discovered. Premature breakdown at the MESA Schottky junction and dislocation induced failure in the active region and their consequences on ESD robustness are reported. Physical mechanisms responsible for snapback instability in transmission line pulsing (TLP) characteristics are discussed. Change in device failure from soft to hard with pulsewidth is revealed. Finally, the role of contact resistivity, surface diffusion, and channel electric field and its fringing effect at contacts are analyzed in context to ESD failure of AlGaN/GaN HEMTs. Various stages of device degradation during TLP stress are captured on-the-fly using high-resolution (HR) optical microscopy and high-speed Si charge-coupled device (CCD) detector. Postdevice failure, damaged regions are analyzed using transmission electron microscopy and scanning electron microscopy together with in situ energy-dispersive X-ray spectroscopy to probe details of failure mechanisms involved. Finally, based on the learning from this article, design guidelines for an ESD robust HEMT are proposed.

Step Bunching Induced by Immobile Impurities in a Surface Diffusion Field

It is well known that impurities attached to a surface cause step bunching, but the effects of a surface diffusion field on step bunching have not been studied sufficiently. In this paper, we carry out Monte Carlo simulations using a simple lattice model and study how the surface diffusion field affects the growth law of the bunch size in the step bunching induced by immobile impurities. We consider a vicinal face with step spacing l. Both impurities and atoms impinge from a vapor phase to the vicinal face, but they do not evaporate. We change the impingement rate of atoms, F, keeping the ratio of the impingement rate of impurities to F constant. When F is smaller than a critical value Fc, the vicinal face becomes unstable and an array of equidistant bunches is formed. In the case of diffusion-limited growth, Fc is inversely proportional to l2. The dependence of Fc on l changes in the case of step-kinetics-limited growth: Fc becomes inversely proportional to l.

Two mechanisms forming a comblike step pattern induced by a moving linear adatom source.

We carry out phase field simulations to study properties of the comblike step patterns induced by an adatom source. When an adatom source advances right in front of a step, step wandering is caused by the asymmetry of the surface diffusion field and small protrusions are formed. If the velocity of the source V_{p} is smaller than a critical value V_{p}^{c}, the protrusions follow the adatom source with coarsening of the step pattern, and a regular comblike pattern with finger-like protrusions is formed. With a sufficiently small V_{p}, the gap of the supersaturation is large at the adatom source. Since the period of protrusions, Λ, decreases with increasing V_{p}, the coarsening of step pattern is irrelevant for the protrusions to catch up with the adatom source. Near V_{p}^{c}, the gap of the supersaturation at the adatom source is small. Taking account of the increase in Λ with increasing V_{p}, the coarsening of the step pattern is essential for the protrusions to follow the adatom source.

Numerical simulations of migration and coalescence behavior of microvoids driven by diffusion and electric field in solder interconnects

A diffuse interface model is developed to simulate the effect of electric field on the morphological evolution and migration behavior of the microvoid in the solder interconnect consisting of the Sn based solder and Cu substrate (i.e., Sn/Cu system). The model takes into account the coupled effect of surface diffusion and electric field, and the validity of the model is confirmed by good agreement between the simulation and theoretical predictions in terms of evolution behavior of the noncircular microvoid driven by surface energy. The results show that the coalescence of microvoids driven only by surface energy occurs when the microvoids contact each other. The evolution and migration of the microvoid under electric field are governed by the magnitude of electric field and the initial size of the microvoid. The microvoid migrates at a constant velocity under a weak electric field, while the strong electric field results in the shape change of the microvoid from circular to narrow crack-like. In addition, the migration velocity of the microvoid increases linearly with the voltage and is inversely proportional to the size of the microvoid; a small microvoid can catch up with a large one, and finally they merge to form a larger microvoid, which may promote the open circuit failure near the solder/Cu interface in solder interconnects.

Microstructure of Pyrocarbon with Chemical Vapor Infiltration

The carbon/carbon (C/C) composites were rapidly fabricated by multi-factor coupling fields CVI in a self-made furnace from propylene without carrier gas. The microstructure of different composites has been investigated with polarized light microscopy (PLM), scanning electron microscopy (SEM), X-ray diffraction (XRD) and Raman spectroscopy. The results showed that the carbon/carbon composites obtained at 650°C and 12kPa satisfied both the deposition efficiency and matrix quality. The increasing regenerative cones were observed with the raised pressures. A new pyrocarbon was observed under the PLM with graphitization degree of 77.9% and crystallite size of 30.5nm after heat treatment temperature at 2300°C for 2 hours. Its formation mechanism was briefly analyzed based on the influence of the surface diffusion and electromagnetic field.

Electromigration-induced surface evolution in bamboo lines with transgranular and intergranular edge voids

The evolution of a surface intersected by transgranular (TG) and intergranular (IG) edge voids under isotropic surface diffusion and electric field effects is simulated numerically under both mass-conserving and non-mass-conserving boundary conditions. A surprising similarity is found in the surface topology of transgranular voids between our non-mass-conserving model and Schimschak and Krug's [J. Appl. Phys. 87 (2000) 695] mass-conserving model. The electric field is found to slow the development of an intergranular groove along a positively tilted grain boundary (GB), and to cause thinning or thickening of grains under non-mass-conserving conditions.

Step wandering due to the gap in diffusion coefficient on the upper and the lower terraces

In a vicinal face of a crystal, wandering instability of steps may occur under nonequilibrium conditions when asymmetry in the surface diffusion field exists. Near the transition temperature of Si(1 1 1) surface between 1×1 and 7×7 structures, wandering instability is observed in growth. We provisionally attribute this instability to the gap in diffusion coefficient on the upper and the lower terraces whose surface structures are different. With linear stability analysis and Monte Carlo simulation, we show that the instability occurs in growth if the diffusion coefficient of the lower terrace is larger. The wandering pattern in a vicinal face is chaotic when evaporation is allowed, but is rather periodic when evaporation is absent. The latter result agrees with the experimental observation.

Wandering and Bunching Instabilities of Steps Described By Nonlinear Evolution Equations

We study wandering and bunching instabilities of steps in a surface diffusion field with a direct electric field applied perpendicular to the steps. The drift of adatoms induced by the electric field modifies the surface diffusion length in the upper terrace and that in the lower terrace. This asymmetry causes wandering instability of an isolated step when the drift is opposite to the step motion. Near the critical point the time evolution of a step obeys the Kuramoto–Sivashinsky equation, which gives rise to spatiotemporal chaos. The asymmetry also causes bunching instability of an array of repulsive straight steps. The instability near the critical point is an amplification of density large wavelength. The step density after the instability obeys the Benney equation, which shows a stable array of solitons corresponding to the formation of stable bunches.

Control of Chaotic Wandering of an Isolated Step by the Drift of Adatoms

The drift of adatoms strongly influences the wandering pattern of an isolated step moving in a surface diffusion field. When the drift velocity has a component against the step motion and exceeds a critical value, the straight step becomes unstable with long wavelength fluctuations, and wanders. This wandering pattern can be controlled by changing the direction of the drift. When the drift has no component parallel to the step edge, the unstable step obeys the Kuramoto-Sivashinsky equation and shows a chaotic pattern. When the drift has a component parallel to the step edge, the step obeys the Benney equation. If the parallel component is sufficiently large, the step shows a regular pattern.

An Experimental Study of Step Dynamics under the Influence of Electromigration: Si(111)

The velocity of monoatomic step motion in the neighborhood of a bunch has been measured in situ using a UHV electron microscope. The width of step bunches at different temperatures and the intrinsic time that lead to step bunching have also been determined. Direct and alternating current were used to heat the Silicon(111) between 1000°C and 1300°C. The results show that the diffusion regime prevails. The asymmetry of the surface diffusion of adatoms is proved experimentally. It is consistent with the adatom electromigration effects. The surface diffusion field under the influence of an electric current can induce an attractive force between the steps. This force balances the step-step repulsive interactions (entropic and energetic) inside the bunch and stabilizes its width. The effective charge on the adatom has been estimated from the critical frequency of AC when the step bunching does not operate. It is around 0.001 electron.

Computer simulation of surface growth

A Monte Carlo model has been used to study surface growth in thin film epitaxy. The model accounts for atom attachment, detachment, and surface diffusion. By varying the deposition temperature and impingement rate, we have explored the surface roughening transition in a nonequilibrium situation and the conditions under which normal, lateral, and step flow growth occurs. The results show that reentrant oscillation occurs as a result of the variation of surface diffusion length with deposition temperature, and that it is a natural phenomenon in kinetic thin film deposition on substrates with permanent steps. We have also examined the morphological instability in step flow growth and found that it is related to the step height. Steps with multi-atomic layers are seen to be less stable in a surface diffusion field, due to a decrease in the attachment rate of growth units from the upper terrace.

Instabilities of Atomic Steps in the Surface Diffusion Field

Instabilities of Atomic Steps in the Surface Diffusion Field

Wandering Instability of an Isolated Step with Direct Electric Current

We study wandering instability of an isolated step in a surface diffusion field with a direct electric current applied perpendicular to the step. The drift of adatoms caused by the electric current modifies the surface diffusion length. In sublimation the difference between the modified surface diffusion length in the upper terrace and that in the lower terrace causes an instability with respect to fluctuation along the step. This instability occurs when the drift is opposite to the step motion and its strength is within a limited range. Near the lower critical current the step obeys the Kuramoto-Sivashinsky equation, which gives rise to spatiotemporal chaos.

Nonlinear Effect in Step Bunching Caused by Electric Current

We study nonlinear effects in step bunching in a surface diffusion field with a direct electric current. Linear stability analysis shows that the bunching instability occurs in sublimation at long wavelength if the step distance is smaller than the surface diffusion length and the drift of adatoms induced by the electric current is in the step down direction. When we take account of the nonlinear effect, the density of steps obeys the Benney equation, which shows an array of step bunches or spatiotemporal chaos. This feature is similar to the step bunching caused by the asymmetry of step kinetics except that the surface profile may change with the sign of the dispersion term.

Structural feature of surface in MBE growth Monte Carlo simulation

The Monte Carlo study of the surface structure under MBE growth conditions is carried out. Characteristic surface diffusion field is obtained with respect to each growth mode. Two-dimensional nucleation on the terrace is investigated in atomic level using the time evolution of the density of clusters. Concerning the anisotropy of surface structure, the main reason for this is not the surface diffusion anisotropy but the anisotropic bond energy. The stoichiometric A-B crystal with the layer-by-layer mode is obtained in a range Ø AA = Ø AB = Ø AB r , r ≥ 1, J A = J B , where Ø AA, Ø BB and Ø AB are the bond energies of A-A, B-B and A-B bonds, J A and J B are the flux of A and B atoms, respectively. It is found that the orderliness S of A-B crystal is a function of ( 2Ø AB kT − Δμ kT ), where Δμ kT is the parameter representing the intensity of the flux.

Morphological instability caused by asymmetry in step kinetics.

We study motion of a train of linear repulsive steps in a surface diffusion field. With asymmetric step kinetics (Schwoebel effect) and repulsive step interaction, fluctuations of step density at long wavelengths become unstable if undersaturation exceeds a critical value. This leads to a morphological instability, in which the diffusion takes place along the interface in contrast to the usual Mullins-Sekerka instability. The instability develops a step bunch with a diffuse front and a sharp end.

Fluctuation and instability of steps in a diffusion field.

Fluctuation and morphology of steps growing in a surface diffusion field are studied theoretically and by the Monte Carlo simulation. Owing to the asymmetry in step kinetics (Schwoebel effect), a morphological instability takes place for advancing steps at a critical impingement rate ${\mathit{f}}_{\mathit{c}}$ of gas atoms. The fluctuation of a step is reduced for receding steps with f${\mathit{f}}_{\mathrm{eq}}$, and enhanced for advancing steps with f>${\mathit{f}}_{\mathrm{eq}}$. The width of a single step shows critical divergence at ${\mathit{f}}_{\mathit{c}}$. Above the instability f>${\mathit{f}}_{\mathit{c}}$, the step motion exhibits spatiotemporal chaos, in which the crystal anisotropy influences the morphology. For a vicinal face, when the step advancement rate increases, the motion of consecutive steps is strongly correlated and the terrace width becomes stable although the fluctuation of each step is enhanced. When steps recede in sublimation, bunching of the steps is observed, which is analyzed as an instability of antiphase oscillation.

Evolution of a train of interacting steps in a surface diffusion field

We study the time evolution of a train of parallel straight steps interacting with an elastic interaction. A general formula for the step velocity is given as a function of the step distances, the interaction strength and the kinetic coefficients of the step. If the attachment kinetics from the lower terrace of the step is faster than that from the upper terrace, the interference of diffusion field gives rise to an effective attraction in sublimation. There is a critical undersaturation below which two repulsive steps can form a bound state. When a step collides with a bound pair, recombination of the steps takes place, which looks like billiards. For an equidistant step train, under a similar condition, an instability occurs and the steps form pairs, which has a significant effect on the growth law of the vicinal surface.

Fluctuation of steps in a surface diffusion field

Nonequilibrium fluctuation of advancing or receding steps is controlled by the growth mechanism in contrast to the equilibrium fluctuation. For a Burton-Cabrera-Frank type model, we adopt a linear stochastic equation to describe the step fluctuation δy k ( t). If the step kinetics is fast from the lower terrance (Schwoebel effect), a step becomes smooth when it recedes, whereas it becomes rough when it advances. The rougheness diverges when the supersaturation approaches the Mullins-Sekerka instability point. We perform Monte Carlo simulations with a lattice model. The growth velocity agrees very well with the theoretical value, and the expected step smoothing and roughening are confirmed. Fluctuation of equidistant parallel steps in a vicinal face is also studied.

Kinematical binding transition of steps in a surface diffusion field.

The motion of steps in a surface diffusion field with asymmetric step kinetics is studied. An effective attraction from interference of the diffusion field causes a kinematical binding transition of two repulsive steps if undersaturation exceeds a critical value. This binding transition leads to a nonlinear growth law, V\ensuremath{\sim}-\ensuremath{\Vert}\ensuremath{\delta}c${\mathrm{\ensuremath{\Vert}}}^{2/3}$, for \ensuremath{\delta}c0. If there is a third step at a distance, it collides with the pair and recombination takes place. In a step train this recombination is repeated.