over from the direct release mechanism by over an order of magnitude. Other parameters had negligible effect on the simulation results. Using this method of combining first principles calculations with a sensitivity analysis in FLOORS, key parameters and key controlling mechanisms can be identified in degradation systems. The results presented here were for MOS regions of specialized test structures in which H2 concentrations could be controlled and trap densities could be easily and reliably extracted. However, this method is applicable to similar systems in other materials and interface.

16.4FLOORS Example: Gate Degradation and Diffusion Under Piezoelectric Strain

GaN high electron mobility transistors, although having impressive RF power densities, currently suffer observed and documented output degradation. This long-term reliability is currently being addressed, and a number of mechanisms have been proposed which attempt to theorize the problem. Diffusion of metal and other impurities from under the gate, enhanced by mechanical strain from the inverse piezoelectric effect, has been proposed as a mechanism for electrical degradation of AlGaN/GaN HEMTs in the off state [33]. Ni diffusion from Ni/Au gates has been observed in degraded areas of devices, and characteristic bulk diffusion models have been matched to increases in trap concentration over time. These observations have been linked to documented unrecoverable decreases in drain current and corresponding increases in gate current.

Recent electron energy-loss spectroscopy (EELS) line scans performed by [34] show clear signs of increased concentration of Ni and O in the AlGaN layer under the Au/Ni gate after off-state biasing conditions. These areas exhibit a distinctive diffusion-like shape as shown in Fig. 16.14. UV light-assisted trapping analysis has been employed by [33] to determine trap densities and activation energies. The amplitude, indicating density, of the dominant trap was measured as a function of time and temperature and yielded classic diffusion behavior [35]. This diffusion behavior was also observed at room temperature and indicates an additional potential driving the diffusion of these impurities other than temperature. This additional potential is the increasing mechanical strain in the AlGaN layer due to the inverse piezoelectric effect.

Off-state fields were computed with FLOORS, and the piezoelectric effect was incorporated to generate mechanical strain in a full elastic computation. The strain results were used to simulate the diffusion that would occur in a step-stress experiment. The altered structure was then used to sweep the I–V current to predict the corresponding drop in drain current, IDS.

The mechanical strain due to the inverse piezoelectric effect, ei, is incorporated via a first-order expression relating strain and electric field. See Eq. (16.31) in Table 16.2. The corresponding inverse piezocoefficients for GaN [36] are listed

Fig. 16.14 TEM image of the region with Ni and oxygen diffusion and the associated threading dislocation

Table 16.2 Governing equations and constants used in simulation

16.31ei ¼ dij Ej, where j ¼ 1, 2, i ¼ 1, 2, 3 in 2D formulation

The impurity profile is included in Eq. 16.2 as an additive term expressed as “+ Impurity (x)”. The relative permittivity of GaN, eGaN, was taken as a static value of 9.0. This value is frequency dependent and tends to decrease at high frequencies such as the typical cutoff frequencies, fT, of industrial HEMTs of ~40 GHz. Subsequent models will account for this. In Eq. 16.3, “D0” represents the modified diffusivity due to imposed strain. In all off-state simulations, temperature, T, was held at 300 K

in Table 16.2. The electric field Ej, given by ðdc=dxÞ , is derived from the spatially varying electrostatic potential c, found as a solution to Poisson’s equation given by Eq. 32 in t.IV.2. For a given set of bias conditions and device dimensions, the electrostatic potential within the device is determined, and electric field is subsequently derived. The strain distribution within the structure is then determined as a function of bias. Figures 16.15 and 16.16 respectively show the strain distributions around the gate for an off-state bias condition of VDS ¼ 30 V, VG ¼ 5 V, and a VDS ¼ 0 state (VD ¼ VS ¼ 30 V) where VG was held at 5 V.

Modified diffusivity of impurity species as a function of strain [37] is given by Eq. (16.33) in Table 16.2 where Q is the species-dependent energy per unit strain.

Fig. 16.15 Simulation figure of GaN HEMT in the off state with VGS ¼ 5 V and VDS ¼ 30 V. Mechanical strain contours due to the inverse piezo effect show highest compressive strains of ~ 7e 4 in the AlGaN layer at both edges under the gate but much more pronounced on the drain edge (right side)

–0.2

Fig. 16.16 Simulation figure of GaN HEMT in the VDS ¼ 0 state with VG ¼ 5 V, VD/VS ¼ 30 V. Mechanical strain contours due to the inverse piezo effect show highest compressive strains of ~ 7e 4 in the AlGaN layer equally at both edges under the gate