1 AlGaN/GaN HEMT Degradation: an Electro-thermo-mechanical Simulation Matthias Auf der Maur, Member, IEEE, and Aldo Di Carlo, Member, IEEE, Abstract—We present fully selfconsistent simulation results based on an electro-thermo-mechanical model of a typical AlGaN/GaN HEMT structure. The mechanical stress state is analyzed under different DC operating conditions in view of possible dislocation formation and movement by comparing simulated elastic energy densities and resolved shear stresses with theoretically predicted values. In particular, we find non-zero resolved shear stress on all wurtzite slip systems, with relevant values especially at high DC power. This could allow formation and movement of dislocations, leading to device degradation. Index Terms—HEMT, nitrides, strain, defects, dislocation glide, device simulation I. I NTRODUCTION D URING the last decades AlGaN/GaN High Electron Mobility Transistors (HEMTs) have been studied ex- tensively for the use in high power microwave applications, and the nitride material system is currently one of the most promising technologies both for electronic and optoelectronic applications [1]–[3]. The reliability of GaN-based HEMTs, however, still remains a major issue, especially at high voltage operation. Usually degradation mechanisms are assumed to be associated with strain- and temperature-related effects [4]–[7]. Simulation models including these effects are therefore of high interest for the understanding of device reliability. Traditionally, simulation of GaN-based HEMTs has been based on the drift-diffusion or hydrodynamic model coupled to a thermal one, normally based on the Fourier model. Degra- dation mechanisms have usually been introduced in such sim- ulations by means of electronic trap states both at the device surface and in the bulk, fitting the trap parameters to reproduce e.g. experimentally measured transient currents [8]. In the last years, several coupled electro-mechanical simulation models for HEMTs have been proposed [9], [10]. More recently, increasing interest has been devoted to fully coupled electro- thermo-mechanical models [11]–[15]. These models allow the prediction of the internal inhomogeneous mechanical stress distribution in dependence on device operating conditions. All models consistently predict increased mechanical stress under the gate region with increasing negative gate voltage due to converse piezoelectric effect, and an overall decrease of strain due to Joule heating. On the other hand, a detailed insight into the nature and dynamics of dislocations in (Al,In)GaN systems both on This work was supported by the ESA GREAT 2 project, contract number 21499. The authors are with the Department of Electronic Engineering, University of Rome “Tor Vergata”, Rome, Italy (phone: +39-06-72597456, e-mail: auf.der.maur@ing.uniroma2.it, aldo.dicarlo@uniroma2.it) Final published version at http://www.dx.doi.org/10.1109/TED.2013.2267547 polar and nonpolar substrates has been gained in the last decade, mostly based on experimental techniques such as nanoindentation and on optical characterisation methods [16]– [21]. The movement of dislocations is due to glide of atomic planes against each other, as illustrated in Fig. 1 [22]. As such, the driving force for glide is the shear stress on the glide plane resolved along the glide direction. Several ef- fective forces counteract the shear force driving this glide motion. In particular, glide is impeded by a friction-like force, since the atoms have to move in the potential landscape of the crystal. This force is described by the Peierls-Nabarro model [23]. On the other hand, when a dislocation line glides in a strained epitaxial layer, the total dislocation line length increases, leading to an increase in energy. This results in a line tension which also counteracts the glide force, and is decribed by the Matthews-Blakeslee model [24]. Thus, the formation of dislocations, their movement and multiplication can be understood approximately by the balance of these different forces. In this work we attempt to establish a connection between results of electro-thermo-mechanical simulations and disloca- tion related properties in order to get insight into possible microscopic effects leading to device degradation. A selfcon- sistently coupled electro-thermo-mechanical simulation model implemented in a single device simulation software has been used for the simulations [25], [26], and elastic energy densities and resolved shear stresses have been extracted from the results to compare them with the critical energies and stresses based on Matthews-Blakeslee and Peierls-Nabarro model. II. SIMULATION MODEL Our simulation model is based on the self-consistent solution of the mutually coupled equations of the drift- diffusion/Poisson model for electronic transport (1)-(2), the Fourier model for heat transport (3) and the equations of linear elasticity (4) given by the set of conservation laws (using index notation and Einstein summing convention) −∂ i (ε ij ∂ j ϕ − P i ) = −e(n + C ) (1) −∂ i (µn (∂ i φ n + S∂ i T )) = 0 (2) −∂ i (κ ij ∂ j T ) = H (3) −∂ i (C ijkl ∂ l u k ) = f j , (4) where ∂ i ≡ ∂/∂ xi , ε ij is the permittivity, P i is the total electric polarization, e the elementary charge, and n and C are the electron and net ionized doping/trap densities, respectively. For the indices we use the convention x → 1, y → 2, z → 3. µ is the mobility and S the thermoelectric power (Seebeck coefficient) of the electrons. We treat the device as