IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 49, NO. 11, NOVEMBER 2002 1849A Model for Hydrogen-Induced Piezoelectric Effectin InP HEMTs and GaAs PHEMTsSamuel D. Mertens and Jesus A. del Alamo, Senior Member, IEEEAbstract—We have developed a model for the impact of the hy-drogen-induced piezoelectric effect on the threshold voltage of InPHEMTs and GaAs PHEMTs. We have used two-dimensional (2-D)finiteelementsimulationstocalculatethemechanicalstress causedby a Ti-containing metal gate that has expanded due to hydrogenabsorption.Thishasallowed usto mapthe 2-D piezoelectricchargedistribution in the semiconductor heterostructure. We then used asimple electrostatics model to calculate the impact of this piezo-electric polarization charge on the threshold voltage. The modelexplainsexperimental observationsof hydrogen-inducedthresholdvoltage shifts, both in InP HEMTS and in GaAs PHEMTs. It alsosuggests ways to mitigate the hydrogen sensitivity of these devices.Index Terms—HEMT, hydrogen (H), InP, piezoelectric effect,reliability.I. INTRODUCTIONHYDROGEN (H) degradation has been identified as a se-rious reliability concern in III-V FETs in general and InPHEMTs in particular [1]. In applications, demanding hermeti-cally-sealed packaging, such as satellite or fiber-optic systems,exposure occurs when H out-gasses from the packaging mate-rial and becomes trappedinside the package cavity.With enoughtime, H diffuses into the transistor and alters its electrical char-acteristics eventually leading to parametric module failure.Recent research has shown that among other effects, H ex-posure results in the formation of TiHin Ti/Pt/Au gates com-monly used in III-V FETs [2]. This produces compressive stressin the gate, which generates a tensile stress in the heterostruc-ture underneath. The resulting piezoelectric polarization chargecauses a threshold voltage shift.The few reports of the sign and magnitude ofin InPHEMTs and GaAs PHEMTs that have been published seemcontradictory (all devices have Ti/Pt/Au gates). While reportson [011]-oriented GaAs PHEMTs indicate a positive[3],[011]-oriented InP HEMTs have been found to display posi-tive [4], negative [3], and even negligibleshifts [5]. Whenall the data are graphed together, however, a compelling pic-ture emerges (see Fig. 1). It appears that for GaAs PHEMTs,is always positive and increases as the gate length is re-duced. However, no data exists for long devices. For long gatelength InP HEMTs,is negative and increasing in magni-tude with decreasing. At a certain , however, there is a signreversal and H-inducedbecomes positive. For shorter de-vices,increases.Manuscript received July 8, 2002. This work was supported in part by NTT,Triquint, and HRL. The review of this paper was arranged by Editor M. Anwar.The authors are with the Massachusetts Institute of Technology, Cambridge,MA 02138 USA (e-mail: [email protected]; [email protected]).Digital Object Identifier 10.1109/TED.2002.804698Fig. 1. Reports of1Vcaused by hydrogen degradation as a function of gatelength for InP HEMTs and GaAs PHEMTs with gates oriented along the [011]direction [2]–[5].In this work, we present a model for H-induced piezoelectriceffectin InP HEMTs and GaAs PHEMTs that explains the pecu-liar behavior ofshown in Fig. 1. Our model sheds light onthe key parameters of the problem and provides design guide-lines for minimizing H sensitivity of these devices. This paperexpands on the work presented in [6].II. MODELOur modeling approach involves:1) performing two-dimensional (2-D) mechanical stresssimulations of the device structure;2) computing the resulting piezoelectric charge in the semi-conductor heterostructure;3) estimating its effect on.First, a 2-D finite-element simulation tool, ABAQUS, wasused to calculate the mechanical stress in the device layer struc-ture introduced by an expanding Ti/Pt/Au gate caused by theformation of TiH. We modeled the expansion of the Ti layer asa thermal expansion of the bottom layer of the gate stack (thisapproach neglects the second-order coupling between the elec-trical field in the semiconductor and its displacement). The me-chanical properties of the materials used in the simulations canbe found in Table I. We used a finer mesh near the surface ofthe heterostructure and directly under the gate to provide a de-tailed picture of the mechanical stress where it has the biggestimpact on. We exploited the symmetry of the structure andwe only simulated half of it. The center of the gate was fixed,so no displacement can take place in the horizontal directionfor any point in the heterostructure underneath the center of thegate. The mesh extends by 20m in the vertical direction and50m in the horizontal direction, from the center of the gate.The structure was fixed mechanically at the bottom and on the0018-9383/02$17.00 © 2002 IEEE1850 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 49, NO. 11, NOVEMBER 2002TABLE IMECHANICAL MATERIAL CONSTANTS USED IN THIS STUDYside far away from the gate. This is a fair assumption as thedevice is surrounded by material that is not expanding. Thereare 16 000 mesh nodes in the semiconductor heterostructure and6400 mesh nodes in the gatestack and passivation layer. The endresult of this simulation is the atomic displacementsandperpendicular and parallel to the gate, respectively.In our second step, we useand to compute the polariza-tion vector fieldand the polarization charge distributionthroughout the device [7]. The and components of the po-larization vector for a III-V semiconductor with a [011] surfaceare, respectively, given by(1)(2)In these equations,is the Voight average shear modulusandthe piezoelectric constant of the material [8]–[11].The values of these constants are specific to each layer. Forthe ternary compounds studied in this work,and wereobtained by interpolation from the binaries (see Table II).The piezoelectric charge can be calculated using(3)As discussed below, computing the piezoelectric chargeis notessential to deriving. However, , since it is a scalar,provides for a compact way of visualizing and understandingthe impact of stress on the electrostatics of the problem.The final step is to compute the effect of the polarizationcharge on. For simplicity, we assume a one-dimensional(1-D) model in whichis calculated at the center of thegate. This is a fair assumption particularly ifis experimen-tally extracted in the linear regime, as is commonly done [2],[4]. Symmetry arguments show that at the center of