ORIENTATION DEPENDENT CHARACTERISTICS OF HIGH QUALI TY FACTOR SINGLE-CRYSTAL SILICON BULK MODE RESONATORS

This paper presents an empirical comparison in the characteristics between identical square-plate reso nators aligned along different crystal orientations for si licon, namely the <100> and <110>. We show that Q drops b y 42% and power handling capability is reduced result ing from the change in orientation when exciting the La mé mode. In the square-extensional (SE) mode, orienta t o shows little impact on Q and power handling for the same orientation change. The measured eigenfrequencies in both orientations closely agree with those predicte by finite element (FE) simulations and the analytical form. INTRODUCTION Single-crystal silicon (SCS) resonators are typical ly transduced along the <100> or <110> direction due t o efficient transmission of compressional and dilatio nal acoustic waves [1]. For bulk mode resonators, most of the research has been so far focused on devices aligned n <110> direction [2-3]. This orientation has had gr eater appeal over other orientations within the (100) pla ne s it offers higher Young’s modulus and smaller Poisson’s ratio [4]. These in turn lead to high Q’s in bulk mode resonators. However, it has been recently reported that devices aligned to the <100> will be a better choic e when repeatability of Q across various batches of fabric tion is of prime importance [1]. In addition, it has also b een postulated that <100> oriented devices surpass thos e in <110> in terms of obtaining high Q above ~750MHz [5 ]. Thus, more extensive research on bulk mode resonato rs aligned in the <100> is of great interest. This pap er investigates the effect of crystal orientation (<10 0> and <110>) on the characteristics of square-plate reson ators excited in the Lamé and SE modes. METHOD AND RESULTS Two square-plate resonators, each 360μm in length were fabricated on the same die in a foundry SOI ME MS process. Each square-plate was suspended by T-shap ed tethers on all 4 corners. The dimensions of the sq uare plates were designed to be identical, including tho se for the tethers, with each one rotated 45 o with respect to the other. Hence one resonator was aligned along <110> while the other in <100>. Optical micrographs of t he devices are depicted in Fig 1. Using the stiffness coefficients for SCS, the eigenfrequencies for the Lamé and SE modes were computed by FE using COMSOL for both orientations as shown in Figs 2 and 3 respecti vely. The devices were characterized in vacuum. Figs 4 an d 5 show the measured electrical transmission for the L amé mode for <110> and <100> aligned devices respective ly. Figs 6 and 7 show the measured electrical transmiss ion for the SE mode for the same pair of devices. Tabl e 1 summarizes the measured Q for each mode for each device. It can be seen that Q for the device in <1 00> is almost half that of the <110> device. However, cha nge in orientation has no obvious effect on Q for the SE m ode. These trends have been observed in measurements fro m a 2 die as well. Table 2 compares the eigenfrequencie s derived analytically, by FE, and by measurement. W e can see a general close agreement between each of them. The difference between the analytical and FE or measure d value for the SE mode stems from the effects of anc hors unaccounted for in the analytical equation. The ch ange in Q caused by rotation in the Lamé and not in the SE mode stems from the effect of orientation on stiffness f or each given mode. In the Lamé mode, stiffness is governe d by the shear modulus which drops from 79.4GPa to 50.8G Pa from <110> to <100> (37% drop). The SE mode stiffn ess is governed by the bi-axial modulus which is invari ant. In addition, we have also observed from our measuremen ts (not shown here) that the onset of mechanical nonli earity occurs earlier in the <100> (at -5dBm) compared to the <110> (at 3dBm) for the Lamé mode under the same DC bias conditions. ACKNOWLEDGMENT This work was supported by a grant from the City University of Hong Kong (Project No. 9667049) REFERENCES [1] A. K. Samarao and F. Ayazi, "Quality Factor Sensitivity to Crystallographic Misalignments in Silicon Micromechanical Resonators," Hilton Head 2010, pp. 479-482, 2010. [2] V. Kaajakari et al, “Square extensional mode single-crystal silicon micromechanical resonator fo r low-phase noise oscillator applications,” IEEE Elect. Dev. Lett. , vol. 25, no. 4, pp. 173–175, Apr. 2004. [3] J. E. -Y. Lee, J. Yan, and A. A. Seshia, "Low l oss HF band SOI wine glass bulk mode capacitive square-plate resonator," J. Micromech. Microeng. , vol. 19, 074003, July 2009. [4] M. A. Hopcroft, W. D. Nix, and T. W. Kenny, “What is the Young’s modulus of silicon? ” J. MEMS, vol. 19, pp. 229-238, 2010. [5] R. Tabrizian, M. Rais–Zadeh, and F. Ayazi, “Eff ect of Phonon Interactions on Limiting the fQ Product o f Micromechanical Resonators,” Proc., Transducers ‘09, June 2009, pp. 2131–2134. CONTACT * C. Tu, tel: 852-21942656; chengtu3@cityu.edu. hk