Temperature Compensation of Silicon Resonators via Degenerate ...
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 59, NO. 1, JANUARY 2012
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Temperature Compensation of Silicon Resonators via Degenerate Doping Ashwin K. Samarao, Member, IEEE, and Farrokh Ayazi, Senior Member, IEEE
Abstract—This paper demonstrates the dependence of temperature coefficient of frequency (TCF) of silicon micromechanical resonators on charge carrier concentration. TCF compensation is demonstrated by degenerate doping of silicon bulk acoustic resonators (SiBARs) using both boron and aluminum dopants. The native TCF of −33 ppm/◦ C for silicon resistivity of > 103 Ω · cm is shown to reduce to −1.5 ppm/◦ C at ultralow resistivity of ∼ 10−4 Ω · cm using relatively slow diffusion-based boron doping. However, the faster thermomigration-based aluminum doping offers TCF reduction to as low as −2.7 ppm/◦ C with much reduced processing time. A very high Q of 28 000 at 100 MHz is measured for a temperature-compensated SiBAR. Index Terms—Aluminum thermomigration, degenerate boron doping, silicon micromechanical resonators, temperature compensation.
I. I NTRODUCTION
A
FTER nearly two decades of research and development, the manufacturability and reliability of silicon resonator technology are successfully established to enable their widespread commercialization and insertion. Currently, they are being used as drop in replacements for quartz crystals as well as integrated modules for frequency and timing applications [1], [2]. Their small size, ease of fabrication, frequency scalability, and high-quality factors (≥ 10 000) along with moderate motional resistances (∼ a few 100 Ω at ≥ 100 MHz) persuaded efforts to tailor these devices for oscillators and resonant sensor applications [3]–[5]. However, one of the most dominant drawbacks of silicon resonators has been their large temperature coefficient of frequency (TCF). The resonance frequency of the silicon microresonator decreases with increasing temperature, thereby exhibiting a negative yet almost linear TCF of approximately −30 ppm/◦ C. Such a TCF is significantly larger in magnitude than that of the worst AT-cut quartz crystals [6]. Hence, considerable research has been carried out to reduce the TCF of single-crystal silicon (SCS) microresonators. There exist system-level approaches to temperature compensation that require tuning or ovenization of the resonator. One approach to temperature compensation is to use the sili-
Manuscript received July 11, 2011; revised October 7, 2011; accepted October 11, 2011. Date of publication November 3, 2011; date of current version December 23, 2011. This work was supported by Integrated Device Technology (IDT), Inc. The review of this paper was arranged by Editor A. M. Ionescu. A. K. Samarao is with Robert Bosch Research and Technology Center, Palo Alto, CA 94304 USA. F. Ayazi is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2011.2172613
con microresonator-based oscillator in a feedback loop and to tune its frequency electronically to compensate for temperature changes [7]. This is somewhat more challenging to accomplish in bulk- than in flexural-mode resonators because the electrostatic tunability of the bulk-mode resonators is substantially less than that of the flexural-mode resonators [8]. Another possible approach is to enclose the resonator in a thermally isolated “micro oven” whose temperature is kept constant through the use of heating elements [9], [10] or by running a current through the structural body of the resonator [8]. However, need for additional circuitry (and thereby chip area) and an increase in the overall power consumption are the two most significant problems in these active temperature compensation techniques. Hence, it is desirable to have passive techniques that compensate for most of the TCF, if not entirely, so that active compensation techniques can be used in conjunction to compensate for the rest to achieve zero-TCF resonators without excessive power consumption and calibration. The most common passive TCF compensation technique is based on using a composite structure, such as silicon dioxide and silicon, whose respective stiffness changes with temperature in opposite ways. Such an approach of using a positive TCF material to compensate for negative TCF dates back to the early 1980s [11] but is still the object of much active research [12]–[14]. However, the acoustic loss at the interface of the different materials in the composite structure loads quality factor Q, while the stress mismatch at such an interface might lead to hysteresis. Further, dielectric charging has been reported in thermally oxidized capacitive silicon resonators, which are known to cause a drift in frequency over time [15]. Thus, since passive temperature compensation techniques are desired, an alternative to composite resonator structures is needed. This paper addresses the issue by identifying the dependence of TCF on charge carrier concentration in the resonating silicon microstructure and proposes degenerate doping of silicon for TCF compensation. II. SiBAR Temperature compensation via degenerate doping is demonstrated using single-crystal silicon bulk acoustic resonators (SiBARs) (see Fig. 1). A SiBAR consists of a resonating suspended SCS bar separated by narrow air gaps from two identical drive/sense polysilicon electrodes. The suspended microstructure is supported using narrow tethers at its shorter edges, which also provide electrical contact to dc polarization voltage Vp that is applied at the Vp pads. Now an ac signal applied at the drive electrode results in a time-varying electrostatic force applied across the air gap onto the corresponding face
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Fig. 1. SEM image of a 100-MHz SiBAR. (W = 40 μm; L = 10 × W = 400 μm; T = 10 μm). E and ρ are the Young’s modulus and density of silicon. Fig. 3. Illustration showing (a) equivalent HH and LH energy surfaces of the valence band in silicon that are (b) permanently split due to the large compressional strain from the very high boron doping of the silicon crystal. E and k are the electronic energy and wave vector, respectively.
Fig. 2. Illustration showing (a) equivalent HH and LH energy surfaces of the valence band in silicon that contain most of the holes at steady-state and (b) propagation of acoustic waves splits the equivalent surfaces leading to a flow of holes from HH to LH. E and k are the electronic energy and wave vector, respectively.
of the resonator. At target frequency f0 determined by W , the resulting width-extensional mode (WEM) of resonance [see Fig. 2(b)] modulates the transduction air gap on the other side inducing a voltage on the sense electrode. The SiBARs used in this work were transduced using very narrow 100-nm air gaps fabricated using the HARPSS process [16]. III. TCF C OMPENSATION VIA D EGENERATE D OPING The propagation of an acoustic wave through a solid material is typically characterized by an alternating set of compressional and dilational forces that perturb the periodicity of the atomic lattice during wave propagation. In a semiconductor such as silicon, such a perturbation of atomic periodicity directly impacts its electronic band structure. For example, at steady-state, the valence band of silicon is made up of three energy surfaces in k-space, two of which are equivalent and are energetically favorable to contain almost all the holes [see Fig. 2(a)]. The resulting longitudinal strain due to the WEM of resonance in a SiBAR splits the equivalent energy bands, leading to a flow of holes from the heavy-hole (HH) to the more energetically
favorable light-hole (LH) band [see Fig. 2(b)] [17], [18]. The net flow of holes and thereby the electronic energy of the system increases with increasing temperature. A similar analogy exists for the electrons in the conduction band of silicon. Per the conservation of energy principle, such a temperature-dependent increase in the electronic energy manifests itself as a corresponding decrease in the elastic energy of the system. Thus, a progressive reduction in the stiffness (i.e., Young’s modulus (E)) of the resonating silicon microstructure and thereby its resonance frequency is observed with increasing temperature (i.e., TCF). Although linear thermal expansion coefficient α of silicon also contributes to the TCF, its contribution is negligible compared with the temperature coefficient of Young’s modulus (TCE). Temperature compensation techniques that have been reported to date combat the effect of TCE, whereas this work targets the manipulation of charge carriers that cause it in the first place [19]. Thus, a momentary strain produced by the propagation of the acoustic waves is understood to create a temperature-dependent change in the electronic and elastic energies of the system. Such an effect of the momentary strain could be made minimal in comparison if a larger permanent strain could be created in the silicon crystal. For example, a boron atom that has a smaller radius than silicon atom strongly bonds to only three of the four adjacent silicon atoms when diffused into the crystal lattice. At very high doping levels, such an atomic arrangement produces a strong shear strain in the silicon lattice, which is sufficient to create a large permanent separation between the equivalent LH and HH valence bands. As a result, the majority of the holes permanently shift from the HH to the LH band, thereby almost depleting the holes from the former (see Fig. 3) [20]. The effect of any additional band splitting caused by the propagation of acoustic waves in such a highly-doped SiBAR now becomes minimal in comparison for two reasons: first, very few holes are available in the almost depleted HH band of a highly doped silicon to flow to the LH band; second, the energy required to flow from HH to LH is much larger compared with a
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TABLE I M EASURED TCF IN SiBARs FABRICATED ON S ILICON WAFERS W ITH V ERY L OW TO V ERY H IGH B ORON D OPING L EVELS
Fig. 4. Illustration of the minimized flow of holes in the valence band of silicon during acoustic transduction in a very highly boron-doped SiBAR.
nonhighly doped silicon, thereby making such a transition least energetically favored (see Fig. 4). As a result, the momentary flow of holes from HH to LH is significantly minimized. Thus, a considerable reduction in the variation of the electrical and elastic energies of the system with temperature is effected, thereby resulting in TCF compensation. At degenerate levels of boron doping, the acoustic wave can potentially be shielded entirely from the k-space contours of the valence band, which, in turn, should completely compensate the TCE component of the TCF, i.e., TCF =
TCE + α . 2
TABLE II B ORON D OPING R ECIPE U SING S OLID AND L IQUID B ORON S OURCES
(1)
The native silicon TCE of ∼ −57 ppm/◦ C and α of ∼ −3 ppm/◦ C yield a TCF of ∼ −30 ppm/◦ C in silicon microresonators. Upon complete TCE compensation via degenerate doping, a TCF as low as ∼ −1.5 ppm/◦ C could be achieved. IV. TCF C OMPENSATION VIA D EGENERATE B ORON D OPING Both Czochralski and float-zone silicon wafer manufacturing processes typically involve an in situ doping with either n- or p-type dopants. Such predoped silicon wafers can be procured as is from the wafer vendors to verify the TCF compensation in silicon microresonators with increasing doping levels (i.e., decreasing resistivities). Thus, the proposed solution of very high doping for TCF compensation can be easily verified for any SCS microresonator design with no additional need for processing capabilities to dope silicon. Table I summarizes the measured TCF across various resistivities from SiBARs fabricated on a 20-μm-thick boron-doped device layer of SOI wafers as-procured from Ultrasil Corp. (USA). Although only a minimal TCF reduction of ∼ 4 ppm/◦ C is observed from very high to low resistivity silicon substrates, substantial TCF reduction has been measured at very low and ultralow resistivities. As shown in Table I, an overall TCF reduction of 24 ppm/◦ C can be readily achieved in silicon microresonators by opting for ultralow resistive substrates. No significant impact was measured on the Q and insertion loss of these microresonators across such wide range of doping levels. It is worth mentioning that such very low and ultralow resistivity substrates were specially ordered for the purpose and are typically more expensive compared with the relatively higher resistivity substrates. Such very high levels of doping can be also achieved starting from a low resistivity substrate
by repeated doping/annealing processes. For example, a borondoped resistivity of ∼ 0.01 Ω · cm resistivity has been measured to reduce to ∼ 0.001 Ω · cm after five repetitions of the solid boron dope/anneal recipe shown in Table II. For further reduction in resistivity, liquid spin-on-dopant boron sources were used [Futurrex Inc. (USA), BDC1-2000]. After six repetitions of spin-on-dope/anneal recipe, the boron-doped resistivity could be further reduced from ∼ 0.001 to ∼ 0.0001 Ω · cm. In both cases of solid and liquid dopants, the borosilicate glass layer that forms after every dope/anneal cycle was removed using hydrofluoric acid. All the reported resistivities in this paper were accurately measured using four-point probe measurement. Although longer hours of processing are needed to achieve a resistivity of ∼ 0.0001 Ω · cm (see Table II), such a resistivity is lower than any commercially available silicon wafer. At such doping levels, the diffusion depth of boron in silicon is typically limited to 7 ∼ 8 μm [22]. Hence, 5-μm-thick substrates were chosen to fabricate uniformly doped SiBARs at such degenerate doping levels of boron in silicon. A 5-μm-thick 0.0001 Ω · cm SiBAR is found to measure a TCF of −3.56 ppm/◦ C, which is an order of magnitude lower than that measured at a very high resistivity of 1000 Ω · cm (see Fig. 5). The increase in resonance frequency after heavy doping is due to the increase in the Young’s modulus of silicon and is indicative of the degenerative doping [23]. As seen from the square of correlation coefficient of linearity R2 reported in Fig. 5, the linearity of the TCF curve is compromised to some extent due to degenerate boron doping.
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Fig. 5. Order of magnitude reduction in TCF measured at a boron-doped SiBAR resistivity of 0.0001 Ω · cm compared with 1000 Ω · cm. Fig. 7. SEM images showing the observed outdiffusion of boron from the silicon surface after seven repetitions of the spin-on-dope/anneal processes.
Fig. 8. Saturation of TCF at ∼ −1.5 ppm/◦ C of the 5-μm-thick SiBAR after seven repetitions of spin-on-dope/anneal processes. Fig. 6. Measured response of the degenerately doped SiBAR with a TCF of −3.56 ppm/◦ C showing a quality factor Q of 33 000 in vacuum.
Such degenerately doped 0.0001 Ω · cm 5-μm-thick SiBARs measure a Q of 33 000 (versus 35 000 for a nondegenerately doped 5-μm-thick SiBAR with a resistivity of 0.01 Ω · cm) at Vp of 20 V in vacuum (see Fig. 6). This indicates a minimal effect on the acoustic loss in silicon microresonators from longer hours of repeated thermal cycling during the doping process. However, upon any further doping, boron is observed to outdiffuse from the surface of the silicon, leaving behind a relatively porous silicon surface. Such a surface of silicon as-observed after seven repetitions of the spin-on-dope/anneal processes is shown in Fig. 7. The outdiffusion is indicative of doping levels that surpass the solid solubility limit of boron in silicon (∼ 2 × 1020 atoms/cm3 ). At such levels of doping, the resistivity values could not be accurately measured and hence are not reported. The SiBARs fabricated at such doping levels measure the lowest recorded TCF of −1.43 ppm/◦ C. Interestingly, no further reduction in TCF was measured even after ten repetitions of spin-on-dope/anneal processes (see Fig. 8). Interestingly, Wang et al. had theoretically predicted a positive TCF with increasing levels of boron doping in silicon microresonators [24]. To the contrary, this work experimentally proves that positive TCFs were not measured even at degenerate levels of boron doping in silicon. Further, the lowest measured TCF value of ∼ −1.5 ppm/◦ C is understood to be the sole contribution of linear thermal expansion component α after
complete compensation of TCE [see (1)]. It is to be noted that such outdiffusion of boron results in lattice damage to silicon that reflects as a relatively reduced Q of 20 000 in vacuum. Thus, degenerate boron doping has been successfully demonstrated to offer a reduction from a native TCF of −33 to −1.5 ppm/◦ C in silicon micromechanical resonators. Similar temperature compensation has been also recently demonstrated in thermally actuated silicon microresonators using degenerate phosphorous doping [25]. However, the longer hours of processing needed to achieve such degenerate doping levels call for a faster alternative. Further, the difficulty in achieving very high doping levels for thicker substrates limits the proposed TCF compensation technique to substrates that are thinner than 7 ∼ 8 μm. The next section addresses both these issues by presenting a boron-assisted aluminum doping technique that is capable of achieving very high doping levels within few minutes of processing in much thicker substrates. V. TCF C OMPENSATION VIA B ORON -A SSISTED A LUMINUM D OPING Boron diffuses as an interstitial dopant [26], which demands for longer hours of annealing to become electrically active. On the other hand, aluminum (also a p-type dopant) becomes readily electrically active by diffusion via self-interstitial mechanism [27]. It has been shown that aluminum can thermomigrate against a temperature gradient into hundreds-of-micrometersthick silicon within few tens of minutes [28]. Thermomigration
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Fig. 9.
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Schematic of the wafer-level aluminum thermomigration process.
is typically performed by patterning aluminum on one side of the wafer while the other side is radiatively heated to approximately 1000 ◦ C. Such one-sided heating results in a temperature gradient across the thickness of the wafer. Once above the eutectic point (577 ◦ C), the aluminum melts and dissolves some of the silicon at the surface. The resulting droplet follows the thermal gradient toward the hot surface. As the droplet moves, the warmer side of the droplet dissolves more silicon, and the cooler side of the droplet epitaxially resolidifies; the resolidified material has an aluminum concentration determined by the solid solubility limit for aluminum in silicon at the solidification temperature, which is approximately 2 × 1019 atoms/cm3 [29]. The process is known to be highly anisotropic and relatively fast, with droplets traveling through a 300-μm-thick silicon wafer in less than 10 min [30]. The uniformity and speed of aluminum thermomigration is known to be enhanced by the presence of boron atoms in silicon [27]. Further, both boron and aluminum dopants are electrically active and will contribute to TCE compensation. Thus, such a boron-assisted aluminum thermomigration is a faster alternative to degenerate boron doping for TCF reduction. This was investigated by evaporating 200 Å of aluminum onto the surface of 20-μm-thick SiBARs fabricated on a borondoped ∼ 0.01 Ω · cm silicon wafer. The required temperature gradient is created in a furnace by turning off one of the many coil heaters of the furnace (see Fig. 9). The wafer is positioned in the furnace at the boundary of the hot and cold regions, with the aluminum-deposited side facing away from the heat. The temperature gradient across the thickness of the wafer drives the aluminum to thermomigrate into the resonating silicon bulk. After 1 h of thermomigration in nitrogen ambient, the TCF of the SiBAR reduces by 24 ppm/◦ C, from −27.8 to −3.8 ppm/◦ C. The reduced TCF is equivalent to that measured at a borondoped resistivity of ∼ 0.0001 Ω · cm (see Fig. 6). Thus, a boron doping duration of approximately 90 h (see Table II) for a similar TCF reduction on a 5-μm-thick substrates can be alternatively realized using an hour of aluminum thermomigration on substrates that are 20 μm or thicker. On the downside, due to the rapid thermomigration and the large temperature gradient across the entire wafer, some structural damage could be observed on the surface of the resonators. As a result, a considerably reduced Q of 16 000 has been observed at vacuum in wafer-level thermomigrated SiBARs. Unlike boron doping that is performed on a plain SOI wafer prior to the fabrication of the resonators, the wafer-level
Fig. 10. Schematic of the device-level aluminum thermomigration process. (a) Released SiBAR. (b) Blanket deposition of 500 Å aluminum. (c) Joule heat the support tethers and SiBAR at 120 mA for 10 min. (d) Aluminum thermomigrated SiBAR at room temperature; wirebond traces are visible in (d) since the same device was used for SEM images.
aluminum thermomigration was carried out postfabrication. Hence, stress due to thermal gradients impacts the Q and long-term stability of these resonators. On the other hand, a device-level thermomigration process could circumvent the problem while offering the expected reduction in TCF. Fig. 10 shows the schematic and SEM images of such a device-level aluminum thermomigration process developed for SiBARs. A 500-Å-thin layer of aluminum was evaporated onto the SiBAR [see Fig. 10(b)]. A current of 120 mA was passed for 10 min through the SiBAR resonator element via the support tethers [see Fig. 10(c)] [31]. At such high currents, the narrow support elements Joule heat to ∼ 1000 ◦ C while the wider SiBAR reaches the Al–Si eutectic temperature, thereby creating the necessary temperature gradient [see Fig. 10(c)]. Aluminum on top of the relatively cold SiBAR laterally diffuses through the silicon toward the hot support elements, thereby doping it [see Fig. 10(d)]. A closer look at the thermomigrated surface (see Fig. 11) shows regions of Al–Si eutectic alloy alongside exposed silicon where aluminum has completely diffused into the bulk of the resonator. The short duration of the process is insufficient to thermomigrate the entire thickness of aluminum, thereby leaving behind some residues (due to thicker than desired Al), which could be thermomigrated with further Joule heating. Although aluminum is deposited on the Vp pads as well [see Fig. 10(b)], its relatively larger cross section remains below the Al–Si eutectic temperature during Joule heating. Hence, no thermomigration has been observed to occur on the Vp pads. A reduction in TCF by 14 ppm/◦ C (from −22.13 to −7.93 ppm/◦ C) has been measured over 10 min of device-level thermomigration on a ∼ 0.001 Ω · cm SiBAR. From the values in Table I, it can be inferred that a TCF value corresponding to very low resistivity of a silicon wafer can be reduced to its ultralow resistive counterpart within few minutes of aluminum thermomigration. The passage of current for longer durations
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Fig. 11. SEM showing a close-up of the aluminum thermomigrated SiBAR in Fig. 10(d).
Fig. 12. Measured response of a 20-μm-thick [∼ 0.001 Ω · cm; boron-doped] SiBAR after device-level thermomigration with 500 Å of aluminum at 120 mA for 10 min.
might lead to plastic deformation at the narrow support tethers, thereby causing a failure of resonator operation. However, if the supports are redesigned to be wider, thermomigration could be performed for longer durations to achieve further reduction in TCF. Unlike boron doping and wafer-level thermomigration processes, device-level aluminum thermomigration is best suited to be a postfabrication postpackaging technique, wherein the TCF can be programmed to a desired value using Joule heating as an electrical calibration step. Minimal or no structural damage has been observed from the device-level thermomigration process as evident from a Q of 29 000 measured from these devices in vacuum. The measured insertion loss of 39.5 dB is typical of 20-μm-thick SiBARs with a capacitive air gap of ∼100 nm at Vp of 20 V (see Fig. 12). A similar device-level thermomigration was also performed on a 20-μm-thick degenerately boron-doped ∼ 0.0001 Ω · cm SiBAR. The TCF curve before thermomigration exhibits an interesting anomalous behavior, as shown in Fig. 13. This is thought to arise due to the nonuniform doping profile at such very high doping levels along the 20-μm thickness of the device. Aluminum thermomigration is found to restore the linearity of the TCF curve and offer a TCF as low as −2.72 ppm/◦ C while maintaining a high Q of 28 000 in vacuum (see Fig. 14).
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Fig. 13. TCF of a 20-μm-thick [∼ 0.0001 Ω · cm; boron-doped] SiBAR before and after device-level thermomigration with 500 Å of aluminum at 120 mA for 10 min.
Fig. 14. Measured response of a 20-μm-thick [∼ 0.0001 Ω · cm; borondoped] SiBAR after device-level thermomigration with 500 Å of aluminum at 120 mA for 10 min.
VI. C ONCLUSION Temperature compensation of silicon micromechanical resonators has been achieved using degenerate boron doping and boron-assisted aluminum doping. A starting TCF of −33 ppm/◦ C is reduced to −1.5 ppm/◦ C by degenerate boron doping of the silicon microresonator. Both wafer- and devicelevel aluminum thermomigration techniques are developed as faster alternatives to the relatively slower diffusion-based boron doping process. Although the former is found to compromise on the Q due to stress from the thermal gradient, the latter circumvents the problem and offers low TCF along with low insertion loss and high Q. ACKNOWLEDGMENT The authors would like to thank the staff of the Nanotechnology Research Center (NRC) at the Georgia Institute of Technology for their assistance. R EFERENCES [1] F. Ayazi, “MEMS for integrated timing and spectral processing,” in Proc. IEEE CICC, 2009, pp. 65–72. [2] B. Kim, R. Melamud, R. A. Candler, M. A. Hopcroft, C. M. Jha, S. Chandorkar, and T. W. Kenny, “Encapsulated MEMS resonators—A
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[25] A. Hajjam, A. Rahafrooz, and S. Pourkamali, “Sub-100 ppm/◦ C temperature stability in thermally actuated high frequency silicon resonators via degenerate phosphorous doping and bias current optimization,” in IEDM Tech. Dig., 2010, pp. 170–173. [26] O. Krause, H. Ryssel, and P. Pichler, “Determination of aluminum diffusion parameters in silicon,” J. Appl. Phys., vol. 91, no. 9, pp. 5645–5649, May 2002. [27] B. Sadigh, T. J. Lenosky, S. K. Theiss, M.-J. Caturla, T. Diaz de La Rubia, and M. A. Foad, “Mechanism of boron diffusion in silicon: An ab initio and kinetic Monte Carlo study,” Phys. Rev. Lett., vol. 83, no. 21, pp. 4341– 4344, Nov. 1999. [28] W. Pfann, Zone Melting. Huntington, NY: Krieger, 1978. [29] D. Lischner, H. Basseches, and F. D’Altroy, “Observations of the temperature gradient zone melting process for isolating small devices,” J. Electrochem. Soc., vol. 132, no. 12, pp. 2997–3001, Dec. 1985. [30] C. C. Chung and M. G. Allen, “Thermomigration-based junction isolation of bulk silicon MEMS devices,” J. Microelectromech. Syst., vol. 15, no. 5, pp. 1131–1138, Oct. 2006. [31] A. K. Samarao and F. Ayazi, “Post-fabrication electrical trimming of silicon bulk acoustic resonators using joule heating,” in Proc. IEEE Int. Conf. MEMS, 2009, pp. 892–895.
Ashwin K. Samarao (S’07–M’11) was born in Chennai, India, on February 18, 1983. He received the B.E. (Hons.) degree in electrical and computer engineering from the Birla Institute of Technology and Science, Pilani, India, in 2004, the M.S. degree in electrical and computer engineering from the University of Cincinnati, Cincinnati, OH, in 2006, and the Ph.D. degree in electrical and computer engineering from the Integrated Microelectromechanical Systems Laboratory, Georgia Institute of Technology, Atlanta, in May 2011. Subsequently he joined Integrated Device Technology, Inc., San Jose, CA, as an intern, where he worked on implementing the ideas he developed as a graduate student to engineer a MEMS-based timing solution. He is currently a MEMS Research Engineer with Robert Bosch Research and Technology Center, Palo Alto, CA. His research interests include micro- and nanoelectromechanical resonators, RF-MEMS and inertial sensors, CMOS-MEMS integration, and micro- and nanofabrication process development. Dr. Samarao was the recipient of the Best Student Paper Award at the IEEE International Frequency Control Symposium in 2010.
Farrokh Ayazi (S’96–M’00–SM’05) received the B.S. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 1994 and the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 1997 and 2000, respectively. He joined the faculty of the Georgia Institute of Technology, Atlanta, in December 1999, where he is currently a Professor in the School of Electrical and Computer Engineering. His research interests are in the areas of integrated micro- and nanoelectromechanical resonators, interface IC design for MEMS and sensors, inertial sensors, RF MEMS, and microfabrication techniques. Prof. Ayazi is a 2004 recipient of the NSF CAREER Award, the 2004 Richard M. Bass Outstanding Teacher Award (determined by the vote of the ECE senior class), and the Georgia Tech College of Engineering Cutting Edge Research Award for 2001–2002. He is an editor for the IEEE/ASME J OURNAL OF M ICROELECTROMECHANICAL S YSTEMS. He served on the technical program committee of the IEEE International Solid State Circuits Conference for six years (2004–2009). He and his students won the best paper awards at Transducers 2011, the IEEE International Frequency Control Symposium in 2010, and IEEE Sensors conference in 2007. He is the CoFounder and Chief Technology Officer of Qualtré Inc., a spin-out from his research laboratory that commercializes multiaxis bulk-acoustic-wave silicon gyroscopes and multidegrees-of-freedom inertial sensors for consumer electronics and personal navigation systems.
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Temperature Compensation of Silicon Resonators via Degenerate Doping Ashwin K. Samarao, Member, IEEE, and Farrokh Ayazi, Senior Member, IEEE
Abstract—This paper demonstrates the dependence of temperature coefficient of frequency (TCF) of silicon micromechanical resonators on charge carrier concentration. TCF compensation is demonstrated by degenerate doping of silicon bulk acoustic resonators (SiBARs) using both boron and aluminum dopants. The native TCF of −33 ppm/◦ C for silicon resistivity of > 103 Ω · cm is shown to reduce to −1.5 ppm/◦ C at ultralow resistivity of ∼ 10−4 Ω · cm using relatively slow diffusion-based boron doping. However, the faster thermomigration-based aluminum doping offers TCF reduction to as low as −2.7 ppm/◦ C with much reduced processing time. A very high Q of 28 000 at 100 MHz is measured for a temperature-compensated SiBAR. Index Terms—Aluminum thermomigration, degenerate boron doping, silicon micromechanical resonators, temperature compensation.
I. I NTRODUCTION
A
FTER nearly two decades of research and development, the manufacturability and reliability of silicon resonator technology are successfully established to enable their widespread commercialization and insertion. Currently, they are being used as drop in replacements for quartz crystals as well as integrated modules for frequency and timing applications [1], [2]. Their small size, ease of fabrication, frequency scalability, and high-quality factors (≥ 10 000) along with moderate motional resistances (∼ a few 100 Ω at ≥ 100 MHz) persuaded efforts to tailor these devices for oscillators and resonant sensor applications [3]–[5]. However, one of the most dominant drawbacks of silicon resonators has been their large temperature coefficient of frequency (TCF). The resonance frequency of the silicon microresonator decreases with increasing temperature, thereby exhibiting a negative yet almost linear TCF of approximately −30 ppm/◦ C. Such a TCF is significantly larger in magnitude than that of the worst AT-cut quartz crystals [6]. Hence, considerable research has been carried out to reduce the TCF of single-crystal silicon (SCS) microresonators. There exist system-level approaches to temperature compensation that require tuning or ovenization of the resonator. One approach to temperature compensation is to use the sili-
Manuscript received July 11, 2011; revised October 7, 2011; accepted October 11, 2011. Date of publication November 3, 2011; date of current version December 23, 2011. This work was supported by Integrated Device Technology (IDT), Inc. The review of this paper was arranged by Editor A. M. Ionescu. A. K. Samarao is with Robert Bosch Research and Technology Center, Palo Alto, CA 94304 USA. F. Ayazi is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2011.2172613
con microresonator-based oscillator in a feedback loop and to tune its frequency electronically to compensate for temperature changes [7]. This is somewhat more challenging to accomplish in bulk- than in flexural-mode resonators because the electrostatic tunability of the bulk-mode resonators is substantially less than that of the flexural-mode resonators [8]. Another possible approach is to enclose the resonator in a thermally isolated “micro oven” whose temperature is kept constant through the use of heating elements [9], [10] or by running a current through the structural body of the resonator [8]. However, need for additional circuitry (and thereby chip area) and an increase in the overall power consumption are the two most significant problems in these active temperature compensation techniques. Hence, it is desirable to have passive techniques that compensate for most of the TCF, if not entirely, so that active compensation techniques can be used in conjunction to compensate for the rest to achieve zero-TCF resonators without excessive power consumption and calibration. The most common passive TCF compensation technique is based on using a composite structure, such as silicon dioxide and silicon, whose respective stiffness changes with temperature in opposite ways. Such an approach of using a positive TCF material to compensate for negative TCF dates back to the early 1980s [11] but is still the object of much active research [12]–[14]. However, the acoustic loss at the interface of the different materials in the composite structure loads quality factor Q, while the stress mismatch at such an interface might lead to hysteresis. Further, dielectric charging has been reported in thermally oxidized capacitive silicon resonators, which are known to cause a drift in frequency over time [15]. Thus, since passive temperature compensation techniques are desired, an alternative to composite resonator structures is needed. This paper addresses the issue by identifying the dependence of TCF on charge carrier concentration in the resonating silicon microstructure and proposes degenerate doping of silicon for TCF compensation. II. SiBAR Temperature compensation via degenerate doping is demonstrated using single-crystal silicon bulk acoustic resonators (SiBARs) (see Fig. 1). A SiBAR consists of a resonating suspended SCS bar separated by narrow air gaps from two identical drive/sense polysilicon electrodes. The suspended microstructure is supported using narrow tethers at its shorter edges, which also provide electrical contact to dc polarization voltage Vp that is applied at the Vp pads. Now an ac signal applied at the drive electrode results in a time-varying electrostatic force applied across the air gap onto the corresponding face
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Fig. 1. SEM image of a 100-MHz SiBAR. (W = 40 μm; L = 10 × W = 400 μm; T = 10 μm). E and ρ are the Young’s modulus and density of silicon. Fig. 3. Illustration showing (a) equivalent HH and LH energy surfaces of the valence band in silicon that are (b) permanently split due to the large compressional strain from the very high boron doping of the silicon crystal. E and k are the electronic energy and wave vector, respectively.
Fig. 2. Illustration showing (a) equivalent HH and LH energy surfaces of the valence band in silicon that contain most of the holes at steady-state and (b) propagation of acoustic waves splits the equivalent surfaces leading to a flow of holes from HH to LH. E and k are the electronic energy and wave vector, respectively.
of the resonator. At target frequency f0 determined by W , the resulting width-extensional mode (WEM) of resonance [see Fig. 2(b)] modulates the transduction air gap on the other side inducing a voltage on the sense electrode. The SiBARs used in this work were transduced using very narrow 100-nm air gaps fabricated using the HARPSS process [16]. III. TCF C OMPENSATION VIA D EGENERATE D OPING The propagation of an acoustic wave through a solid material is typically characterized by an alternating set of compressional and dilational forces that perturb the periodicity of the atomic lattice during wave propagation. In a semiconductor such as silicon, such a perturbation of atomic periodicity directly impacts its electronic band structure. For example, at steady-state, the valence band of silicon is made up of three energy surfaces in k-space, two of which are equivalent and are energetically favorable to contain almost all the holes [see Fig. 2(a)]. The resulting longitudinal strain due to the WEM of resonance in a SiBAR splits the equivalent energy bands, leading to a flow of holes from the heavy-hole (HH) to the more energetically
favorable light-hole (LH) band [see Fig. 2(b)] [17], [18]. The net flow of holes and thereby the electronic energy of the system increases with increasing temperature. A similar analogy exists for the electrons in the conduction band of silicon. Per the conservation of energy principle, such a temperature-dependent increase in the electronic energy manifests itself as a corresponding decrease in the elastic energy of the system. Thus, a progressive reduction in the stiffness (i.e., Young’s modulus (E)) of the resonating silicon microstructure and thereby its resonance frequency is observed with increasing temperature (i.e., TCF). Although linear thermal expansion coefficient α of silicon also contributes to the TCF, its contribution is negligible compared with the temperature coefficient of Young’s modulus (TCE). Temperature compensation techniques that have been reported to date combat the effect of TCE, whereas this work targets the manipulation of charge carriers that cause it in the first place [19]. Thus, a momentary strain produced by the propagation of the acoustic waves is understood to create a temperature-dependent change in the electronic and elastic energies of the system. Such an effect of the momentary strain could be made minimal in comparison if a larger permanent strain could be created in the silicon crystal. For example, a boron atom that has a smaller radius than silicon atom strongly bonds to only three of the four adjacent silicon atoms when diffused into the crystal lattice. At very high doping levels, such an atomic arrangement produces a strong shear strain in the silicon lattice, which is sufficient to create a large permanent separation between the equivalent LH and HH valence bands. As a result, the majority of the holes permanently shift from the HH to the LH band, thereby almost depleting the holes from the former (see Fig. 3) [20]. The effect of any additional band splitting caused by the propagation of acoustic waves in such a highly-doped SiBAR now becomes minimal in comparison for two reasons: first, very few holes are available in the almost depleted HH band of a highly doped silicon to flow to the LH band; second, the energy required to flow from HH to LH is much larger compared with a
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TABLE I M EASURED TCF IN SiBARs FABRICATED ON S ILICON WAFERS W ITH V ERY L OW TO V ERY H IGH B ORON D OPING L EVELS
Fig. 4. Illustration of the minimized flow of holes in the valence band of silicon during acoustic transduction in a very highly boron-doped SiBAR.
nonhighly doped silicon, thereby making such a transition least energetically favored (see Fig. 4). As a result, the momentary flow of holes from HH to LH is significantly minimized. Thus, a considerable reduction in the variation of the electrical and elastic energies of the system with temperature is effected, thereby resulting in TCF compensation. At degenerate levels of boron doping, the acoustic wave can potentially be shielded entirely from the k-space contours of the valence band, which, in turn, should completely compensate the TCE component of the TCF, i.e., TCF =
TCE + α . 2
TABLE II B ORON D OPING R ECIPE U SING S OLID AND L IQUID B ORON S OURCES
(1)
The native silicon TCE of ∼ −57 ppm/◦ C and α of ∼ −3 ppm/◦ C yield a TCF of ∼ −30 ppm/◦ C in silicon microresonators. Upon complete TCE compensation via degenerate doping, a TCF as low as ∼ −1.5 ppm/◦ C could be achieved. IV. TCF C OMPENSATION VIA D EGENERATE B ORON D OPING Both Czochralski and float-zone silicon wafer manufacturing processes typically involve an in situ doping with either n- or p-type dopants. Such predoped silicon wafers can be procured as is from the wafer vendors to verify the TCF compensation in silicon microresonators with increasing doping levels (i.e., decreasing resistivities). Thus, the proposed solution of very high doping for TCF compensation can be easily verified for any SCS microresonator design with no additional need for processing capabilities to dope silicon. Table I summarizes the measured TCF across various resistivities from SiBARs fabricated on a 20-μm-thick boron-doped device layer of SOI wafers as-procured from Ultrasil Corp. (USA). Although only a minimal TCF reduction of ∼ 4 ppm/◦ C is observed from very high to low resistivity silicon substrates, substantial TCF reduction has been measured at very low and ultralow resistivities. As shown in Table I, an overall TCF reduction of 24 ppm/◦ C can be readily achieved in silicon microresonators by opting for ultralow resistive substrates. No significant impact was measured on the Q and insertion loss of these microresonators across such wide range of doping levels. It is worth mentioning that such very low and ultralow resistivity substrates were specially ordered for the purpose and are typically more expensive compared with the relatively higher resistivity substrates. Such very high levels of doping can be also achieved starting from a low resistivity substrate
by repeated doping/annealing processes. For example, a borondoped resistivity of ∼ 0.01 Ω · cm resistivity has been measured to reduce to ∼ 0.001 Ω · cm after five repetitions of the solid boron dope/anneal recipe shown in Table II. For further reduction in resistivity, liquid spin-on-dopant boron sources were used [Futurrex Inc. (USA), BDC1-2000]. After six repetitions of spin-on-dope/anneal recipe, the boron-doped resistivity could be further reduced from ∼ 0.001 to ∼ 0.0001 Ω · cm. In both cases of solid and liquid dopants, the borosilicate glass layer that forms after every dope/anneal cycle was removed using hydrofluoric acid. All the reported resistivities in this paper were accurately measured using four-point probe measurement. Although longer hours of processing are needed to achieve a resistivity of ∼ 0.0001 Ω · cm (see Table II), such a resistivity is lower than any commercially available silicon wafer. At such doping levels, the diffusion depth of boron in silicon is typically limited to 7 ∼ 8 μm [22]. Hence, 5-μm-thick substrates were chosen to fabricate uniformly doped SiBARs at such degenerate doping levels of boron in silicon. A 5-μm-thick 0.0001 Ω · cm SiBAR is found to measure a TCF of −3.56 ppm/◦ C, which is an order of magnitude lower than that measured at a very high resistivity of 1000 Ω · cm (see Fig. 5). The increase in resonance frequency after heavy doping is due to the increase in the Young’s modulus of silicon and is indicative of the degenerative doping [23]. As seen from the square of correlation coefficient of linearity R2 reported in Fig. 5, the linearity of the TCF curve is compromised to some extent due to degenerate boron doping.
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Fig. 5. Order of magnitude reduction in TCF measured at a boron-doped SiBAR resistivity of 0.0001 Ω · cm compared with 1000 Ω · cm. Fig. 7. SEM images showing the observed outdiffusion of boron from the silicon surface after seven repetitions of the spin-on-dope/anneal processes.
Fig. 8. Saturation of TCF at ∼ −1.5 ppm/◦ C of the 5-μm-thick SiBAR after seven repetitions of spin-on-dope/anneal processes. Fig. 6. Measured response of the degenerately doped SiBAR with a TCF of −3.56 ppm/◦ C showing a quality factor Q of 33 000 in vacuum.
Such degenerately doped 0.0001 Ω · cm 5-μm-thick SiBARs measure a Q of 33 000 (versus 35 000 for a nondegenerately doped 5-μm-thick SiBAR with a resistivity of 0.01 Ω · cm) at Vp of 20 V in vacuum (see Fig. 6). This indicates a minimal effect on the acoustic loss in silicon microresonators from longer hours of repeated thermal cycling during the doping process. However, upon any further doping, boron is observed to outdiffuse from the surface of the silicon, leaving behind a relatively porous silicon surface. Such a surface of silicon as-observed after seven repetitions of the spin-on-dope/anneal processes is shown in Fig. 7. The outdiffusion is indicative of doping levels that surpass the solid solubility limit of boron in silicon (∼ 2 × 1020 atoms/cm3 ). At such levels of doping, the resistivity values could not be accurately measured and hence are not reported. The SiBARs fabricated at such doping levels measure the lowest recorded TCF of −1.43 ppm/◦ C. Interestingly, no further reduction in TCF was measured even after ten repetitions of spin-on-dope/anneal processes (see Fig. 8). Interestingly, Wang et al. had theoretically predicted a positive TCF with increasing levels of boron doping in silicon microresonators [24]. To the contrary, this work experimentally proves that positive TCFs were not measured even at degenerate levels of boron doping in silicon. Further, the lowest measured TCF value of ∼ −1.5 ppm/◦ C is understood to be the sole contribution of linear thermal expansion component α after
complete compensation of TCE [see (1)]. It is to be noted that such outdiffusion of boron results in lattice damage to silicon that reflects as a relatively reduced Q of 20 000 in vacuum. Thus, degenerate boron doping has been successfully demonstrated to offer a reduction from a native TCF of −33 to −1.5 ppm/◦ C in silicon micromechanical resonators. Similar temperature compensation has been also recently demonstrated in thermally actuated silicon microresonators using degenerate phosphorous doping [25]. However, the longer hours of processing needed to achieve such degenerate doping levels call for a faster alternative. Further, the difficulty in achieving very high doping levels for thicker substrates limits the proposed TCF compensation technique to substrates that are thinner than 7 ∼ 8 μm. The next section addresses both these issues by presenting a boron-assisted aluminum doping technique that is capable of achieving very high doping levels within few minutes of processing in much thicker substrates. V. TCF C OMPENSATION VIA B ORON -A SSISTED A LUMINUM D OPING Boron diffuses as an interstitial dopant [26], which demands for longer hours of annealing to become electrically active. On the other hand, aluminum (also a p-type dopant) becomes readily electrically active by diffusion via self-interstitial mechanism [27]. It has been shown that aluminum can thermomigrate against a temperature gradient into hundreds-of-micrometersthick silicon within few tens of minutes [28]. Thermomigration
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Fig. 9.
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Schematic of the wafer-level aluminum thermomigration process.
is typically performed by patterning aluminum on one side of the wafer while the other side is radiatively heated to approximately 1000 ◦ C. Such one-sided heating results in a temperature gradient across the thickness of the wafer. Once above the eutectic point (577 ◦ C), the aluminum melts and dissolves some of the silicon at the surface. The resulting droplet follows the thermal gradient toward the hot surface. As the droplet moves, the warmer side of the droplet dissolves more silicon, and the cooler side of the droplet epitaxially resolidifies; the resolidified material has an aluminum concentration determined by the solid solubility limit for aluminum in silicon at the solidification temperature, which is approximately 2 × 1019 atoms/cm3 [29]. The process is known to be highly anisotropic and relatively fast, with droplets traveling through a 300-μm-thick silicon wafer in less than 10 min [30]. The uniformity and speed of aluminum thermomigration is known to be enhanced by the presence of boron atoms in silicon [27]. Further, both boron and aluminum dopants are electrically active and will contribute to TCE compensation. Thus, such a boron-assisted aluminum thermomigration is a faster alternative to degenerate boron doping for TCF reduction. This was investigated by evaporating 200 Å of aluminum onto the surface of 20-μm-thick SiBARs fabricated on a borondoped ∼ 0.01 Ω · cm silicon wafer. The required temperature gradient is created in a furnace by turning off one of the many coil heaters of the furnace (see Fig. 9). The wafer is positioned in the furnace at the boundary of the hot and cold regions, with the aluminum-deposited side facing away from the heat. The temperature gradient across the thickness of the wafer drives the aluminum to thermomigrate into the resonating silicon bulk. After 1 h of thermomigration in nitrogen ambient, the TCF of the SiBAR reduces by 24 ppm/◦ C, from −27.8 to −3.8 ppm/◦ C. The reduced TCF is equivalent to that measured at a borondoped resistivity of ∼ 0.0001 Ω · cm (see Fig. 6). Thus, a boron doping duration of approximately 90 h (see Table II) for a similar TCF reduction on a 5-μm-thick substrates can be alternatively realized using an hour of aluminum thermomigration on substrates that are 20 μm or thicker. On the downside, due to the rapid thermomigration and the large temperature gradient across the entire wafer, some structural damage could be observed on the surface of the resonators. As a result, a considerably reduced Q of 16 000 has been observed at vacuum in wafer-level thermomigrated SiBARs. Unlike boron doping that is performed on a plain SOI wafer prior to the fabrication of the resonators, the wafer-level
Fig. 10. Schematic of the device-level aluminum thermomigration process. (a) Released SiBAR. (b) Blanket deposition of 500 Å aluminum. (c) Joule heat the support tethers and SiBAR at 120 mA for 10 min. (d) Aluminum thermomigrated SiBAR at room temperature; wirebond traces are visible in (d) since the same device was used for SEM images.
aluminum thermomigration was carried out postfabrication. Hence, stress due to thermal gradients impacts the Q and long-term stability of these resonators. On the other hand, a device-level thermomigration process could circumvent the problem while offering the expected reduction in TCF. Fig. 10 shows the schematic and SEM images of such a device-level aluminum thermomigration process developed for SiBARs. A 500-Å-thin layer of aluminum was evaporated onto the SiBAR [see Fig. 10(b)]. A current of 120 mA was passed for 10 min through the SiBAR resonator element via the support tethers [see Fig. 10(c)] [31]. At such high currents, the narrow support elements Joule heat to ∼ 1000 ◦ C while the wider SiBAR reaches the Al–Si eutectic temperature, thereby creating the necessary temperature gradient [see Fig. 10(c)]. Aluminum on top of the relatively cold SiBAR laterally diffuses through the silicon toward the hot support elements, thereby doping it [see Fig. 10(d)]. A closer look at the thermomigrated surface (see Fig. 11) shows regions of Al–Si eutectic alloy alongside exposed silicon where aluminum has completely diffused into the bulk of the resonator. The short duration of the process is insufficient to thermomigrate the entire thickness of aluminum, thereby leaving behind some residues (due to thicker than desired Al), which could be thermomigrated with further Joule heating. Although aluminum is deposited on the Vp pads as well [see Fig. 10(b)], its relatively larger cross section remains below the Al–Si eutectic temperature during Joule heating. Hence, no thermomigration has been observed to occur on the Vp pads. A reduction in TCF by 14 ppm/◦ C (from −22.13 to −7.93 ppm/◦ C) has been measured over 10 min of device-level thermomigration on a ∼ 0.001 Ω · cm SiBAR. From the values in Table I, it can be inferred that a TCF value corresponding to very low resistivity of a silicon wafer can be reduced to its ultralow resistive counterpart within few minutes of aluminum thermomigration. The passage of current for longer durations
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Fig. 11. SEM showing a close-up of the aluminum thermomigrated SiBAR in Fig. 10(d).
Fig. 12. Measured response of a 20-μm-thick [∼ 0.001 Ω · cm; boron-doped] SiBAR after device-level thermomigration with 500 Å of aluminum at 120 mA for 10 min.
might lead to plastic deformation at the narrow support tethers, thereby causing a failure of resonator operation. However, if the supports are redesigned to be wider, thermomigration could be performed for longer durations to achieve further reduction in TCF. Unlike boron doping and wafer-level thermomigration processes, device-level aluminum thermomigration is best suited to be a postfabrication postpackaging technique, wherein the TCF can be programmed to a desired value using Joule heating as an electrical calibration step. Minimal or no structural damage has been observed from the device-level thermomigration process as evident from a Q of 29 000 measured from these devices in vacuum. The measured insertion loss of 39.5 dB is typical of 20-μm-thick SiBARs with a capacitive air gap of ∼100 nm at Vp of 20 V (see Fig. 12). A similar device-level thermomigration was also performed on a 20-μm-thick degenerately boron-doped ∼ 0.0001 Ω · cm SiBAR. The TCF curve before thermomigration exhibits an interesting anomalous behavior, as shown in Fig. 13. This is thought to arise due to the nonuniform doping profile at such very high doping levels along the 20-μm thickness of the device. Aluminum thermomigration is found to restore the linearity of the TCF curve and offer a TCF as low as −2.72 ppm/◦ C while maintaining a high Q of 28 000 in vacuum (see Fig. 14).
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 59, NO. 1, JANUARY 2012
Fig. 13. TCF of a 20-μm-thick [∼ 0.0001 Ω · cm; boron-doped] SiBAR before and after device-level thermomigration with 500 Å of aluminum at 120 mA for 10 min.
Fig. 14. Measured response of a 20-μm-thick [∼ 0.0001 Ω · cm; borondoped] SiBAR after device-level thermomigration with 500 Å of aluminum at 120 mA for 10 min.
VI. C ONCLUSION Temperature compensation of silicon micromechanical resonators has been achieved using degenerate boron doping and boron-assisted aluminum doping. A starting TCF of −33 ppm/◦ C is reduced to −1.5 ppm/◦ C by degenerate boron doping of the silicon microresonator. Both wafer- and devicelevel aluminum thermomigration techniques are developed as faster alternatives to the relatively slower diffusion-based boron doping process. Although the former is found to compromise on the Q due to stress from the thermal gradient, the latter circumvents the problem and offers low TCF along with low insertion loss and high Q. ACKNOWLEDGMENT The authors would like to thank the staff of the Nanotechnology Research Center (NRC) at the Georgia Institute of Technology for their assistance. R EFERENCES [1] F. Ayazi, “MEMS for integrated timing and spectral processing,” in Proc. IEEE CICC, 2009, pp. 65–72. [2] B. Kim, R. Melamud, R. A. Candler, M. A. Hopcroft, C. M. Jha, S. Chandorkar, and T. W. Kenny, “Encapsulated MEMS resonators—A
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Ashwin K. Samarao (S’07–M’11) was born in Chennai, India, on February 18, 1983. He received the B.E. (Hons.) degree in electrical and computer engineering from the Birla Institute of Technology and Science, Pilani, India, in 2004, the M.S. degree in electrical and computer engineering from the University of Cincinnati, Cincinnati, OH, in 2006, and the Ph.D. degree in electrical and computer engineering from the Integrated Microelectromechanical Systems Laboratory, Georgia Institute of Technology, Atlanta, in May 2011. Subsequently he joined Integrated Device Technology, Inc., San Jose, CA, as an intern, where he worked on implementing the ideas he developed as a graduate student to engineer a MEMS-based timing solution. He is currently a MEMS Research Engineer with Robert Bosch Research and Technology Center, Palo Alto, CA. His research interests include micro- and nanoelectromechanical resonators, RF-MEMS and inertial sensors, CMOS-MEMS integration, and micro- and nanofabrication process development. Dr. Samarao was the recipient of the Best Student Paper Award at the IEEE International Frequency Control Symposium in 2010.
Farrokh Ayazi (S’96–M’00–SM’05) received the B.S. degree in electrical engineering from the University of Tehran, Tehran, Iran, in 1994 and the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 1997 and 2000, respectively. He joined the faculty of the Georgia Institute of Technology, Atlanta, in December 1999, where he is currently a Professor in the School of Electrical and Computer Engineering. His research interests are in the areas of integrated micro- and nanoelectromechanical resonators, interface IC design for MEMS and sensors, inertial sensors, RF MEMS, and microfabrication techniques. Prof. Ayazi is a 2004 recipient of the NSF CAREER Award, the 2004 Richard M. Bass Outstanding Teacher Award (determined by the vote of the ECE senior class), and the Georgia Tech College of Engineering Cutting Edge Research Award for 2001–2002. He is an editor for the IEEE/ASME J OURNAL OF M ICROELECTROMECHANICAL S YSTEMS. He served on the technical program committee of the IEEE International Solid State Circuits Conference for six years (2004–2009). He and his students won the best paper awards at Transducers 2011, the IEEE International Frequency Control Symposium in 2010, and IEEE Sensors conference in 2007. He is the CoFounder and Chief Technology Officer of Qualtré Inc., a spin-out from his research laboratory that commercializes multiaxis bulk-acoustic-wave silicon gyroscopes and multidegrees-of-freedom inertial sensors for consumer electronics and personal navigation systems.
