Intrinsic Temperature Compensation of Highly Resistive High-Q Silicon Microresonators via Charge Carrier Depletion

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1 Intrinsic Temperature Compensation of Highly Resistive High-Q Silicon Microresonators via Charge Carrier Depletion Ashwin K. Samarao and Farrokh Ayazi School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, GA, USA Abstract We report on a novel temperature compensation technique that exploits the dependence of TCF on the free charge carriers in silicon bulk acoustic resonators (SiBARs). The free charge carriers are considerably minimized by creating single and multiple pn-junction based depletion regions in the body of the resonator. The TCF of a highly resistive (>1000 Ω-cm) conventional rectangular SiBAR has been reduced from -32 ppm/ C to -3 ppm/ C. We previously exploited the dependence of TCF on silicon resonator geometry for TCF compensation. However, at large charge carrier depletion levels achieved in this work, the TCF is found to become independent of silicon resonator geometry. I. INTRODUCTION Silicon micromechanical resonators have evolved tremendously since their introduction as possible alternatives to quartz resonator technology [1]. Silicon resonators come with the definitive advantage of on-chip integration with mature silicon microelectronics while maintaining a very small form-factor and very high fq product [2]. These enable a potential for insertion of such microresonators into ultra lowphase noise oscillators and other frequency references for timing applications [3-5]. Active devices like transistors are being incorporated into a resonating silicon microstructure to generate an electronically amplified signal output [6] that is also being explored in closed-loop configuration for selfsustained self-oscillating resonators [7]. Also, unlike quartz, silicon resonators can be coupled mechanically, capacitively and electrostatically for band-pass filtering [8] and mixing applications [9]. Although considerable research has gone into perfecting the microfabrication processes to match silicon with quartz resonators in terms of quality factor (Q), power handling and motional impedance (R m ), the temperature co-efficient of frequency (TCF) of silicon resonators still remains a significant problem. The TCF of silicon microresonators (-30 ppm/ C) is significantly larger in magnitude than that of the worst AT-cut quartz crystals [10]. Perhaps the most natural approach to temperature compensation is to insert the silicon resonator in a feedback loop, and to tune its frequency electronically so as to compensate for temperature changes [11]. This is somewhat more challenging to accomplish in bulk- than in flexural-mode resonators, because the electrical tunability of the former is substantially less than that of the latter, but this problem can /10/$ IEEE 334 be mitigated by deliberately shaping the resonator to increase its tunability albeit at somewhat lower frequencies [12]. 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 [13, 14]. However, need for additional circuitry (and thereby chip area) and an increase in the overall power consumption are two most significant problems in these active temperature compensation techniques. The most common passive temperature compensation technique in silicon resonators is based on the use of composite structures consisting of materials whose stiffness changes with temperature in opposite ways. This approach dates back at least to the early 1980 s [15], but is still the object of much active research [16]. However, the acoustic loss at the interface of the different materials in the composite structure considerably damps the Q, while the stress mismatch at such an interface leads to hysteresis. Also dielectric charging has been observed in thermally oxidized silicon resonators which cause a drift in frequency over time [17]. Transduction in silicon microresonators typically involves the propagation of longitudinal acoustic waves through its bulk. Such an acoustic wave 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 like silicon, the perturbation of atomic periodicity directly impacts its electronic band structure. As a result, a net flow of free charge carriers exists between the sub-bands within the valence and conduction bands in silicon during acoustic transduction which increases the overall electronic energy of the resonator [18]. The increase in electronic energy of the resonator system due to acoustic transduction increases with temperature due to the additional thermal generation of free charge carriers at higher temperatures [19]. The law of conservation of energy dictates a corresponding decrease in the mechanical energy of the system with the increase in temperature which causes a negative temperature coefficient of Young s modulus (TCE) in silicon. Since the mechanical resonance frequency of silicon microresonators are predominantly determined by the Young s modulus of silicon, a negative TCE reflects as a negative TCF. Thus, there exists a possibility to explore a charge carrier based TCF compensation technique in silicon micromechanical resonators.

II. MOTIVATION FOR CHARGE CARRIER DEPLETION A conventional rectangular silicon bulk acoustic resonator (or SiBAR) consists of a long rectangular bar resonating element placed between two identical

A very narrow air-gap of ~100 nm is achieved between the resonator and the electrodes (Figure 2) using the HARPSS process [3].

When an AC voltage is applied to the drive electrode, the resulting time-varying electrostatic force applied to the corresponding face of the resonator induces an acoustic wave that propagates

Small changes in the air gap on the other side of the device induce a voltage on the sense electrode whose amplitude peaks at the mechanical resonance frequency.

2 II. MOTIVATION FOR CHARGE CARRIER DEPLETION A conventional rectangular silicon bulk acoustic resonator (or SiBAR) consists of a long rectangular bar resonating element placed between two identical electrodes (drive & sense), and supported symmetrically by two narrow support tethers on the sides (Figure 1(a)). A very narrow air-gap of ~100 nm is achieved between the resonator and the electrodes (Figure 2) using the HARPSS process [3]. A DC polarization voltage (V p ) applied to the resonator generates an electrostatic field in these narrow capacitive gaps. When an AC voltage is applied to the drive electrode, the resulting time-varying electrostatic force applied to the corresponding face of the resonator induces an acoustic wave that propagates through the bar, resulting in a width-extensional resonance mode (Figure 3(a)) whose frequency is primarily defined by width (W) of the SiBAR. Small changes in the air gap on the other side of the device induce a voltage on the sense electrode whose amplitude peaks at the mechanical resonance frequency. Figure 1 : SEM Images of a (a) conventional rectangular SiBAR and (b) concave SiBAR (or CBAR). Figure 2 : SEM showing the very narrow capacitive air-gap (~100 nm) between the resonator and the electrodes, fabricated using the HARPSS process [3]. Figure 3 : Simulated width-extensional-mode (WEM) of the (a) rectangular SiBAR and (b) concave SiBAR (CBAR). We have previously demonstrated TCF compensation in Silicon Bulk Acoustic Resonators (SiBARs) via degenerate boron doping [20]. By creating such a permanent charge surplus, the charge flow that results due to acoustic transduction in silicon can be made minimal in comparison. Thus, by minimizing the temperature dependent increase in the electronic energy of the silicon resonator, a corresponding decrease in mechanical energy and thereby the TCF could be minimized. The TCF of the SiBAR was shown to reduce from -30 ppm/ºc at a moderately boron doped substrate resistivity of 10-2 Ω-cm to -1.5 ppm/ºc at a degenerately boron doped resistivity of <10-4 Ω-cm. Figure 4 : Simulated shear strain along the xy-plane in a (a) rectangular SiBAR and (b) concave SiBAR (CBAR). We also reported that TCF compensation can also be accomplished via resonator geometry engineering [21]. Figure 1(b) introduces a concave SiBAR (or CBAR) geometry where the long edges of a conventional rectangular SiBAR are curved such that the central frequencydetermining width is retained the same as a SiBAR while the shorter edges are extended to form a concave geometry. At appropriate curvatures, it was shown that the WEM of the resonator can be completely confined to near the central region in a CBAR (Figure 3(b)) as opposed to the entire length in a SiBAR (Figure 3(a)). Such a construction minimizes acoustic loss at the narrow support tethers, thereby greatly enhancing the quality factor (Q) of the resonator. Interestingly, a considerable reduction in TCF was measured from the CBAR compared to that of a SiBAR. At a substrate resistivity of 10-3 Ω-cm, the TCF of -21 ppm/ºc of a SiBAR was reduced to -6 ppm/ C in a CBAR while exhibiting a Q of 101,000 at 100 MHz. Such a reduction in TCF was understood to arise from the additional shear strain components that are generated in the CBAR geometry in the xy-plane (Figure 4(b)) during acoustic transduction unlike a SiBAR (Figure 4(a)). Such shear strain was hypothesized to minimize the charge flow during acoustic transduction that results in a compensation for TCF. Thus, there exists a two fold motivation for depletion of charge carriers in silicon microresonators (Figure 5). First, to verify if TCF compensation could also be achieved via charge carrier depletion by a similar principle of minimizing the effect of charge carrier flow during acoustic transduction as was possible by creating a charge surplus via degenerate doping. Second, to verify if the advantages of shear strain in CBAR would reduce with increasing charge depletion eventually rendering the TCF to be independent of resonator geometry at very high depletion levels. Highly resistive silicon with very low doping levels is more suitable for depletion of charge carriers. A boron-doped silicon substrate with a resistivity >1000 Ω-cm was used as the starting substrate in this work. 335

pn-junction. As the next step, the single pn-junction was created using liquid phosphorous dopants to increase the amount of dopants in the diffusion process.

PN-JUNCTION BASED CHARGE CARRIER DEPLETION In this work, pn-junction based depletion regions were created in the body of the microresonator to deplete charge carriers (Figure 6).

Multiple pn-junctions were also explored by successively doping with alternating doping polarity to increase the number of depletion regions for achieving higher levels of charge depletion.

3 pn-junction. As the next step, the single pn-junction was created using liquid phosphorous dopants to increase the amount of dopants in the diffusion process. Figure 5 : Motivation for charge carrier depletion in silicon microresonators. III. PN-JUNCTION BASED CHARGE CARRIER DEPLETION In this work, pn-junction based depletion regions were created in the body of the microresonator to deplete charge carriers (Figure 6). Boron doped substrates were diffused with phosphorous dopants to create a pn-junction. 5 µm thick substrates were used to achieve considerable depletion of charge carriers via wider depletion regions. Multiple pn-junctions were also explored by successively doping with alternating doping polarity to increase the number of depletion regions for achieving higher levels of charge depletion. Figure 7 : TCF of a SiBAR and CBAR as-fabricated on a 5 µm thick borondoped silicon substrate with a resistivity of >1000 Ω-cm. Figure 8 : Schematic of creating a single pn-junction using solid phosphorous dopant sources. Figure 6 : A cross-section of the SiBAR showing an illustration of pn-junction based charge carrier depletion in silicon microresonators. IV. RESULTS SiBAR and CBAR fabricated as-is on a 5 µm thick boron doped silicon substrate with a resistivity of >1000 Ω-cm show a starting TCF of ppm/ C and ppm/ C respectively (Figure 7). The starting difference between the two TCFs was ~12 ppm/ C. As the first step, a single pn-junction was created on such highly resistive substrate using solid phosphorous sources as illustrated in Figure 8. A 5 hour doping at 1050 C was followed by a drive-in for 6 hours at 1100 C. SiBARs and CBARs fabricated on such a substrate measured a TCF of ppm/ C and ppm/ C respectively. No considerable reduction in the absolute TCF value or in the difference between the two TCFs was measured as compared to the substrate without a Figure 9 : TCF of a SiBAR and CBAR on a 5 µm thick highly resistive silicon substrate with a single pn-junction created using solid phosphorous dopant sources. As illustrated in Figure 10, the highly resistive p-type substrate was doped using Futurrex Phosphorous Dopant Coating solution (PDC1-2000). The solution was spun onto 336

78 ppm/ C and -11.95 ppm/ C respectively (Figure 11). A reduction in the difference between the two TCFs (~8.83 ppm/ C) was also measured.

4 the wafer at 3000 rpm for 40 seconds, followed by baking at 200 C for 3 minutes. The dopants were driven-in by annealing the wafer at 1100 C for 6 hours. The liquid phosphorous dopants are found to be more effective in creating a depletion region for the same duration of annealing. As a result, the TCF of the SiBAR and CBAR reduced to ppm/ C and ppm/ C respectively (Figure 11). A reduction in the difference between the two TCFs (~8.83 ppm/ C) was also measured. Such a reduction in the difference was understood to indicate a reduction in the effect of resonator geometry on the TCF. To further verify the claim, an increased depletion of charge carriers had to be effected. boron doping and an annealing for 9 hours. Similarly, the dopant polarity was reversed with every consecutive doping step while progressively reducing the duration of annealing by an hour, until the last step of boron doping was followed by one hour of annealing. Annealing was performed at 1100 C for all these steps. Equal thickness of the different doped layers is not a significant requirement for this work. Such multiple pn-junctions were created on both 10 µm and 5 µm thick substrates. Figure 10 : Schematic of creating a single pn-junction using liquid phosphorous dopant sources. Figure 12 : Multiple pn-junctions created on a highly resistive p-type silicon substrate with consecutive doping with opposite polarity and progressively reducing in the duration of annealing. The TCF of the SiBAR and CBAR on the 10 µm substrate was measured to be ppm/ C and ppm/ C respectively (Figure 13). Thus, the difference in the TCF reduces to just 3.9 ppm/ C indicating the increasing independence of TCF on resonator geometry at increased depletion levels. The Q of the SiBAR and CBAR are measured to be 24,000 and 67,000 respectively, in vacuum at an input power level of -10 dbm and at a V p of 10 V (Figure 14). Figure 11 : TCF of a SiBAR and CBAR on a 5 µm thick highly resistive silicon substrate with a single pn-junction created using liquid phosphorous dopant sources. Figure 13 : TCF of a SiBAR and CBAR on a 10 µm thick highly resistive silicon substrate with multiple pn-junctions. Multiple pn-junctions can be stacked on top of each other in a starting silicon substrate by successively doping with opposing polarities of dopants with a progressive reduction in annealing time for every drive-in step (Figure 12). The multiple depletion regions that result are expected to considerably deplete the free charge carriers. In this work, multiple pn-junctions were created using liquid phosphorous and boron dopants on a starting highly resistive p-type substrate. The first step involved phosphorous doping followed by annealing for 10 hours. This was followed by 337

5 CBAR geometry during acoustic transduction effects a charge carrier based TCF compensation which becomes absent at such very high depletion levels. Finally, the longer hours of annealing involved in the creation of multiple pn-junctions degrade the Q of the resonators. However, since the CBAR is designed for minimal support-loss and thereby a very high Q to start with, it sustains a much higher Q compared to a SiBAR even after Q degradation. Figure 14 : Measured response of a (a) SiBAR and (b) CBAR on a 10 µm thick highly resistive silicon substrate with multiple pn-junctions. The charge carriers might still not be appreciably depleted along the entire thickness of a 10 µm thick substrate, as the diffusion depths of doping processes are limited to 6-7 µm using liquid dopants [22]. However, at the substrate thickness of 5 µm, the TCF of the SiBAR and CBAR become equal and measure -3 ppm/ C (Figure 15). Thus, the TCF is found to eventually become completely independent of the resonator geometry at very high depletion levels. As seen from Figure 15, the linearity of the TCF curve is compromised to some extent with increasing levels of charge carrier depletion. Also, longer hours of annealing on a thin substrate degrade the Q of the resonators compared to the 10 µm substrate. The Q of the SiBAR and the CBAR are measured to be 13,000 and 50,000 respectively, in vacuum at an input power level of -10 dbm at a V p of 10 V (Figure 16). Figure 16 : Measured response of a (a) SiBAR and (b) CBAR on a 5 µm thick highly resistive silicon substrate with multiple pn-junctions. Figure 15 : TCF of a SiBAR and CBAR on a 5 µm thick highly resistive silicon substrate with multiple pn-junctions. CONCLUSION Three important conclusions can be drawn from this work. First, depleting the charge carriers in a silicon microresonator is a viable technique for TCF compensation. The TCF of a SiBAR was measured to reduce from -32 ppm/ C at a substrate resistivity of >1000 Ω-cm to -3 ppm/ C with multiple pn-junctions based charge carrier depletion. Second, the TCF of the SiBAR and CBAR were found to measure the same value at very high depletion levels indicating the independence of TCF on the resonator geometry. It also confirms that the additional shear strain in a ACKNOWLEDGMENT This work was supported by Integrated Device Technology (IDT), Incorporated. The authors would like to thank the staff at the Nanotechnology Research Center (NRC) at the Georgia Institute of Technology for assistance with microfabrication. REFERENCES [1] F. Ayazi, MEMS for Integrated Timing and Spectral Processing, Invited Paper, Proc. IEEE Custom Integrated Circuits Conference (CICC 2009), Sep. 2009, pp [2] R. Tabrizian, M. Rais-Zadeh, and F. Ayazi, Effect of Phonon Interactions on Limiting the fq Product of Micromechanical Resonators, IEEE International Conference on Solid-state Sensors, Actuators and Microsystems (Transducers), June. 2009, pp

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