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Micromachined polysilicon resonating xylophone bar magnetometer
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Acta Astronautica 52 (2003) 421 – 425 www.elsevier.com/locate/actaastro
Micromachined polysilicon resonating xylophone bar magnetometer D.K. Wickenden∗ , J.L. Champion, R. Osiander, R.B. Givens, J.L. Lamb, J.A. Miragliotta, D.A. Oursler, T.J. Kistenmacher The Johns Hopkins University, Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723-6099, USA
Abstract The basic device principles, including response sensitivity and transduction schemes, are outlined for a resonating xylophone bar magnetometer. Advanced design emphasis is on a polysilicon version with dimensions of order microns fabricated by microelectromechanical systems (MEMS) processing techniques. All polysilicon devices tested to date have performed extremely well in static magnetic 4elds and exhibit mechanical quality factors, Q, of up to 30,000 at reduced pressures. The resonance frequencies of the fundamental mode of vibration of these polysilicon xylophone bars have been found to be sensitive functions of the torsional sti5ness of the support arms, in accord with an analytical model based on Bernoulli– Euler theory. The output response of the polysilicon xylophone magnetometer as a function of impressed magnetic 6ux density has been shown to be linear up to 150 T; however, sensitivity is currently limited by the signi4cant resistivity of the polysilicon xylophone bar. Various strategies are being implemented to bring the magnetometer sensitivity into the applications-dominated nT regime. c 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction There are a number of pragmatic motivations directing the development of miniature magnetometers including conservation of mass, volume, power, and cost. Some applications where these factors are of fundamental importance include determination of orientation and spin rate of ordinance, tracking of surface and subsurface vessels, oceanographic mapping, measurement of extraterrestrial 4elds, imaging on-board satellite currents, microsurgery, and bio4eld imaging. Importantly, whether the particular application requires a single magnetometer or an array
∗
Corresponding author.
of magnetometers, the realization of optimal performance at reduced mass, size and cost will necessitate micromachining and microfabrication, as well as the integration of the associated electronic circuitry. Several contemporary magnetic sensors have been shown to be capable of being miniaturized using microelectromechanical systems (MEMS) processing techniques and include the -magnetometer [1], a magnetostrictive 4eld sensor [2], a wide dynamic range, high sensitivity xylophone bar magnetometer [3–5], a high-4eld, rapid “trampoline” device [6], and an amplitude detecting microbeam magnetometer [7]. In this report, the current status of the miniaturization of the resonating xylophone bar magnetometer [3–5] through MEMS processing is outlined.
c 2002 Elsevier Science Ltd. All rights reserved. 0094-5765/03/$ - see front matter PII: S 0 0 9 4 - 5 7 6 5 ( 0 2 ) 0 0 1 8 3 - 2
D.K. Wickenden et al. / Acta Astronautica 52 (2003) 421 – 425 200
0.10
F B Magnitude (a.u)
0.08
I
150
0.06 100 0.04 50
0.02
Fig. 1. Operating principle of the resonating xylophone bar magnetometer.
0.00 78.05
Phase (deg.)
422
78.10
78.15
0 78.20
Frequency (kHz)
Fig. 2. Displacement and phase outputs as a function of the frequency of the drive current to the xylophone bar.
2. Basic principles For the detection of static magnetic 4elds, the active element of the xylophone magnetometer [3,4] is a conductive bar supported at the nodes of its fundamental mode of mechanical vibration [8], and a sinusoidal current is supplied to the bar at this frequency (f0 ) through the support arms. In the presence of a 4eld component parallel to the surface of the xylophone bar but normal to the direction of the drive current (Fig. 1), the Lorentz force [F = B × I = BI cos(2f0 t)] causes the bar to vibrate at its fundamental frequency with an amplitude according to Eq. (1) [8]: d(f0 ) =
5Fl42 384EIB
Q;
(1)
where, l2 is the length of the xylophone bar between the supports, E is Young’s modulus, IB is the area moment of inertia of the bar, and Q is the mechanical quality factor. From this equation, it can be seen that amplitude is linearly proportional to the drive current (I ), the magnetic 4eld (B), and the mechanical Q-factor. Because the xylophone bar’s normal mode frequencies for oscillations in other directions are di5erent, the technique discriminates against these components of the magnetic 4eld extremely well so that any second-order cross coupling between di5erent 4eld components is extremely small.
3. Signal transduction The amplitude of the de6ection of the xylophone bar, Eq. (1), can be measured by a number of established, position-sensitive detection techniques [9]. Thus far, optical methods (beam de6ection [3–5] and interferometry [10]) have been the principal experimental techniques, with capacitive methods under active investigation. In magnetic 4elds of order T to nT, the displacement of the xylophone bar resulting from the Lorentz force is of order 1–0:01 nm at the resonant frequency. Therefore, any proposed optical transduction mechanism must be capable of resolving xylophone bar displacements that are signi4cantly less than the wavelength (typically, several hundred nanometers) of the probing optical radiation. Optical beam de6ection has been extensively utilized. In this technique. a laser diode beam is re6ected (the incident angle is about 5◦ from vertical incidence, and the laser diode and detector are about 20 cm away from the xylophone bar) from one of the free ends of the bar. The re6ected laser beam is collected in a position sensitive detector, with the di5erence in photogenerated current used as the signal to a lock-in ampli4er. In this case the output signal can be detected using homodyne detection at the resonance frequency. The ability to detect the resonantly enhance signal from the magnetic 4eld sensor is illustrated in Fig. 2. Here the variation in the detector amplitude and phase are plotted as functions of the frequency of the driv-
D.K. Wickenden et al. / Acta Astronautica 52 (2003) 421 – 425
Fig. 3. SEM Image of an MEMS fabricated polysilicon xylophone bar resonator, current leads, and mounting pads. The polysilicon xylophone bar is 500 m in length, 50 m in width, and 2 m in thickness.
ing current to the xylophone bar. As the frequency is tuned through the fundamental mechanical resonance, the displacement amplitude is resonantly enhanced while the phase angle (with respect to the current source) displays a 180◦ shift. In this measurement, the xylophone bar magnetometer was oriented to maximize the Lorentz force, arising from the interaction between the earth’s magnetic 4eld (∼ 30 T) and the alternating current in the bar. 4. MEMS processing, signal response, mechanical modeling The polysilicon xylophone bars, support arms and mounting pads reported on here were fabricated at the MCNC MEMS foundry [11]. An SEM image of a typical device is shown in Fig. 3. The lower electrode consists of a 0:5 m thick polysilicon layer patterned on the silicon nitride-coated silicon substrate. The xylophone bar, support electrodes, and mounting pads are fabricated from 2 m thick polysilicon suspended (after release of the sacri4cial silicon dioxide) 2 m above the silicon nitride layer. The mounting pads are attached to the lower electrode by the indicated patterns to provide a rigid anchor which minimizes vibrational coupling from the xylophone bar [12].
423
Physical contact between the xylophone bar and the silicon nitride layer is minimized by having 0:75 m deep “dimples” in the center and toward the ends of the xylophone bar. Lastly, etch holes are incorporated to facilitate release of the completed structure. The SEM micrograph clearly displays the anchor structure, etch holes, topographical evidence of the dimples, and the clean release of the xylophone bar and support electrodes. Evaluation of these micromachined xylophone bar resonators has been carried out in an evacuated test chamber, using a bench-top beam de6ection microscope [3,4]. Magnitude and phase outputs were initially obtained in an mT static magnetic 4eld by scanning and detecting at the frequency of the sinusoidal drive current through a 500 m × 50 m xylophone bar with 4 m × 45 m support arms, where the current through the device was 22 A (rms) and the chamber pressure was 35 mTorr. From these data, a resonance frequency of 78:2 kHz and a Q-factor of almost 7000 were obtained from a least-squares 4t to the amplitude resonance equation (1). For reference, the predicted frequency for a free– free polysilicon resonating bar (assuming a Young’s modulus of 160 GPa) is 69:2 kHz. Experimental results were also obtained from xylophone bars with 6 and 10 m wide support arms, under identical conditions. The resonance frequencies of these supported xylophone bars were 84.9 and 95:6 kHz, respectively. It was conjectured that the increasing resonance frequencies were largely determined by the increasing torsional sti5ness of the wider xylophone bar support arms. As a test of this supposition, an analytical model was derived based on Bernoulli–Euler theory, as the wavelength of vibration is much larger than the thickness of the resonant beam. The variation in natural frequency of the fundamental oscillation mode with support arm thickness was obtained from a numerical solution to the analytical model [5,13] and is compared to measured values in Fig. 4. The excellent agreement (to within 1% on average) between the theoretical results and the experimental data suggests that the analytical model very successfully describes the dynamics of the supported xylophone bar. It is also well known that pressure markedly in6uences the performance of MEMS resonators, and the e5ect of pressure on the resonance properties of a xylophone bar with 4 m wide support arms has been
424
D.K. Wickenden et al. / Acta Astronautica 52 (2003) 421 – 425 0.40
Normalized output signal (a.u)
110
Frequency (kHz)
100 90 80 70 60
0.35
0.30
0.25
0.20 0
2
4
6
8
10
12
Support width (µm)
Fig. 4. Measured and predicted resonance frequency of xylophone bar resonators as a function of support arm width at constant length and thickness.
determined. For this measurement, the magnetic 6ux density was on the order of 10 T (owing to the presence of the Earth’s plus other background 4elds), and the xylophone drive current was again 22 A (rms). The pressure in the test chamber was varied between 15 and 85 mTorr, and the resulting Q factors showed maximum and minimum values of 21,950 and 2780. A small (9 Hz) decrease in resonance frequency from the highest to the lowest pressure is believed to be due to thermal e5ects (lower torsional sti5ness of the xylophone bar, vide supra). Moderate temperature sensitivity of the xylophone bar resonance frequency has also been observed at constant pressure by varying the intensity of a broad illumination source or by repositioning the beam de6ection laser. There has also been evidence that mechanical energy losses at resonance contribute enough thermal energy to measurably lower the resonance frequency of a xylophone bar device. Finally, a plot of the response of the polysilicon xylophone magnetometer as a function of impressed magnetic 6ux density up to 150 T is shown in Fig. 5. The superimposed line is a least-squares 4t to the data, and it is apparent that the magnetometer response is linear over the range of magnetic 6ux density shown. An estimate of the ultimate noise 6oor of the xylophone bar magnetometer, based on thermomechanical noise (Brownian motion due to the Langevin force) and to a lesser extent Johnson noise (current noise that couples with√the magnetic 4eld), yields a value of order 100 pT A= Hz. This estimate calls out the very
0
40
80
120
160
Impressed field (µT)
Fig. 5. Output response of a polysilicon xylophone bar magnetometer as a function of impressed magnetic 6ux density.
important role that the amplitude of the drive current plays in determining the ultimate 4eld sensitivity of a xylophone bar magnetometer. Two remarks are appropriate: (a) earlier versions of the xylophone bar magnetometer (chemically milled from low resistivity CuBe, with Q values more typically near 3000 –5000) have successfully √ measured calibrated 6ux densities in the 0:1 nT= Hz range [5,14]; and, (b) the length and width dimensions of the polysilicon xylophone bar magnetometer presented here are proportionally scaled from these earlier versions, while the thickness is an order of magnitude smaller than for direct √ scaling. The limiting factor in achieving nT= Hz sensitivity is, then, de4nitely identi4ed as the high resistivity of the polysilicon xylophone bars and their lower current carrying capability. 5. Potential aeronautical and aerospace applications There are several advantageous points to be considered in the development of an ultrasensitive micromachined xylophone bar magnetometer for aeronautical and aerospace applications: • Simplicity of the basic device physics, design rules and functionality; • As a resonant sensor, the amplitude of the response is ampli4ed by the mechanical Q; • Wide dynamic range achieved in a device free of magnetic materials and hysteresis;
D.K. Wickenden et al. / Acta Astronautica 52 (2003) 421 – 425
• Resonant frequency size selectable to reduce crosstalk in multidimentional designs; • The xylophone bar sensor has essentially no zero 4eld drift; • There are a number of detection techniques (optical beam de6ection, interferometry, capacitance) capable of being miniaturized in parallel with xylophone bar resonators; • The xylophone bar magnetometer can be used as a narrow-band mixer for the detection of alternating magnetic 4elds, detecting resonances at either the sum or the di5erence between the frequency of the driving current and that of the alternating magnetic 4eld.
Acknowledgements Support of this work by the US Department of the Navy under contract N00039-91-5301 and by the Defense Advanced Research Project Agency under contract F49620-98-1-0500 and extremely helpful discussions with A. P. Pisano are all gratefully acknowledged. References [1] L.M. Miller, J.A. Podosek, E. Kruglick, T.W. Kenny, J.A. Kovacich, W.J. Kaiser, Proceedings of IEEE Workshop on Micro Electro Mechanical Systems, IEEE, New York, 1996, p. 467.
425
[2] R. Osiander, S.A. Ecelberger, R.B. Givens, D.K. Wickenden, J.C. Murphy, T.J. Kistenmacher, Applied Physics Letters 69 (1996) 2930. [3] R.B. Givens, J.C. Murphy, R. Osiander, T.J. Kistenmacher, D.K. Wickenden, Applied Physics Letters 69 (1996) 2755. [4] R.B. Givens, D.K. Wickenden, D.A. Oursler, R. Osiander, J.L. Champion, T.J. Kistenmacher, Applied Physics Letters 74 (1999) 1472. [5] D.K. Wickenden, J.L. Champion, R.B. Givens, T.J. Kistenmacher, J.L. Lamb, R. Osiander, SPIE Vol. 3876 (Micromachined Devices & Components V) (1999) 267–273. [6] V. Aksyuk, F.F. Balakirev, G.S. Boebinger, P.L. Gammel, R.C. Haddon, D.J. Bishop, Science 280 (1998) 720. [7] J.W. Kang, H. Guckel, Y. Ahn, Proceedings of IEEE Workshop on Micro Electro Mechanical Systems, IEEE, New York, 1998, p. 372. [8] W.C. Young, Roark’s Formulas for Stress & Strain, 6th Edition, McGraw-Hill, New York, 1989. [9] A. Garcia-Valenzuela, M. Tabib-Azar, Proceedings of SPIE Conference on Integrated Optics and Microstructures II (Pub # 2291), 1994, pp. 125 –142. [10] J. Miragliotta, R. Osiander, J.L. Champion, D.A. Oursler, T.J. Kistenmacher, Materials Research Society Symposium Proceedings, 605 (2000) 217. [11] Cronos Integrated Microsystems, Inc. (MCNC MEMS Technology Applications Center), 3021 Cornwallis Road, P. O. Box 12889, Research Triangle, NC 20779. [12] “Five of Hearts” anchor design based on results from D. Sherman, “An Investigation of MEMS Anchor Design for Optimal Sti5ness Damping,” Master’s Project, University of California, Berkeley, May 1996. [13] J.L. Lamb, D.K. Wickenden, J.L. Champion, R.B. Givens, R. Osiander, T.J. Kistenmacher, Materials Research Society Symposium Proceedings, 605 (2000) 211. [14] D.K. Wickenden, R.B. Givens, R. Osiander, J.L. Champion, D.A. Oursler, J.L. Lamb, T.J. Kistenmacher, Second International Conference on Integrated Micro/Nantechnology for Space Applications, 1999, in press.
Acta Astronautica 52 (2003) 421 – 425 www.elsevier.com/locate/actaastro
Micromachined polysilicon resonating xylophone bar magnetometer D.K. Wickenden∗ , J.L. Champion, R. Osiander, R.B. Givens, J.L. Lamb, J.A. Miragliotta, D.A. Oursler, T.J. Kistenmacher The Johns Hopkins University, Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723-6099, USA
Abstract The basic device principles, including response sensitivity and transduction schemes, are outlined for a resonating xylophone bar magnetometer. Advanced design emphasis is on a polysilicon version with dimensions of order microns fabricated by microelectromechanical systems (MEMS) processing techniques. All polysilicon devices tested to date have performed extremely well in static magnetic 4elds and exhibit mechanical quality factors, Q, of up to 30,000 at reduced pressures. The resonance frequencies of the fundamental mode of vibration of these polysilicon xylophone bars have been found to be sensitive functions of the torsional sti5ness of the support arms, in accord with an analytical model based on Bernoulli– Euler theory. The output response of the polysilicon xylophone magnetometer as a function of impressed magnetic 6ux density has been shown to be linear up to 150 T; however, sensitivity is currently limited by the signi4cant resistivity of the polysilicon xylophone bar. Various strategies are being implemented to bring the magnetometer sensitivity into the applications-dominated nT regime. c 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction There are a number of pragmatic motivations directing the development of miniature magnetometers including conservation of mass, volume, power, and cost. Some applications where these factors are of fundamental importance include determination of orientation and spin rate of ordinance, tracking of surface and subsurface vessels, oceanographic mapping, measurement of extraterrestrial 4elds, imaging on-board satellite currents, microsurgery, and bio4eld imaging. Importantly, whether the particular application requires a single magnetometer or an array
∗
Corresponding author.
of magnetometers, the realization of optimal performance at reduced mass, size and cost will necessitate micromachining and microfabrication, as well as the integration of the associated electronic circuitry. Several contemporary magnetic sensors have been shown to be capable of being miniaturized using microelectromechanical systems (MEMS) processing techniques and include the -magnetometer [1], a magnetostrictive 4eld sensor [2], a wide dynamic range, high sensitivity xylophone bar magnetometer [3–5], a high-4eld, rapid “trampoline” device [6], and an amplitude detecting microbeam magnetometer [7]. In this report, the current status of the miniaturization of the resonating xylophone bar magnetometer [3–5] through MEMS processing is outlined.
c 2002 Elsevier Science Ltd. All rights reserved. 0094-5765/03/$ - see front matter PII: S 0 0 9 4 - 5 7 6 5 ( 0 2 ) 0 0 1 8 3 - 2
D.K. Wickenden et al. / Acta Astronautica 52 (2003) 421 – 425 200
0.10
F B Magnitude (a.u)
0.08
I
150
0.06 100 0.04 50
0.02
Fig. 1. Operating principle of the resonating xylophone bar magnetometer.
0.00 78.05
Phase (deg.)
422
78.10
78.15
0 78.20
Frequency (kHz)
Fig. 2. Displacement and phase outputs as a function of the frequency of the drive current to the xylophone bar.
2. Basic principles For the detection of static magnetic 4elds, the active element of the xylophone magnetometer [3,4] is a conductive bar supported at the nodes of its fundamental mode of mechanical vibration [8], and a sinusoidal current is supplied to the bar at this frequency (f0 ) through the support arms. In the presence of a 4eld component parallel to the surface of the xylophone bar but normal to the direction of the drive current (Fig. 1), the Lorentz force [F = B × I = BI cos(2f0 t)] causes the bar to vibrate at its fundamental frequency with an amplitude according to Eq. (1) [8]: d(f0 ) =
5Fl42 384EIB
Q;
(1)
where, l2 is the length of the xylophone bar between the supports, E is Young’s modulus, IB is the area moment of inertia of the bar, and Q is the mechanical quality factor. From this equation, it can be seen that amplitude is linearly proportional to the drive current (I ), the magnetic 4eld (B), and the mechanical Q-factor. Because the xylophone bar’s normal mode frequencies for oscillations in other directions are di5erent, the technique discriminates against these components of the magnetic 4eld extremely well so that any second-order cross coupling between di5erent 4eld components is extremely small.
3. Signal transduction The amplitude of the de6ection of the xylophone bar, Eq. (1), can be measured by a number of established, position-sensitive detection techniques [9]. Thus far, optical methods (beam de6ection [3–5] and interferometry [10]) have been the principal experimental techniques, with capacitive methods under active investigation. In magnetic 4elds of order T to nT, the displacement of the xylophone bar resulting from the Lorentz force is of order 1–0:01 nm at the resonant frequency. Therefore, any proposed optical transduction mechanism must be capable of resolving xylophone bar displacements that are signi4cantly less than the wavelength (typically, several hundred nanometers) of the probing optical radiation. Optical beam de6ection has been extensively utilized. In this technique. a laser diode beam is re6ected (the incident angle is about 5◦ from vertical incidence, and the laser diode and detector are about 20 cm away from the xylophone bar) from one of the free ends of the bar. The re6ected laser beam is collected in a position sensitive detector, with the di5erence in photogenerated current used as the signal to a lock-in ampli4er. In this case the output signal can be detected using homodyne detection at the resonance frequency. The ability to detect the resonantly enhance signal from the magnetic 4eld sensor is illustrated in Fig. 2. Here the variation in the detector amplitude and phase are plotted as functions of the frequency of the driv-
D.K. Wickenden et al. / Acta Astronautica 52 (2003) 421 – 425
Fig. 3. SEM Image of an MEMS fabricated polysilicon xylophone bar resonator, current leads, and mounting pads. The polysilicon xylophone bar is 500 m in length, 50 m in width, and 2 m in thickness.
ing current to the xylophone bar. As the frequency is tuned through the fundamental mechanical resonance, the displacement amplitude is resonantly enhanced while the phase angle (with respect to the current source) displays a 180◦ shift. In this measurement, the xylophone bar magnetometer was oriented to maximize the Lorentz force, arising from the interaction between the earth’s magnetic 4eld (∼ 30 T) and the alternating current in the bar. 4. MEMS processing, signal response, mechanical modeling The polysilicon xylophone bars, support arms and mounting pads reported on here were fabricated at the MCNC MEMS foundry [11]. An SEM image of a typical device is shown in Fig. 3. The lower electrode consists of a 0:5 m thick polysilicon layer patterned on the silicon nitride-coated silicon substrate. The xylophone bar, support electrodes, and mounting pads are fabricated from 2 m thick polysilicon suspended (after release of the sacri4cial silicon dioxide) 2 m above the silicon nitride layer. The mounting pads are attached to the lower electrode by the indicated patterns to provide a rigid anchor which minimizes vibrational coupling from the xylophone bar [12].
423
Physical contact between the xylophone bar and the silicon nitride layer is minimized by having 0:75 m deep “dimples” in the center and toward the ends of the xylophone bar. Lastly, etch holes are incorporated to facilitate release of the completed structure. The SEM micrograph clearly displays the anchor structure, etch holes, topographical evidence of the dimples, and the clean release of the xylophone bar and support electrodes. Evaluation of these micromachined xylophone bar resonators has been carried out in an evacuated test chamber, using a bench-top beam de6ection microscope [3,4]. Magnitude and phase outputs were initially obtained in an mT static magnetic 4eld by scanning and detecting at the frequency of the sinusoidal drive current through a 500 m × 50 m xylophone bar with 4 m × 45 m support arms, where the current through the device was 22 A (rms) and the chamber pressure was 35 mTorr. From these data, a resonance frequency of 78:2 kHz and a Q-factor of almost 7000 were obtained from a least-squares 4t to the amplitude resonance equation (1). For reference, the predicted frequency for a free– free polysilicon resonating bar (assuming a Young’s modulus of 160 GPa) is 69:2 kHz. Experimental results were also obtained from xylophone bars with 6 and 10 m wide support arms, under identical conditions. The resonance frequencies of these supported xylophone bars were 84.9 and 95:6 kHz, respectively. It was conjectured that the increasing resonance frequencies were largely determined by the increasing torsional sti5ness of the wider xylophone bar support arms. As a test of this supposition, an analytical model was derived based on Bernoulli–Euler theory, as the wavelength of vibration is much larger than the thickness of the resonant beam. The variation in natural frequency of the fundamental oscillation mode with support arm thickness was obtained from a numerical solution to the analytical model [5,13] and is compared to measured values in Fig. 4. The excellent agreement (to within 1% on average) between the theoretical results and the experimental data suggests that the analytical model very successfully describes the dynamics of the supported xylophone bar. It is also well known that pressure markedly in6uences the performance of MEMS resonators, and the e5ect of pressure on the resonance properties of a xylophone bar with 4 m wide support arms has been
424
D.K. Wickenden et al. / Acta Astronautica 52 (2003) 421 – 425 0.40
Normalized output signal (a.u)
110
Frequency (kHz)
100 90 80 70 60
0.35
0.30
0.25
0.20 0
2
4
6
8
10
12
Support width (µm)
Fig. 4. Measured and predicted resonance frequency of xylophone bar resonators as a function of support arm width at constant length and thickness.
determined. For this measurement, the magnetic 6ux density was on the order of 10 T (owing to the presence of the Earth’s plus other background 4elds), and the xylophone drive current was again 22 A (rms). The pressure in the test chamber was varied between 15 and 85 mTorr, and the resulting Q factors showed maximum and minimum values of 21,950 and 2780. A small (9 Hz) decrease in resonance frequency from the highest to the lowest pressure is believed to be due to thermal e5ects (lower torsional sti5ness of the xylophone bar, vide supra). Moderate temperature sensitivity of the xylophone bar resonance frequency has also been observed at constant pressure by varying the intensity of a broad illumination source or by repositioning the beam de6ection laser. There has also been evidence that mechanical energy losses at resonance contribute enough thermal energy to measurably lower the resonance frequency of a xylophone bar device. Finally, a plot of the response of the polysilicon xylophone magnetometer as a function of impressed magnetic 6ux density up to 150 T is shown in Fig. 5. The superimposed line is a least-squares 4t to the data, and it is apparent that the magnetometer response is linear over the range of magnetic 6ux density shown. An estimate of the ultimate noise 6oor of the xylophone bar magnetometer, based on thermomechanical noise (Brownian motion due to the Langevin force) and to a lesser extent Johnson noise (current noise that couples with√the magnetic 4eld), yields a value of order 100 pT A= Hz. This estimate calls out the very
0
40
80
120
160
Impressed field (µT)
Fig. 5. Output response of a polysilicon xylophone bar magnetometer as a function of impressed magnetic 6ux density.
important role that the amplitude of the drive current plays in determining the ultimate 4eld sensitivity of a xylophone bar magnetometer. Two remarks are appropriate: (a) earlier versions of the xylophone bar magnetometer (chemically milled from low resistivity CuBe, with Q values more typically near 3000 –5000) have successfully √ measured calibrated 6ux densities in the 0:1 nT= Hz range [5,14]; and, (b) the length and width dimensions of the polysilicon xylophone bar magnetometer presented here are proportionally scaled from these earlier versions, while the thickness is an order of magnitude smaller than for direct √ scaling. The limiting factor in achieving nT= Hz sensitivity is, then, de4nitely identi4ed as the high resistivity of the polysilicon xylophone bars and their lower current carrying capability. 5. Potential aeronautical and aerospace applications There are several advantageous points to be considered in the development of an ultrasensitive micromachined xylophone bar magnetometer for aeronautical and aerospace applications: • Simplicity of the basic device physics, design rules and functionality; • As a resonant sensor, the amplitude of the response is ampli4ed by the mechanical Q; • Wide dynamic range achieved in a device free of magnetic materials and hysteresis;
D.K. Wickenden et al. / Acta Astronautica 52 (2003) 421 – 425
• Resonant frequency size selectable to reduce crosstalk in multidimentional designs; • The xylophone bar sensor has essentially no zero 4eld drift; • There are a number of detection techniques (optical beam de6ection, interferometry, capacitance) capable of being miniaturized in parallel with xylophone bar resonators; • The xylophone bar magnetometer can be used as a narrow-band mixer for the detection of alternating magnetic 4elds, detecting resonances at either the sum or the di5erence between the frequency of the driving current and that of the alternating magnetic 4eld.
Acknowledgements Support of this work by the US Department of the Navy under contract N00039-91-5301 and by the Defense Advanced Research Project Agency under contract F49620-98-1-0500 and extremely helpful discussions with A. P. Pisano are all gratefully acknowledged. References [1] L.M. Miller, J.A. Podosek, E. Kruglick, T.W. Kenny, J.A. Kovacich, W.J. Kaiser, Proceedings of IEEE Workshop on Micro Electro Mechanical Systems, IEEE, New York, 1996, p. 467.
425
[2] R. Osiander, S.A. Ecelberger, R.B. Givens, D.K. Wickenden, J.C. Murphy, T.J. Kistenmacher, Applied Physics Letters 69 (1996) 2930. [3] R.B. Givens, J.C. Murphy, R. Osiander, T.J. Kistenmacher, D.K. Wickenden, Applied Physics Letters 69 (1996) 2755. [4] R.B. Givens, D.K. Wickenden, D.A. Oursler, R. Osiander, J.L. Champion, T.J. Kistenmacher, Applied Physics Letters 74 (1999) 1472. [5] D.K. Wickenden, J.L. Champion, R.B. Givens, T.J. Kistenmacher, J.L. Lamb, R. Osiander, SPIE Vol. 3876 (Micromachined Devices & Components V) (1999) 267–273. [6] V. Aksyuk, F.F. Balakirev, G.S. Boebinger, P.L. Gammel, R.C. Haddon, D.J. Bishop, Science 280 (1998) 720. [7] J.W. Kang, H. Guckel, Y. Ahn, Proceedings of IEEE Workshop on Micro Electro Mechanical Systems, IEEE, New York, 1998, p. 372. [8] W.C. Young, Roark’s Formulas for Stress & Strain, 6th Edition, McGraw-Hill, New York, 1989. [9] A. Garcia-Valenzuela, M. Tabib-Azar, Proceedings of SPIE Conference on Integrated Optics and Microstructures II (Pub # 2291), 1994, pp. 125 –142. [10] J. Miragliotta, R. Osiander, J.L. Champion, D.A. Oursler, T.J. Kistenmacher, Materials Research Society Symposium Proceedings, 605 (2000) 217. [11] Cronos Integrated Microsystems, Inc. (MCNC MEMS Technology Applications Center), 3021 Cornwallis Road, P. O. Box 12889, Research Triangle, NC 20779. [12] “Five of Hearts” anchor design based on results from D. Sherman, “An Investigation of MEMS Anchor Design for Optimal Sti5ness Damping,” Master’s Project, University of California, Berkeley, May 1996. [13] J.L. Lamb, D.K. Wickenden, J.L. Champion, R.B. Givens, R. Osiander, T.J. Kistenmacher, Materials Research Society Symposium Proceedings, 605 (2000) 211. [14] D.K. Wickenden, R.B. Givens, R. Osiander, J.L. Champion, D.A. Oursler, J.L. Lamb, T.J. Kistenmacher, Second International Conference on Integrated Micro/Nantechnology for Space Applications, 1999, in press.