Е-Публикации
Технически университет - София

Abstract: In this paper, the impact of Lorentz forces and temperature on the natural frequencies of a piezoresistive sensor composed of two microcantilevers with integrated U-shaped thin-film aluminum heaters are investigated. Two types of experiments were performed. In the first, the sensor was placed in a magnetic field so that the current flowing in the heater, in addition to raising the temperature, produced Lorentz forces, inducing normal stresses in the plane of one of the microcantilevers. In the second, which were conducted without magnetic fields, only the temperature variation of the natural frequency was left. In processing of the results, the thermal variations were subtracted from the variations due to both Lorentz forces and temperature in the natural frequency, resulting in the influence of the Lorentz forces only. Theoretical relations for the Lorentz frequency offsets were derived. An indirect method of estimating the natural frequency of one of the cantilevers, through a particular cusp point in the amplitude–frequency response of the sensor, was used in the investigations. The findings show that for thin microcantilevers with silicon masses on the order of 4 × 10−7 g and currents of 25 µA, thermal eigenfrequency variations are dominant. The results may have applications in the design of similar microsensors with vibrational action.

References

1. Breuer K.S. Park J. Henoch C. Actuation and Control of a Turbulent Channel Flow Using Lorentz Forces Phys. Fluids 2004 16 897 907 10.1063/1.1647142
2. Herrera-May A. Soler-Balcazar J. Vázquez-Leal H. Martínez-Castillo J. Vigueras-Zuñiga M. Aguilera-Cortés L. Recent Advances of MEMS Resonators for Lorentz Force Based Magnetic Field Sensors: Design, Applications and Challenges Sensors 2016 16 1359 10.3390/s16091359 27563912
3. Kwang W.O. Chong H. Ahn Magnetic Actuation Comprehensive Microsystems Gianchandani Y.B. Tabata O. Zappe H. Elsevier Ltd. Amsterdam, The Netherlands 2008 Volume 2 42 43
4. Allen J.J. Micro Electro Mechanical System Design 1st ed. Taylor & Francis Group, LLC. New York, NY, USA 2005 Volume 1
5. Basha H. Nandeppanavar M.M. Reddy G.J. Dissipative Lorentz Force Influence on Mass Flow over a Micro-cantilever Sensor Sheet under Magnetic Ohmic Heating ZAMM J. Appl. Math. Mech. Z. Angew. Math. Mech. 2024 104 55 10.1002/zamm.202300055
6. Lv X. Wei W. Mao X. Yang J. Yang F. A Novel MEMS Actuator with Large Lateral Stroke Driven by Lorentz Force J. Micromech. Microeng. 2015 25 025009 10.1088/0960-1317/25/2/025009
7. Keplinger F. Kvasnica S. Jachimowicz A. Kohl F. Steurer J. Hauser H. Lorentz Force Based Magnetic Field Sensor with Optical Readout Sens. Actuators A Phys. 2004 110 112 118 10.1016/j.sna.2003.10.025
8. Gkotsis P. Lara-Castro M. López-Huerta F. Herrera-May A.L. Raskin J.-P. Mechanical Characterization and Modelling of Lorentz Force Based MEMS Magnetic Field Sensors Solid State Electron. 2015 112 68 77 10.1016/j.sse.2015.02.004
9. Treutler C.P.O. Magnetic Sensors for Automotive Applications Sens. Actuators A Phys. 2001 91 2 6 10.1016/S0924-4247(01)00621-5
10. Li M. Nitzan S. Horsley D.A. Frequency-Modulated Lorentz Force Magnetometer with Enhanced Sensitivity via Mechanical Amplification IEEE Electron. Device Lett. 2015 36 62 64 10.1109/LED.2014.2372617
11. Mbarek S.B. Alcheikh N. Ouakad H.M. Younis M.I. Highly Sensitive Low Field Lorentz-Force MEMS Magnetometer Sci. Rep. 2021 11 21634 10.1038/s41598-021-01171-z
12. Tu C. Ou-Yang X. Wu Y. Zhang X. Single-Structure 3-Axis Lorentz Force Magnetometer Based on an AlN-on-Si MEMS Resonator Microsyst. Nanoeng. 2024 10 58 10.1038/s41378-024-00696-3
13. Lee B. Prater C.B. King W.P. Lorentz Force Actuation of a Heated Atomic Force Microscope Cantilever Nanotechnology 2012 23 055709 10.1088/0957-4484/23/5/055709 22237044
14. Alunda B.O. Lee Y.J. Review: Cantilever-Based Sensors for High Speed Atomic Force Microscopy Sensors 2020 20 4784 10.3390/s20174784
15. Somnath S. Liu J.O. Bakir M. Prater C.B. King W.P. Multifunctional Atomic Force Microscope Cantilevers with Lorentz Force Actuation and Self-Heating Capability Nanotechnology 2014 25 395501 10.1088/0957-4484/25/39/395501
16. Zhang W. Lee J.E.-Y. Frequency-Based Magnetic Field Sensing Using Lorentz Force Axial Strain Modulation in a Double-Ended Tuning Fork Sens. Actuators A Phys. 2014 211 145 152 10.1016/j.sna.2014.01.022
17. Liepe M. Moeller W.D. Simrock S.N. Dynamic Lorentz Force Compensation with a Fast Piezoelectric Tuner Proceedings of the 2001 Particle Accelerator Conference (Cat. No.01CH37268) Chicago, IL, USA 18–22 June 2001 IEEE New York, NY, USA 2001 1074 1076
18. Mehdizadeh E. Kumar V. Pourkamali S. Sensitivity Enhancement of Lorentz Force MEMS Resonant Magnetometers via Internal Thermal-Piezoresistive Amplification IEEE Electron. Device Lett. 2014 35 268 270 10.1109/LED.2013.2293349
19. Shiraishi N. Kimura M. Ando Y. Basic Characteristics of Polycarbonate-Based Dual Cantilever Sensors for Detecting VOC Mech. Eng. J. 2014 1 MN0055 10.1299/mej.2014mn0055
20. Gurjar M. Jalili N. Toward Ultrasmall Mass Detection Using Adaptive Self-Sensing Piezoelectrically Driven Microcantilevers IEEE/ASME Trans. Mechatron. 2007 12 680 688 10.1109/TMECH.2007.911635
21. Toda M. Inomata N. Ono T. Voiculescu I. Cantilever Beam Temperature Sensors for Biological Applications IEEJ Trans. Electr. Electron. Eng. 2017 12 153 160 10.1002/tee.22360
22. Abedinov N. Grabiec P. Gotszalk T. Ivanov T. Voigt J. Rangelow I.W. Micromachined Piezoresistive Cantilever Array with Integrated Resistive Microheater for Calorimetry and Mass Detection J. Vac. Sci. Technol. A Vac. Surf. Film. 2001 19 2884 2888 10.1116/1.1412654
23. Ramos D. Calleja M. Mertens J. Zaballos A. Tamayo J. Measurement of the Mass and Rigidity of Adsorbates on a Microcantilever Sensor Sensors 2007 7 1834 1845 10.3390/s7091834
24. Jin D. Li X. Liu J. Zuo G. Wang Y. Liu M. Yu H. High-Mode Resonant Piezoresistive Cantilever Sensors for Tens-Femtogram Resoluble Mass Sensing in Air J. Micromech. Microeng. 2006 16 1017 1023 10.1088/0960-1317/16/5/019
25. Banchelli L. Todorov G. Stavrov V. Ganev B. Todorov T. Investigating a Detection Method for Viruses and Pathogens Using a Dual-Microcantilever Sensor Micromachines 2024 15 1117 10.3390/mi15091117 39337776
26. Banchelli L.F. Ganev B.T. Todorov T.S. Sustainability Validation of a LabVIEW Based System for Biomarkers Detection Proceedings of the 2023 XXXII International Scientific Conference Electronics (ET) Sozopol, Bulgaria 13–15 September 2023 IEEE New York, NY, USA 2023 1 6
27. Stavrov V. Stavreva G. Tomerov G. Tester for Detection of Infectious Agents in Fluid Bulgarian Patent BG113123A 16 April 2020
28. Liu C. Foundations of MEMS 2nd ed. Prentice Hall, 2 Pearson Education, Inc. Upper Saddle River, NY, USA 2011
29. McCarter D.R. Paquin R.A. Isotropic Behavior of an Anisotropic Material: Single Crystal Silicon Proceedings SPIE Material Technologies and Applications to Optics, Structures, Components, and Sub-Systems Robichaud J.L. Krödel M. Goodman W.A. SPIE Paris, France 2013 Volume 8837 883707
30. Volterra E. Zachmanoglou E.C. Dynamics of Vibrations C.E. Merrill Books New York, NY, USA 1965 Volume 1
31. Meirovitch L. Elements of Vibration Analysis 2nd ed. McGraw-Hill New York, NY, USA 1986
32. Lindroos V. Tilli M. Lehto A. Handbook of Silicon Based MEMS Materials and Technologies Elsevier Amsterdam, The Netherlands 2010 9780815515944
33. Keyes R.W. Electronic Effects in the Elastic Properties of Semiconductors Solid State Physics Seitz F. Turnbull D. Ehrenreich H. Elsevier Amsterdam, The Netherlands 1968 Volume 20 37 90

Issue