Valle et al. Microsystems & Nanoengineering (2022)8:103 https://doi.org/10.1038/s41378-022-00423-w Microsystems & Nanoengineering www.nature.com/micronano ARTICLE Open Access Design, fabrication, characterization and reliability study of CMOS-MEMS Lorentz-force magnetometers 1✉ 1,2 ✉ 3✉ 1✉ J. J. Valle , J. M. Sánchez-Chiva , D. Fernández and J. Madrenas Abstract This article presents several design techniques to fabricate micro-electro-mechanical systems (MEMS) using standard complementary metal-oxide semiconductor (CMOS) processes. They were applied to fabricate high yield CMOS-MEMS shielded Lorentz-force magnetometers (LFM). The multilayered metals and oxides of the back-end-of-line (BEOL), normally used for electronic routing, comprise the structural part of the MEMS. The most important fabrication challenges, modeling approaches and design solutions are discussed. Equations that predict the Q factor, sensitivity, Brownian noise and resonant frequency as a function of temperature, gas pressure and design parameters are presented and validated in characterization tests. A number of the fabricated magnetometers were packaged into Quad Flat No-leads (QFN) packages. We show this process can achieve yields above 95 % when the proper design techniques are adopted. Despite CMOS not being a process for MEMS manufacturing, estimated performance (sensitivity and noise level) is similar or superior to current commercial magnetometers and others built with MEMS processes. Additionally, typical offsets present in Lorentz-force magnetometers were prevented with a shielding 1234567890():,; 1234567890():,; 1234567890():,; 1234567890():,; electrode, whose efficiency is quantified. Finally, several reliability test results are presented, which demonstrate the robustness against high temperatures, magnetic fields and acceleration shocks. Introduction research interest during the past decades that led to several Today, the most common form of mass-production developments, generally categorized depending on when semiconductor device fabrication is CMOS technology. The the MEMS are built, compared to the CMOS circuitry: dedicated integrated circuit (IC) interfaces of commercial ● Pre-CMOS or MEMS before CMOS4–6: The MEMS sensors are realized using this technology. However, the are built before CMOS. Once finished, the wafer can sensing elements need to be manufactured using specialized undergo standard CMOS processing. The MEMS is micro-machining processes. For a number of applications, free of CMOS thermal budget limitations7,8, but it integration of CMOS electronics and MEMS devices on a must be compatible with the subsequent standard single chip (CMOS-MEMS) has the potential of reducing CMOS processing steps. Unfortunately, CMOS fabrication costs, size, parasitics and power consumption, foundries tend to be reluctant to work with already along with higher speed, compared to other integration MEMS-processed wafers. approaches1–3. These advantages have attracted a lot of ● Intra-CMOS or MEMS between FEOL and BEOL9–14: The CMOS process is interrupted for MEMS processing. Again, close colaboration with the Correspondence: J J. Valle (juanvallefraga@gmail.com) or J M. Sánchez- CMOS foundry is required, but several products are Chiva (jose.sanchez_chiva@sorbonne-universite.fr) or D Fernández (dfernandez@ifae.es) or J Madrenas (jordi.madrenas@upc.edu) under volume production3. 1 Department of Electronic Engineering, Universitat Politècnica de Catalunya, ● Post-CMOS or MEMS after CMOS: MEMS are Jordi Girona 1 i 3, Edifici C4, 08034 Barcelona, Spain 2 created only once the standard CMOS process is Sorbonne Université, CNRS, Laboratoire de Recherche en Informatique (LIP6), UMR7606, 4 place Jussieu, 75005 Paris, France finished, so the CMOS foundries do not need to Full list of author information is available at the end of the article © The Author(s) 2022 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 2 of 25 modify the standard process. However, the MEMS process cannot surpass the CMOS thermal budget7,8, B K D Lorentz which limits the MEMS processing options. Movable structure current - MEMS on top15–17: Several foundries like TSMC, magnetic XFAB, UMC and DALSA, and IMEC’s SiGe MEMS L1 RL2 (Wire) Fm Vw RL1 L2 driving followed this route18. The DMD from Texas Cws iL Zsh iL Instruments19 is another well known example. (Shield) Vsh Fe - BEOL CMOS-MEMS6,20–26: Remarkably, a CMOS- + g Css V Vs MEMS device may be built with the back-end-of-line – AC (Sense) (BEOL) layers of the finished CMOS process. This + Zs – VDC Electrostatic approach minimizes the number of post-processing driving isense steps and is the one discussed in this work. Fig. 1 Principle of operation of a shielded Lorentz-force Despite its advantages, the BEOL CMOS-MEMS magnetometer. The structure moves under the action of the electrostatic and/or magnetic driving, and the movement is sensed by approach has proven to be very challenging given the cur- the sense electrode. rent lack of commercial products in the market. The most important reasons are two: Firstly, achieving a competitive performance with a fixed process, which is not optimized The system behaves as a damped harmonic oscillator. for MEMS, is challenging. Secondly, cost advantages vanish In this work, the movable structure is formed by several if the MEMS yield is not sufficiently high or its area too (nB) clamped beams, and the Lorentz current passes large. Both issues are addressed in this work. along each beam nw times. This increases the effective We present and discuss the challenges, modeling and Lorentz current nw × nB times. Only a single wire and design techniques used to fabricate high-yield BEOL beam are depicted in Fig. 1 for clarity reasons. CMOS-MEMS devices. They were applied to fabricate Additionally, iL is applied as a square wave whose integrated Lorentz-force magnetometers (LFM) which frequency is coincident with the first resonant fre- were packaged, characterized and subjected to several quency of the structure (fr) in order to maximize the reliability tests. These are missing in most technical works output or sensed current (isense), produced by the sense in the literature, yielding the practical commercialization capacitance variation Css. The Lorentz wire is shielded of LFMs still unknown. The measured performance is very from the sense electrode, so isense is independent of iL, competitive compared to current products in the market. and this provides some important benefits that will be All commercial magnetometers are non-Lorentz-force examined later. ones. They are typically based on the Hall effect, aniso- In order to sustain the oscillation when ~B ¼ 0, or simply tropic magnetoresistance (AMR), giant magnetoresistance to characterize the device, an electrostatic driving is (GMR), or, recently, tunnel magnetoresistance (TMR)27, applied between the shield and sense electrodes. This also called magnetic tunnel junction (MTJ). They all have creates an electrostatic force labeled as Fe in Fig. 1, which some sort of magnetic material, like flux concentrators28. allows to track the resonance frequency as done in many The magnetic material may be damaged by high magnetic works31,33–38. fields, imposes temperature limitations and is susceptible Also, the figure shows the most important electrical to magnetic hysteresis, which in turn, may lead to reduced parameters of the whole system. accuracy and require tedious re-calibration from the user. Although LFM do not require magnetic materials, they Sensitivity and offsets induced by the Lorentz current suffer from other offsets related to electrical inter- The electrostatic force Fe is a function of the gap (g) ference29–32. This will be analyzed, solutions will be pre- between plates, the sensing area (A) and the voltage dif- sented and their efficiency quantified. ference (ΔV = Vsh − Vs). For the typical impedance values and operating frequencies Vsh/Vs > 104, so ΔV ≈ Vsh. Lorentz-force magnetometers: principle of operation and Additionally, the Lorentz wire AC voltage (Vw) induces an analysis interference voltage (V int sh ) in the shield electrode, yielding The operational principle of the shielded LFM discussed V sh  V DC þ V AC þ V int sh , assuming small Zsh. These in this work is illustrated in Fig. 1. The magnetic field ~ B is considerations allow to write isense and Fe as: sensed with a current ~ iL (Lorentz current) that flows along a wire (Lorentz wire) of length L inside a movable isense ¼ dQss d ðCss ΔV Þ ¼  Css dVAC þ Css sh dV int þ Vsh dCss structure, which experiences a force Fm given by: dt dt dt ffl} |fflfflfflfflffl{zfflfflfflffl dt ffl} |fflfflfflfflffl{zfflfflfflffl dt |fflfflfflffl{zfflfflfflffl} Electrical coupling Electrical interference Motional currentðim Þ F~m ¼ L  i~L ´ ~ B ð1Þ ð2Þ Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 3 of 25 where Qss is the charge of Css. The motional current (im) is In this work, the Lorentz current iL must be applied at caused by the magnetic field (B) and its associated Lorentz resonance, generating an alternating force on the beam. force (Fm), and/or by the electrostatic force (Fe)39: This alternating force creates an alternating output  Electrostatic driving zfflfflfflffl}|fflfflfflffl{ Electrostatic interference zfflfflfflffl}|fflfflfflffl{ ∂ 1 2 Vsh2 ∂Css ϵ0 A 2 ϵ0 A ϵ0 A Fe ¼ Css ðVsh  Vs Þ    2 VDC  2 ð VDC VAC þ VDC Vshint Þ  2 ðVAC þ Vshint Þ2 ∂g 2 2 ∂g 2g g 2g |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Fdc ðω¼0Þ Fωr ðω¼ωr Þ F2ωr ðω¼2ωr Þ ð3Þ where a simple parallel plate configuration was assumed current at the resonant frequency that can be amplified for now. Only the F ωr terms excite the device at its by the electronics. Hence, the sensor information is not at resonant frequency and therefore contribute to motional DC, despite the magnetic field is, thus avoiding flicker 1/f current at ωr. The VDCVAC term corresponds to the noise effects and offsets. No other frequencies or mixing expected electrostatic driving force. The V DC V int sh term is byproducts are present. an electrostatic interference caused by the Lorentz wire: it causes an undesired mechanical resonance (magnetic Noise and heading accuracy offset) that is, unfortunately, indistinguishable from the Three devices aligned along the three Cartesian axes one caused by a constant external magnetic field B in un- form a three-axis magnetometer that can work as a shielded LFM. The underlying reason is that B and V int sh magnetic compass. In our case, one device (z) detects out- are both proportional to the Lorentz current. Interest- of-plane magnetic field, and two devices (xy) detect the in- ingly, in a shielded LFM this current is in quadrature with plane components. They all can be monolithically inte- the magnetic field sense current. However, its suppresion grated in a single die, so the alignment is straightforward, with electronic techniques is challenging. as the two xy devices are orthogonal by mask design. Two interference mechanisms due to the Lorentz wire The best heading accuracy, or angle error, of a magnetic have been identified: the electrical interference in Eq. (2) compass sensor is limited by the Brownian noise. It can be and the electrostatic interference in Eq. (3). Ultimately, calculated as the ratio between the equivalent magnetic both processes appear as an offset in the measured field noise (Bnoise) and the Earth’s magnetic field (Bearth): magnetic field. In conventional unshielded magnet-   RMS  ometers this offset is generally orders of magnitude larger  pffiffiffiffiffiffi B BRMS 180 θRMS 1= Hz ¼ atan noise  noise  ð6Þ than the magnetic signal30,40. In fact, this is a well-known noise Bearth Bearth π drawback of resonant Lorentz-force magnetometers29–32. The offset can be compensated, for example, using a DC where a linear approximation is valid given that Bnoise < compensation voltage applied to the MEMS structure to < Bearth. Earth’s magnetic field horizontal intensity ranges null the electrostatic force29,40, but it is difficult to elim- from around 40 μT in Southeast Asia to 15 − 20 μT in inate its associated drift reliably and cheaply30. There is a areas like South America, South Africa, Siberia and patented technique31,33,41, based on current chopping, northern Canada42,43. So, regarding heading accuracy, we that reduces this effect greatly. It will be used in the Offset think that considering Bearth = 20 μT in Eq. (6) is a and shielding efficiency section. The motional current in reasonable assumption. Eq. (2) depends on the applied force (Fm + Fe). For a To calculate BRMSnoise let us first calculate the total Lorentz damped harmonic oscillator driven at the resonant fre- force Fm per unit of magnetic field B: quency: F RMS 4 1 dC ss dC ss dg dC ss Fm þ Fe m ¼ iRMS  L  nw  nB ¼ iL   pffiffiffi  L  nw  nB im ¼ V sh ¼ V sh ¼ V sh jωr Q B L π 2 dt dg dt dg K ð7Þ ð4Þ where j indicates 90∘ phase and Q is the quality factor of where L is the length of the beams and the RMS Lorentz the resonator, and K the spring constant. current component at the resonant frequency (iRMSL ) is The sensitivity S of the device to the external magnetic calculated with the square wave Lorentz current iL: field B may now be derived by combining Eqs. (1) to (4): 4 1 ∂im dC ss iL nw nB L iRMS ¼ iL   pffiffiffi ðSquare waveÞ ð8Þ S¼ ¼ V sh jωr Q ð5Þ L π 2 ∂B dg K Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 4 of 25 A D Post-CMOS sealing layer E M6 capping layer M6 C G I M5 J M4 B Bcal M3 F K M2 H M1 SiN Sealing Metal Continuous via Unetched oxide Fig. 2 General cross-section. CMOS BEOL and post-CMOS sealing layer. which was used to obtain the last term of Eq. (7). On the repeatability, excessive curvature and creep26. In addition, other hand, the Brownian noise force (Fnoise) is given by44: although the IMD oxide etching rate is uniform, the vHF sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi etch is highly catalyzed along the metals45 producing a pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4K B TMωr runaway etch that must be stopped. This increases hor- F RMS noise ¼ 4K B TD ¼ ð9Þ izontal etching speed and reduces greatly etching isotropy. Q We refer to this as the capillarity effect. where D = Mωr/Q is the damping coefficient of the considered 1-D or lumped system of mass M. Design techniques to overcome the CMOS-MEMS Using the previous equations allows us topffiffiffiffiffiffi write the fabrication process challenges equivalent magnetic field noise in units of T= Hz as: Continuous vias to stop vHF Vias (or plugs) are generally square, tungsten-based and pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F RMS π K B TMωr used for connecting two different metal levels in CMOS BRMS noise ¼ RMS noise ¼ peak pffiffiffiffiffiffi ð10Þ design. However, vias may be made very long in one F m =B iL  L  nw  nB  2Q direction (continuous vias) and thus fill completely the Equations (6) and (10) will be evaluated for the fabri- gap between two metal layers with tungsten, which is a cated devices later in the Results and discussion section. vHF-resistant material. Vertical metal walls that stop the advance of vHF can be created this way. Although via Materials and methods detaching problems have been observed with other release CMOS-MEMS fabrication process agents47, vHF has never caused these issues in our The CMOS-MEMS process used in this work uses the experience. This technique opens a myriad of possible back-end-of-line (BEOL) of a standard 6-metal 0.18 μm structures for CMOS-MEMS design. One example are CMOS process to build the MEMS. The unwanted inter- anchors, as the one supporting the sensing electrode in metal-dielectric (IMD) oxide is etched away with a vapor detail H of Fig. 2. HF (vHF) process already described in previous works26,45,46. The vHF enters through small holes in the Anchors to attach mechanically and isolate electrically last metal of the BEOL (detail E of Fig. 2), dissolving the The resonating beams and driving/sensing electrodes oxide selectively and releasing the MEMS structure must be mechanically attached to something and, typi- (details F and G of Fig. 2). For fabrication reasons, each cally, electrically isolated. Attaching them to unetched BEOL layer is composed of several sub-layers26, which oxide proved unreliable and complicated due to the makes the mechanical modelization of the final multi- capillarity effect, which leads to very fast etching around layered structure difficult. Finally, the MEMS devices are the edges of the metals, and quick detachment from any sealed in vacuum with a post-CMOS layer of Aluminum unetched oxide. When electrical isolation is not needed, (detail D of Fig. 2) deposited on top of the last metal, diced one option is to attach them to vertical walls created with and packaged23. metals and continuous vias. When it is needed, one We mostly used 200 mm wafers from the 1P6M compact option is to use anchors as in detail H of Fig. 2, 0.18 μm CMOS process from Global Foundries (GF), but where they provide mechanical support to the sensing similar processes from LFoundry (1P6M 0.15 μm) and electrode. They work by forcing the vHF to travel upwards TSMC (1P6M 0.18 μm) worked well, also. and downwards, taking advantage of the slower vertical The fabrication process is simple, but using the BEOL as etch rate, and keeping under control the capillarity effect structural layers has important drawbacks such as non this way45. Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 5 of 25 Anchors leave some oxide exposed to the MEMS cavity rest of the vibrating structure, the damping coefficient which may outgas if the device undergoes sufficiently high D is proportional to the number of coupled beams nB. and long temperature excursions. We have found that, in Therefore, the Brownian force noise (Eq. (9)) is only pffiffiffiffiffi devices that require a vacuum level under 1 mbar the proportional to nB . By contrast, the total Lorentz exposed oxide should be minimized. Therefore, using as force Fm is proportional to nB (Eq. (7)). As a con- few anchors as possible may be a good design strategy in sequence, the equivalent magnetic noise (Eq. (10)) is pffiffiffiffiffi terms of outgassing minimization. proportional to 1= nB , which implies that coupling more beams lowers the noise of the system. In addition, improved repeatability is also expected as variations in Clamped-clamped beams to overcome curvature issues geometric or material properties are averaged when Large curvature and variability are observed in several beams are coupled. On the other hand, the CMOS-MEMS BEOL structures24–26,46. Fortunately, device occupies larger space, and power consumed by clamped-clamped (c-c) beams made of several stacked the Lorentz current is increased. BEOL layers may be an excellent design option to cir- cumvent these issues. The reason is that, as long as a given critical tem- Beam design: Offset prevention via shielding and Lorentz perature/compressive residual stress is not reached, the multiwire c-c beams will remain very flat even when there is a very The two inherent offsets present in LFM which are large stress gradient. Simulations predict that c-c beams caused by the Lorentz current were discussed in the below the buckling load display deformations in the introduction. In the present work both offsets and their nanometer range (see Fig. 3) while, if only clamped at drifts are prevented by design: firstly, the Lorentz wires one end, they would deform from a few to hundreds of are decoupled from the sensing electrodes using a metal microns (as predicted by equation 7 from Valle et al.26). shield around the wires as described in Sánchez-Chiva All long structures are doubly clamped in this work. et al.46, and as depicted in the cross-section of the beam in detail F of Fig. 2, 4, 6a, b and 7. Secondly, a symmetric Lorentz wire routing design with respect to the shield Several beams coupled to improve SNR and repeatability electrode was adopted (RL1 = RL2 in Fig. 1). This way, If nB beams are mechanically coupled they will behave the central point of the wire may be kept at constant as a single resonating structure. Given that the coupling voltage: half the total voltage drop (Vw = 0.5 ⋅ Vdrop). is far from any surface and very small compared to the Then, the interference due to the AC voltage in the rest of the wire would cancel out due to symmetry, apart Compressive residual stress (MPa) from fabrication variability. Hence, little or no com- 1 10 100 pensation techniques are needed. Later on, this will be 2.5 C-c beam with large stress gradient shown experimentally. C-c beam with uniform stress Equation (11) was derived from the model in Fig. 4. It 2.0 quantifies the shielding efficiency, which depends on the μm) BUCKLED Maximum displacement (μ capacitance between the shield and the Lorentz wire (Cws), and on the impedance between the shield and its 1.5 grounding (Zsh). As it turns out, the capacitance between m m m m m 00 μ 00 μ 00 μ 00 μ 00 μ the shield and the sense electrodes (Css) is irrelevant in L=1 practice as its associated impedance is substantially larger L=2 L=8 L=5 L=3 1.0 0.5 Wire Shield Sense (Vw) int (Vsh ) (Vsint ) 0.0 0.1 1 10 100 Cws Css Temperature increase (°C) Cws Css Vw Zsh Zs Fig. 3 Deformation effect of stress gradient on clamped-clamped Zsh Zs ioff (c-c) beams. FE simulations prove the negligible effect of stress gradient on c-c beams below the critical stress or temperature, above which the beam buckles. The critical temperature depends on the Fig. 4 Simplified equivalent AC circuit for shielding efficiency ( beam length, but for tensile stress (negative temperature increase) all int Vsh =Vw ) calculation. Left: cross-section of beam and sense electrode. beams remain flat regardless of stress gradient level. Right: electrical equivalent. Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 6 of 25 than Zsh. Typical values yield Vsh/Vw < 10−5. In order to maximize the ratio capacitance variation versus static capacitance, the sensing electrodes of some devices are only at the central part of the beams, where V int sh  jω  Z sh  C ws ð11Þ the vibration amplitude is maximum, as in the devices of Vw Fig. 6a, b. This is also beneficial in terms of Q and, The metal shield provides additional advantages: it therefore, sensitivity enhancement. encloses unetched oxide along with one or two metal layers that can be used to route several Lorentz wires Electrical routings (nw > 1) along each beam (multiwire beams), as illustrated Output from vHF area The sensing electrodes are in the in the beam cross-sections of Figs. 6a, b and 7. Increasing etched area. As a consequence, connecting them to the the Lorentz current per beam delivers several obvious electronics while avoiding the capillarity effect and thus, benefits, such as sensor area reduction and improvement containing the vHF, proved challenging. The technique of sensitivity (Eq. (5)), signal-to-noise ratio (SNR) (Eq. used in this work takes advantage of the vHF etching (10)) or heading accuracy (Eq. (6)). The number of wires anisotropy, as the anchors previously described do: The per beam has limitations, though, such as electromigra- output routing describes a vertical zigzag as detail I of Fig. tion current, maximum resistance allowed for the Lorentz 2 and bottom-right cross-section in Fig. 7 show. wire due to maximum supply voltage, or filtering limitations due to the impedance of the wire at high Lorentz routing The Lorentz wires run along all beams frequency. Usually, electromigration current is the limit- and each beam multiple times (detail B of Fig. 2), ing factor. increasing this way, the total Lorentz force/current ratio substantially. For example, for a 6-beam 4-wire per beam Electrostatic sensing/actuation techniques device as in Fig. 6a, this ratio is increased 24 times with A 3D magnetometer demands both vertical and hor- respect to a conventional LFM. Similar multiwire izontal sensing electrodes. Devices that vibrate vertically approaches were followed in some works32,48,49. This will detect in-plane xy magnetic field. Conversely, devices achieve a very low noise floor, only surpassed when using that vibrate horizontally detect out-of-plane z magnetic piezoelectric amplification to increase SNR50,51. field as Eq. (1) dictates. Fortunately, the CMOS BEOL Each Lorentz wire has a return path along the external layers allow multiple design options (see yellow elec- parts of the device (detail B of Fig. 2). The magnetic field trodes of devices in Figs. 6a, b and 7). The cross-section created by the Lorentz wires is at frequency much higher of a typical lateral sensing design is depicted in the than Earth’s magnetic field. Thus, their associated zoomed orange box of Fig. 7. Two different vertical magnetic forces, detected by adjacent beams, should be sensing designs are shown in Figs. 6a, b. Note that the mechanically filtered. In addition, the return wires are sensing electrode in Fig. 6a has a vertical flange at each placed symmetrically at both sides of the device in such a end: they act as stiffeners that reduce potential curling way that the total magnetic force on the beams is zero. caused by the stress gradient. One advantage of the Also, as already stated previously, the Lorentz wire was vertical sensing design of Fig. 6b is that it allows to use 4 designed symmetric with respect to the shield electrode layer beams and, therefore, have 2 layers dedicated for as a first step to suppress its interference and associated the Lorentz current-carrying wires. offsets. While a large variation of capacitance versus displace- Running many more wires along each beam could ment is generally desired to maximize sensitivity (Eq. (5)), further increase the force vs current ratio, but ohmnic other aspects such as damping and Q factor need to be resistance and available voltage impose limitations on the taken into account. In this respect, the aforementioned maximum length and minimum width of the Lorentz designs may be improved by adding through-holes that wires. For the case of devices with only one or few beams, reduce air squeezing and, therefore, damping. The vertical electromigration is typically the bottleneck, and limits the sensing electrode shown in Figs. 2 and 6a has these holes, minimum width for a given Lorentz current (around for instance. Also, two z devices with g = 0.35 μm with 1 − 2 mA/μm in the processes we have used). lateral sensing electrodes solid as in Fig. 7 showed Q The Lorentz wire impedance imposes another important factors 1.5 smaller than the same device with sensing limitation: it increases quite abruptly above a given pole electrodes formed by layers joined with standard vias frequency (ωpole = 1/(RLCws)). The pole may fall close to which let the air flow through. the mechanical resonance frequency if the device has too The sensing electrodes are supported on anchors at many coupled beams and/or turns, or its resonance both ends and at intermediate points. They were designed frequency is too high. For the devices considered in this as clamped-clamped structures given that this was found work it is at least one order of magnitude above the to be the most mechanical reliable design. resonance frequency, so it is not a problem. Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 7 of 25 a b c TOP M6 surface and release holes Sealing layer M6 (over M6) M6 (Over pass) SiN passivation d e f 45 min DIE_12_06 ANCHOR Sealing layer Sealing layer passivation M6 Sealing layer SiN H1 = 8.705 μm M6 Fig. 5 Thin-film aluminum sputtering sealing results. a XY device before sealing. b Z device before sealing. c Sealed device on wafer. d XY device after 3.5 μm sealing. e Z device after 3.5 μm sealing. f Sealed device on wafer: FIB cut. Joule heating due to the Lorentz current is proportional protection is given by covering the whole device with to the intensity squared and, therefore, takes place at the top metal layer (M6 capping), as seen in detail E of twice the resonance frequency and higher, so its effects Fig. 2. In Fig. 6a most of the top metal covering has are filtered out both mechanically and electronically. been hidden to show the structures underneath. The top metal layer is grounded and it is part of the elec- Autocalibration routing Some kind of autocalibration trical shield. is generally very desirable in commercial sensors to Enhanced performance requires vacuum encapsulation. compensate inherent sensitivity variations and/or off- This is achieved with an outgassing step followed in less set drifts. We have implemented it by adding wires that than 4 hours by a 3 μm aluminum sputtered layer (sealing run along the device in specific arrangements that can layer) deposited on top of the device, which takes place at create a known magnetic field, or autocalibration around 6.4 μbar. The outgassing step consists on heating magnetic field. These can be seen in the white oxide the wafer at the highest temperature possible while the areas cut in Fig. 6a. The horizontal field that is created wafer is kept at very low vacuum, so the outgassed and can be seen in detail C of Fig. 2. When it is activated sublimated species are pumped out. The CMOS process the sensitivity can be measured and readjusted, and the MEMS yield limit the maximum temperature which is a unique feature of the presented LFM. The that can be applied7,8. In our case, we chose 350 ∘C. This coupled-beam arrangement of our devices allows to step reduces the trapped gasses in the materials exposed add the autocalibration routing very close to the to the MEMS cavity and therefore reduces future out- Lorentz wires, reducing this way the power consumed gassing processes. The sealing aluminum layer is pre- by the autocalibration field. ceded by a titanium/titanium nitride thin layer. The deposition temperature needs to be high in order to improve step coverage and seal the release holes properly. M6 capping and sealing layer to protect MEMS before wafer We found that 0.9 μm holes are sealed well with a 2 μm- sawing and packaging thick layer deposited at 350 ∘C. However, 3 μm-thick The packaging step in MEMS products will often be layers were used for improved safety margin. This is the decisive one in terms of yield. The design must be shown in the focused-ion-beam (FIB) cuts of Fig. 5 and robust enough to withstand wafer sawing, manipulation detail D in Fig. 2. The sealing layer provides additional and final encapsulation conditions32. Our magnet- mechanical robustness for further post-processing, along ometers have a robust design but additional mechanical with a very good vacuum level that will be partially lost Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 8 of 25 The z device is comprised of 4-metal stack beams. The a two xy devices have different sensing techniques: par- allel plate in the xy device and fingers in the xy-4m device. Also, the number of stacked layers differs: 3 layers in the xy device versus 4 layers in the xy-4m Fm device. These differences will be critical in terms of reliability as it will be demonstrated later. Most of the By characterization, analysis and tests were focused on the iL z and xy variant. Modeling In this section, the resonance frequency of clamped- clamped beams, which comprise the basic elements of the fabricated LFMs, is expressed as a function of design b parameters and residual stress/temperature. Additionally, an electrical model of the MEMS, used for measuring the LFMs is developed and the most important equations derived. Resonance frequency Fm The resonant frequency of beams under no axial load is very well known (Blevins and Plunkett52, Table 8-1): iL By  12  1 λ2i EI 4:730042 Et 2 2 ð12Þ Fig. 6 3D perspective of the xy magnetometer: vertical f0 ¼ ¼ 2πL2 m 2πL2 12ρ resonance. Arrows indicate direction of sensed magnetic field, magnetic force and Lorentz current. Cross-section and SEM images for where i is the mode number, E the Young’s Modulus, I each device are shown. a XY device. b XY-4M device. the moment of inertia (I = wt3/12 for a rectangular section of thickness t and width w), m the mass per unit length, ρ is the density and λ = 4.73004 for the after final packaging due to outgassing. It is patterned and fundamental mode (i = 0) and clamped-clamped etched using the passivation SiN (detail A in Fig. 2) as the conditions. etch barrier. Only the pads and the devices remain However, dealing with axially stressed clamped- covered. clamped structures is very common in MEMS and nano At this point the wafer is ready for undergoing standard design. Tensile stress (σ > 0) increases the resonant fre- packaging processes. In our case, the wafers were sub- quency and compressive stress (σ < 0) decreases it. This is jected to a back-grinding process to decrease their a very important effect in MEMS structures that often thickness down to 280 μm, and divided into dice with renders Eq. (12) insufficient for correct predictions. For a standard wafer sawing at an assembly house. Then, each given compressive load, called the critical load (Fcr) the die was attached to a leadframe, wire-bonded and over- resonant frequency is zero and the beam buckles due to molded to obtain the final QFN packaged devices. Char- elastic instability53. The most accurate formula that acterization and yield measurements of QFN devices are describes the frequency-residual stress dependency was later presented in this work. given by the authors54. It works in the full range of axial load (Fa), from the buckling point to the high-tension or string-limit regime: Variants of Lorentz-force CMOS-MEMS magnetometers The three variants analyzed in this work are shown in !12 Fa 1 Figs. 6a, b and 7. The first two are xy devices that detect f r ðF a Þ  f 0 1þγ þ 1 F cr 1 ð13Þ F þβ F cr αγ in-plane magnetic field and, therefore, resonate vertically. a The third one is a z device that detects out-of-plane magnetic field and vibrates horizontally. For each type, where f0 is given by Eq. (12) and α = 0.19514, β = 1.2114 devices with beam lengths from 80 μm to 800 μm were and γ = 0.81626 are given in Table A.3 of Valle et al.54 for manufactured. This allowed to characterize and obtain the fundamental mode and clamped-clamped (c-c) reliability data as a function of the beam length. conditions. The buckling axial load of a rectangular c-c Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 9 of 25 Bz iL Fm Coupling Fig. 7 3D perspective of the z magnetometer: lateral resonance. Arrows indicate direction of sensed magnetic field, magnetic force and Lorentz current. Cross-sections and SEM images for each device are shown. beam is Fcr = 4π2EI/L2 = π2wt3E/(3L2), as can be found in contraction as: Table A.3 and Appendix C of Valle et al.54. Eq. (13) will be used to explain the observed resonant frequency of c-c RT P beams as a function of their length and their temperature. σðT Þ ¼ σðT 0 Þ  T0 E i ðαi  αsubs Þ AAi dT i By using Eq. (13), the dependence with beam length can P be obtained, yielding:  σðT 0 Þ  E i ðαi  αsubs Þ AAi ðT  T 0 Þ i sffiffiffi ð16Þ t E fr / 2 ; when jF a j  F cr ðSmall stressÞ ð14aÞ where sub-index i refers to the material number, α is the L ρ beam CTE, αsubs is the substrate CTE, Ai/A is the fraction rffiffiffi of the beam section occupied by material i, and σ(T0) is 1 σ the stress at an arbitrary reference temperature T0. Note fr / ; when jF a j  F cr ðStress  dominatedÞ L ρ that the substrate also expands/contracts and needs to be ð14bÞ taken into account in the fr(T) calculation. Typically, the Young Modulus decreases with temperature and the CTE Note that for the beams where the tension/residual stress increases with temperature. Interestingly, their product is the main contributor to their stiffness, the Young’s E ⋅ α for the CMOS BEOL materials remains approxi- Modulus E or the beam thickness t are of no importance mately constant, so the integral in Eq. (16) may be for fr dependence with beam length L. substituted by the temperature increment (T − T0). By assuming that the thickness t, the density ρ and the length L of the beam are constant, the resonance fre- quency dependence on temperature can be readily derived MEMS electrical model from Eq. (14a) and (14b): The equation of motion of a driven damped spring- mass system is: pffiffiffiffiffiffiffiffiffiffiffi fr / EðT Þ; when jσj  σ E ðSmall stressÞ ð15aÞ pffiffiffiffiffiffiffiffiffiffi ∂2 x ∂x ð17Þ M þ D þ Kx ¼ f ðtÞ f r / σðT Þ; when jσj  σ E ðStress  dominatedÞ ∂t 2 ∂t ð15bÞ where M, D and K are the mass, damping coefficient and stiffness of the system, respectively, and f(t) is the applied An implicit temperature-dependency on E and the lin- lumped force. ear coefficient of thermal expansion (CTE) is contained in Let’s now assume we apply a voltage V = VDC + VAC to Eq. (15b): the axial stress σ of a clamped-clamped beam a movable capacitor of capacitance C that is part of a depends on temperature due to the thermal expansion/ damped spring-mass system, as in Fig. 1. The current flow Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 10 of 25 through this moving capacitor is: nodes 1-2 may show calibration/interference offsets that are absorbed by Rp and Cp, respectively. In this case, they no ∂CV ∂V ∂C ∂V AC ∂x longer represent the physical resistance and capacitance of i¼ ¼C þV ¼C þη ð18Þ ∂t ∂t ∂t ∂t ∂t the MEMS. In practice these offsets are unavoidable when where η ¼ V DC ∂C ∂x is the electromechanical coupling there is capacitive coupling between the Lorentz current factor. wire and the sensing electrodes, as described in this and The component of the electrostatic force between the many other works31,33,41,46. In this work, the Lorentz wire is plates of the capacitor at the frequency of VAC is: coupled only to the shield electrode, as shown in the explicit electromechanical model of Fig. 8a. This creates an inter-   ference signal created by Vw which changes the admittance ∂U ∂ 1 ∂C Fe ¼ ¼ CV 2 ¼ V AC V DC ¼ ηV AC of the system seen from 1-2. Fortunately, the model in ∂x ∂x 2 ∂x Fig. 8a can be simplified to the model in Fig. 8b, which is the ð19Þ one used in this work to fit G-B curves of MEMS magnet- ometers with and without interferences. When no current It is important to note that x refers to the lumped flows through the Lorentz wire there is no interference and displacement used in Eq. (17), which is 0.542 times the Css = Cp and Rp → ∞. Finally, the impedance components central displacement xc of the real clamped-clamped ∂C r Zsh and Zs represent the output impedance of the mea- beam. This value was calculated so that ∂C ∂x ¼ ∂xc , where surement instrument connected to 1-2. Cr and C are the real and lumped capacitance values, The motional parameters are related to the mechanical respectively. This way, the lumped force f(t) is equiva- and electrical properties of the system and also to Ω. This lent to the total uniform load acting on the real beam. is described by the following equations, derived from Eq. This is convenient for the considered devices given that (21): the electrostatic and the Lorentz forces are applied uniformly along the beam span. pffiffiffiffiffiffiffiffi D 1 KM 1 1 Now, defining imot ¼ η ∂x ∂t and substituting into Eq. (17) Rm ¼ 2 ¼ ð22Þ yields: η 1þΩ Q η2 1 þ Ω M 1 Z Lm ¼ ð23Þ M ∂imot D K η2 1 þ Ω þ imot þ imot dx ¼ f ðtÞ ð20Þ η t η η η2 Cm ¼ ð 1 þ ΩÞ ð24Þ Let us assume that the force f(t) is the combination of K the electrostatic force Fe produced by the measurement where Q is the quality factor of the system: signal of an impedance analyzer and a magnetic force Fm. If we define the ratio Ω = Fm/Fe, by substitution of rffiffiffiffiffiffiffi 1 Lm f(t) into Eq. (20) it is straightforward to arrive at: Q¼ ð25Þ Rm Cm Z M ∂imot D K Note that the Lm, Cm and Rm values seen by an þ imot þ imot dx η2 ð1 þ ΩÞ ∂t η2 ð1 þ ΩÞ η2 ð1 þ ΩÞ impedance analyzer depend on the ratio Ω = Fm/Fe. Z ∂imot 1 When the MEMS is just characterized with an impe- ¼ Lm þ Rm imot þ imot dx ¼ V AC ∂t Cm dance analyzer, and no Lorentz current is injected ð21Þ Fm = 0 and so Ω = 0. In some experiments in this work Fm ≠ 0, like when extracting the sensitivity of the MEMS which corresponds to an inductor Lm, capacitor Cm and to magnetic fields. resistor Rm in series. They represent the motional In addition, the magnetometer sensitivity (Eq. (5)) may inductance, capacitance and resistance values of the be rewritten in a much simpler form as a function of the MEMS, respectively, and they simulate the mechanical parameters measured directly with the IA in units of dynamics of the MEMS resonator. It is the dashed Amperes per Tesla (A/T): region of the MEMS electrical model55 used to fit the measurements in this work (see Fig. 8a, b). ∂im ΩV AC S¼ ¼ ð26Þ Components Rp and Cp in Fig. 8b generally represent the ∂B Rm B physical electrical resistance and capacitance between the shield and sense electrodes. However, under some circum- which can be further generalized in units of Amperes stances, the conductance G and/or susceptance B seen from per Tesla and per DC voltage and Lorentz current used Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 11 of 25 a b (Shield ) (Sense) Css Rp (Wire) Cp (Shield ) (Sense) Cws Lm Cm Rm Lm Cm Rm III Vw Zsh Zs Zsh Zs 1 2 1 2 c 0.5 r Conduc. G Rm Rm BW ≈ Lm = Q 1/Rm 0.5 BW Rm 1/Rp r = 1/ Cm Lm ) + Cm Suscep. B 0.5  (C p Rm 0.5 Rm Frequency () Fig. 8 MEMS Electrical equivalent. Electrical equivalents of a MEMS resonator with Lorentz wire interference included (a, b). a Interference is included explicitly. Css is the shield-sense capacitance. Cws is the wire-shield coupling capacitance. b Lorentz current interference effects are built in Rp and Cp. c Admittance G-B versus frequency example curves. (A/(TV A)), as Eq. (5) shows: lumped vibration amplitude X may be written as:   S ΩV AC f ðωÞ 1 S0 ¼ ¼ ð27Þ XðωÞ ¼ G  þ jðB  ωC p Þ ð30Þ V DC iL Rm BV DC iL ωη2 Rp The admittance (Y = G + jB) of the circuit in Fig. 8b is: Methodology and measurement setup 1 Rm The status of the CMOS-MEMS devices was assessed GðωÞ ¼ þ  2 Rp ð28Þ by measuring their admittance vs frequency curve Y(ω), R2m þ wLm  wC1 m also called G-B curve, that typically showed a resonance peak. Then, the electrical equivalent of Fig. 8b was fitted wLm  wC1 m to the obtained curve. This allows accurate extraction of BðωÞ ¼ wC p   2 ð29Þ R2m þ wLm  wC1 m important electrical and mechanical parameters of the beams, like their resonant frequency and residual stress, or the capacitance between the beam and the excitation where ω is the angular frequency. The G-B curves are electrode, from where the status of the beam can be plotted in Fig. 8c along with the circuit parameters that inferred. For example, a deformed beam which is determine their shape. Finally, and for completeness, the touching the adjacent metal electrode would lead to Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 12 of 25 voltages were adjusted experimentally depending on a a number of factors, such as quality factor, resonance fre- quency, parasitic capacitance, noise level and non-linear behavior of the system. A Lorentz current in phase with the AC voltage of the impedance analyzer was injected into the MEMS in some tests, namely sensitivity, offset and magnetic robustness tests. This was accomplished with the system described in Sánchez-Chiva et al.56, for which additional equations were derived in the MEMS electrical model section: the Ω parameter plays a key role Wafer in all the tests with injected Lorentz current while the IA measures the device. Results and discussion Characterization Q factor versus pressure, resonance frequency/beam length: Q(P, fr) b Accurate on-wafer characterization of the Q factor as a function of the pressure (P) was carried out. Please see the Supplementary Material for a detailed explanation. This allowed to extract a formula that predicts very well the Q factor as a function of the device type, resonance fre- quency fr and pressure that may range from 1 μbar to se t (S adou ) Electrostatic ambient pressure. At pressures over a few millibar, only en Re driving air damping needs to be considered. At lower pressures, (shield) Volt. comparator thermoelastic damping becomes dominant and the mea- & Lorentz current sured quality factors reach a plateau. The total Q factor generator can be expressed as: L2 L1 1 1 1 QFN ¼ þ ð31Þ iL Qtotal Qair QTED Fig. 9 Measurement setups. a On-wafer: cascade probe station where QTED is given in Table 1 and Qair is: 12,000b and impedance analyzer HP 4294A. b Socket for QFN measurement, impedance analyzer and optional Lorentz current   ! generation (sensitivity, offset and magnetic robustness tests). fr 5λg f 2r Qair ¼γ 1þ 1þ 2 ð32Þ μ0 Lc fc higher conductance and no resonance peak at the where the pressure dependence is contained in the mean expected frequency. free path length of the gas molecules λg ∝ T/P. The The G-B curve measurement was carried out with dynamic viscosity of the gas (μ0 = f(T)) may be considered impedance analyzers (HP 4294A or Agilent E4990A) set independent of P. The characteristic length of the to measure admittance values. Radio-frequency (RF) structure (Lc) is considered to be equal to the sensing probes were used for a reduced measurement noise. A gap g. Table 2 provides experimental data for five different Cascade probe station 12000b was used for wafers or devices. It shows γ, which is a proportionality parameter single dice (Fig. 9a). A socket was used for packaged that depends on the considered geometry. It also shows fc, samples (Fig. 9b). The beams were excited with a sinu- which is the cut-off frequency. soidal test voltage (VAC) superimposed to a DC bias vol- tage (VDC), which results in an excitation force at the Resonance frequency versus length: fr(L) frequency of VAC (as in Eq. (3)). The test voltages were The resonance frequency of magnetometers built using applied between the beams and an electrode (used for clamped-clamped beams of different lengths is plotted in both driving and sensing) which was placed either on top Fig. 10. It was done for two types of beam sections and for of the beam for exciting vertical out-of-plane vibration, or out-of-plane and in-plane vibrations. The obtained data to one side for horizontal in-plane vibration excitation. In was fitted using Eq. (13). The fit is very good, which order to achieve the cleanest resonance curve, the test indicates that both the Young’s Modulus (E) and the Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 13 of 25 tension (Pa) (or residual stress σr = Pa/(wt)) are indepen- proportional to the length squared52; another one for long dent of the beam length. beams or high tensile stress (jP a =P cr j > 50), where it Optical methods have been used to determine E and σr mostly depends on Pa or σr and it is inversely proportional in several studies57–59. Unfortunately, these methods can to the length, like for cables and membranes52; and a third only extract the effective values of composite beams mixed region (0:2 < jP a =P cr j < 50) in which neither E nor applicable to the out-of-plane direction. Fortunately, the Pa can be neglected. The dependence for the 3 regimes presented method also allows determination along the in- may be readily derived from Eq. (13) by taking the plane direction. appropriate limits. Note that longer beams converge to Three mechanical behaviors or regions may be dis- the same fr because their ratio σr/ρ is very similar, by tinguished in Fig. 10: one, for short beams or low tensile coincidence. Longer beams were not fabricated due to die stress (jP a =P cr j < 0:2), where the resonant frequency (fr) size limitation, so the maximum length achievable mostly depends on the value of E and it is inversely remains to be studied. Remarkably, beams as long as 800 μm remained func- Table 1 Quality factors due to TED (QTED) used in Eq. (31) tional, indicating a planarity better than 0.9 μm (vertical gap between beam and electrode). Tensile residual stress L= 100 μm 200 μm 400 μm 800 μm was used in order to achieve long structures that are planar and robust against temperature excursions as was Z devices QTED = 2850 8200 23,000 50,000 put forward in Fig. 3 and confirmed with these XY devices QTED = 1090 1160 2000 7000 measurements. Temperature experiments: Q(T) and fr(T) Table 2 Parameters used in Eq. (32) Maximum working temperature. Closed cavity A QFN Lc(nm) γ fc(MHz) z device (600 μm-long beams with 0.5 μm gap) was put inside an oven and heated up from 26 ∘C to 198 ∘C in steps Z devices 350 4.4 × 10−11 ≈ 1.6 of 10 ∘C, approximately. Its resonance curve was perma- Z devices* 350 6.8 × 10 −11 ≈ 2.3 nently monitored. After each temperature increment we waited between 20 min and 34 min until a stable Z devices 500 8.3 × 10−11 ≈ 2.0 −11 temperature was reached and then the measurement Z devices 1000 26 × 10 ≈ 2.0 was taken. Finally, the device was removed from the oven −11 XY devices** 900 35 × 10 ≈ 3.0 and measured again. The obtained resonance frequencies *Sensing electrode is hollow between layers and air can flow through. **Double and Q factors are plotted in Fig. 11b. The device survived vertical gap of 900 nm, one of them with holes and air can flow through the test. 3.0 Pa / Pcr = 0.19 Measured resonant frequency data (XY device) Eq. (13) fit (E = 81.97 GPa, Pa = 1234 μN, fr ∝ t 2 2.5 E  = 3667 kg m–3, t = 3.533 μm, w = 3.5 μm) L  Resonance frequency (MHz) Measured resonant frequency data (Z device) Eq. (13) fit (E = 153.3 GPa, Pa = 1285 μN, 2.0  = 5861 kg m–3, t = 1.5 μm, w = 5.01 μm) Pa / Pcr = 0.96 1.5 1.0 Pa / Pcr = 19 Pa / Pcr = 1.2 Pa / Pcr = 96 Pa / Pcr = 6.0 r 0.5 fr ∝ 1 L  0.0 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 μm) Beam length (μ Fig. 10 Beam to string transition. Measured resonance frequencies of clamped-clamped beams of different lengths, and fitted with Eq. (13), which allows to obtain Young’s modulus E and tension or axial load Pa. Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 14 of 25 Eq. (32) given that fr < < fc (fr = 140 kHz and fc is in the a 250 order of MHz). In a closed cavity, the pressure increases linearly with temperature. So, the mean free path λg ∝ T/P 200 remains constant when the temperature changes. Contra- XY d ev. ( rily, in an open cavity at constant pressure the mean free g = 1. 150 0 μm ) path increases linearly with temperature. By taking into Q factor Z dev. account these considerations, Q factor dependence with (g = 1 .0 μm temperature may be greatly simplified from Eq. (32) to: ) 100 Z dev. (g = 0.5 μm) 8 > Closed Cavity > > f 50 Z dev. (g = 0.3 5 μm) f μ0 < ðλg / T =P ¼ constantÞ Q /  λg / Q (T ) with Eq. (33) (open cavity) μ0 > > Open Cavity 0 > f : μ0  T –30 27 85 ðλg / T ; P ¼ constantÞ Temperature (°C) ð33Þ b 150 Note that this approximation is not valid in other 1500 situations such as lower pressures where TED dominates, in the fluidic regime or when the resonant frequency is Resonance frequency (kHz) comparable to the cut-off frequency. Full Eq. (31) shall be 100 1000 Q after test used in those cases. (P = 0.35 mbar) Initially, the gas in the cavity is Argon at 1.4 μbar. But Q factor Ou during the packaging steps other species are out-gassed, the tga ss ing pressure rises to generally more than 100 μbar and the final 50 500 Measured fr gas composition is unknown. In Eq. (33), the viscosity of the fr (T ) with Eq. (15b) (thermal stress) surrounding gas μ0 was calculated using the formulas given Measured Q factor in Lemmon and Jacobsen60 for air. For Nitrogen or using Q (T ) with Eq. (33) (closed cavity) 0 0 the tabulated values for air61 the results are very similar. 50 100 150 200 The viscosity of gases increases with temperature and it Temperature (°C) does not change appreciably with pressure. Fig. 11 Measured fr and Q factor as a function of temperature Using Eq. (33) the predicted Q factor as a function of the and predicted values using Eq. (15b) (fr) and Eq. (33) (Q). a Q(T): temperature is plotted in Fig. 11b. The measured values Open cavity (z device on wafer at constant P = 4 mbar). b Q(T) and fr(T) Closed cavity (QFN sealed z device at P = 0.28 mbar when T = follow the curve within 7%, except in the higher 26 °C before the test). temperature region, where the measured Q factor drops appreciably. This indicates that, above 150 − 175 ∘C an outgassing mechanism is exacerbated. As a consequence, The resonant frequency decreased as the temperature after the device is cooled down to room temperature, the rose. Eqs. (15b) and (16) predicted well the resonant Q factor decreased from 1436 to 1146, indicating that the frequency as it can be appreciated in Fig. 11b. It is pressure inside the cavity increased from 0.28 mbar to important to note that the CTE of the substrate (Silicon) 0.35 mbar, approximately. The datapoint at 198 ∘C can be must be included in the equation. Otherwise, the fr used to estimate the Q factor once the device returns to decrease with temperature will be overestimated. Con- room temperature using the closed cavity case of Eq. (33): stant values of Eiαi with respect to temperature can be assumed given that this is approximately true for the    ð26 CÞ μ ð198 CÞ C f BEOL materials of the beams. If not, their temperature Q26 C ¼ Q198  0  f ð198 CÞ μ0ð26 CÞ ¼ 546 94:3 138 25:95 18:47 ð34Þ dependence (Ei(T) and αi(T)) should be introduced into  Eq. (16). ¼ 1123  Q26 measured ¼ 1143 C Equation (32), with the values listed in Table 2 for the xy which confirms the validity of Eq. (33) for a closed cavity. device with g = 0.5 μm and Q = 1436, was used to estimate the pressure inside the cavity at the beginning Maximum working temperature. Open cavity In order of the experiment: 0.28 mbar. At this pressure, TED to confirm the validity of Eqs. (32) and (33) for the open (QTED > 20000) is negligible compared to air damping cavity case, four devices were measured at wafer level (Qair ≈ 1400). Therefore, we can rely on Eq. (32), rather before sealing at 3 different temperatures and constant than Eq. (31), for Q estimation and its dependence with pressure (4 mbar). The results are shown in Fig. 11a. The temperature. In addition, the fc effect may be neglected in error bars represent the Q uncertainty caused by the Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 15 of 25 measurement noise. The dashed lines predict reasonably curves of the measured devices.pTheffiffiffiffiffiffi lowest limiting noise well the measured data and were produced using Eq. (32) values are around 2  3 nT= Hzpffiffiffiffiffiffi and the best case and a γ 10% smaller than in Table 2. Note that the on- heading accuracy around 0:006 1 = Hz were achieved for wafer measured devices are from a wafer and lot different the z and xy longest devices, and using a Lorentz current from the QFN devices, and that 10% is accountable for the of 600 μA. These numbers are state-of-the-art for 3 axis expected process variability. In the open cavity case the Q Lorentz-force pffiffiffiffiffiffi magnetometers: the lowest noise ( factor variation is significantly smaller (around 2-4 times) 10 nT= Hz) had been reported in Kyynarainen et al.32. than for the QFN devices (closed cavity). The reason is They could be potentially improved with longer beams or that the fr/μ0 variation is partially compensated by the higher current which does not necessarily mean higher mean free path variation in the open cavity case, as Eq. power consumption if the Lorentz wires are designed (33) shows. wider accordingly. Actually, small improvements ( < 10) can be achieved by increasing the width of the wires. The approximate pressure range of a QFN device is Performance depicted in Fig. 12 as a light gray area. For QFN pffiffiffiffiffiffi devices, Noise and heading accuracy the lowest noise values are around 7-10 nT= Hz p with ffiffiffiffiffiffi an The heading accuracy (Eq. (6)) and the noise floor (Eq. associated heading accuracy around 0:02-0:03 1= Hz. (10)) were plotted in Fig. 12 using data from the measured The Lorentz current can be reduced as desired and the devices, which provided Q, fr, η and Lm. The continuous noise floor will increase linearly. The dissipated power curves were calculated using the Q factor from Eq. (31) ( ∝ I2R) will decrease quadratically. So the system may be and the lumped mass M = η2Lm obtained from the G-B run in a number of different configurations depending on a b 10–6 10–6 1 1 Heading accuracy, rms (° / √Hz) Heading accuracy, rms (° / √Hz) 10–7 10–7 Noise floor (T / √Hz) Noise floor (T / √Hz) 0.1 0.1 10–8 10–8 L = 100 μm, 0.35 mW L = 100 μm, 0.36 mW L = 200 μm, 0.59 mW 0.01 L = 200 μm, 0.58 mW 0.01 L = 400 μm, 1.08 mW L = 400 μm, 1.03 mW L = 600 μm, 1.58 mW L = 600 μm, 1.48 mW L = 800 μm, 2.07 mW L = 800 μm, 1.95 mW 10–9 10–9 10–6 10–4 10–2 100 10–6 10–4 10–2 100 Pressure (bar) Pressure (bar) Fig. 12 MEMS brownian noise floor and heading accuracy versus pressure for different designs. Lorentz current = 0.6 mA (square wave), which respects maximum electromigration current. Noise is inversely proportional to Lorentz current. The continuous lines were obtained using the lumped mass derived from G-B curves and the Q given by Eq. (31), which models well experimental data. The data points were obtained from G-B curves at different pressures. In dark gray, range of pressures of QFN packaged devices. Heading accuracy or angle error is calculated assuming Bearth = 20 μT. a Z device: g = 0.35 μm, nB = 10, nw = 2. b XY device: g = 0.9 μm, nB = 6, nw = 4. Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 16 of 25 the requirements. For example, if power consumption calculated analytically quite accurately, with parallel plate specs are stringent, ipeak L ¼ 100μA may be used, and the assumption. For illustration purposes, its Ω value may be voltage drop along the MEMS would be less than 0.5 V. In calculated as follows: that case, the current may be reused for the electronics. The equations presented in this work allow to calculate Ωz ¼ FFme ¼ iL nw LB V DC V AC Lw ¼ 101; 5  BðT Þ ð35Þ ϵ0 g2 the expected performance for other configurations. System-level simulations at the resonant frequency where w = 5 μm is the width of the electrostatic area of show that SNR (Signal-to-Noise Ratio) due to the one beam. The parallel plate assumption yields Ωz = mechanical pffiffiffiffiBrownian noise decreases with Q with a 0.048 for B = 473 μT, similar to the measured and factor of Q as Eq. (10) shows, while the SNR of the simulated values shown in Table 3. electronics increases linearly with Q, as its noise only The maximum conductance value Gmax may be used to depends on the parasitic capacitances and the circuit obtain the sensitivity as in Sánchez-Chiva et al.56. It is not current consumption. With a low-noise amplifier of used given that variability in the Rp values, for example 50 μA biasing (ibias), the Brownian noise dominates at the due to electrostatic coupling between sense and Lorentz pressure level inside the QFN packaged devices. For a wire, introduces errors in the measurement that are given device size and power constraint, system-level overcome using the Rm, Lm and Cm values. power-noise optimization shall redistribute the ibias/iL Finally, the very high coefficient of determination current ratio for optimal overall SNR for minimum obtained in non-weighted fits (R2 > 0.999) confirms the power consumption. high linearity of Lorentz-force magnetometers62,63, mainly limited by the non-linearity of the motion Sensitivity detection capacitors (C(x)). It also proves that this new The sensitivity to magnetic fields was measured using a method for measuring the sensitivity of Lorentz-force Helmholtz coil. The applied magnetic field ranged magnetometers works well. In fact, the Ω ratio may be from − 473 μT to + 473 μT. A square Lorentz current of found with very good accuracy (we estimate better than 50.14 μA (45.14 μARMS at fr) was injected in phase with 2% in our case). the Vac voltage of the impedance analyzer (10 mVRMS). Phase alignment was achieved with the system described Offset and shielding efficiency in Sánchez-Chiva et al.56. The Lorentz force is added to One the best features of the presented magnetometers the electrostatic force and modifies the measured G-B is their Lorentz current shielding from the sense elec- curve (and Rm, Lm and Cm values) as described in the trode. The theoretical models have been already pre- MEMS electrical model section. Eight magnetic sweeps sented. Now, in order to check the shielding efficiency were performed so the G-B curve was measured eight experimentally, the G-B curve was measured while a times at each of the seven B values to reduce measure- Lorentz current of 52 μA (peak value of square wave) in ment noise and/or temperature drifts. The variance of phase with impedance analyzer alternating voltage (V1−2 each group of 8 points was used to perform a weighted in Fig. 8) was injected into the MEMS. The external linear regression that yielded the 1/Rm, 1/Lm and Cm magnetic field was compensated with Helmholtz coils. values (R2 > 0.999) as a function of the magnetic field (see The experiment was repeated but this time using a Lor- Table 3). It was done for one z and one xy device. The Ω entz current in anti-phase. The resultant admittance value obtained from the fit is displayed in the table, along curves are shown in Figs. 13c, g for the z device, and in with the sensitivity calculated using Eqs. (26) and (27). It Fig. 13a, e for the xy device. is important to note that the Q factor of the chosen z and An appreciable constant offset due to the Lorentz cur- xy devices is low: the worst case scenario after QFN rent interference effect was measured, especially in the packaging. The expected sensitivity of a nominal QFN susceptance (B) curves. This corresponds to the electrical device is between 1.25 and 2.5 times higher than the interference term in Eq. (3). The interference magnitude ( measured ones for the xy and z devices, respectively. V int int sh ) and the shielding efficiency (V sh /Vw) can be The measured Ω is similar to the theoretical value deduced from the G-B curves as follows: (within 15%). This similarity is an indication that our The impedance analyzer extracts the admittance from theoretical estimation of the electrostatic and magnetic the nodes 1-2 of Fig. 8 by applying an AC voltage (V1−2) forces (and associated Brownian noise) are correct. This and measuring the current flow. The interference caused 15% discrepancy is perfectly accountable by the inherent by a Lorentz current + iL introduces an additional process variability, which affects lateral gaps and layer unwanted current iint flowing through 1-2 and this, in thicknesses. In general, Ω must be calculated using turn, is seen as an admittance change. The admittance simulations to estimate the electrostatic force correctly. offsets (Yoff = Goff + jBoff) shown in the figures are pro- Fortunately, the electrostatic force of the z device may be duced by a 2 ⋅ iL current, so the offset must be divided by a Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 17 of 25 Table 3 Measured Ω and sensitivity S (Eqs. (26)) and S0 (Eq. (27)) of two QFN-packaged devices Device type Setup Helmholtz coil Measurement Fitted linear eq. (Eqs. (22) to (24)) Magnetic conditions (RMS) Ym ¼ Ym B¼0  ð1 þ ΩÞ sensitivity (RMS) Z VAC = 10 mV 1/Rm = 1.075 × 10−6 ⋅ (1 + 96.00 ⋅ B(T)) Ωz = 96.89 ⋅ B(T) L = 600 μm VDC = 0.5 V 1/Lm = 1.255 × 10−3 ⋅ (1 + 97.77 ⋅ B(T)) Sz = 1.05 μA/T g = 0.5 μm iL = 45.14 μA Cm = 1.543 × 10−15 ⋅ (1 + 97.80 ⋅ B(T)) S 0z ¼ 46:3 μA/(T V mA) Q = 770 nw = 2, nB = 10 XY VAC = 10 mV 1/Rm = 0.3958 × 10−6 ⋅ (1 + 311.0 ⋅ B(T)) Ωxy = 308.9 ⋅ B(T) L = 600 μm VDC = 1 V 1/Lm = 1.9287 × 10−4 ⋅ (1 + 306.8 ⋅ B(T)) Sxy = 1.22 μA/T g = 0.9 μm iL = 45.14 μA Cm = 2.851 × 10−16 ⋅ (1 + 306.8 ⋅ B(T)) S 0xy ¼ 27:1 μA/(T V mA) Q = 1700 nw = 4, nB = 6 a ⋅10–7 b ⋅10–7 c ⋅10–6 d ⋅10–7 +iL – (G G –iL) /2 (G +iL – G –iL)/2 Conductance G (S) Conductance G (S) G +iL 2.3 4 G +iL 1 1.60 G –iL 2 2.2 G –iL XY 1.50 0 Goff z 0 Goff 2.1 –2 124.6 125 125.4 124.6 125 125.4 142 143 144 142 143 144 e ⋅10–6 f ⋅10–6 g ⋅10–6 h ⋅10–6 3 1.45 (B +iL – B –iL) /2 4 B +iL (B +iL – B –iL)/2 Susceptance B (S) Susceptance B (S) B +iL 1.71 2 XY 1.44 Z Boff 2 Boff 1.7 1 B –iL 1.43 1.69 0 0 B –iL 1.68 124.6 125 125.4 124.6 125 125.4 142 143 144 142 143 144 Frequency (kHz) Frequency (kHz) Frequency (kHz) Frequency (kHz) Fig. 13 Offsets in the G-B curves due to positive (black) and negative (orange) Lorentz current interference. Their difference shows a resonance (gray). a Offset in conductance (G) due to Lorentz current (XY Device). b Magnetic resonance related to +iL and fit. Conductance (G). XY. c Offset in conductance (G) due to Lorentz current (Z Device). d Magnetic resonance related to +iL and fit. Conductance (G). Z. e Offset in susceptance (B) due to Lorentz current (XY Device). f Magnetic resonance related to +iL and fit. Susceptance (B). XY. g Offset in susceptance (B) due to Lorentz current (Z Device). h Magnetic resonance related to +iL and fit. Susceptance (B). Z. Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 18 of 25 Table 4 Interference/offset reduction achieved with Lorentz routing symmetric design (*) and Lorentz current shielding (**) Device Measurement Device Admittance Vdrop Vw (RMS) V int sh (RMS) Magnetic type conditions impedances offset (iLRwire) Eq. (38) Eq. (37) offset Z iL ¼ 51:1μApeak Cws = 6.20 pF GZoff ¼ 0:459 μS 295 mV → 3.08 mV → 0.428 μV 0.43 μT L = 600 μm ¼ squarewave Css = 1.36 pF g = 0.5 μm 12 ¼ 0:5V V dc Zsh = 25Ω BZoff ¼ 3:39 μS 1  1  45 7184 Q = 770 V ac 12 ¼ 10mV RMS Rwire = 4.50 kΩ nw = 2, nB = 10 XY iL ¼ 52:5μApeak Cws = 3.56 pF GZoff ¼ 0:321 μS 282 mV → 5.17 mV → 0.362 μV 0.13 μT L = 600 μm ¼ square wave Css = 2.9 pF g = 0.9 μm 12 ¼ 1V V dc Zsh = 25Ω BZoff ¼ 2:88 μS 1  1  26 14301 Q = 1575 V ac 12 ¼ 10 mV RMS Rwire = 4.22 kΩ nw = 4, nB = 6 factor of two in order to calculate iint: are shown in Table 4. We can see that the shielding electrode reduced the interference voltage by a 4 order Y off Goff þ jBoff magnitude factor, approximately. This value is highly iint ¼  V 12 ¼  V 12 ð36Þ 2 2 dependent on the impedance connected to the shield electrode. In an ASIC we estimate similar shielding Consequently, an interference voltage V int sh is also added attenuation factors. Additionally, the Lorentz routing on top of the shield voltage Vsh. We can calculate this design reduced the interference between 25 and 50 times. voltage simply as: In total, a 5-6 order of magnitude reduction was achieved. The interference adds an offset to the admittance sh ¼ Z sh  i V int int ð37Þ curves (electrical interference term in Eq. (2)). This offset may be almost eliminated by using the current where Zsh is the output impedance of the impedance chopping technique33,41 mentioned in the introduction. analyzer. The coupling capacitance between wire and Unfortunately, this technique cannot eliminate the shield Cws was measured. Then, Vw can also be readily magnetic offset (electrostatic excitation term in Eq. (2)). deduced after substituting equations Eqs. (36) and (37) Let us apply this technique to the measured data by into Eq. (11), which yields: subtracting the + iL and − iL curves, and dividing by V 12 two, so the result corresponds to + iL: the resultant V w  Boff  jGoff  ð38Þ curves were plotted in Figs. 13b, d, f and h. A small 2ωC ws resonance peak was found. The peak was fitted to the Note that Vw is an equivalent AC voltage that creates the MEMS electrical model and, by using the sensitivity observed interference. It is just a fraction of the real voltage equations from Table 3, we found that it corresponds to drop Vdrop along the Lorentz wire, caused by the fabrication a magnetic field of approximately 100 μT. We think this inherent variability resulting in a small lack of symmetry, is caused by the permanent magnetization of the pro- non-compensated AC voltage and its associated interfer- totyping package and/or measuring setup. One reason is ence, already mentioned in the Materials and methods that the magnetic field has the same magnitude but section. The real voltage drop is readily calculable with the opposite direction for the z and xy device: note that the resistance value of the Lorentz wire. Therefore, the interference AC voltage would excite electrostatically interference reduction achieved with symmetric Lorentz the device and create peaks in the same direction, so is routing design can also be estimated as Vw/Vdrop. an indication that they correspond to a physical mag- By looking at Eq. (38), if Vw is perfectly in phase or in netic field. Additionally, the observed peaks (100 μT) are anti-phase with V1−2, then Goff should be zero. It turned between 2 and 3 orders of magnitude larger than the one out to be small, but not zero. From the ratio Boff/Goff we created by the interference voltage V intsh (0.1 − 0.4 μT), can deduce that Vw was in 83∘ phase with V1−2 during the not observed in these measurements. The magnetic measurements, and not perfectly in phase. offsets were calculated by setting Ω = 1 (in Eq. (35) for The measurement conditions and the amount of elec- the z device) and obtaining the correspondence between trical interference obtained from Eqs. (11) and (36) to (38) magnetic field and VAC. Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 19 of 25 In conclusion, the current chopping technique in con- Also, Aluminum suffers a significant Young’s modulus junction with the beam shielding successfully eliminated the softening at those temperatures65. Withstanding high electrical interference. In addition, the magnetic offset was temperatures for several minutes is very important so the reduced almost 6 orders of magnitude (4 orders due to device may be subjected to outgassing thermal treatments shielding and 2 orders due to symmetric Lorentz routing), (annealings)66,67 and other post processes. In our experi- down to, at most, 0.4 μT, approximately. We believe this is an ence, a MEMS device that shows high yield after these important achievement given that this magnetic offset cannot tests also shows high yield after packaging into QFN, and be compensated with the current chopping technique. viceversa. Therefore, it can be used as a quick and cheap method to foresee yield issues before QFN packaging. Yield and reliability tests The devices were measured before and after the Yield after QFN packaging experiment and the yield results are summarized in Tables The two types of z and xy devices shown in Fig. 6a and 6, 7, 8. The number of mechanical couplings and length of 7 and in Table 3 were packaged into QFN packages. The the sensing structures (sensing plate length x number of chosen variants were formed by 600 μm-long c-c repetitions) is shown for each device type and length. beams. They were measured and the results and Results show that, with proper design, very robust expected cavity pressure, noise floor and associated best CMOS-MEMS structures may be manufactured. For heading accuracy are summarized in Table 5. The cavity example, the length of the sensing electrodes of the xy pressure was deduced from the Q factor and resonant devices had an important effect on the robustness against frequency using Eq. (31) and values from Table 2. Noise high temperature. In fact, older devices (not shown here) floor and heading accuracy can be found in Fig. 12. with longer sensing plates showed much lower yield. Results showed that the z-yield is high but the xy-yield Shortening the sense electrode length allowed to improve was significantly lower. We will show in the following the yield of the 3-metal xy device from 56% to 96% in the section how the xy device was redesigned to improve 400∘C − 1 h test. Also, it was found that the number of this yield. The main failure mode was a too high G couplings should be minimized: it increased the yield of value, indicating a short-circuit between sense and the xy-4m device with sensing fingers from 60% to 96% in shield electrode. Statistical data will show that this may the 450∘C − 0.5 h test, achieving similar yields to the z be caused by a non-optimum sense electrode or cou- device. This is strong evidence that the yield after QFN pling link design. packaging of the xy-4m device would be similar to that of the z device. Temperature robustness and yield improvement Implementing a large number of design variants proved On-wafer devices were subjected to one of the two a decisive factor in the yield optimization process, which stringent thermal profiles shown in Fig. 14, which are also allowed to reduce the number of iterations and close to altering the CMOS electronics performance7,15,64. therefore development time. Table 5 Variability and yield of QFN devices Dev. f r þsample max sample min Qþsample max sample min Pþsample max sample min Noise floor (RMS) Heading accuracy (RMS) Yield pffiffiffiffiffiffi  pffiffiffiffiffiffi Z 144þ15 6 kHz 1687þ1122 1093 270þ520 114 μbar 15þ5 5 nT= Hz 0:045þ0:015 0:015 = Hz 118/124 (95%) pffiffiffiffiffiffi  pffiffiffiffiffiffi XY 133þ9 10 kHz 2049þ935 966 245þ245 157 μbar 9:5þ2:5 2:5 nT= Hz 0:027þ0:009 0:009 = Hz 68/114 (53%) 600 600 Temperature (°°C) Temperature (°°C) 500 Profile 1 500 450 °C30 min Profile 2 400 °C 60 min 400 400 300 300 16.6 °C/min –24.9 °C/min 200 9.2 °C/min –17.6 °C/min 200 –10.2 °C/min 100 100 11.1 °C/min 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Time (min) Time (min) Fig. 14 Temperature profiles applied to test the device robustness against temperatures that are close to altering the CMOS electronics performance. Left: 400 °C for 1 h. Right: 450 °C for 30 min. Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 20 of 25 Table 6 Yield results of the two high temperature tests on xy devices XY device with long sensing plates Dev. L (μm) 300 400 500 600 Sense L (μm) 100 x 4 82 x 6 74 x 8 Couplings 4 6 6 TOTAL Yield before 400 °C 1 h 13/13 (100%) 11/13 (85%) 13/13 (100%) 37/39 (95%) Yield after 400 °C 1 h 7/13 (54%) 5/13 (38%) 10/13 (77%) 22/39 (56%) Yield before 450 °C 0.5 h 13/13 (100%) 13/13 (100%) 12/13 (92%) 38/39 (97%) Yield after 450 °C 0.5 h 5/13 (38%) 2/13 (15%) 0/13 (0%) 7/39 (18%) XY device improved with shorter sensing plates (Fig. 6a) Dev. L (μm) 300 400 500 600 Sense L (μm) 33 x 6 36 x 7 Couplings 2 6 TOTAL Yield before 400 °C 1 h 12/13 (92%) 13/13 (100%) 25/26 (96%) Yield after 400 °C 1 h 12/13 (92%) 13/13 (100%) 25/26 (96%) Yield before 450 °C 0.5 h 12/13 (92%) 13/13 (100%) 25/26 (96%) Yield after 450 °C 0.5 h 5/13 (38%) 3/13 (23%) 8/26 (31%) Table 7 Yield results of the two high temperature tests on xy-4m devices XY-4M device with sensing fingers (Fig. 6b), several couplings Dev. L (μm) 300 400 500 600 Sense L (μm) 28 x 4 28 x 6 28 x 8 28 x 10 Couplings 2 4 4 6 TOTAL Yield before 400 °C 1 h 13/13 (100%) 13/13 (100%) 13/13 (100%) 13/13 (100%) 52/52 (100%) Yield after 400 °C 1 h 13/13 (100%) 10/13 (77%) 5/13 (38%) 3/13 (23%) 52/52 (100%) Yield before 450 °C 0.5 h 13/13 (100%) 13/13 (100%) 13/13 (100%) 13/13 (100%) 52/52 (100%) Yield after 450 °C 0.5 h 13/13 (100%) 10/13 (77%) 5/13 (38%) 3/13 (23%) 31/52 (60%) XY-4M device with sensing fingers (Fig. 6b), 1 coupling Dev. L (μm) 300 400 500 600 Sense L (μm) 28 x 6 28 x 6 28 x 6 28 x 8 Couplings 1 1 1 1 TOTAL Yield before 400 °C 1 h 13/13 (100%) 13/13 (100%) 13/13 (100%) 13/13 (100%) 52/52 (100%) Yield after 400 °C 1 h 13/13 (100%) 13/13 (100%) 13/13 (100%) 13/13 (100%) 52/52 (100%) Yield before 450 °C 0.5 h 13/13 (100%) 13/13 (100%) 13/13 (100%) 13/13 (100%) 52/52 (100%) Yield after 450 °C 0.5 h 13/13 (100%) 13/13 (100%) 13/13 (100%) 11/13 (85%) 50/52 (96%) Magnetic robustness a square wave Lorentz current of 50 μA in the presence In order to test the robustness against large magnetic of a magnetic field of variable intensity. The maximum fields the z device G-B curve was measured while using applied magnetic field was estimated in around 32 mT. Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 21 of 25 Table 8 Yield results of the two high temperature tests on z devices Z device with gap = 0.5 μm (Fig. 7), 1 coupling Dev. L (μm) 300 400 500 600 Sense L (μm) 37 x 8 50 x 8 40 x 12 37 x 16 Couplings 1 1 1 1 TOTAL Yield before 400 °C 1 h 13/13 (100%) 13/13 (100%) 13/13 (100%) 13/13 (100%) 52/52 (100%) Yield after 400 °C 1 h 13/13 (100%) 13/13 (100%) 12/13 (92%) 12/13 (92%) 50/52 (96%) Yield before 450 °C 0.5 h 13/13 (100%) 13/13 (100%) 13/13 (100%) 13/13 (100%) 52/52 (100%) Yield after 450 °C 0.5 h 13/13 (100%) 13/13 (100%) 13/13 (100%) 13/13 (100%) 52/52 (100%) It was created with a magnet placed on top of the QFN pk-pk / 20 g pk min, 20-2000 Hz, 4 sweeps in each of and a Helmholtz coil, generating 24 mT and 8 mT each, 3 mutually perpendicular axes at 3 octaves/min. The 5 devices survived the tests. respectively. No malfunction was found during or after the test. Due to the magnetization of external compo- Finally, one QFN z device underwent a 3 s free fall from nents, offsets of around a few hundreds of μT remained a 5.60 m height and landed on a concrete floor at an when the magnetic field was set to zero. In addition, estimated velocity of 7 km s−1. The acceleration during non-linear behavior became slightly apparent when the impact was not recorded. No appreciable damages vibration amplitudes reached around 20 − 30% of the were observed in the QFN package and the device con- gap which took place when the magnetic field was tinued functioning correctly. around 14 − 20 mT. Performance comparison with other magnetometers Shock tests A list of the commercial magnetometers used in The QFN z-device underwent several shock tests along smartphones may be found in Matyunin et al.69. Some of the 3 directions. The impacts were performed manually. A them are compared with 3 axis MEMS magnetometers in commercial triaxial piezoelectric accelerometer (834M1- Table 9. The recently commercialized TMR technology 6000)68 was used as the reference accelerometer. Its displays the best noise figure-of-merit (FOM) of com- maximum acceleration range is ± 6000 g, so that was the mercial magnetometers. However, the Lorentz-force maximum shock that could be recorded. An Arduino magnetometers built with the presented CMOS-MEMS microcontroller board was also attached to the test process show very competitive results in QFN packages, assembly, which recorded the 3 axis readings when a compared to both MEMS and commercial devices. For given threshold was surpassed and later sent to a PC via example, the sensor area is the smallest found in 3 axis serial communication. The accelerometer bandwidth is MEMS magnetometers. above 6 kHz with analog output and its sensitivity 5 g/ The xy and z devices packaged into QFN occupy an area LSB. Its offset was compensated in the Arduino code. of 680 × 185 μm2 and 690 × 210 μm2, respectively, which Three readings, one for each axis, were taken every 4.5 μs corresponds to a total area of 0.4 mm2. If the MEMS yield and the total recording time was 9 ms. The QFN, accel- is kept high, the area taken by the MEMS has a CMOS erometer and Arduino were assembled together as shown fabrication cost smaller than $0.01 for 200 mm wafers in Fig. 15d. from 0.18 μm CMOS processes. In addition, in multi-die The devices survived all the tests performed. The approaches, a relatively high area is wasted in pads, recorded accelerations of the 3 strongest shocks are especially in a small die. Also MEMS die area is limited by shown in the graphs in Fig. 15. Along the y and z axes they the fact that cutting very small dice is not straightforward. reached 6000 g. The correct functioning after the test was All this is avoided with CMOS-MEMS and highlights the confirmed by measuring the G-B resonance with an area-cost advantage of BEOL CMOS-MEMS integration. impedance analyzer. In addition, 5 QFN z devices where subjected to two Conclusions standard mechanical shock tests: Integration of MEMS on CMOS using the BEOL lay- ● Method 2002.5, Condition B: MIL-STD-883 1500 g ers is a long-sought objective that would provide sig- 0.5 ms Half Sine, 5 shocks in each direction of 3 nificant size, cost, speed and power advantages in some mutually perpendicular axes. (30 total). applications. However, successful commercialization ● Method 2007.3, Condition A: MIL-STD-883 1.5 mm has proven to be difficult due to two main reasons: Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 22 of 25 a b c d 6000 Acceleration (g) 3000 0 –3000 –6000 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 2.0 2.2 2.4 2.6 2.8 3.0 Socket Reference Arduino for QFN accel. Time (ms) Time (ms) Time (ms) 834M1-6000 Fig. 15 Recorded acceleration values for the X, Y and Z shock tests and measurement setup. a X-shock test results. b Y-shock test results. c Z-shock test results. d Setup for recording acceleration during the shock tests. Table 9 Comparison of commercial and in research-state 3 axis magnetometers 3D Magnetometer Technology Full scale Current per axis Figure of merit* Footprint 3 axes Offset (μT) range ( ± mT) (μArms) (μTμArms/√Hz) (mm2) COMMERCIAL STMicroelectronics LIS3MDL70 AMR 1.2 90 ~10 4 100 a a b STMicroelectronics AMR 4.9 33−316 6−20 4 6c 71 LSM303AGR Freescale MAG311072 TMR 1.0 2.9-300a 3.6-19a 4 100 73 AKM AK8975 Hall 1.2 117 ~100 4 300 74 AKM AK09940 TMR 1.2 40−267 0.20−0.76 2.56 No data 75 Honeywell HMC5883 AMR 0.8 33/640 3.4 9 No data Bosch BMM15076 AMR+Hall 1.3 57-1630a 35.6-155a 2.43 40b R&D Kyynarainen et al.32 MEMS LFM 0.2 100 X/Y: 1.0, Z: 7.0 >11.5 25 40 d f d Laghi et al. MEMS LFM 5.5 33 X/Y: 6.1, Z: 6.7 4 5000b Marra et al.49,77 MEMS LFM X: 6.0, Y: 5.5, Z: 70d X: 8.4, Y: 5.2, Z: 7.7f 0.53d No datae 7.0 This work (QFN) CMOS-MEMS LFM Z: 32g 0-600d X/Y: 1.8, Z: 3.0f 0.4d X/Y: 0.13, Z: 0.43 * Normalized for a single axis. For R&D, X, Y and Z axis values are given a Value varies depending on the selected current/bandwidth b 3D magnetometer and 3D accelerometer c Can be reduced to a few μT with manual DC compensation or calibration d ASIC current consumption/area not included e Expected to be in the same order of magnitude as Laghi et al.40 given the design and manufacturing process similarities f Assuming current is reused for the 3 axes. Otherwise the triple value must be taken g Tested with a current of 50 μA MEMS yield and MEMS performance. In this work, the beams as a function of temperature, design parameters, fabrication process and the design techniques to over- and gas pressure from 1 bar to 1 μbar were derived and come the main challenges to build reliable and compe- verified experimentally. TED was the main damping titive CMOS-MEMS Lorentz-force magnetometers mechanism at low pressures as finite element simula- (LFM) have been presented. tions confirmed. Gas viscosity explained Q factor tem- Three-axis Lorentz-force magnetometers were perature variations in the air damping regime. Thermal designed, fabricated and extensively characterized: stress accounted for the variation of resonance fre- equations that accurately predict the Q factor and quency with temperature. The beam-to-string transi- resonant frequency of multilayered clamped-clamped tion of clamped-clamped beams with the same axial Valle et al. Microsystems & Nanoengineering (2022)8:103 Page 23 of 25 stress but different length was measured and fitted Barcelona Institute of Science and Technology (BIST), Edifici Cn. Facultat accurately the expected behavior. This demonstrates Ciències Nord, Universitat Autónoma de Barcelona, 08193 Bellaterra, (Barcelona), Spain that accurate modelization of complex multilayered structures built with the BEOL of CMOS is feasible. Author contributions Lorentz-force magnetometers do not have magnetic J.V. conceived the design techniques, designed the sensors, performed simulations, proposed and analyzed the measurements, established the new materials, which provides several advantages over other theoretical models and wrote the manuscript. J.M.S.-C. and J.V. performed magnetometer technologies. Unfortunately, offsets in measurements. J.M.S-C. and D.F. conceptualized test setups. All authors LFM are, probably, their main drawback. In this work, participated in the testchip designs and in the sensor high-level model development. D.F. and J.M. conceived the system design and supervised the the current chopping technique in conjunction with the research. J.M. obtained public funding for some prototypes and test setup. All beam shielding successfully eliminated the electrical the authors discussed system design and results. All the authors revised the interference. In addition, the electrostatic interference/ manuscript. offset, which cannot be compensated with the current Competing interests chopping technique, was reduced almost 6 orders of The authors declare no competing interests. magnitude (4 orders due to shielding and 2 orders due to symmetric Lorentz routing) down to 0.13 μT and 0.43 μT for the xy and z axes, respectively. Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41378-022-00423-w. Despite CMOS technology not being a MEMS pro- cess, Brownian noise in the final CMOS-MEMS pffiffiffiffiffiffi QFN- Received: 1 February 2021 Accepted: 12 May 2021 packaged devices was between 9:5  15 nT= Hz when using a p current ffiffiffiffiffiffi of 600 μA. A heading accuracy as low as 0:045 = Hz, approximately, may be achieved by a compass formed by the packaged magnetometers. This References is similar or better than what commercial magnet- 1. Baltes, H. et al. CMOS-MEMS: Advanced Micro and Nanosystems. (John ometers and state-of-the-art three-axis LFMs built with Wiley & Sons, 2008) https://onlinelibrary.wiley.com/doi/book/10.1002/ 9783527616718. MEMS-dedicated processes can provide. Apart from 2. Fedder, G. K., Howe, R. T., Liu, Tsu-JaeKing & Quevy, E. P. Technologies for the offset and noise benefits, the sensor area is the cofabricating MEMS and electronics. Proc. IEEE 96, 306–322 (2008). smallest found in 3 axis MEMS magnetometers. The 3. Qu, H. 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