A Silicon MEMS EM vibration energy harvester

A Silicon MEMS EM vibration energy harv ester Y. Y ang, U. Radhakrishna, D. W ard, A. P . Chandrak asan and J. H. Lang MIT, Cam bridge, MA, 02139, USA. E-mail: markyang@mit.edu Abstract. This paper presents an optimized silicon-MEMS electromagnetic vibration energy harv ester suitable for applications such as mac hine health monitoring. The harvester comprises a DRIE-etc hed silicon susp ension, and pick-and-place N42 NdBF e magnets and copp er coils, housed in a 3D-printed pack age. The harvester is designed to op erate near 50 Hz with 0.5-1 g vibrations using a long-stroke suspension. Multi-domain harvester optimization results in an op en-circuit voltage of 1.7 V, a matched-load pow er output of 2.2 mW, and a matc hed-load p o w er-output densit y of 1.23 mW/cm 3 at 1.1 g with a resonance frequency of 76 . 3 H z . 1. In tro duction This pap er presents a vibration energy harv ester, emplo ying a Loren tz-force energy conv erter, that is suitable for p o wering miniaturized autonomous IoT sensors [1][2]. The harvester comprises a DRIE-etc hed silicon suspension, and pic k-and-place N42 NdBF e magnets and copp er coils, all enclosed in a 3D-prin ted plastic pack age. The harvester has an active volume of 1.79 cm 3 , and an output p o wer P Out of 2.2 mW at 1 . 1 g and 76 Hz under matc hed load, yielding a p ow er densit y (PD) of 1.23 mW/cm 3 and a normalized p ow er density (NPD) of 1.02 mW/cm 3 /g 2 , the highest rep orted PD and NPD among silicon-based MEMS harvesters rep orted to date [2]. The high P Out follo ws the use of a four-bar-link age susp ension that lo wers b eam stress compared to our earlier accordion susp ension [3], enabling mm-range strok es and hence mW-level P Out . The k ey con tributions here are: (i) large-stroke (2 mm) silicon susp ensions with stress analysis, (ii) harvester implementation yielding P Out = 2 . 2 mW, and (iii) optimized design guidelines and scaling to further reduce harv ester size while preserving P Out . 2. Design and Optimization As describ ed b elow, harv ester design is based on optimizations o v er mec hanical, magnetic and electrical domains. T o begin, a mechanical optimization of the harvester spring-mass-damp er system is executed following [3]. T o do so, the mec hanical p ow er P M con verted by the harvester is expressed at resonance in sin usoidal steady state in the absence of mechanical loss as P M = B ω 2 X 2 / 2 = ω X M A/ 2 = ρω X A ( L 1 − 2 S ) L 2 L 3 / 2 (1) where damping co efficient B is a pro xy for energy con v ersion through the Loren tz-force energy con verter, ω is the resonance frequency , X is the strok e amplitude, M is the pro of-mass mass, A is vibration acceleration, ρ is the density of the pro of mass, L 1 , L 2 and L 3 are the dimensions of the harv ester with L 1 in the strok e direction, and S ≥ X is the single-sided space within L 1 Figure 1. (a) Cross-sectional side view of the harv ester. (b) T op view of the susp ension and magnets glued together. (c) Individual 3D-prin ted pac k aging parts to b e com bined. (d) Harv ester at its maximum deflection sho wing the b ending of the b eams. allo cated for strok e; the assumption of negligible mechanical loss is supported by exp erimental observ ation. F ollo wing [3], P M is maximized when X = S = L 1 / 4, yielding P M , Max = ρω S A ( L 1 − 2 S ) L 2 L 3 / 2 = ρω AL 2 1 L 2 L 3 / 16 . (2) Th us, L 1 , is allo cated equally to the mass and bi-directional stroke 2 X . This assumes the susp ension/springs p ermit (nearly) all of S to be used for X , which was true for the accordion susp ension [3]. Finally , following (2), the longest harvester dimension is used for the stroke direction L 1 for maxim um P M . Note that to ac hiev e the maximized p ow er in (2), the Loren tz- force energy con v erter m ust provide the damping B required to satisfy (1) and X = L 1 / 4. T o ac hieve P Out in the mW range, the strok e X m ust b e in the mm range. Our previous accordion susp ension [3] did not yield large X as the springs fractured at X = 0 . 6 mm due to high stress caused by the side-bar used to raise the resonant frequencies of the higher-order vibration mo des. A four-bar-link age suspension is c hosen here to ov ercome the spring fracture at large strokes while raising the resonance frequencies of the higher-order mo des. Figures 1(a)- (b) show a cross-sectional side-view of the fabricated harvester and a top-view of the silicon four-bar-link age susp ension. The four-bar link age is not as space efficient as the accordion susp ension as it requires X ≤ S/ 2. P M in (1) is then maximized with X = S/ 2 = L 1 / 8, yielding P M , Max = ρω S A ( L 1 − 2 S ) L 2 L 3 / 4 = ρω AL 2 1 L 2 L 3 / 32 . (3) Ho wev er, the springs in the new susp ension should experience low er stress than in [3] b ecause they are not torqued by the side bar. This is evident from the spring b ending at maximum strok e shown in Figure 1(d). Second, the spring widths are tap ered via narrowing tow ards their middle to create a more uniform stress profile. Third, the joints are designed to hav e symmetric fillets with radius of fiv e spring widths to further reduce stress. F ourth, the spring length is increased to reduce strain. These precautions yield the desired strok e of X = S/ 2 = 2 mm as sho wn in Figure 1(d), the largest strok e reported in a Si-MEMS harv ester suspension [2]. The suspension is dimensioned to ac hieve a near-50-Hz resonance sub ject to the constraints that the spring width exceeds 25 µ m as limited b y etch resolution, and b eam stress is less than 130 MPa. Figure 2(a) shows the resonan t mo dal analysis for the optimized susp ension highligh ting a fundamental resonance translational mode f Res close to 50 Hz and a 5-fold separation b etw een f Res and higher-order resonance frequencies. Solidw orks sim ulations sho w the lo w est resonant mo des are: translational along L 1 at 76 H z ; translational along the L 3 (magnetic pole) direction at 270 Hz; and rotational ab out L 3 at 575 Hz. The stress analysis in Figure 2(b) also shows that the maximum b eam stress at full stroke is 130 MP a compared to 460 MPa in the accordion susp ension. Th us, the mec hanical optimization achiev es optim um resource allo cation for mass and strok e while the susp ension exhibits the desired f Res and X . Tw o an ti-parallel N42 NdBF e p ermanen t magnets are the magnetic flux source through which B is implemented, and the pro of mass because they offer higher mass densit y than lo ose windings. 4.5 7 x10 8 0 Pa 2.0 3 x10 8 1.0 2 x10 8 3.0 5 x10 8 (a) (b) Resonant modal analysis Non -linear stress analysis f 1 =76 .3 Hz f 3 =73 4 Hz f 2 =27 0 Hz x ma x = 2 mm x ma x = 2 mm S max = 0.46 GP a S max = 0.1 3 GP a (c ) X X Figure 2. (a) Resonan t mo dal analysis of the 4-bar-link age susp ension showing go o d mo dal separation betw een higher resonan t modes and the desired fundamen tal mo de. (b) Stress analysis sho wing that the suspension under maxim um strok e has three times low er stress than do es the previous accordion spring suspension [3]. (c) 2D magnetic sim ulation to compute G . Figure 1(a) shows the magnetic energy con verter cross section with mo ving magnets, and t w o stationary coils on the harvester frame. The design parameters of magnet height T , coil height ∆, and airgap betw een magnet and coil δ are optimized for maxim um time-a verage electrical output p ow er P E . Assuming the magnetic thic kness of T + 2∆ + 2 δ is small compared to the magnet widths and lengths, the maximum magnetic flux densit y , and hence the maximum induced coil voltage V at a giv en ω and X , the coil resistance R Coil , and the maximum output p o w er P E = V 2 / 8 R Coil in to a matc hed load, are giv en b y V ∝ N T / ( T + 2∆ + 2 δ ) ; R coil ∝ N 2 / ∆ ; P E ∝ ∆ T 2 / ( T + 2∆ + 2 δ ) 2 (4) with N coil turns. F or a given magnet size and hence T , P E is maximized with the smallest p ermissible δ , and ∆ = T / 2 + δ . A harv ester so optimized pro duces a maxim um induced coil v oltage in sin usoidal steady state giv en b y F araday’s La w according to V = dφ B /dt = B L 2 ω X = Gω X . (5) 2D-magnetic simulation computes the flux distribution and output voltage as describ ed in [3]; a magnetization of 1.3 T is chosen for the p ermanent magnets. The magnetic flux distribution of B x and B y is shown for zero stroke in Figure 2(c). T ogether with the velocity u ( t ), the distribution is used to compute the time-dep endent voltage across eac h coil turn according to V T urn ( t ) = ω L 3 ( A ( x 1 ( t )) − A ( x 2 ( t )) = u ( t ) L 3 ( B y ( x 1 ( t )) − B y ( x 2 ( t )) = u ( t ) G ( t ) . (6) Finally , an optimized coil configuration maximizes the mechanical-to-electrical transduction co efficien t G while minimizing the coil resistance R Coil . The total n um b er of lay ers N Lay ers of 50- µ m-diameter copp er-wire coils within T , and the num b er of turns N T urns in each such la yer, are determined based on this optimization. While thick coils reduce R Coil , they also result in fewer N Lay ers within a giv en T and hence a low er G . The electrical optimization considers this trade-off using the metric G 2 /R Coil as the optimization goal to maximize p ow er output. 3. F abrication and P ack aging Silicon-spring susp ensions are fabricated using a single deep-reactive-ion etc h through a 525- µ m-thic k w afer, with the mask halo ed [3]-[5] using 40- µ m-wide trenches to reduce etc h loading, resulting in essentially vertically-etc hed side walls as shown in Figure 3. Additionally , the mask is biased to accommo date a 5- µ m blo w-out per side w all. This fabrication process allo ws a minim um feature size of 25 µ m, smaller than the minimum spring width of 30 µ m used in the susp ension. SEM images in Figure 3 sho w the tap ering of the b eams along their length, and v ertical smo oth surfaces after etching that prev ent damping. The magnets are glued inside the Si-wrapp er linked to the susp ension using a pick-and-place pro cess with a 3D-printed platform. The spring-mass system is housed within another plastic assembly sho wn in Figure 1(c) along with parts that hold the t wo coils that are wound from 44 A W G wire on a Mandrell using a lathe. Each coil has 400 turns resulting in an individual R Coil = 123 Ω. The full assembly with the plan- and side-views is sho wn in Figure 1. (a) ( c) (b) (d ) 130.4 µ m 121.3 µ m 92.12 µ m 81.18 µ m 89. 2 o 525 µ m 920 µ m (a ) (c) (b ) (d) 130. 4 µ m 121. 3 µ m 92. 12 µ m 81. 18 µ m 89.2 o 525 µ m 920 µ m Figure 3. SEM images. (a) T ap ered spring profile sho wing the spring width v ariation. (b) Angled view of a join t. (c) Side view of an inner susp ension wall sho wing the etch profile. (d) An image of the anchor with the fillet profile. !" # $ % & !' # ( )** & ! + ,- ! + . - /01 - 2 34 - 5 6 7 8 9: + ;3! 3 < 5 3 =)> ?@ < 5 A( B C& . < < # $ % & 3 < . < + , < Du f f ing ' M o d el' f o r' Sp rin g - Ha rd en in g '' (b) (c) ( )** + ( @ # ( B ! < X Figure 4. (a) Measured open-circuit v oltage compared against simulations for differen t ω and g . (b) Harv ester dynamic mo del with the Duffing spring hardening. (c) Harv ester equiv alent circuit mo del with extracted mechanical and electromagnetic parameters. 4. Exp erimen tal P erformance Harv ester parameters are extracted from the measured op en-circuit voltage V OC = Gω X as a function of ω and g ; see Figure 4(a). V arious optimizations in volv ed in harvester design result in the high V OC = 1 . 75 V. Figure 4(a) sho ws that the susp ension springs harden at higher g , exhibiting tw o voltage branches together with a slight increase in ω Res = 2 π f Res with g . The Duffing dynamics [6] used to fit the data and extract X are shown in Figure 4(b) while the harv ester equiv alen t circuit model and its parameters are listed in Figure 4(c). The parameters are extracted from the t wo low er- g data and the mo del fits w ell against the data for g = 0 . 095. The measured loaded output pow er P Out , output v oltage V Load , resonance frequency f Res = ω Res / 2 π , and strok e X are plotted against g for different loads R Load . The measuremen ts, all p erformed at resonance, are compared against mo del sim ulations in Figure 5 showing a goo d matc h. The maxim um P Out of 2.2 mW is obtained with the matched load of R Load = R Coil = 245 Ω at 1.1 g , the highest rep orted v alue to date for Si-based MEMS harvesters, at least at sub-kHz frequencies. The device is curren tly strok e-limited with the side-bar hitting the external frame. If R Load > R Coil , reduced electrical damping causes the strok e to reach its maxim um of X = S/ 2 at a lo wer g with a higher V Load . The opposite holds for R Load < R Coil with low er V Load at X = S/ 2 at higher g . The harvester has a volume of 1.79 cm 3 whic h results in p erformance metrics of: PD = 1.23 mW/cm 3 , NPD = 1.02 mWcm − 3 g − 2 , and PD /g /f Res = 15 µ Wcm − 3 g − 1 s − 1 [7]. The PD is highest among rep orted EM harvesters [2], and the NPD is highest among MEMS harvesters (T able 3 of [2]). The NPD ranks second against non-Si, non-MEMS harv esters (behind [4] in T able I of [2]). A T ungsten wrapp er is added around the magnet/pro of-mass to increase the mass by 2.7 fold, reducing the acceleration to ac hieve X = 2 . 07 mm as shown in Figure 6. The measured P Out and PD /g /f Res compared against scaling-la w sim ulations sho w lo wer PD = 212 µ W/cm 3 , 0 0.5 1 1.5 2 g 0 0.5 1 1.5 2 2.5 x stroke (mm) 0 0.5 1 1.5 2 g 76.2 76.3 76.4 76.5 76.6 f res (Hz) 0 0.5 1 1.5 2 g 0 500 1000 1500 2000 2500 P load ( W) 0 0.5 1 1.5 2 g 0 0.5 1 1.5 2 V load (V) Symbols - Data Lines - Sim u la t io n s 50 W 100 W 150 W 250 W 430 W 500 W 1. 3 K W 2 K W x ma x x ma x - lim it x ma x - limit (a) (b) ( c) (d ) Re s o n a n c e . f r e q u e n c y . s h i f t due . t o . s pr i ng . ha r de ni ng 0 0.5 1 1.5 2 g 0 0.5 1 1.5 2 2.5 x stroke (mm) 0 0.5 1 1.5 2 g 76.2 76.3 76.4 76.5 76.6 f res (Hz) 0 0.5 1 1.5 2 g 0 500 1000 1500 2000 2500 P load ( W) 0 0.5 1 1.5 2 g 0 0.5 1 1.5 2 V load (V) S ym b o l s - Da t a L i n e s - Si m u l a t i o n s 50 W 100 W 150 W 250 W 430 W 500 W 1. 3 K W 2 K W x ma x x ma x - lim it x ma x - lim it (a ) (b ) ( c) (d ) Res o n ance . fre qu en cy.s hi ft due. to. spring . ha rde ning g g g g (c ) (d) Limit% of % X=% 2% m m Limit% of % X=% 2% m m x ( mm) % Limit% of % X =%2%mm Figure 5. Measured and sim ulated (a) P Out , (b) V Load , (c) f Res and (d) x Max as functions of g for different R Load at resonance. 0 0.5 1 1.5 g 0 10 20 30 PD/g ( W/(cm 3 g rad/s) 0 0.5 1 1.5 g 0 1000 2000 3000 P load ( W) m = l m 0 l =2.7 f res = ! l " # f res ,0 P load = ! l P load,0 a max = ! l l " a max ,0 (a) (b) ( c) Op t i m i z e d dev i c e c ont our wi t h P out , 0 Op t i m i z e d dev i c e c ont our wi t h P out , 0 Go l d e n dev i c e Go l d e n dev i c e St r a i n boundar y St r a i n boundar y (d ) St r a i n l i m i t : $ % & '( ) * + '& ,- * + '& . / 0 1 234 Ma s s - di m ens i on l i m i t : 5 67 8 9 : ; < = - * + '& . > % & '( . . " Et c h l i m i t : ? @: 7 6 A ,B # CD 12.5 mm 9.5 mm 0.42 mm 100 µ m cleara nce NPD= l 2 NPD 0 PD/ w a = l PD 0 / w 0 a 0 7. 37 m m 16. 36 m m 18. 67 m m 7. 29 m m 13. 72m m 1. 08 m m X ma x =0 . 8 8 m m 1 m m Hz)) 0 0.5 1 1.5 g 0 10 20 30 PD/g ( W/(cm 3 grad/s) 0 0.5 1 1.5 g 0 1000 2000 3000 P load ( W) m = l m 0 l =2 . 7 f re s = ! l " # f re s ,0 P lo a d = ! l P lo a d , 0 a ma x = ! l l " a ma x , 0 (a ) (b ) ( c) Op t i m i z e d dev i c e c ont our wi t h P out , 0 Op t i m i z e d dev i c e c ont our wi t h P out , 0 Go l d e n dev i c e Go l d e n dev i c e St r a i n boundar y St r a i n boundar y (d) St r a i n l i m i t : $ % & '( ) * + '& ,- * + '& . / 0 1 234 Ma s s - di m ens i on l i m i t : 5 67 8 9 : ; < = - * + '& . > % & '( . . " Et c h l i m i t : ? @: 7 6 A ,B # CD 12. 5 m m 9. 5 m m 0. 42 m m 100 µ m cl e a r a n ce NP D= l 2 NP D 0 PD / w a = l PD 0 / w 0 a 0 7.37 mm 16.36 mm 18.67 mm 7.29 mm 13.72mm 1.08 mm X ma x =0 . 8 8 m m 1 mm Hz)) X= # 0.88 #m m 0 0.5 1 1.5 g 0 10 20 30 PD/g ( W/(cm 3 grad/s) 0 0.5 1 1.5 g 0 1000 2000 3000 P load ( W) m = l m 0 l =2 . 7 f re s = ! l " # f re s ,0 P lo a d = ! l P lo a d , 0 a ma x = ! l l " a ma x , 0 (a ) (b ) ( c) Opt im ized devic e contour with P out,0 Opt im ized devic e contour with P out,0 Gol de n devic e Gol de n devic e Str ain boundary Str ain boundary (d ) St r a i n l i m i t : $ % & '( ) * + '& ,- * + '& . / 0 1 234 Ma s s - di m ens i on l i m i t : 5 67 8 9 : ; < = - * + '& . > % & '( . . " Et c h l i m i t : ? @: 7 6 A ,B # CD 12. 5 m m 9. 5 m m 0. 42 m m 100 µ m cl e a r a n ce NP D= l 2 NP D 0 PD / w a = l PD 0 / w 0 a 0 7. 37 m m 16. 36 m m 18. 67 m m 7. 29 m m 13. 72m m 1. 08 m m X ma x =0 . 8 8 m m 1 m m Hz)) 6 4 2 0 P out ( mW ) 6 4 2 0 PD## ( mW /cm 3 ) Device#with#W - mass # (si m) Device#with# W- mas s# (d a t a ) Ref. # de v i ce # (si m) Ref. # de v i ce # (da t a ) (c )# Str ain #li m it: Mass - dimens ion#l i m it : Et c h # limit : !" # $%&' () $%&' * + ,- ./0 ) '&1 2%3 + ) $%&' * 4 " * 5 6 # $%&' 7 (8 9 :; Figure 6. (a) Pro of mass augmen ted with a T ungsten magnet wrapper. (b) Resulting low er- g op eration yielding increased NPD and PD /g /f ; also scaling rules. (c) Mec hanical optimization to low er the o verall dimensions by making magnet and spring dimensions equal allo ws higher PD for the same P Out . (d) Cross-section of the optimized golden device. but higher NPD = 8951 µ Wcm − 3 g − 2 and PD /g /f Res = 29 µ Wcm − 3 g − 1 s − 1 , the highest among EM-harv esters reported in [2] if sw ept v olume is considered. Shortening the spring and X to reduce the harv ester fo otprint, and increasing magnet width in the un used L 2 direction, yield a “golden-device” pro jected to pro vide similar P Out = 2 . 2 mW at reduced X = 0 . 88 mm and a v olume of 0.59 cm 3 , but at the same f Res and operating g as sho wn. This harv ester has impro v ed PD= 3729 µ W/cm 3 , NPD = 3082 µ Wcm − 3 g − 2 , and PD/ g /f Res = 44 . 5 µ Wcm − 3 g − 1 s − 1 . 5. Summary & Conclusions This paper presents a compact MEMS electromagnetic vibration energy harv ester designed for near 50-Hz operation. Optimization, and design guidelines are pro vided together with fabrication details. The harvester has a volume of 1.79 cm 3 , and demonstrates an op en-circuit v oltage of 1.75 V and a matched-load p ow er of 2.2 mW at 1.1 g near 76 Hz. This demonstrates that small vibration energy harv esters can provide the p ow er required b y autonomous machine health monitoring for industrial IoT and other remote sensing applications. Ac knowledgmen ts The authors wish to thank Analog Devices Inc. for collab oration and pro ject supp ort. References [1] D. P . Arnold, in IEEE T ransactions on Magnetics, vol. 43, no. 11, pp. 3940-3951, No v . 2007. [2] Y. T an et. al., in Journal of Micro electromechanical Systems, vol. 26, no. 1, pp. 1-16, F eb. 2017. [3] A. Shin et al., in Po wer MEMS 2017, Nov. 2017. [4] S. P . Beeby et al., in J. Micromech. Microeng., vol. 17, no. 7, pp. 1257, 2007. [5] R. Gho dssi et. al., MEMS materials and pro cesses handb o ok, Springer, 2011. [6] F. T a jaddo dianfar et. al., in Microsystem T ec hnologies, vol. 23, pp. 1913-1926, Jun. 2017. [7] P . D. 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