durusmail: mems-talk: Ansys for MEMS electrostatic calculations
Ansys for MEMS electrostatic calculations
2013-10-31
2013-11-04
2013-11-05
Youmin Wang (2 parts)
2013-11-05
Youmin Wang (2 parts)
2013-11-11
Daniel Shaw (2 parts)
2013-11-13
Youmin Wang (2 parts)
2013-11-19
Daniel Shaw (2 parts)
2014-01-16
Daniel Shaw (2 parts)
Ansys for MEMS electrostatic calculations
Youmin Wang
2013-11-05
Hi Daniel,


Thank you for you kind help!

After investigations done so far, I recognized that Trans126 element might
not be a good choice to be used in my tilting mirror applications. Though
the Ansys help manual indicated something as below:

[image: Inline image 1]

As you can see, the above figure is using Trans126 elements, though I think
it is a simplified model. I heard that Trans126 is good for attraction,
while difficult to perform the leaving electrodes. Beyond that. I think my
micromirror has more complicated geometry than the parallel plates, I don't
know this parallel-plate simplification would be a good choice for it.

As for now, I am considering to proceed with the Solid226 option, which is
exactly what you have suggested. I am trying to mesh the air gap between
the movable mirror and the fixed electrodes using Solid226 elements, while
leaving the other parts using Solid45. The electroelastic and structural
elements are joined through nodal connectivity at the interface between
them. I am still working on this direction right now, when the geometry
becomes more complicated, seems it get more difficult to converge, I have
many small parts to trim, such as the meshing and boundary conditions...

Another option seems to be multi-field solver, which up-to-now I have not
acquired too much reference materials and did not dive in too deep yet.

Again, thank you very much for your help and suggestions! I am really
grateful to you. If you could provide more insight, that would be really
great.


On Fri, Nov 1, 2013 at 11:22 AM, Daniel Shaw  wrote:

> Hi Youmin:
>
>
>
> To perform an electrostatic-structural simulation using Mechanical APDL
> (aka “classic ANSYS”), you can use either the 22x coupled-field elements,
> the multi-field solver (MFS), or the electro-mechanical transducer element
> (TRANS126).  You could also use the reduced order electrostatic-structural
> element (ROM144).  The 22x elements and the MFS use a sequential coupling
> approach.  TRANS126 and ROM144 use a matrix coupling approach.
>
>
>
> If possible, I recommend using TRANS126.  It is the simplest and most
> robust approach.  With the 22x elements and the MFS, you might have meshing
> issues at pull-down.  ROM144 can be complicated to implement.  If fringing
> effects are significant, TRANS126 might be difficult to accurately
> implement.  In that case, you need to use one of the other methods.
>
>
>
> Regards,
>
>
>
> Daniel Shaw
>
> ANSYS, Inc.
>
>
>
> On Wed, Oct 30, 2013 at 9:50 PM, Youmin Wang  >wrote:
>
> > Dear Friends,
> >
> > I am starting to use Ansys for the modeling of MEMS micromirror
> > static/dynamic analysis. There have been many previous work in this
> field,
> > but according to my observations, 3 key technologies were basically used
> > for MEMS electromechanical coupling, which are 1. using Coupled Field
> > Element (SOLID226); 2. Multi-field solver; and 3. Trans126.
> >
> > Seems for method #1 I have to use air to enclose the whole device if
> fringe
> > electric field needs to be considered, but in "Gyimesi, Miklos, Ilya
> > Avdeev, and Dale Ostergaard. "Finite-element simulation of
> > micro-electromechanical systems (MEMS) by strongly coupled
> > electromechanical transducers." Magnetics, IEEE Transactions on 40.2
> > (2004): 557-560." it says in large deformation bending electrode problem,
> > Trans126 might not be suitable.
> >
> > Do you guys have any previous experience on this selection issue?
> Besides,
> > seems Trans126 also requires the pre-stress definition, which I am still
> > struggling to find out where to apply...
> > _______________________________________________
> > Hosted by the MEMS and Nanotechnology Exchange, the country's leading
> > provider of MEMS and Nanotechnology design and fabrication services.
> > Visit us at http://www.mems-exchange.org
> >
> > Want to advertise to this community?  See http://www.memsnet.org
> >
> > To unsubscribe:
> > http://mail.mems-exchange.org/mailman/listinfo/mems-talk
> >
> _______________________________________________
> Hosted by the MEMS and Nanotechnology Exchange, the country's leading
> provider of MEMS and Nanotechnology design and fabrication services.
> Visit us at http://www.mems-exchange.org
>
> Want to advertise to this community?  See http://www.memsnet.org
>
> To unsubscribe:
> http://mail.mems-exchange.org/mailman/listinfo/mems-talk
>
‰PNG


IHDR˜$‹ÑAZ IDATxíÝ
|ÕÝÿñ!@ÂÅ@@
€‚¶HPTPP±ˆˆŠ­}¼Ñj[ô±ô¥Å՗>­—þՊ­¶ZQÛ¢¢•kED1«&Q¹   ˆˆ @@.
Â~'κ›ìnv73»³»Ÿy½x²;;sæÌ{¦O¿=3çœFG¬EX@@pH
ár(@@#@ÀäF@@pT€€é('
!€ €0¹@@
 `:ÊIa € €Lî@@G˜ŽrR € €“{@@ÀQ¦£œ† €
@Àä
@@pT€€é('
!€ €0¹@@
 `:ÊIa € €Lî@@G˜ŽrR € €“{@@ÀQ¦£œ† €
@Àä
@@pT€€é('
!€ €0¹@@
 `:ÊIa € €Lî@@G˜ŽrR € €“{@@ÀQ¦£œ† €
@Àä
@@pT€€é('
!€ €0¹@@
 `:ÊIa € €Lî@@G˜ŽrR € €“{@@ÀQ¦£œ† €
@Àä
@@pT€€é('
!€ ›ÀW[ÊåÅÉäkfJYÙ±Â^xD Ó#õ  €¤@yù>yãõ2ëßZY³j—ïü‹Wnüüξï|@ Ù
±–d«4õE@ Y4T–|ô¹,˜÷‰¬\±ÕwcÆõ”Ýä÷/1ëžyn’de5õýÎ’I€ÌdºZÔ@ )B
ʧu‹/9Yútñ
Éq—íÇyOJK6É©º'åùRi˜Ü €¸
.TŽ<¿·ô;^rs[Ô9òà!y&`½»€YG‡É"@ÀL–+E=@#àE¦¯
uBHÊʃæq¶¶8j(´}ü
®¥ÒÞ.ØßË'ü@ؼ«9ôÌÞÁ6a
ž `zúòP9@/
„
•Úò¨á0ÔãïHÏE÷×E;0#Uc;/        0½t5¨
 €€gÂ
Êaçô}wRo;±è»™ÃGt•E
7ŠŽéT¹Nԍ2ˆD€€‰Û €¤¥@{R€€éÉËB¥@T T¨
pZy~oë½ÊîIÿø;Ò+Íԑ‘J±˜^¸
Ô@À'P_¨ÔÇÅÚ¢—N‹š|óÍ^sÊL
™NW>yϕ€™¼×Žš#€)#PYyPŠÞ]Wçñ·ÝR™®¡2Ø+Gçf™–Ýt
Ù)s³§É‰0ÓäBsš €€×4T––l²‚å™=kµ¯z„ʺ³‰ïÆàCR        0“êrQY@ ¹B
ʼ^GË
åËiƒz¤åãï`-•„Êä¾×Ó½öÌt¿8@Àep¡rØ9=DgªÑÁÄÓi±Mýg•,Z¸Ñwê„J
’\€€™äê#€^°TíÇßÚR™î¡²¶   ¡Ò‹w0uj¨³¡‚ì
à(+ûBŠWnùs×Èö¯+ÍzBeÝ÷Lm“açä§Ý+¾›
)-@ÀLéËËÉ!€î

•mÛeÉäOMëÇßµ[*íP™Ž¯¸r¯     0½vE¨ ¡BåÄ«
¤ÿ€n’Ÿß9        ι*òJ€s–””ÌÔ¸Žœ
ມ2˜PèÁ7ü˜þ|FøjK¹,_¶Ffý³Ô÷N¥>þ¦¥2pìN
Ü6|A@˜Ü €v¨Ô)  ׬Úe~#T†î¨Ã;•·_0Ln@
*•e̸žR8°›ô-è"YYMÓF*Ôãï;4•sÇõKËÎKisñ9QG˜Ž0R
|„ʺ×콕ëêL]©¿Ïè×Zz<;CzüøZÉUXwGÖ €@€3€ƒ/ €@j
”—ðÏý×÷ø[Ï8][*õ܃u^ªýNåuëdÛ3_éæ, 3$6A’YÀ•
æ}"+Wlõ
¡2p@xû=Ó#û¦Ýԕ¾›‚8$@Àt’b@/       „
•ö´„
»§Õ;•zm‚µTÚ¡2
ÇîôÒýJ]RO€€™zה3B4¨/Tô;>í¦%$T¦é8í„
0~    ¨ »€ÝÛùå?
xüm·T*kæC§¥2ö{Œ=ˆE€€‹û €  °Ceí¹® •Áß©äñwoV¶Ì´½ôœ8$“@¨Pi÷v
vN>¿­
JKe2ÝÕÔ5•˜©|u97HjúBe:Î Ã;•I}KSù4 `¦ÑÅæT@ 9B
ö=ìœ
i9ƒ
¡29î[j‰€¿Ó_ƒÏ €@‚‚
(ûñw:¶T›eˆÇß   º99,10c@c@À       `¡ÒQé8Ø7¡Ò‰»Š2ð†ÓׁZ €@š„
•éØÛ9X¨Ô[!gJ“ÿ(pš).@ÀLñ
Ìé!€@╁׀PèÁ7RQ€€™ŠW•sB„

QöãoZ*wù®-•>
> R̔ºœœ
$R X¨ÔúL¼ª@•„ÊDޛ
x
0ã-Îñ@ ¥B
Êtm™Ã#¥noNƃS§þFrrrdʔ_IvvvЮY³Fžzê¯Ò§Oo™4iRÐmÜ^IÀt[˜ò@
åQ—@¾!à¦@—.åïŸ)C‡•Áƒ=Ô믿.K–¼%Ɲ
ô÷x¬$`ÆC™c €@Ò
”—ï“’>—ó>‘•+¶ú·–ʵ²f¿}7pY`ðàÁ&`>ýôÓAfEE
ù]«Ñ¿—kºxfh~A4 TÞê±âµòÚ+e„Ê@¾!7“O>Y

úJII©lÞ¼Y:uêpìÕ«W›ï“&])­[·ø-ž_˜ñÔæX àyP¡rÀi
däù½¥ ßñ’›ÛÂóçáTCy¤kË­S®”ƒ@Cƍ»ÄÌŋ×yÇò±ÇþdŠÖ–ÎD.ÌDêslð„@¨E¨
|
Àö(
Ø]²²šzâÚQ       ÒQÀ~ô={ö+sçΝ&xj
§¶t&r!`&RŸc#€@Â*+JiÉ&YôŸU²háF_=ìEKe
Iºzøn> àA}ô}æ™CMGžåËßñ½‹Y\\lj{Þyç%¼Ȫ_*€ñ°CeÑ»dö¬š÷”ôØé¢h¹×Çqp^`üøË
MÀüðÃ|sÖ¬́4|&z!`&ú
p|pU T¨Ìëu´
;§‡

’'ÇvÌuµ^*œP饫A]ˆ]@wìx¬é1>~üxÙ¾}»y<®á2Xç

³¬ìciÙ²
tíÚUòòòb?x{0#@bH.Beàõ"Tzð
T3æ"yì±ÇMKæÞ½{Ìii˦ÿ¢ÃÝyç]fÿõDï¼óŽƒµûoËgf,j샞(+ûB–,^ðø›–Êà
uÒí
SOÞ°T

Œ5ÊÌùóç›ÖKmѬݹ硇
6áR;þØïf>ûì³fÏû￯µ¾;3¸
k@ I4T¯Ü ó箑í_WšZ* •IrûRM$ ÂGþ‘¼úê¿M9Ç
(O[/íß4HڏÎ
8UƎ
gB¦njÊɀ¢üBÀŒŒÍ@ ñÁBeÛvY2ñª9chO9áÄö‰¯dœj ¯½»®Î
CéÚq)Nì
Ï蔑vˆ
=zt@½¾øâ
ó][/íp©+tpvmíܲå+!`ñÒM \¨ì? ›äçwN’Pï˜*ÓæàDð
è|äEE+|ßý?tîÜYž}öiÛ¶­ÿj3†ËP
‚6Žñ
-˜1±¸/°þ³m²ô­Õ¿í–JBe¿¾pù„¤Ý
Cîß}
äÐGßµ{‹koò©ScN®°°Ðµ“$`ºFKÁ
‹ÀW[Êeù²5òÆëk}ó]*ÇíL×wLc¹ŸØjt–Ÿ3žð=NŸ:õ×rñÅc\ã!`ºFKÁ
©@°P©ûê|×gžÝ‹Çߖ¡2Ò»‰í@ ¶€Îöó‡?üÁ¼s©Åÿç~Z§e³ö>
ýNÀl¨ û#€@LáBeáÀnÒ· KÚÌw
êJBeL·;!€€Ÿ€†Ë›nºÙ¬™>ý.9÷Üsý~uï#Ó=[JFZ„ÊïA•ß[ð   ÜÐÇâv¸|é¥Y¦÷¸;Gª[*³®
k@ÀAP³ÈèãoZ*k i©tð†£(ð      lÚ´É|®™RòYßzÿ“&Mt%x0ý•ùŒŽ„
•§žÚ^F\p’œ68Çßi:º#7
 €@Dë×o0ÛéDöX™µw¼ä’±µW9ò€é#
 €@¨PiÍ(‡ÈÃw-‘SÿÝJ
óŸ&p`Ý:©\õ©
Z»Nª¿Ý-•s^ómV9çß²Éú§Kf~_ÉìÚUšôì%M»u“fyy’™›ëÛ6ÒÚKÜ͞âáêAÀ
§Ão V ¾Pé?ßµ†.‘%²tÑ:¹èR÷Æ^
[a—´ƒöo%¾#ñøÛGÁÒR ¢´T*ŠŠdÿ«³¥zëÖ;H¬´¾
,~O*ËJ¨nÛbìXi1xHLa³ö1ÜþNÀt[˜òH1P­svK¥¨ô?õ¬¬¦2ò’ÇF IB
Jm‹f™þO0ó]k õdnÅ
*Óu0ø$¹
©&qØgµV–ÿîn_keó+®”ÇK¶,£Y2²²M€Ô™cJÿЪÖõŸÍÜk®­7¬Fs\§¶%`:%I9¤˜@¸P9ìœ
2xHž
e+dŸ‚šùÂ?,ޜt“P™b78§ƒ€Ã‡¶l‘
ø½iiÔ¢µµò(ë‘v,ïN«šÎVgŸmþiˆÝ=ãq2¿²‚f«›o‘œ‹F‹nã•
€é•+A=h€À'¥ŸË  =ŽmpÏl7B¥ÿiécò!#Ž—e
?—]åûäèÜþ?{î3¡Òs—„
!àI=Ö#ìò©·˜ºÅ£U±
5‡¸þ³[K÷<ð{9°²HÚüï-žiÍ$`zòV¥RD'0wö²yãbùÍïF[­Š­£ÛÙÚÚRþSºçåHÏ
­å¸ãŽ²‚`sSfÉ×KùŽ¶
³
ƒO0³ì£Ïeș½£®«Û;ØþïTòøÛmuÊG yv>ù¤ì}âqóŽeΔ›M
c¼ÎFCfö¬eçã3dÿó3eÛÚ5’ûÛÛMøŒW
B
‡€J†õ$™ÀúËåÚ1OË
ӆʈQ?¬·öÁ‚”¾S9hPÙcµ.Îÿ秲¥ì› åä´i&#Æö–qGÝjšßïxSæ¢yŸz&`³
T½ô¬DïôÈ¯o½Õ<×
ÞÇÜsoBZõ±xÛ)SdO¿~¦uÇ
?yôO   ™Lþ£‚@J       4’G§¿%%ÿýB®¹q¸ÕòØ2àìê
R•û*­±*ÿ#»w
#IuF¦õ¯ñ÷e
±zB
9lý~Pþõçä?³?•»ÿx±t;±Ã÷ÛÔóI‹÷ØA>zwkB“×g‘Ÿ_ó¾h=§ÃÏi"Pµc‡9ӌæ5­ùirڜfÿpÙôô3¤Ý
½÷&üýG}?3ó¯Oˎ[#^™Ì7«HFƒM²%óðY:w½àž‘[ï%Ս2¤xå©ï‘oqÑZ¹ë5ƒþ
nÜTª7©KÐH¤Z›ß2’]ßTÊ/®x^îr¬ôî[Ó2Yw§ºk†Ÿ’
˜ñ~LN¨¬{-X™@Õ75­ùM»t‰l¶JY/†K[{ª·â/²íºk
2       ˜öUá/)  ­Ž‡2³¬yÈ´BN½ú%©ÊÈ°ÖeJ›vY2ñªé? ›ÔnûjËÎïÂ¥µ“fV(õkµ
êÒÈ
™M­VÎ
ɬ: ÷N#>÷ã:-¦AwµVڏɋ–¯wý1ùW֘›
”Ö°CՕõ €€¿À®™Ï™Çâ^i¹ô¯›~Öñ5ýCf†ÕªíIµËŒå;35öAÀãÚúxØz´Ý¤ªR2««å¸Meºõ(;T
{o}ŜQUfÓÂå÷'Øz„.˜0û—GÉ-·_ôýa>ُɵ7ùÏo>õ{œaŠ6?i¨\nµùÆëkeͪ]f
ïTÖ§Æï PŸ€ö×=^
—vý5djg}T®Ì;ü}¦cÃ%ÙǨï/³>!~GÀÃvZùöæ:µÔÖEóȼê lÛ´7d }4¾ñÓ]æ]Kë”~Åa+Ì6®>d
Ë_yõΐ!¶v)'÷ïd
“\ò
üpÀ‰µŽú»má*µ1ãzʙg÷ªÓjõØÒZ@ǹԡˆtF

ÈKcN»0ÚüêŽ;e÷]wÊöéwK‡
¶™k똮ÑR0î
RYUU’ôpÖ£ìLë‘wu¦Õšy h âë̞c]ôM}T¾âíUrñeƒ"*f 5Pû3Kñ»ëc˜Á,ôà*
v“¾]
o
èäØRN@Q×E[ë›æÑ+'¯3
xÿ}3 ûnk@vý
¯
€/iŽƒ@Ê­aƒÞx½Ì<ò]k=òm¦=¼
ñ©7æ–ÈòC
A{‚ë¤
s–/Ú`íg•Wï{—!‹7ãõÿ™|¶úëÐÕúEç"ïf
‹¤s“ÿøÚ¡ABe-
H¾"€€ëÎt.p3í£Õ2˜LKë_üR¶¿'{ž˜!-‰Û£rf2Ý%Ô5­4T–Xƒ‘/˜÷‰¬\±Õwîç_x¢,›³^úh/7üâ
³~ɂ2ßï¡>ët鵧˜žàC
* ìúF¦Ãö^¿åö°üxÆðî²aU±Ô÷˜œPÀƈ£@Uy¹
gúhüèŸü$ŽGvæP:U¥¯÷¿}é%i}õÕÎ\O)Ìz€øx
„
•Në _r²ï‘ïží/Å<Ž¤
ËÒ©El#kœÌh–pÉ •ÑH²-¸% ¡¬zëVɱÞgtj^q·êª\
#s5¼vPjqæ™Ò¬{÷P›:¶ž€é%!›@¸P9òüÞR`Í|“[kÎn{
É%Öcó‹.þq ÆÕU±U¼Ö^ŽT‹ÎðÍb?&/zk“\÷
Be4zl«›úÄbÛåÇõx]ŠKâz<( c^ÚÓ@¶><ðÇ$û–sýdÓ«|ߒ%Ì$»vTˆ*+JÑ»ëê<þ֖ÊP¡Ò¿
ðþõ}¾)K­‹)`jYÖðE«›b3¾ûk¾ÄðYïƒê¿~‹zï¼ÞídáËkä§WüM>ÿbŸo:êø(ø€
سh‘9r«ë®÷|¯ñúˆ´WùîïZ1;ÖõÖXZ0ë»"üŽ€C*KK6YÁrƒÌžµÚWj¤¡Ò·ƒõ!+«©Œ¼$ÏtÙjùÝrÄ
ÄÞØŒ]—S†t”–m±Âf•ÕY'¶ÿ—ñ]+èÀÓ5øÖ¿ø·Tn°:-e[×¿Þ¼ß×i‰Þßõ²E
@ªµôÅ»e6P“o¶À>ëñ¸.ÉÞziŸO«‰“Ì»˜{.”ÜË/·W»ò7¶ÿ6q¥*Š@ê        „
•yVïéË'ü èãïHú<ÁÌ7–Fº‹ÕÊXm†+Ò¿]O:Znšv¾Ù÷ƒeÏKãÃc
˜5U
ê{rWS^°ÿêUm©|÷?¤àÔ¾NKÁög
 OŠÒR©*+•–×Mv¥õò³Ï>‹ètŽ;î8«Q!+¢mëۨŠÓD›$*. `ևÅïxM \¨
vNlÿx¬5DOC
œ<÷˜,ycÎZ9©_›z‹ÓËL+DêrÁø“ä'×ó

tÆ'˜Òõw2š%ÓÈ]äˆ\uÓÀ:SE†
•ÃGt•áçöòuZºúZçgó‰æ
ب-PQTdVe»4,ÑW\YûA¿?ÿüL9ñĆOF¡
ëàð:ÔÒ~«L
8ÞÍñÚÂX`u ºåŽÕieÔ
Îm)¿r¼Ürõ
&df
9lµd6³Æ¶l¼\ëwmÕòsÛeÉϧŽhP§¥ a%I, ?juJb†¤­º¶îéãqmísk5j”[E‡-7»_ÍÈ
:ϸ8³3ìeàGê

•m­5ùÆS
{ü]÷¨Á×t;±½™
G;Ê.
yn˜6TFŒúaà&µ¾
Û±µ     ™þß)±voZ½ß
ž^muü±ƒ¦ö×=ú§.y'·•Ì–VÀ¼v¶¯´p-•¾ø€@

”[sۏ?‡
,½{Ÿ$íÛ·—“N:Iœ|Ÿ.
        ~j•«V™:4ë×/áuqºú˜¼éég˜é#ÅÛÓ­
€é–,妔@¨P9ñªé? ›äçwNØùÚ³ád4nlê¬#O·;DT?
™÷<|
­•Ù/¼g‚¦vþ©½dç4•ÝûªåÃO¾µ~úV•µ
øžÎ›7oöþ²eËEÿù/}úXãÛô•îÖ`×ÚÊ©Á“Å[U_×L{Û´KoUÌ¡Ú4íÝÇL}y`Ý:×ÆÄ$`:t±(&õ¼
*ýµÏ<'_žy´XY3\G
ÿ}êû¬ïhê¿]å{¥ÌZéþ_/°vÑÇåGLkæŽ
‘ƒ;F4fg}ÇâwRM yóæríµWË'Ÿ|Z'\ê¹~üñ'æŸ}Þ÷Ýw¯œuÖYöWþz@àÐêïZ0ã0ãM"N·É
'˜ÃVíØAÀLÄà˜é'`Ï8럥¾w*õñ·Z*C]£­Y~Z
ÝDöì:$MªÊQ!:ò„Ú?ØzÿŽ:%oo–
k#bR[GµSÏ´;†Ê™Ãûەu¤½€¶Jú¿©ïcnÚ´IÖ¯_4tîßoý/6O
,~O2­AÉSu±[f«¾©i©uãÞ%Í[6‹*\ÚÃ+-úÏ*Y´p£ï’é;•Ã†çÉß
z[¾ÝYåS;ûhØÜøé.ù¤ôséÝ÷xß>|@Ð¥­Ò
ö IDATÖ Ý·Ý6M¶mÛ&Úñg«`Ö­«h»£‹Cń®¿¤³€=þe՗߿/ì´ÓiQÊó¬@ª
Jèëu®ä¶Yá›:²C˜ÜíPYߔ•Ï>õ¦.X-—MMorûx:F¦O4wöL
¿„¨¬¬4­–/¼ðO³ÅM7ýJF
-C‡Ö¼syÁ5³i
ØÕ     Ў/º4éÙ+GOC0SçZr&Aô±ïŠwÖÊk¯”ù
ëfÉÚRäÍ*
ÇÒêÈ   W°i¨PiÙ9Ìê(”k½Ëi/>Û*ÿúó¦COUãÀÿ7Qݨ±iÅ\:w½\2a«DÚCÝ.›¿¤‹€«¥ö
¿í¶[Í»™þSö왗.
Iwž-¿ÿÿ‰IWyT8ð¿98}ž)¾*³™õ·î`ë:6¦¶b.[ò)³ö
à»ç

O‹k
íVK{>éO?ýÔwü®]»ú>óT `¦ÒÕLãs  *íñ
v÷Í»ªL:Ýâ#N”Wg~,wO{EÞZ²ÙwªvKe¸Pio¼pÎûæ
K}×R[+ƒ-‡­€Ù¸ÑAÓÊyáŧFõÞg°òX‡@*
\vÙe§·î»G°º²sçč¡P)¾ø·ic>Z[ó¨Ü÷¢ `FÅÅÆ^¨/Tô;>౯—êîd]ü[*çÌZ-
ÙVGœ•o})фJ»>:îå£Óß²¾6’C¦õÒþ¥î_}7Sç"íå÷dâÿÔ¼OVw+Ö à=¢¢ŽWJßµ|õÕWåÁ
6e×nµô?`II©ï+
||žù™›kêRýínÏÔÉéŠTWº?4Óé«Fy®
h˜*zw,˜÷‰ØCéèí–Êt
•³­Pi/*+¶WšùÄzäÒ¨[mÿòÈ"S”ŽyìѸ}
ý{ØjáÌ´‚¨¾«9nÂਏå_ŸHf}§òž{î5ƒ§û¿kìœ4ˆê@ëºhor!phó—æ°nvd"`&âÊr̨ü[èüᲆ
±vKå+ÿ*23û|õe¹õ~dûˆ­uzHí¸cyYÿŽÌؘ:•ä[‹Jëë¼þò؁䈦ÕÒ>³/¿¬ù/vý®s”³xS
su'òÌ«+jZ0ÝìÈDÀLäæØ!B
J
S^”/§
ê‘v¿ýÃuíPé9òG§ˆþÓw2#]ÔûÓ_7›WY¾#]´‡¹NO9sF‘
µfö‰æ˜‘
ƒíð¢@4­–þõ×Aן~¦™Ù§KŠÎsí¾Éú9#'ÇT]%gde'ëi„¬÷ÁÏ7šßš
ß5ä6
ý€ÙPAöwL \¨
vN‰¤ƒŠc•IpAï­\g½
°A"
•þՍ%äÍzn¹ìú¦²Î˜—þåÿlµbZÊuß²>7ó—ߎµ¤†@íVKs|„     Öÿ¸ÊŠøí™}"ށ
ã.Ðì‡?”Ê9¯É«£Ovßԛ2ÒîÀÔ¤S'×l   ˜®ÑRp¤
        S‘
#¶++ûBŠWnùs×øæA×RéÔ9
ó2’chg>ò™Çß&`FÆ6I+àßjÙ¾}{ë½ËéÒ7ÃGÒ^ +n·ìiK_<æΝ;¥¸¸Xtت¼¼<Ï$xQ•‹IF‡bwh
¾UÃÖ0æÇÞ1
$*LÅX]×v
æ`σ>bd_96̌ªVˤ:a*+Ízt7
‹KΨ
]Ù¾}»L›v‡LŸ~—ëóЖ-¢s­7¿âJWϋ€é*/
û
x!Lù×'QŸÃ9ô
ÐMòóã7.ž=æ¥Z49TÙ`’ÿë}fƒ)ÀK´Zzéjį.úÞ¥vô9øöR©*/wµ¥Ïÿ¬öîÝçÿՕϕ«V™r³
r¥|»P¦-Á_W¼¦\9Á
õ¢ƒ¾óZòß/äŒ
Nˆð,"ÛLÇÒÔ©+YHv9sæX-J÷˜Ó Õ2Ù¯fôõoaµ\jÀ¬øàiuöÙÑÃ
-ã0=å>ëÝR]š¹ü(ž€Ã
À.ἦÂ×؝_½î n¹ý"wNžRHb-Ö#Ä
xP–-[.¼k™Ä²UÏ>å)·ÊÐ@¯€év
¦>
×Мe
g7ß¿Tzfo@v¯øjK¹,_¶FÞx}­¬YµË¬´ß%Œ÷cßD^¯‡ÊDÚpl¼"Í\äÛ¶m“«¯¾¶AUwcæ
Uˆ#ЦAL{“k0kÒ±cDûE²Ñ‡~(ë×om±ÔP¹wï
³Û*ëñõË/Ïö­×ßÏ=÷ÜHŠŒh›=óæ™íZŒ‘•+¶úΐP)B¨ôÝ|@ ©hµLê˗°Êçþìç²Íê}]þàÒìqë=F—æ'w£yEi©ì~¦×3^½áõB0v»z
ãÀ¡Bå€Ó:ÈÈó{KA¿ã­ÿUß•u±ÁZ*õpé®]$¦h.ðæ›oÊo~s«©­–  ¿
IUfÝ»K«›o‘=ü^v>>CÚN™âJýnÁÔGã;ný©«†äx.Ìxj{äX„Êš
A¨ôÈ
I5pY Üú/ÙG
yTæΝgƵä]K—ÁS´øœ‹FKŦ5pŸ5
Ž“=±uþñڝϜ`Ü>ýn3-dŽõäx.Ìxj'ðX:kKiÉ&yùÅ
ÓRYsQh©LàÍÉ¡pQ@[-z菢ãYÒjé"t­Å¹ç^ÙvÝ5¦ÓOæ
ÿŒ{h‹†yç“OúUÇ|êµëFÀ¬-’BßíPYôî™=kµïÌ•5„Jß-ÁRR੧ž’?ÿùIÓjyß}÷ÒC<%¯r|OJ[Ïýí
í&`~c:Ðþ‰¿8:»Sg£áRǼÔùÔÛNêT±Q•CÀŒŠËû‡
•y½Ž–açô°þåóNe×éý;–"àžÀ€äË/·ÐCÜ=â´,Ù<ôO&djk¦×B¦
.3:t6ÿ{‹k
’ê»øŽXK}ñ»·ê
•ƒ‡äɱ
Sø
Þ©ôö}JípC`SÿSl—â7ŠOX™©z^     uáÀûŠŠLÈÔ §­šN¾“Kuu¦ž]3ŸóÍ֓èàK
f,WÑ#ûèÀßK¯
xüm·T*Ókf!Ü’THÿ–L
ˆý ÕË<÷òËrþÚ[\;ô
´†RÒÇâÚréäÜ鱜-˜±¨%pŸ`³É¤[¨Ô^ð+ÞY+¯½R–ÖƒÀ'ð6äÐxFÀnéóL

®HªµÌ:Ìã‰â¬['ú>fõÖ­            w{/–Ý=`ŽŸ5êBóÎ¥[ãtFNÀŒF+AÛ
•:ð÷yäɈ‘}Óâñw¨¡•è¨“ ›’Ã"à¦G.DšWCOo¿ÿ~3ۏR蘙:¬‘›AOƒíîçfúŽ©C%¢·x¨KOÀ
%“àõáBeÿÝ$?¿s‚kèþáC
J»|áÀÕÔýŠpH{ÝsæXs9ß%í_xÁÓCÓ¤ý
J0€k¢¾›Ùêºë¥Åà!’éà4¤µƒ¥¶Zæ^sm‰צç
ÌÚ"     ü¾þ³m²ô­Õ2îÙþu¥©IºMQX_¨L—™
xrh@t*ƃN“=‹ɞ'fXÿ£äNÙm•ÕüŠ+%Ûœ=»_AL­šúŽeÅȞgÿ.Ue¥¦v™ù}%çúÉ
ï\ŠŠ€J&Nëƒõ|&TÖàÛ-•„Ê8݌
@ ÁúX\U·>ÜÍ}/½dfÿÑùÀuÑN8ÍJf»vÒ´K³®I§ãLðÔ
yxdz®rÕ§rhí:9Xò‘/TêÚbÙêⱒݷ¯ÙΫÿ‡€™€+,Tj5ô}Â3ÏîÅãï4š=·‡Dˆƒ€
45l
Ú²Eö.]*V™žÞÚÛ;šECe¶L³O9ÅÑÇíÑÔ!Úm
˜ÑŠÅ¸}¸PY˜&óø;ƛ‡Ý@’ZÀ̤CYÿ´CСÍ_ÊÁM›¤zÿ>©Þ»OöYu´zó+&H“
Ý͹6=¾«d¶iã¹w+#½ÌH¥b؎P)B¨ŒáÆa@”ЖÍfÝ»t;´zµÕ|Ž´2%eΛ€éð¥
¨Òi8P¼SéðÍFq €xT€€éÀ
        ¨†è*ÃÏí%}
º¤üp::]eÑ»ëdÁ¼Od劭>UB¥‚ Ä‡Ö®5µol=²dAú˜õÝ"T¨L§@jôt2zs°RN
úÛoÍ999žaÊ!qBø       0ý0"ý¨ƒ ÿrò«¾ÍÓ)P

•:]åå~
)ä»-ø€ €@Ú
0c¸ôÇ
×Ú쥡êÞÿ#¹¹-b(%yv      *‡ÓCÉK‹é*“çŠQS@+@ÀŒÁ_¥¶Z껆ÙÙMb(Áû»*½¨!
€^ `ÆxeNÚÝÌҒMrê€î1–â­Ý•Þº
Ô@d
`ÆxåN9åxkÏeòqٖ¤˜„ÊovC@̐4á8¶c®èœáó箑ŸüôŒð{ìWB¥Ç.ÕA@ Ř
¸ ç]'Ïþ­DÖ¶MN8±}JrWB¥ûÆ
@j˜
¸úäw´ö.‘ÿ¾¿Ñ““Pـ‹Ë® € ³3f:13ôèîï!—\Z؀’œÝUÇé,^¹Á´®Ú%ëJ
)dkð@Ü `6@7+«©o¸"Ù'‘ãaÚ¡Rß     Ýþu¥9+Be..»"€
€@Ì̘éjv´‡+Z·ö«¸÷&*µãÑÄ«
¤ÿ€n’Ÿß¹gÇî € €@ô!æÔ©¿‘œœ
™2åWÖ`âÙAK^³f<õÔ_¥OŸÞ2iÒ¤
Û¤úJ{¸¢¢w7Ä%`*SýŽâü@H~³K—Îò÷¿Ï”¡C‡ÊàÁƒ‚žé믿.K–¼%Ɲ
ô÷tXiWôö[ŸË
¿pçŒ    •î¸R* €¸#2`
<Ø̧Ÿ~:hÀ¬¨¨0¿kµú÷ïïN풤T7†+"T&Éŧš € PG dÀ<ù䓥
¯”””Êæ͛¥S§N;¯^½Ú|Ÿ4éJiݺuÀoéöũንévçp¾
€¤¦@Ȁ©§;nÜ%&`.^¼¸Î;–=ö'#¢-n,[óóÝ(֕2Û5j!rôʆ+
*s3«­Ž:'ÓQǕ«E¡ € à¶@؀i?úž=û•€€¹sçN<µ
S[:Ó}ivdŸ
ªÚ!﬉d¸¢P¡ò¢ƒ_JÁ¡Ï¥çÁ2éðÓ²tgåü@@
IÂL}ô}æ™CMGžåËßñ½‹Y\\lN÷¼óÎsý´;”%GоäygÚb   5\ÑW[Êeá‚R3w¹=Ne°!
’©åÖõ‹Ï@@ )ÂL=£ñã/7óÃ?ðÌY³^4'«á“¥F /ïXóÁ¸"
•Ë—­‘7^_+kVí2¿
•"€ €©$PoÀÔGà
;
kzŒ?^¶oßn
k¸
Õ¹G¡k+§>bµM*!ê¹èpE:sÎìY«¥C‡£B¥þ>f\O9óì^
~®, € àÈ8ê(󹪼\2ss}ë“ùC½SOn̘‹ä±Ç
7-™{÷î1ç«-›¡–9sæ˜í_ziVÚLµ(<­‹i©|ü‘÷
†ÊÝ̜å:­$
 € P[ I
fÕá
;Ò+`Ž5ÊÆùóç›ÖKmÑ
Ö¹G‡3ÒN
£ºìß¿ßüM—ÿsÆО²wïBeº\pÎ@‚
DԂ©¹Gþ‘¼úê¿M!Ç«SØË/ϖûïÿ¿€õ͛7øžê_N8±½5›Ï9©~šœ € V
#ì¯~?ꔑö2zôhû£ïo~~™:õ×2}ú]¦ç¹þn-˜>
> € €i,Q
¦úè|äEEÖ@!–¼¼<Ñö¢s”§[
¦}îüE@ÒY â€
ÒÞ½ûÌæÑ´`VWVȁµëäàçåõ÷P³&¦Œ¯ïºS2ë$;´—¬^'I³îÝ£©
Û"€ €ÄYÀ•€Ù²¥5u¢µD҂¹¯¨H*ÞyGö??3ðÔ3jžÞWÎyÍ·~÷wŸZ^7YZœy&aÓ'Ã@@À;®Ì
HZ0¬[';îùT••Ìü¾’=b¤dõé#M:u
è¦hË©²ºîWXatÿ«³eY£.”Ük®•&
;zG”š € €i.àJÀ
ׂ©ÂwÍ|ÎDµ×˜3áÊ°­‘ õ_vß¾Òúê«E[=wÏx\´uó+ë_Î
wJŽU
 € €@â\   ˜¡Z05\~}ë­rðí¥¢-–mnûmØ`Š§Ea¡è¿=‹Ëî‡
ÝÖ{š‡·n“£¯œ YÙ¡vc= € €@
\      ˜ÁZ05\n<Ù<o~ŕÒzòõ
ƒ­Î>ÛêøÓKvüá÷¦Eôà'K»{ïmp¹Ñ¸oê_Íæõo›Uóî©ãåú
¹Kq‰ß7>"€ €Î
D<f4‡­Ý‚i·\êû–ÚA§í”)Ž
@}t®¡²éég˜–Q}ü΂ € 8WZ0/¾xŒè?{Ùùø
þ4\ê;”N/úX\C¦>~×@:¤Q¼ßÉL†VA7[E¾¦”‡ €É+àJ
¦?‡¾'©Ci
£¾#éÖ¢!³í´Û%£CóN¦ö
ÏÎζÞÇ\bÂe‹-ÌOÚÂI륭Ä_@ˆ—€+óÀºu¦þYƒ‡Äë<ê
G‡-²_¯ócŠ­˜3gŽŒ3V–-[.ãÇ_&§Ÿ>؜a¤¯
¤§ƒ €
påùÁM›Ìi5³zt'riÚ»à]¯¾—™j‹ö$àM°lß¾½ÜsÏték™žfNµk×®©vʜ
€$€+³zÿ>sê™mÚ$”@gôñÒb?§ë¤Âo¼ñÓk\C§½tîÜÙþÈ_@@ n®<"¯Þ[0ãv!”yL;ó‹
Ý¢b³¤_­Ã6é{˜ºèðEöÒњ§@ˆ·€+-˜‡V¯2çѐÇÒÚ+º¸¸Xô1o^^dCÕƳ[PíÕÚ¿Çû{Qъ
Rßµœ>ý
S†«¥¡7nôýÏ € €@¼\
˜™Çu2õ×ùÀcíE¾}ûv™6í+PÝsÀŒ¢ÛÇ©ý®å”)¿”³Î:+èaW¯^cÖÓÁ'(+@@ ®LûÝÇêýû|
{ð¸½rÕ§æøMïÚàz$ª
ò¡‡þhSÕjé_·_ÿú™0á
ÿU|F@â*àJÀ´Ï º¢Âþóߖ-kÆtŒ¹kÇ
kŒÈd[tðôG
yÔLŸ©=Äï»ïސ­–þç¦ã^ê ì, € €@¢\     ˜v‹áÁÏ7Jv‡*jH
æ÷ß7®M:
—(ߘŽm«eLa'@@À%Wf“N5ï`š€7ꈪþá‡ÊúõD[,5TîÝ»Çì·jÕ*yùåÙ¾õúû¹çžQ™‹ß3³
é ëÉ°ÄÚj™
çF
@@ }\     ˜™Ö9:Mdåœ×¤zêT‰$à͛7_^}õßuäu]íõ‘̊ÒR©ÞºUš
S§L/®ðoµ
2d°üö··ù†
òb}© € JÀ•€©Ë
1Rö”•JÅG%Ò¢°0Ôñ}ë'Mš(—\2Ö÷]‡ÛÑ^ä?ÿùd8p o}¤*Šjæ ώàؑ–ÙÐí"
h]§|
9òüˆ×Ðá">"€ €¸0[!{
ø½ìùç?"
˜¾{¬^»Î-[¶Šz˜¢êÊ
ÙÿêlÉèСÁï€Ö®ß@@Â
¸0õ1y–õþ¥>&×ÇÕ±vö‰¥ùžE‹Ìãñœ;î
öqþÕniô×R«0mÚm2jÔ¨8׆Ã!€ €î¸2U¤]՜      Wšå>`¯Šúo´½È«¬á}ö<1ô^¶><êã¹½
C©¶üã«ÌðCú®åìÙ/.ÝF§|@ˆ«€k-˜z:Udó+®”ýÏϔòüCr/¿<꓋¶sçÿû£i½Ì½ÿ÷u.ŠºB1
îPYY)3f̐^ø§)VË!Ù
@*oóèŸÌ£ëm×]#\v[­–;nø™
—íŸø‹h£D/Újy饗›Gâ¼k™è«Áñ@@ žq   ˜zB:¦
25
j(lè¢Ãmè!Ù}ם¾pÙÄ#žgÏ~Å´ZÞtÓ¯äž{~G«eC/6û#€ €@ÒÄ-`ªˆ†Ìcþú´        ƒ
·\õ9°n]LXÚ
ºeÜ%¦‘¾s©-—^   —zB7Þxƒå”°·õýͽK—JÅÂReͤK«›o‘œ‹F'¼Çø¦þµOUšXk6ÕYË
@@ µâ
0•S;þ´2E\x¡ì~n¦éù]>õ)·~Ó9Ì3»v•Ìã:IãíåðÖmRõåf9Xüžy‡Ó¾
-¯›,G
6ÚÛò@@ ~             ˜öéiçŸvÖl;U¿ø¥T|ðT¼½ÔÉÊïZ'ííô¯ö×15³
’ì~    o±´ëÖ¥¸ÄþèÈß­ùù¦œeeŽ”G! €
€@¼0í“Õ^ß:n¥ÿؕ_Ôapø @@ zfôfì €
F€€‡Ÿ@@¢ `FoÆ
 € €a˜apø       @@ zfôfì € F€€‡Ÿ@@¢ `FoÆ
 € €a˜apø       @@ zfôfì € F€€‡Ÿ@@¢ `FoÆ
 € €a˜apø       @@ zfôfì € F€€‡Ÿ@@¢ `FoÆ
 € €a˜apø       @@ zfôfì € F€€‡Ÿ@@¢ `FoÆ
 € €a˜apø       @@ zfôfì € F€€‡Ÿ@@¢ `FoÆ
 € €a˜apø       @@ zfôfì € F€€‡Ÿ@@¢ `FoÆ
 € €a˜apø       @@ zfôfì € F€€‡Ÿ@@¢ `FoÆ
 € €aþ?³Ð
–¯+ÍLIEND®B`‚
_______________________________________________
Hosted by the MEMS and Nanotechnology Exchange, the country's leading
provider of MEMS and Nanotechnology design and fabrication services.
Visit us at http://www.mems-exchange.org

Want to advertise to this community?  See http://www.memsnet.org

To unsubscribe:
http://mail.mems-exchange.org/mailman/listinfo/mems-talk
reply