lec 3 design issues for mems 2

7/22/2019 Lec 3 Design Issues for MEMS 2

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HVI CIN T(VI H THNG)MICROSYSTEMS

MICRO-ELECTRO-MECHANICAL SYSTEMS

MICROMACHINING


2/67

VI H THNG

MEMS

Mt th gii rng m v quyn r

(An fascinating and wide world)


3/67

III. Thit k trong MEMS

1. Mu/ Introduction2. Cc h qu khi thu nh kch thc /

Scaling issues for MEMS

3. M hnh ha v m phng/Modeling and Simulation

4. Thit k qui trnh ch to/Process integration

5. Kt lun/Conclusions


4/67

3. M hnh ha v m phng

Php bin i Lagrange S dng h cc phng trnh vi phn Lagrange trong h ta chung(generalized coordinates) qk (k= 1,2,n) m t tng thi ca h

c inTa chung (qi) x Q V hoc

ng nng (T)

Thnng (U)

Hm suy haoRaleigh (D)

Cng (W) F.x T. V.Q i.

2

2

1xM&

2

2

1&M 2

2

1QL&

22

2

1

2

1= &CCV

2

2

1Kx 2

2

1K

C

Q2

2

1L

2

2

1

22

1xC&

22

1&C 221

QR& R

2

2

1&

Slng cc ta c lp m t hng hc gi l bc t do ca

h (degree of freedom - DOF)

Xy dng m hnh tng qut(concept to first design)


5/67

Phng trnh Lagrange tng qut


Php bin i Lagrange

i

N

i iii

dqq

U

q

T

q

T

dt

dUTd

=

+

=+1

)(&&

Trong h ta chung: T l hm caqi v vn tc ,U l hm ca qi,iq&

0=+

iii q

UqT

qT

dtd

&&

i vi hbo ton khng thuc trng lc th:

Khi h thc hin cng bng lc bnh thng Qi, c: =

==+N

i

iidqQdWUTd1

)(

iiii

Qq

U

q

T

q

T

dt

d

=

+

&& Phng trnh Lagrange:


Tnh lut bo ton nng lng, c: d(T+U) = 0


6/67


Php bin i LagrangeLc ma st (khng th- nonpotential force)+ Lc ma st trong h ta Descartes: xCF &=

Hm suy hao: = =

=n

r

n

s

srrs qqCD1 12

1 &&

Lc ma st trong h ta chung:i

iq

DQ

=

i

iiii

Qq

D

q

U

q

T

q

T

dt

d=

+

+

&&

Phng trnh Lagrange c lc khng th:

Xy dng m hnh tng quat(concept to first design)


7/67


Php bin i Lagrangeiu kin rng buc (constrain equation)

=

+=+=

+

+

M

l i

li

con

ii

iiii q

gQQQ

q

D

q

U

q

T

q

T

dt

d

1&&

Phng trnh Lagrange i vi cc lc khng thuc trng th

+ Trng hp sta n v sbc tdo N khng nhnhau, tc l: n > N

iu kin rng buc: gl (q1, q2, , qN) = 0 (l = 1, 2,,M)

+ iu kin c hphng trnh gii c xc nh mt h: n M = N

=

=M

l i

lcon

i q

gQ

1

Suy hao do lc ging



8/67


Php bin i LagrangeV d: xy dng m hnh ca cm bin gia tc

Hdao ng c, 1-DOF, ngoi lc F c thllc qun tnh, lc tnh in hoc lc in t

2

2

1xMT &=

2

2

1KxU=

2

21 xCD &=

xFW = .

+ ng nng ca h:

+ Thnng ca h:

+ Suy gim NL ca h:

+ Cng h thc hin:

Phng trnh vi phn dao ng bc 2: 0=++ FKxxCxM &&&



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M hnh kt khi (lumped-model) Linh kin MEMS trong thgii thc

C kch thc 3 chiu

C nguyn l hot ng tun theo cc nh lut Vt l

M hnh kt khi cho thit k- s dng l thuyt mch :

n gin ha mt hphc tp (c, nhit, ha) bng cc phn t

mch in M hnh ha tng tc gia cc dng nng lng (energy domain)mt cch hiu qu

M hnh ha tnh cht Tnh v ng ca h m khng cn phi xy

dng v th



10/67


M hnh kt khi (lumped-model)Phn t kt khi Vt thn l c thtrao i NL vi ccvt thkhc

Tc trao i nng lng: nng lng/thi gianPAB = r1

2 PBA = r22 (r1 v r2 l cc sthc, PAB > 0 v PBA > 0)

Mng nng lng gia A v B

P = PAB - PBA = r12 - r22 = (r1+r2)(r1-r2) NL gia A v B lun c vitdi dng tch ca 2 sthc,

Bin NL lin hp Cp i lng m tch ca chng bng tch tc trao i NL mng

gia 2 phn t



11/67


M hnh kt khi (lumped-model)Nng lng (generalized power variable) Tc ng (effort): e(t)

Bin i (flow):f(t)

Bin lin hp: e(t).f(t) = NL

Xung lng v chuyn v (momentum and displacement)=t

t

dttetp

0

)()(Xung lng

Chuyn v =t

t

dttftq

0

)()(

e(t).q(t) = NL hay f(t).p(t) = NL



12/67


M hnh kt khi (lumped-model)

Tc ng Bin i Xung lc Dchchuyn

Hchc Lc(F)

Vn tc(v)

Xung lng(p)

V tr(x)

Mch in Th(V) Dng(I) in tch(q)

Cht lu p sut(P)

Dng chy khi(Q)

p lc()

Th tch(V)

NL lin hp tng ng cc dng NL c th khc nhau



13/67

2 bin cho mi port:


M hnh kt khi (lumped-model)Phn t mt cng (1-port element) Cng (port): cp li vo/ra ca mt phn tmch in cho php dng i vo v i ra.

Ngang qua (across) Xuyn qua (through)

in Tc ng = thBin i = dng

C Tc ng = lc Bin i = vn tc

Cht lu Tc ng = p sut Bin i = dng chy khi



14/67


Ngun (source): phn t kchhot cung cp NL cho cc phnt khc khi e(t).f(t)


15/67


Trong chuyn ng (dao ng) c, m hnh in trng vai tr l lmb gim chn (damper) dp tt dao ng (do ma st, nht cht lu).


f (I, v hoc Q)

e (V,F hocP) e.f > 0 gc I v III NL sbtiu th (disipated/absorbed)

e = Rf

Th hin mi quan h tuyn tnh gia tcng v bin i:

M hnh kt khi (lumped-model)M hnh in tr (generalized resistor)


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e (V,F hocP)

q (q,x hoc V) Th hin mi quan h gia tc ng vdch chuyn: e = (q)

Khi t c tng tc 0 cchuyn v0 t tch trNL

NL lu tr: ==11

1

00

)(qq

q dqqedqW

NL tng ng (co-energy):

==1

0

* )(.)(e

qdeqWqeeW


M hnh kt khi (lumped-model)M hnh T (generalized capacitor)


17/67


QC= CV

g

AC

=

C

QQW

2)(

2

= )(2

)(2

*QW

CVQW ==

e (V)

q (Q)

Q = CV

Q ca t l dng in

M hnh T p dng cho tin phng

Theo L Hook: F = kx

NL lu tr trong l xo: 10

1 2

1)()(

1

kxdxxFxW

x

==

x ca l xo l dng c

M hnh T p dng cho dao ng c


M hnh kt khi (lumped-model)


18/67


Th hin mi quan h gia bin i vxung lng

f = (p)

V d:p = mvm

pp = )( m

ppW

2)(

21

1 =

211

*

2

1)( mvpW =

=1

0

1 )()(p

dpppW

)(.)(* pWpfpW =

NL lu tr:

NL tng ng (co-energy):

Trong Ccm hnh cun cm ng vai tr l khi lng (gia trng) dochuyn ng qun tnh


M hnh kt khi (lumped-model)M hnh cun cm (generalized inductor)


19/67


S mch in

Mc ni tip (serires): p dng cho trng

hp cng chia sbin dng chy (flow) vdch chuyn

Mc song song (paralell): p dng cho trnghp cng chia sbin tc ng (effort)

nh lut Kirschhoff p dng cho dng ti nt i: 0= iI p dng vi thca mch kn: 0= iV

-F + ek+ em+ eb= 0


M hnh kt khi (lumped-model)Gn kt cc phn t (circuit connection)


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Php bin i Laplace (Lapalace transform) Phng php ton hc c dng ph bin phn tch hoc m hnhha hng hc.

Php bin i t vng ph thuc thi gian (time-domain) trong thng

tin a vo (inputs) v ly ra (outputs) l hm ph thuc thi gian sang vngtn s (frequency-domain) ngha l cc thng tin ni trn trthnh hm catn s gc phc (hay rad/s).

Bin i php vi phn (hoc tch phn) thnh php nhn (chia) vi s phng trnh a thc d dng gii s dng php bin i Laplace

nghch chuyn ngc v qu trnh ph thuc thi gian.

nh ngha: bin i Lapalce ca hm ph thuc thi gian, f(t), l hm

F(s), c dng: ==0

)(}{)( dtetxxsX stsL (s l sphc)



21/67


Php bin i Laplace (Lapalace transform)Cc tnh cht Tuyn tnh (linear)

(t) = .x(t) + y(t)(t) l t hp tuyn tnh cax(t) v y(t):

W(s) = .X(s) + Y(s) Bin i Laplace ca (t): Vi phn (differentiation)

)0()(}{)( xssXxtx s = && LBin i Laplace ca )(tx&

Hm n v bc thang (Heaviside unit-step function )

=


22/67


Php bin i Laplace (Lapalace transform)Hm truyn (transfer function)

)}({

)}({

)(

)()(

tx

ty

sX

sYsH

s

s

L

L==

H lin tc: x(t): hm li vo, y(t): hm li ra

H ri rc:

)(

)()(

zX

zYzH =

Biu din ton hc (php nh x tuyn tnh ca bin i Laplace) th hinmi quan h gia li vo v li ra (ph thuc thi gian) di dng hm tn s:

Y(s) = H(s)X(s)

H(s): hm ph thuc tn s



23/67


Khi gia trng di chuyn (moving mass)

Gii phtr xc nh X(s)

)()()( txmtmatf &&==L 2 Newton:

Bin i Laplace caf(t) }{)()( xmsFtf s &&L=

)]0()0()([

)}0()]0()([{

)]0(}{[)(

2 xsxsXsm

xxssXsm

xxsmsF s

&

&

&&

=

==

== L

00)0( vxx == &&x(0): v tr ban u v l vn tc ban u

p dng nh l vi phn, c:


Php bin i Laplace (Lapalace transform)ng dng cho cc m hnh


24/67


Nuf(t) = 0, c: 22)0()0()0()0(

)( s

v

s

x

s

x

s

xsX +=+=

&

p dng nh l unit step function v tr khi gia trngx(t):

x(t) =x(0).u(t) + v(0).t.u(t)

v tr ban ux(0) = x0, v v(0) = 0 x(t) = x0 vit 0 vt ng yn

Khi gia trng di chuyn (moving mass)

v(0) kt hp vi thi gian vt Ckhng ngng vi vn tc ban u

phtr vi phn m tC ca vtphtr i s tuyn tnh




25/67


Bdao ng gia trng-l xo (mass-spring)

Bin i Laplace

)()0()0()(

)()}0()]0()([{

)()]0(}{[

}{}{

}{0

2 skXxmmsxsXms

skXxxssXsm

skXxxsm

xkxm

kxxm

s

ss

s

+=

=+=

=+=

=+=

=+=

&

&

&&

&&

&&

L

LL

L



)()()( txmtmatfm &&== L 2 Newton cho m:

L Hook cho k: )()( tkxtfk =

L 3 Newton: 0)()( =+ tftf km 0)()( =+ tkxtxm&&


26/67

Php bin i Laplace (Lapalace transform)ng dng cho cc m hnh Bdao ng gia trng-l xo (mass-spring)


00)0( vxx == &&x(0): v tr ban u v l vn tc ban u

00

200

/)(

js

r

js

r

mks

vsxsX

++

=+

+=

mk/0= rj

reRv

jxr

=+=

00

0

220

20

20

20

2

xvRr

+=

=

00

01tanx

vr

v tr khi gia trngx(t):

+=

==+=

00

010

0

20

20

20 tancos

}{2)( 000

x

vt

xv

rereerretx tjtjtj

v(0) = 0 x(t) = x0cos(0t)

x(0) = 0 x(t) = (x0/0)sin(0t) vv(t) = v0cos(0t)



27/67


Php bin i Laplace (Lapalace transform)

Bin trng thi:

x1: v tr

x2 = dx1/dt: vn tc

dx2/dt: gia tc

u vo (input) = tc ng

u ra (output) = dch chuyn

12 xx &=

F

m

x

m

bx

m

kx

1212 +=& (L 2 Newton cho h)

ng dng cho cc m hnh Bdao ng l xo-gia trng-gim chn (mass-spring-damper)



28/67


Php bin i Laplace (Lapalace transform)ng dng cho cc m hnhF

mx

x

m

b

m

kx

x

+

=

1010

2

1

2

1

&

&

Fx

x

x

x

+

=

00

1001

2

1

2

1

-x: bin trng thi (ma trn ct) th hin v tr, vn tc,

-U: thng tin u vo (ma trn ct) th hin lc

-y: thng tin u ra (ma trn ct) th hin gia tc,

-A, B, C, D cc i lng thi gian, c ngha lin kt c h.

Phng trnh trng thi tng qut BUAxx +=&

DUCxy +=

(1)

(2)



29/67



Bin i Laplace vi phng trnh (1): )()()0()( sBUsAXxssX +=

Bin i Laplace th hin p ng ca h:[ ])()0()()( 1 sBUxAsIsX +=

p ng iu kin ban u (cha c li vo): )0()()( 1xAsIsXzir=

)()()( 1 sBUAsIsXzsr=p ng tc ng li vo:

iu kin c nghim: 0)det( AsI

Bi ton tr ring: tn ti gi tr s sao cho: 0)det( =AsI



30/67

p li ra:i vi h l xo/gia trng/gim chn: D = 0

)()()()()()( 1 sUsHsBUAsICsCXsY zsrzsr ===



BAsICsH 1)()( =Hm truyn:

Bin i Laplace vi phng trnh (2):

[ ] )()()(

)()()(

sDUsXsXC

sDUsCXsY

zsrzir ++=

=+=

H(s) l ma trn c: s hng = sbin trng thi, s ct l bin li vo

=

++

++=

))((

1))((

111

)(

21

21

ssss

s

m

ssssm

kbsms

skbsmssH

2

0

2

2

2,1 22

=

=

=m

k

m

b

m

bs



31/67


Cc phng php m phng

3 phng php phbincng dng cho MEMS

Sai phn hu hn (finite differantial method - FDM)

Phn t hu hn (finite element method - FEM)

Th tch hu hn (finite volume method - FVM)

cim Bini cc phng trnh vi phn thnh phng trnhi s xp x

Chia nh cu trc thnh mng li (grid hay mesh)

Gii h cc phng trnhi s

Cc bi ton chc cu trcc m t bng cc phng trnh o hmring mt slng ln cc phng trnh cn c gii tm nghim chomi im trn ton b m hnh (hay mt min) phc tp kh thc hin viphng php gii tch thng thng cc phng php gii s gn ngc s dng vi cng c l my tnh thng qua mt ngn ng lp trnh hocmt phn mm ng dng.


32/67

FDM

FEM

FVM


Cc phng php m phng


33/67

Phng php FDM

Xut pht t cch xcnh khong cch gia 2 im = php trphpsai phn

nh ngha php lyo hm

+=

)()(lim)('

0PFPPFPF

Nu hu hn:

+

=)()(

)(' PFPPF

PF


Cc phng php m phng

Sai phn gia: F(P)=- F(P-1/2P) - F(P-1/2P)P P + P -

Sai phn tin: F(P) = F(P+P) - F(P)

Sai phn li: F(P) = F(P) - F(P-P)P P+PP-P


34/67


Cc phng php m phngPhng php FDM

Bi tonng: bini hin (explicit method)

Bi tonng: binin (implicit method)

S dng php sai phn tinthiimtj

2

11

1 2

h

uuu

k

uu n

j

n

j

n

j

n

j

n

j

+

+ +=

nj

nj

nj

nj ruruuru 111 )21( ++ ++= Vi 2/ hkr=

S dng php sai phn lithiimtj+1

2

11

11

11

1 2

h

uuu

k

uu i

j

i

j

i

j

n

j

n

j

+

+

+ +=

11

11

1)21( +++

+ ++=+ iji

j

i

j

n

j ruruuur Vi2/ hkr=


35/67


Cc phng php m phng

Phng php FDM

S dng php sai phn giathiimt(j+1)/2

++

+=

+

+

++

+

+

2 112

1

1

11

1

1 22

21 h

uuu

h

uuu

k

uu n

j

n

j

n

j

n

j

n

j

n

j

n

j

n

j

Vi 2/ hkr=

)()()22()22( 111111

1 ++

++

+ ++++=+ njn

j

n

j

n

j

n

j

n

j uuruururur

Bi tonng: bini Crank-Nicolson


36/67

Phng php FDM

Cc bc thc hin

Xy dng thut ton.

M ha thut ton bng cch s dng cc ngn ngbin dch (C, pascal,Fortran) hoc cc phn mmng dng (MatLAB, Mathematica) vitchng trnh tnh ton cho yu cu ca bi ton (lp trnh).

a bi ton v dng khng th nguyn.

Thc hin gii bi ton v phn tch kt qu.


Cc phng php m phng


37/67


Cc phng php m phng10

4

+1-1

i+1

i-1

i

2 3

5 11

12

678

9 1 0

(i,j)

Mng

2

501

2

02 2

+

= www

x

w

2

703

2

02 2

+

= www

y

w

Xy dng thut ton thng qua php sai phn

1 2 1

2

1

1

Phng php FDMng dng FDM m phng lch (un cong)mng mng ca cm bin p sut Phng trnh lch mng khi c p sut

),(24

4

22

4

4

4

yxPy

wD

yx

wD

x

wD =++

Phng trnh lch mng khng th nguyn

124

4

22

4

4

4

=++y

w

yx

w

x

w


38/67


Cc phng php m phngPhng php FDMng dng FDM m phng lch (un cong)mng mng ca cm bin p sut

1 1

1

1

8 820

8

8

2 2

22

1 4 6 4 1

1

6

4

4

1

2 24

2

2

1 1

11

4

115019

4

04 464

++

= wwwww

x

w

4

654703812

22

04 2222

++++=

wwwwwwwww

yx

w

4

1270310

40

4 464

++= wwwww

y

w


39/67


Cc phng php m phngPhng php FDMng dng FDM m phng lch (un cong) mngmng ca cm bin p sut

a x + a x + ... + a x = b

a x + a x + ... + a x = b

...

a x + a x + ... + a x = b

11 1 12 2 1N N 1

21 1 22 2 2N N 2

N1 1 N2 2 NN N N

=

NNNN

N

N

aaa

aaa

aaa

A

,...,,

...

,...,,

,...,,

21

22221

11211

=

Nx

x

x

X

...

2

1

=

Nb

b

b

B

...

2

1

Phng trnhi s tuyn tnh:

Hay: AX = BVi:

X = B.A-1

Gii bi ton xcnhn s:


40/67


Cc phng php m phngPhng php FEM

tng chia mt cu trc phc tp thnh nhng khi nh (phn t) c

cu trcn gin v d dng khng ch.Hnh trn = hnh tam gic, c din tch:

Din tch hnh trn:

ii RS = sin21 2

Element

Si

22

1

2sin

2

1R

NNRSS

N

i

iN

== =

khi N

Mt cu trccc trng bi ma trn h s cng (stifffness). Mi phn t, ma trn h s cng lin kt c cu trc bng phngtrnh cbn.


41/67



Khi mt cu trcc chia (mesh) thnh cc phn t, ma trn cng ca

ton b cu trc c mi thnh phn l cng ca mi phn t tngng.

Nu cu trc chu tc dng ca mt ngoi lc F phng trnh quan hgia F v dch chuyn (chuyn v) vi h s t l l h s cng.

{F} = {k}.{x} {x}= {k}-1

.{F}

Ta, kch thc, sutn hi Young, t s Poisson hay khi lng ring(density) l cc thng s u vo gii phng trnh ny.

FEM l phng php ri rc ha mt min phc tp thnh cc min conn gin, c cng tnh cht, gi l cc phn t (element) m c m tbngcc phng trnh ton, th hin hnh vi ca n vi mt ti xc nh. Tng hptt c cc hnh vi trong m hnh s cho ta hnh vi chung ca c h vt l.


42/67



Cu trc c to t cc phn t c s gm: mt phng 4 cnh

(quadrilateral plates), mt phng tam gic (triangular plates), khi (solid brickelement), hay thanh mng (beam).

Phn t1 chiu1-D (line) element

(spring, beam, truss, pipe)

Phn t2 chiu

2-D (plane) element

(membrane, plane, shell)

Phn t3 chiu3-D (solid) element

(trng vt l 3 chiu: nhit,chuyn v, ng sut, dng chy)

Nt (node)


43/67



H s n hi - cng (stiffness) ca l xo

L xo (phn t n hi) chu tc dng cangoi lc F dch chuyn (bin dng) on:

)( ij uukkF ==

L 3 Newton cp lc cn bng ti 2 v trca chuyn di - nt (node) i vj:

jiiji kukuuukFf === )(

jiijj kukuuukFf +=== )(

Hay:

=

j

i

j

i

f

f

u

u

kk

kk Fku=

u

Fk=

3 M h h h h


44/67


Cc phng php m phngPhng php FEMH s cng ca thanh (bar)

Thanh (bar) c diL, thit din ngangA, h sn hiE, dch chuynu(x),bin dng(x) vng sut(x).

LL

uu

dx

du ji =

==

L

EE

==

c

v Mt khc:A

F= === k

L

EAAF vi:

L

EAk=

Thanhng x nh l xo

=

=

= 11

11

L

EA

L

EA

L

EAL

EA

L

EA

kk

kk

k

Phng trnh cn bng phn t:

=

j

i

j

i

f

f

u

u

L

EA

11

11 Ct thj (=1, 2) ca ma trnkthhin lctc dng ln bar duy tr tnh trng bin dng

ti ntj v khng bin dng ti cc nt khc

3 M h h h h


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Hm hnh dng v nng lng bin dng

ji uLxu

Lxxu +

= 1)( Chuyn vu(x) dc theo trc x:

Hm hnh dng: =

1)(iN =

)(jN ViL

x= 10

[ ] Nuuu

NNuNuNuxuj

i

jijjii =

=+== )()()()()()(

B: ma trn (h st l) bin dng-chuyn v

[ ]LLB /1/1=

Khi BuuNdx

d

dx

du=

==

v EBuE == NL bin dng: th nng lu tr trong h bin dng n hi, c gi tr bng cng h thc hintorab in dng.

VLAFWU ====

2

1

2

1.

2

1 Vi thanh c

II C s c in

3 M hnh ha m phng


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II. Cs vcin3. M hnh ha v m phng


H s cng tng qut

( ) ( ) udVEBBudVEBuBudVUV

TT

V

TT

V

T

=== 2

1

2

1

2

1

Hm nng lng bin dng tng qut:

Trong: T

vuT

vBT

l cc ma trn hon v (hng ct) Cng thc hin bi 2 lc nt fuufufUW Tjjii 2

1

2

1

2

1=+==

hay ( ) fuudVEBBu TV

TT

2

1

2

1=

( ) kufudVEBB

V

T ==

Ma trn cng phn t: ( )=V

TdVEBBk

Hm nng lng bin dng thu gn kuuU T

2

1=

p dng chung chomi loi phn t

II C s v c in

3 M hnh ha v m phng


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Thc hin xy dng m hnh (modeling) i tng cn tnh ton, nhp ccthng s vt liu c trng (Material Properties), xc lp kiu phn t (ElementType), chia nhi tng thnh mt slng cc phn t(Mesh), t cc iukin bin (Boundary Condition) xc lp vng khng chu ti (Constrains) v

vng chu ti (Load), cng nhiu kin ban u (Initial Condition).

Cc bc thc hin

Gii h cc phng trnh i s tuyn tnh (p dng phng php loi trGauss) tm bin chnh l chuyn v{u} v bin ph l bin dng, ng sut,moment

Phn tch v x l kt qu tnh ton.

Phn mmng dng ca FEM ANSYS, NASTRAN, ABAQUS, COSMOS, ALGOR, PATRAN,hyperMESH, Dyna-3D

c vit ch yu bng ngn ng FORTRAN

II C s v c in

3 M hnh ha v m phng


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Cc phng php m phngPhng php FEMng dng FEM trong cc bi ton k thut

II C s v c in

3 M hnh ha v m phng


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ng dng FEM (ANSYS) trong MEMSM phng hotng ca cm bin gia tc

M phng hotng ca cm bino pH do

hiung swelling ca polymer hydrogel

M phng hotng ca bnh rng vi c

II C s v c in

3 M hnh ha v m phng


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Cc phng php m phngSo snh FDM v FEM FDM v FEM u c h o li gii trn ton b min tnh ton v khng cn tnhlin tc. FEM mnh v kh nng x l cc bi ton c hnh hc phc tp trongkhi FDM ch gii hn nhngi tng c hnh dngn gin

FEM c la chn ch yu cho cc bi ton cu trc chc trong khiFDM oph hp hn cho cc ton v ng hc cht lu (computational fluiddynamics - CFD).

Cs ton hc ca php gnng trong FEM cho php vic chia nh itng thc hin tnh ton mnh hn FDM. Tuy nhin FDM d thc hin,trong khi FEM i hi qu trnh tnh ton nhiu hn v lu hn sai s trong

cc tnh ton ca FEM nh hn so vi FDM.

C rt nhiu phn mmc vit sn cho FEM, tch hp (nhng) phn x l ha (CAD), km theo cc b th vin cha tngiy cc loi phnt, cc dng bi ton k thut trong thc t nn rt thun li cho ngi s dng kt qu tnh tonc biu din bng s liu, th, hnhnh 2,3 chiu v

c bit lnhng (animation) di dng file ui .avi.

III Thit k trong MEMS


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III. Thit k trong MEMS

1. Mu/ Introduction2. Cc h qu khi thu nh kch thc /

Scaling issues for MEMS

3. M hnh ha v m phng/Modeling and Simulation

4. Thit k qui trnh ch to/Process integration

5. Kt lun/Conclusions

II C s v c in

4 Thit k qui trnh ch to


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II. Cs vcin4. Thit k qui trnh ch to

Thit k qui trnh ch to

Xy dng cc bc cng ngh chi tit cho ch tolinh kin (fabrication layout)

Thit kb MASK (mt n) quang hc

II. C s v c in

4. Thit k qui trnh ch to


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Cc nguyn l thit k qui trnh Chn cch thc th hin cu trc linh kin d dng phc tho hnh dnglinh kin cho qui trnh ch to:

- Hnh v 3 chiu bng cc cng c thit k trn my tnh (CAD)

- Hnh v mt ct th hinc cu trcy ca linh kin

La chn cng ngh v cch thc ch to:

- Vi ckhi kh (hoct) hay vi cb mt

- Thc hin to cu trcin trc (front-end process) hay cu trc c trc(back-end process).

- Cn nhc cc bc cng ngh sao cho bom an ton ca cu trc cn chto (do c tnh ca cu trc linh kin MEMS rt mnh mai, db gy hay v).

Lun kt hp gia thit k v kim tra mt qui trnh ch tom botnhn nhng yu t cng ngh lm tng tnh chnh xc ca qui trnh.

Lu n tnh cht khngngu ca b mt phin trc v ngay trongqu trnh ch to (cc bc cng ngh lm thay i phn b b mt phin)

trnh b tr linh kinst mp phin

II. C s v c in



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Gii hn ca k thut quang khc (photolithography) Cc chi tit ca linh kin MEMS cnh dng, tonh vn mn hoc

bc lp (lift-off) bng qui trnh quang khc Gii hn quang khc l kh nng to ra kch thcnh nht c th cho linh kin kch thc chi tit(feature size - FS) hay kch thc ti hn (critical

dimension CD), xcnh bng rng vch (linewidth - w) v qui tc thit k khong cch (spacedesign rules - s) .

Vi phm qui tc

khng t c cu trcmong mun

Chi tit trn

MASK quang hc

a < FS

Chi titc

nh dng

nh hng ca cng ngh ch to

II. Cs vcin



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q

Gii hn ca k thut quang khc (photolithography) Hiung quang hc (giao thoa, nhiu x) lm cho chi tit cncnh

dng trong qui trnh quang khc b thay i khu vc vin mp (distortededge effect).

Chi tit sau khicnh dng

Dng hnh hctrn MASK quang


II. Cs vcin



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q

Gii hn ca k thut quang khc (photolithography) Gii hn khong cch tiu c (depth focus) ca knh hin vi trn thit b

quang khc Du so MASK (alignment marks) quytnh tnh chnh xc ca qui trnhch tophn gii ca h quang hc trn thit b quang khc cnctnhn khi thc hin thit kb MASk quang hc.

Hin tngng sut ni xut hin khi ph lp cm quang (photoresist) cth lmnh hngn tnh chnh xc ca chi tit cn ch to .


II. Cs vcin



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q

nh hng ca cng ngh ch toGii hn ca k thutn mn (etching) Vt liu bo v (mask) b mt phin thch hpm bo:

- Chungc thi gian di trong qui trnhn mnt.- Chuc nhit cao ca mi tr ng plasma trong qu trnhn mn kh.

Convex corner

Hin tngn mn ngang:

- Notching effect trong k thutn mn kh.

- Undercutting lm cu trc cnn mn b lmgc () trong k thutn mnt

Notching effect

II. Cs vcin



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Thc hin m hnh ha qui trnh ch to da trn nguyn l vt l (physic-based process modeling tool): Ch yu l cc phng php m hnh ha vphng qu trnh to mng mng cng nh n mn cung cp cc thng tin vthng s qu trnh gip xy dngc hnhnh c th ca linh kin s cch to.

Thc hin m hnh ha qui trnh ch to da trn cc bc cng ngh(geometric emulation of MEMS processes): m t hnh dng nhn c saumi bc cng ngh kt ni vi nhau xy dng cu trc hnh hc hon

chnh ca linh kin s c ch to.

Kim tra thit k (design rule checking)

II. Cs vcin



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Kim tra thit k (design rule checking)

Cng c tonho

Hnh hc caMASK (2 D)

nho 3D

nh o 2-D(mt ct dc)

Xc inhqui trnh

II. Cs vcin



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Cc cng c thit k (design tools)

Thit k MASK: Corel Draw, LEdit,

Thit k qui trnh: SUMMiT, MEMCAD, SIMULINK

II. Cs vcin



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Qui trnh ch to cm bin p sutpin tr (back-end process)

Ch to cu trc c (mngmng nhy p sut) trc, cutrcin sau.

Ch to theo cng ngh vi ckhi (bulk microfabrication) s dng qui trnh n mn t(wet etching)

Thc hin trn thit bquang khc 1 mt (one-sidealigner)

II. Cs vcin



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Thit kb MASK (corel draw)

II. Cs vcin



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Thit kb MASK (corel draw)

II. Cs vcin



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Qui trnh ch to cm bin p sutpin tr (front-end process)

Ch to cu trcin trc,cu trc c (mng mng nhyp sut) sau.

Ch to theo cng ngh vi c

khi (bulk microfabrication) sdng qui trnhn mn t (dryetching)

Thc hin trn thit bquang khc 2 mt (two-sidealigner)

Si

Buried SiO2

SiO2

Boron doping layer

Al

1

2

3

54

6

7

8

II. Cs vcin



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Thit kb MASK (LEDit)

MASK 1

MASK 2

II. Cs vcin



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Thit kb MASK (LEDit)

MASK 4

MASK 3

5. Kt lun


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Thit k MEMS l cng vic phc tpi hi cc kh nng tduy tru tng v ton hc thng qua thc hin m hnh ha vm phng (tnh ton) ccng x ca linh kin.

Nhng nhu cu ca th trng, kh nng cng ngh kt hpvi tng sng to l cscho vic thc hin thit k mt linhkin MEMS.

Cc nguyn l, nh lut vt l kch thc vi m s ancc hiung khc so vi mc v mi hi cc tnh ton vthit kph hp.

Thit k qui trnh ch to cn tun th cc qui tc thit k vkim tra thit k nhmt to rac mt qui trnh cng nghch to tiu, ph hp cciu kin thc t.

lec 3 design issues for mems 2

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