1 n dn dt = f v = 4 π m 2kT 3/ 2 v 2 mv exp 2kT 2 f v dfv = 0 v = 0, v = /// fv = max = 0 dv 2kT v p = m 1/ 2 vfvdv 0 2 2kT = = vav = v f dv π m

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1 n dn dt f v 4 π m kt 3/ v mv exp kt f v dfv 0 v 0, v /// fv max 0 dv kt v p m / vfvdv 0 kt vav. 8v f dv π m k m 0 v / R0 4 T vav.45 0 cm / sec M M p v v fvdv 0 3 fvdv 0 kt m / 3kT v v. 5 m rms v p

2 n dn dv v f m πkt / mv exp kt x v x x V n R k W M V T R N φ vxdnx 0 0 v x v x fndv V W N n kt a RT n RT n N M V π m a nvav T nkt 4 / kt π kt m MT a x 0 m πkt / nv / x mv exp kt # cm x sec dv π MkT x /

3 φ 3 T q φa nvav A A 4 M / dv dt q n 3 T M / A dv dt.6a

4 (flow regimes) I R e R e ρ vd /η ρµ d 4mQ 4 QM.53 0 η πdktη dt η Q v( πd / 4) ρ nm M /(RT ) η nmv av λ ρv 3 3 η πξ mkt π / η av ξ M d m 3 T / Q d λ Q R e [ M /( RT )][4Q /( πd R e air [ 4M /( πrtη]/( Q / D) M η.89 0 )]( D / η) R e D 4 poise R Torr liter / K

5 (/4) : (knudsen knudsen Number, Kn) Knudsen _ number Kn D / λ λ e ipe, R ρµ D e η

6 (/4) (conductance) : ( ) / / + /, + conductance( conductance( pipe) : conductance(/sec), L : (cm) 4 air 8( D / L) D : (cm), : A : (cm ), M : gas T :, K : 3 3.8( T / M ) / ( D / L) /[ +.33( D / L)] (Qthroughput) : D : pumping speed ( S ) : Q ressure x S torr liter / sec n v A sccm ST cc.69 x 0 9 #/min torr liter/sec sccm.3 x 0 #/min

7 onductance N A vn Sn N Avn Sn A v S Av Sn Sn N N N N N ( n ) n / ( n n) / N (/ S / S)

8 N a N N a b + (arallel) N a a b ( n ) n ( n n) N p ( n ) n N (Series) n n ) ( n ) a ( b n3 / s (/ a ) + (/ b) +Λ Λ p a + b +Λ

9 Q ( i f ) Q + Q + +Λ Q ( j,,3 ) j Κ Q ( ) + ( 3 ) +Λ Q Q Q + + +Λ 3 Κ ( j j,,3 )

10 Q S p ( dv / dt) N ( n ) n kt NkT ( nkt n kt) NkT N / n S Q ( )

11 (3/4) > S > M 3 [ m / s] [ / s] > Γ > Q a [ kg / s] µ A ns nµ A nms mγ nmµ A 3 [ m / s] S µ A Q S S Q S S m [kg] n [ /m 3 ] A [m ] u [m/s] S S Q Q ( n n ) kt ( n ) n Γ

12 (4/4) conductance Angle valve (l/s) 5/8 (6mm) 5 ½ (40 mm) 45 ½ (63 mm) 60 Gate valve (l/s) ½ (63 mm) (00 mm) (60 mm) (00 mm) (50 mm) 6000

13 Q S e S e ) S p + ( S S e p S p + S p >> S p S e / ds e ds p S p ds e / d 0 << S p S e / 0 ds e ds p ds e / d

14 ( / γ γ γ γ γ M RT A Q V c c γ /( ) Q ( / ) / ( 9.3 γ γ γ γ γ M T A γ [ ] { } ) / ( /.6 76 A

15 Q A / γ γ γ M RT ( γ γ / Q 0, γ /( γ ) [ /( γ + ] γ c ) ritical value For air at 0 o / > / / < γ c Q c 0A {.6A/[ ( / )]} 0A ( / ) 0A A (cm ), (torr), Q (torr liter/sec)

16 ,. df ( d / dx) πr dr dx F ηa( dv / dr) A πrdx F dv η πrdx πη r dt F ' df dv dx dr δf dv d dv F + dr πηdx r + r dr δr dr dr dr d πη dr r dv drdx dr

17 df d dx d dv πrdrdx + πη r drdx 0 dr dr r + ( dv / dr) ( r / η )( d / dx) K ( dv / dr) ( r / η )( d / dx) + ( K / r) v η + + ( r / 4 )( d / dx) K ln r K d dr r dv dr df r d η dx dv / dr 0 v max, r0 K 0 v0 (wall), ra K ( a / 4η )( d / ) v (/ 4η )( d / dx)( a dx r ) Gas, Gas, zero

18 gas flowing : throughput dv / dt 0 a πrvdr ( πa 4 / 8η )( d / dx) 4 Q ( dv / dt) ( πa / 8η )( d / dx) L 4 Q ( πa / 8η ) d / 0 L dx [ πa 4 /(6ηL)]( ) ( )( + ) ( + )/ Q 4 4 [ πa /(6ηL)] ( ) [ πd /(8ηL )] ( ) oiseuille law 4 Q /( ) [ πd /(8 L)] D, L (cm), (dyne/cm ), (cm 3 /sec), in poises η [ D /( ηl)] (torr), L (cm), D (cm), (poise), (liter/sec) η η At 0 o air 4 air 8( D / L)

19 d f πr dx dµ f r dx dx π η dr dµ ( r) dr r d η dx d 4 η dx u ( a) 0 u( r) ( r a )

20 µ(r) 4 a πa d πrµ ( r) dr 0 6η dx 4 πa 6η L 4 πa 8ηL av ( ) 4 πd 8ηL av ( d / dx ( ) / L av ( + ) / ) Q /( ) 4 πa 8ηL 4 πd 8ηL av av dm ( MT ) / d L 4 av [ a]

( < ) ( A) gas Q Q ( A 3 / dv / dt) 3.64 0 ( T / M ) gas Q Q ( dv dt T M A 3 / / ) 3.64 0 ( / ),. Q Q > 0 3 3.

21 ( < ) ( A) gas Q Q ( A 3 / dv / dt) ( T / M ) gas Q Q ( dv dt T M A 3 / / ) ( / ),. Q Q > ( T / M ) / A( ) Q onductance of an aperture of area A (in molecular flow) 3 Q /( ) ( T / M ) / 3.64( T / M ) A / A A (cm ) cm 3 /sec liter/sec conductance

22 For air, at 0 o, (T/M) / 3.8 air. 6A liter/sec, A πd / 4.86( T / M ) D air 9.6D / liter/sec Aperture pumping speed S Q / ( ) / [ ( / )] For air, at 0 o, S.6A[ ( / )]. 0 S. 6A A (cm ), S (liter/sec) umping speed /.6 A pumping speed (.6A) (0A)

23 -, 3, A 0 - A diaphragm 3 -A 0 order A e -3 A conductance --3 conductance / (/ ) + (/ ) + (/ ) A 0 e 3-- conductance / (/ A ) + (/ ) conductance,,, 3 flow. / (/ ) + (/ ) + (/ ) (/ ) (/ ) 0 e A 0 A + / e (/ A) (/ A ) > /[ A/ A ] 0 e A 0 At 0 o air.6a/[ A/ A ] e 0 A << A 0 e A A A A 0.5A 0 e 0 e A aperture No resistance to the flow diaphragm effect

24 ., vav φ nv av / 4 q φbl BLnv av / 4 B, v flow drift velocity, L mv / 4 q ' qmv BLnv N A N q' F F A 4AkT n N / n Avn / n [4A N / n v av BLnv av mv /( BL)][ kt /( mv av ( / π )(kt / m) av Avn AkT n / [ A /( BL)][ kt /(m)] [A /( BL)][ RT /(M π uniform drift velocity v random Maxwell-Boltzman distributuin. π )] / )] /

25 Knudsen drift velocity random velocity 8/3π. conductance 3 8 π kt m / A BL π 4 T m / A BL GS unit AπD /4, B D conductance 3.8( T / M ) / ( D 3 / L) D (cm), L (cm), (liter/sec) For air at 0 o, (T/M) / 3.8 air.( D 3 / L) D (cm), L (cm), (liter/sec) conductance

26 zero, conductance aperture conductance. conductance / e (/ L A e L /( ) + (/ L + e ) e ) L /[ + ( L / e )] L K'' 3 /[ ( A / A )] ( / ) / 0 T M A /[ ( A / A0 )] conductance L, K" L / e 5.3[ A/( BL)][ ( A/ A0 )] ( / ) L K" L conductance, e aperture conductance A, A 0 [ + 5.3A/( BL)( A/ )] + L e A0 : AπD /4 ; B D ; A 0 D v /4 K" /{ +.33( D / L)[ ( D / D V ) ]} K Knudsen s factor

27 D < 0. D v (Dv D ) conductance 3.8( T 3.8( T 3.8( T For air at 0 o, (T/M) / 3.8 K " /[ +.33( D / L)] / M ) / M ) / M ) / / / ( D ( D D / L) K" / L) /[ +.33( D / L)] /[ L +.33D] L (cm) ; D (cm) ; (liter/sec) 3 air.d /( L +.33D).( D Kinetic gas theory K lausing s factor K 3 / L) K" K' 5( L / D) + ( L / D) ( L / D) + ( L / D)

28 lausing s factor K K.0 lausing' Factor K K exp ( -x /.5) x L/a L ipe Length (cm) a ipe Radius (cm) X-axis (x L/a)

29 3.8( T 3.8( T / M ) / / M ) ( D / 3 ( D / L) 3 / L) K" 3.8( T / M ) / D D /[( D + D ) / L] / 3 3.8( T / M ) ( D / L) e D e [ D + D /3 D /( D )] : 3.8( T / M ) / D /[ L + L +.33D] ( T / M ) / D /[ L + L ] / 3 3.8( T / M ) D / L e L + L +.33D( L e θ /80)

31 Gas flow flow meter meter calibration (Q QnVAS) -, gas ( V V ) 0 cc ST final 39 mtorr : 0 x x 0 - x V V 9.4 liter Gas Flow rate Slope : 3. mtorr / sec, V 9.4 liter Flow rate 3. x 0-3 x x 0 - t /sec ressure slope sccm/(t /sec) 4.8 sccm Residence Time : : chamber : Time τ V S V S V Q torr, V 00 liter Q 60 sccm ( tl/s) ( x 00) / 50 sec

32 : : leakage 3 : 4 : roughing 0 9 <<<< : 6 : roughing 7 : 8 : 9 : main 0 : water : : fore-line

33 onductance : 4 air 8( D / L) + T M 3 3.8( T / M ) / D /[ L +.33D]

34 umping Speed conductance Angle valve (l/s) 5/8 (6mm) 5 ½ (40 mm) 45 ½ (63 mm) 60 Gate valve (l/s) ½ (63 mm) (00 mm) (60 mm) (00 mm) (50 mm) 6000

35 umping Speed (760 ~ 0-3 ) :,,, K 760 ~.0 torr :..0 ~ 0. torr :.5 0. ~ 0.00 torr : 4.0

36 o e -st/v + ( u + Q / S) ( e -st/v ) Q/S sus

37 (residual gas)

39 (Oil Diffusion)

42 (/7) Ex) 500 mm, 500 mml sus 60 x 0-5 torr,, valve, Sol) 5, 45 ) Sn (.3V/t) log ( / ) (.3 x 98 / 5) log(760/0 - ) 73 liter / min x 0 - torr 73 liter/min. if pump(gh-40) 0 liter/min Sn(.3 KV/t)log(/) K π (π/4) x (50) +πx50x cm min 760 torr l / min 50l / min 70l /.0torr 0.torr 0. 0 torr

43 (/7) GH-40 rotaty pump

44 (3/7) min 760 torr l / min 50l / min 70l /.0torr 0.torr 0. 0 torr t.3( VK / Sn)log( / ) log( ) + log( ) + log( ) 9.min ) 5 mm, valve 000 mm, 4 D (.5 /00) 705liter / sec 450liter / min L real : S S /( + S ) /( ) 94.7liter / min x0 - torr p n n 73l / min 94.7l / min 0l / min 0 torr 5min (?) 9.min GH-40.7 min

45 (4/7) 4 D : 3.D 50liter / sec L +.33D Sn (Sp x )/(Sp + ) 50 x 570 / ( ) 73.8 l/sec pumping hr x (36/73.8).36 hr

46 (5/7) 4 D 6 D

47 (6/7) 60 mm (6 ), 880 liter/sec Sn346 liter/sec t hr x (36/346) 0.68 hr 40.9 min T.3 min min 53. min 6 D (00 l/sec) 00 mm (4 ), Sn (50 x 00)/(50+00)07 liter/min t hr x (36/07).4 hr68.4 min T.3 min min 80.7 min 60 mm (6 ), Sn (880 x 00)/(880+00) 508 liter/min t hr x (36/508) 0.46 hr 7.6 min T.3 min min 39.9 min

48 (7/7) 4) backing pump 4 D 0 - torr 60 liter/min, fore-pressure x 0 - torr throughput : 60 x 0 - torr liter/min back-streaming x 0 - torr 60 x 0 - torr liter/min. Sp 60 x 0- / ( x 0 - ) 3 liter/min rotary pump GH-40 (90 liter/min) x 0 - torr 30 liter/min back-streaming.

(Vacuum) Vacuum)? `Vacua` (1 ) Gas molecular/cm 3

(Vacuum) Vacuum)? `Vacua` (1 ) Gas.5.5 10 19 molecular/cm 3 & Medium high vacuum High vacuum Very high vacuum 760 5 1 10-3 10-6 10-7 10-9 Low vacuum Medium vacuum High vacuum Very high vacuum Ultra-high