_&WordMicrosoft Word  6&"Systemf. &$-X@Bookman Old Styleww 0wf.- 12 ~ &6Vacuum Deposition ChamberPOyTkTOk 2 C&6 F,@Bookman Old Styleww 0wf.-&2 ?&6Problem raised by gFyKgFyyK~K- 3f12 8&6Galileo Vacuum System spaPOTOOOykOy-  2 ?&6 - D2  &&6Coordinating teachers of the problem: gFYF~KYyyygyKKKYyKgFyKK8,@Bookman Old Styleww 0wf.- 2 &6 x -U2 t 1&6Riccardo Ricci (Universit degli Studi di Firenze8FyygKFyyFKFFyygyFYKy~FFKYFKFKFgypy 2 t &6)F 2 t &6 _2  !8&6Miguel ngel Herrero (Universidad Complutense de Madrid)F~yFK~yFKyggygKFFyygyFKFYyyyKyKgFF 2  &6  2 &6 8X@Bookman Old Styleww 0wf.-22 ?&6Exposition of the problem:{|hH\H|D|LD\tD\|xDtD 2 ?i&6 8@"Arial Narrowww 0wf.-2  &6Physical Vam[RR$R[$cm[2  N&6cuum Deposition (PVD) is industrially used for the generation of a coating on R[[cv[[[R$.$[[c7mmv7c$Rc$[[[R.7$[$$Rc[R[[b.[7b.[[b[[[[7[.$[[b[.b[bR[[.$[[b[[.6&'@2 #&6substrates of different materials. R[[R.7[.[R.[..[$..[7[[..[.[7$[$R.. 2 &6 X6&'2 m[&6In the particular case we have to deal with, the coating is a constituted by a sandwich of .[Z.[[Y[[7.$R[$[7YR[R[Yv[Y[[R[Y.[Y[[[$Yv$.[.Y.[[YR[[.$[[Y$RY[YR[[R.$.[.[[Y[RY[YR[[[v$R[Y[..6&'X2 R3&6Aluminium and a polymeric film (HMDSO) upon a substm$[$[$[1[[[1[1[[$R[7$R0.$$07vvm70[[[[0[0R[[R.M2 RP,&6rate of polycarbonate. The final product of 7[.[0[.0[[$RR[7[[[[.[.0d[[0.$[[$0[7[[[R.0[..6&'}2 8L&6the industrial process is the reflecting part of projectors for automotive. .[[.$[[[R.7$[$.[7[R[RR.$R..[[.7[.$[R.$[[.[[7..[..[7[$[R.[7R..[7.[[.[[.$R[.. 2 8&6 X6&'j2 ?&6The deposition of the final coating is achieved in three steps:d[[.[[[[R$.$[[.[...[[..$[[$.R[[.$[[.$R.[R[$[R[[.$[..[7[[.R.[[R. 2 &6 X6&'v2 G&61. Within a cylindrical metallic chamber, the atmosphere is brought to [..$.[$[.[.RR$$[[7$R[$.[.[$$$R.R[[[[7...[[.[.[R[[[7[.$R.[7[[[[...[.)2 E&6a very low pressure [.R[7R.$[v.[7[RR[7[. 2 &6 X6&'2 ^&62. Within the chambers, aluminium is vaporised by means of the Joule Effect. In this way, the [.D$.[$[D.[[DR[[[[7R.D[$[$[$[D$RDR[[[7$R[[D[RD[[[RD[.D.[[DR[[$[Cm..[R..C.[C.[$RCv[R.C.[[.6&'2 M&6Aluminium covers up the surface of the substrates located within the chamber.m$[$[$[.R[R[7R.[[..[[.R[7.[R[.[...[[.R[[R.7[.[R.$[R[.[[.v$.[$[..[[.R[[[[7. 2 &6 X6&'j2 ?&63. A monomer flows through nozzles at relatively high pressure.[.TmT[[[[7T.$[vRT.[7[[[[S[[RR$[RS[.S7[$[.$R[$RS[$[[S[7[RR[7[.42 &6 In the plasma atmosphere, S.[S.[[S[$[R[S[.[R[[[7[..6&'2 a&6generated by the strong electric field, the monomer polymerise on the substrate, covering up the d[[[[7[.[[6[R6.[[6R.7[[[6[$[R.7$R6.$[$[.6.[[6[[[[76[[$R[7$R[6[[6.[[6R[[R.7[.[.6R[R[7$[[5[[5.[[.6&'2 ~Z&6surface. In this way a thin (~ 10 nm) film of HMDSO is made to protect the surface of the R[7.[R[.R.[R.[$RRv[RR[R.[$[R7`R[[R[7R.$$R[.QvvmQ$RQ[[[Q.[Q[7[.[R.Q.[[QR[7.[R[Q[.Q.[[.6&' 2 d&6projectors. [7[$[R.[7R.... 2 d &6 X6&' 2 I&6 X6&'22 /&6At the end of the process,m...[[.[[[.[...[[.[7[R[RR.t2 / F&6 the chamber is opened and the projectors are ready to be assembled. ..[[.R[[[[7.$R.[[[[[[.[[[..[[.[7[$[R.[7R.[7[.7[[[R..[..[[.[RR[[$[[.. 2 /(!&6 X6&'2 [&6The scope of the model and simulations, should be to suggest new and better setting of the d[[LRR[[[L[.L.[[K[[[$K[[[KR$[$[.$[[R.KR[[[$[K[[K.[KR[[[[R.K[[vK[[[K[[..[7KR[..$[[K[.K.[[.6&'2 [&6chamber and electrodes, such as shape, position and size of the electrodes, and optimised R[[[[7O[[[O[$[R.7[[[R.NR[R[N[RNR[[[[.N[[R$.$[[N[[[NR$R[N[.N.[[N[$[R.7[[[R.N[[[NN[[.$$R[[.6&'2 &6pro[7[2 w]&6cess parameters (such as pressure and voltage applied to the electrodes), in order to have a R[RR8[[7[[.[7R87R[R[8[R7[7[RR[7[7[[[7R[$.[[[7[[[$$[[7.[7.[[7[$[R.7[[[R7.7$[7[7[[77.[7[[R[7[.6&'2 a&6mostly uniform energy and charge density, a uniform potential, a uniform distribution of current d[R.$RA[[$.[7A[[[7[RA[[[AR[[7[[A[[[R$.R.A[A[[$.[7A[[.[[.$[$.A[A[[$.[7A[$R.7$[[.$[[A[.AR[77[[..6&'n2 B&6lines and so on, so to reduce the possible inhomogeneities in the $$[[R.[[[.R[.[[..R[..[.7[[[R[..[[.[[RR$[$[.$[[[[[[[[$.$[R.$[..[[."2 &6final coating. .$[[$.R[[.$[[.. 2 &6 X6&'2 !d&6Clearly, the real situation would not allow for the resulting model to be actually solved. However, v$[[7$R.7.[[77[[$7R$.[[.$[[7v[[$[7[[.7[$$[v7.[77.[[77[R[$.$[[7[[[$7.[7[[7[R.[[$$R7R[$R[[.6v[v[R[7..6&'2 u"e&6as the aim of the model is to analyse the distribution of potential and charged particles within the [R5.[[5[$5[.5.[[5[[[$5$R5.[5[[[$RR[5.[[5[$R.7$[[.$[[5[.4[[.[[.$[$4[[[4R[[7[[[4[[7.$R$[R4v$.[$[4.[[.6&'F2 [#'&6chamber, one can drastically reduce theR[[[[7..[[[.R[[.[7[R.$R[$$R.7[[[R[..[[R2 [#/&6 complexity by making some simple assumptions. .R[[$[R$.R.[R.[R$[[.R[[.R$[$[.[RR[[.$[[R.. 2 [#&6 X6&' 2 @$&6 X6&'2 &%Y&6The activity we propose is to start the construction of the model under some simplifying d[[f[R.$R$.Rfv[f[7[[[R[f$Rf.[fR.[7.f.[[eR[[R.7[R.$[[e[.e.[[e[[[$e[[[[7eR[[eR$[$$.R$[[.6&'2 &\&6assumptions like stationary field, plasma at equilibrium and simple boundary conditions and [RR[[.$[[RY$$R[YR.[.$[[[7RX.$[$[.X[$[R[X[.X[[[$$$[7$[X[[[XR$[$[X[[[[[[7RXR[[[$.$[[RX[[[.6&'22 &&6develop analytical and num[[R[$[[.[[[$R.$R[$.[[[.[[+2 &K &6erical descriptions. [7$R[$.[[RR7$[.$[[R.. 2 &&6 X6&' 2 '&6 X6&'-82 (&6Scheme of the work to be done:tttD|LD\tD|\D\|DxtD|tD 2 (n&6 6&' 2 )&6 6&'-2 *&61) [7.8@Times New Romanww 0wf.-,2 *J&6Set the physical modeloY828dY2dddN8YY82ddY8- 2 *d &6 0X6&' 2 x+&6 0X6&'-2 [,&62) [7.-F2 ^,J'&6Discuss the appropriate simplifications8NYdNN28dY2YddCddC8Y8Y2N8d88B8YY88ddN- 2 [,{&6 0X6&' 2 D-&6 0X6&'-2 (.&63) [7.-D2 +.J&&6Solve numerically the simplified modelod8dY2ddYC8YY88d28dY2N8d88B8Yd2ddY8 2 +.&6 0[6&' 2 /&6 0[6&'-R2 //&64) Draw consequences from the numerical resultsdC2CY2YddNYddYdYYN2BCd28dY2ddYC8YY82CYNd88N- 2 / &6 0X6&' 2 0&6 0X6&'-66&&66&&66&&66&&66&&66&&66&&66&&66&& 6 6& &  6 6& &  6 6& &  6 6& &  6 6& & 66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&&66&& 6 6& & !!6!6&!&!!""6"6&"&""##6#6&#&##$$6$6&$&$$%%6%6&%&%%