ECE507 - Plasma Physics and Applications

Transcription

1 ECE57 - Pasma Physics ad Appicatios Lecture 9 Prof. Jorge Rocca ad r. Ferado Tomase epartmet of Eectrica ad Computer Egieerig

2 Low temperature pasmas Low temperature pasmas are a very iterestig subject ivovig physics, chemistry, ad materias sciece. I the past, research i pasmas was maiy cetered i the study of high-temperature, coisioess pasmas. The iterest o these pasmas was fueed by appicatios such as ucear fusio ad others. More recet techoogica deveopmets, maiy reated to semicoductor maufacturig, have ed to a revived iterest i ow temperature pasma physics ad techoogy. Some appicatios icude: Pasma etchig/depositio i microeectroics, Low-pressure discharge ight sources, High-pressure pasma ight sources, Pasma dispay paes, High-pressure pasmas: dieectric barrier ad coroa discharges, Low temperature pasmas for poymer surface modificatio, Pasma-assisted diese ehaust remediatio, Abatemet of ehaust gases from semicoductor maufacturig, Io impatatio, Pasma-ehaced depositio of hard thi fims, ad may, may others ECE 57 Lecture 9

3 Semicoductor maufacturig: scaig Number of trasistors doubig every years G. Lisesky - Beoit Coege ECE 57 Lecture 9 3

4 ECE 57 Lecture 9 4

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7 3 Eea dieectric etch system (LAM) ECE 57 Lecture 9 7

8 Custer too for metaizatio process (AMAT) ECE 57 Lecture 9 8

9 ECE 57 Lecture 9 9

10 ECE 57 Lecture 9 1

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16 Trech etch (. µm wide by 4 µm deep) i sige-crysta siico ECE 57 Lecture 9 16

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20 Outie for the et casses Partice ad eergy baace i discharges Itroductio iffusio Sheath dyamics Eectropositive pasma equiibrium Eectroegative pasma equiibrium C discharges Capacitive discharges Iductive discharges ECE 57 Lecture 9

21 iffusio ad trasport Remember from Lecture 6 the epressio for mometum coservatio u m t ( u) u q( E ub) P m f v t co For sow time variatio, ad egectig iertia ad magetic forces, we have qe p m u The ast term represets the mometum oss of the eectros i coisios with backgroud ios ad eutras, which are supposed to be at rest. ν m is the coisio frequecy for mometum trasfer: it tes us how may times per secod (i average) the eectro oses a its directed motio (mometum). If we further assume that the pasma is isotherma (such that gradiets i pressures are oy caused by gradiets i desity) we obtai u qe m m kt m m m ECE 57 Lecture 9 1

22 We ca rewrite this epressio as E u Partice fu q m m (m Mobiity costat /V s) kt m m (m iffusio costat /s) A coupe of particuar cases: Free diffusio (eutras, or E = everywhere) t Substitutig i the cotiuity equatio ad assumig positio idepedet. Show it! ECE 57 Lecture 9

23 Ambipoar diffusio Sovig for E, ad the substitutig i the io equatio ECE 57 Lecture 9 3 e e i i E E What are we assumig here? e i e i E ambipoar e i e i i e i e i e i i

24 iffusio some particuar cases iffusio i a sab ECE 57 Lecture 9 4 A X A X A X B A X X d X d T e T T dt dt s m d X d X dt dt T d X d T dt dt X t t T X t t t a cos ; si ; cos si cos ] [ 1 1 so ) ( ) ( ), ( propose we / -/ +/

25 Boudary coditios: X = /, -/ ECE 57 Lecture 9 5 owest mode domiates 1 1) ( 1) cos( ow characteristic time, its Assumig eah mode decays at the desity profie chage with time? How does. which satisfies ) si( 1) cos( desity profie for a arbitrary iitia cos ) ( ) ( The compete soutio for the owest diffusio mode is 1 / cos / / j j A e () j B j A e t T X (,t) j t j j j j j j t j -/ +/ t

26 iffusio some particuar cases Steady-state soutios ECE 57 Lecture 9 6 A A B B A B A d d t so idepedet of we say easy soutio +/

27 iffusio some particuar cases Source i the regio of iterest: ioizatio iz so we ca write iz ioizatio frequecy d iz (same form as before) d The soutio here is aso of the form cos where here the fu ad veocity are iz, 1 iz d d si we eed to appy boudary coditios, say, u si 1 cos ta cos ad the iz ECE 57 Lecture 9 7

28 Peope aso defie 1 iz How ca this be whe both ν iz ad are fuctios of the medium? They are both fuctios of T e. Ca we reay ask for (±/) =? O the oe had si O the other had so u u B d d ad we fiay obtai At the edge of the sheath ( ta u ) B u u aso a equatio for T B e kt m e ECE 57 Lecture 9 8