MODELING OF MICRODISCHARGE DEVICES: PLASMA AND GAS DYNAMICS*

Transcription

1 MODELING OF MICRODISCHARGE DEVICES: PLASMA AND GAS DYNAMICS* Mark J. Kushner Dept. Electrcal and Computer Engneerng Urbana, IL USA October 2004 * Work supported by the Natonal Scence Foundaton and Ar Force Research Labs. IWM04_01

2 AGENDA Scalng of Mcrodscharge Devces Descrpton of model The annular sandwch MD The pyramdal MD Concludng Remarks. Acknowledgements: Ramesh Arakon, Ananth Bhoj, Bran Lay IWM04_02

3 MICRODISCHARGE PLASMA SOURCES Mcrodscharges have demonstrated great promse for photon, radcal and onzaton sources, and laboratores for plasma and optcal physcs. Mcrodscharges leverage pd scalng to operate as dc atmospherc glows 10s 100s µm n sze. MEMS enable nnovatve structures for dsplays and detectors. Although smlar to PDP cells, MDs are dc devces whch largely rely on nonequlbrum beam components of the EED. Electrostatc nonequlbrum results from ther small sze. Debye lengths and cathode falls are commensurate wth sze of devces. IWM04_03 L 1/ 2 T ev λd 750 cm 10µ m, 3 ne( cm ) 1/ 2 ( 2V ε / ( qn )) m cathode Fall = c 0 I µ

4 WHAT CAN BE LEARNED FROM MODELING MICRODISCHARGES? Progress n other felds of low temperature plasmas has greatly benefted and been facltated by modelng. Plasma materals processng Lasers Polluton abatement Development of mcrodscharge technologes has been extremely successful wthout a strong legacy of modelng. What can be learned from modelng mcrodscharges (that we ddn t already know)? What capabltes n modelng are requred? IWM04_34

5 GOAL FOR THIS TALK: MODELING AS A BASIS OF FUNDAMENTAL UNDERSTANDING AND SCALING Dscusson of modelng MDs wth goals of Fundamental parameters and operatng characterstcs Scalng Use of MDs as sources of radcals and thrust Modelng Platform: Nonpdpsm 2-dmensonal plasma hydrodynamcs model IWM04_06

6 DESCRIPTION OF nonpdpsim To nvestgate scalng processes n mcrodscharge sources, nonpdpsim has been developed, a 2-dmensonal model. Rectlnear or cylndrcal unstructured mesh Implct drft-dffuson-advecton for charged speces Naver-Stokes for neutral speces Posson s equaton (volume, surface charge, materal conducton. Crcut model Electron energy equaton coupled wth Boltzmann soluton Monte Carlo beam electrons Optcally thck radaton transport wth photoonzaton Secondary electrons by mpact, thermoncs, photo-emsson Surface chemstry. GEC04_05

7 DESCRIPTION OF MODEL: CHARGED PARTICLE, SOURCES Contnuty (sources from electron and heavy partcle collsons, surface chemstry, photo-onzaton, secondary emsson), fluxes by modfed Sharfetter-Gummel wth advectve flow feld. N t Posson s Equaton for Electrc Potental: v = r φ Photoonzaton, electrc feld and secondary emsson: v v v v r r 3v N ( r ) σ j N j ( r )exp d r v λ S P ( r ) = v v 2 4π r r ( ( ) ) 3 1/2 2 ΦW q E/ ε 0 S = = S j, je AT exp, js = γ jφ j kts j + S ε Φ = ρ V + ρ S GEM_0204_32

8 DESCRIPTION OF MODEL: ELECTRON ENERGY, TRANSPORT COEFFICIENTS Electron energy equaton mplctly ntegrated usng Successve- Over-Relaxaton: ( n ε) e t = r j r E + σe 2 EM n e N κ 5 2 εϕ λ T e, r j = r qφ e Electron transport coeffcents obtaned from 2-term sphercal harmonc expanson of Boltzmann s Equaton. Ion transport coeffcents obtaned from tabulated values from the lterature or usng conventonal approxmaton technques. ECOIL_0803_25

9 DESCRIPTION OF MODEL: MCS AND MESHING Transport of energetc secondary electrons s addressed wth a Monte Carlo Smulaton. IWM04_07 Supermpose Cartesan MCS mesh on unstructured flud mesh. Construct Greens functons for nterpolaton between meshes. Electrons and ther progeny are followed untl slowng nto bulk plasma or leavng MCS volume. Electron energy dstrbuton s computed on MCS mesh. EED produces source functons for electron mpact processes whch are nterpolated to flud mesh.

10 DESCRIPTION OF MODEL: NEUTRAL PARTICLE TRANSPORT Flud averaged values of mass densty, mass momentum and thermal energy densty obtaned usng unsteady, compressble algorthms. ( ρc T ) t p ( ρv) t r ρ r = ( ρv ) + ( nlets, pumps ) t rr = NkT ρvv µ + q = ( ) ( ) ( κ T + ρvc T ) + P v R H + j Alternately, f only heat conducton s consdered. ( ρc T ) t p r p ( T ) R H + j = κ f r N r E v E r r E GEM_0204_33

11 DESCRIPTION OF MODEL: NEUTRAL PARTICLE UPDATE Transport equatons are mplctly solved usng Successve-Over- Relaxaton: ( ) ( ) + = r N + ( t t) N t t N t v f D NT + SV + N T Surface chemstry s addressed usng flux-n/flux-out boundary condtons wth reactve stckng coeffcents SS = j ( ) φ r j γ j S S ECOIL_0803_26

12 METHOD OF SOLUTION Fnte volume technques are used for flux conservaton at all nodes. dn dt r 1 r r 1 = φ = Ajφj, φj = 2 φ V Jacoban elements are numercally derved to produce a matrx of dfferental updates for tmestep t. N N ( t + t) = N ( t) = N t j ( t ) t + + N Iteratve Newton s method s used to solved coupled charged partcle transport and Posson s equaton. j N N j ( φ ) + âj N j ECOIL_0803_32

13 METHOD OF SOLUTION Tme splcng acceleraton technques are used n whch modules are sequentally executed. Charged Partcles and Potental Electron Temperature Neutral Denstes Surface Chemstry t Electron Monte Carlo t2 Electron Transport Coeffcents t 3 [ Electromagnetcs] 5 1 t If only the steady state s desred, the tme steps taken n each module are usually dfferent. t 4 Naver Stokes t5 Neutral Denstes IWM04_08

14 ANNULAR SANDWICH MICRODISCHARGE MDs wth 10s - 100s µm spacng wth crcular/annular electrode cavty. Operaton of up to 1 atm n rare and molecular gases V, a few ma Ref: Kurt Becker, GEC 2003 IWM04_04

15 BASE CASE MICRODISCHARGE PARAMETERS A sandwch mcrodscharge devce s the base case: Sloped delectrc (flow ssues) 200 µm Hole: 200 µm dameter at anode to 300 µm at cathode. Anode Cathode Delectrc: 200 µm thck Anode/Cathode 100 µm thck Cylndrcally symmetrc Argon, 250 Torr, 2 ma (set by adjustng ballast resstor) IWM04_09

16 MESHING IS CRITICAL Anode Cathode 200 µm The choce of meshng s crtcal n resolvng plasma transport n the dscharge zone. Must resolve cathode fall as well as electrcal and flow boundary condtons at large dstances. Dynamc range Total nodes: 5424 Plasma nodes: 3693 IWM04_10

17 ELECTRIC POTENTIAL AND FIELDS Anode potental penetrates nto lower plenum, producng hollowcathode-lke structure. Geometrcal enhancement and space charge produce felds approachng 100 kv/cm. IWM04_11 Electrc Potental E/N (Electrc Feld/Gas Densty) Max = 80 kv/cm

18 ELECTRON TEMPERATURE AND IONIZATION SOURCES In the bulk plasma, T e of 3.5 ev suggests postve column condtons. Large contrbutons to onzaton occur from both bulk and beam electrons Electron Temperature Bulk Ionzaton Beam onzaton APL_0904_23

19 ELECTRON DENSITY Peak electron denstes of >10 14 cm -3 are produced n the steady state. These hgh cw denstes enable large rates of exctaton of hgh lyng electronc states. Electron densty APL_0904_24

20 VISIBLE AND UV EMISSION Vsble emsson s constraned to an annulus due to short lfetmes of states. UV emsson from excmer s more dstrbuted due to the large range of Ar(4s) metastable precursor. Ar(4p) Densty (Vsble Emsson) IWM04_12 Ar 2 * Densty (UV Emsson)

21 THERMODYNAMIC PROPERTIES Current denstes of 5-10 A/cm 2 and power of 10 s-100 kw/cm 3 produce sgnfcant gas heatng and rarefacton. Rarefacton ncreases range of secondary electrons. IWM04_13 Gas Temperature Relatve Mass Densty

22 ADVECTIVE FLOWFIELD Cataphoress entrans gas, producng pumpng acton from above the plenum, through the hole to below the plenum. The jet experences resstance n the stagnaton zone below the plenum and recrculaton results. Axal Gas Speed Flow Drecton IWM04_14

23 Beam Ionzaton MD PROPERTIES vs PRESSURE Electron Densty Decreasng pressure enables deeper penetraton of beam electrons n spte of the lower cathode voltage. The result s more confnement at hgher pressure and hgher peak electron densty. Ar, 2 ma 125 Torr 1.3 x Torr 2.1 x APL_0904_ Torr 3.5 x 10 14

24 MD PROPERTIES vs PRESSURE: VISIBLE EMISSION Vsble emsson s sgnfcantly more extended at low pressure, penetratng far out the hole. Peak emsson s greater at hgher pressure due to confnement of beam component. 125 Torr 250 Torr 500 Torr IWM04_15

25 62.5 Torr 250 Torr 125 Torr 500 Torr MD PROPERTIES vs PRESSURE: VISIBLE EMISSION Expermental trends are reproduced for contracton of optcal emsson at hgh pressure. Ref: Mara Crstna Penache, Thess, 2002 Ar, 2 ma, syntheszed sde vews IWM04_16

26 MD PROPERTIES vs PRESSURE: VISIBLE EMISSION Expermental trends are reproduced for contracton of optcal emsson wth ncreasng pressure. Ref: Mara Crstna Penache, Thess, 2002 IWM04_17

27 MD PROPERTIES vs PRESSURE: Ar(4s) DENSITY Large metastable denstes produce effcent excmer emsson at hgher pressures. Ref: Mara Crstna Penache, Thess, 2002 IWM04_18 Ar, 2 ma

28 MD PROPERTIES vs PRESSURE: UV-EXCIMER EMISSION The dsparty between unformty of and peak emsson s greater for the UV-excmer due to greater dffusvty of Ar(4s) at low pressure and hgher rate of dmer formaton at hgh pressure. 125 Torr 250 Torr 500 Torr IWM04_19

29 MD PROPERTIES vs CURRENT: BEAM IONIZATION Thermodynamcs cannot be gnored n operaton of MDs. Contrastng, low (0.15 ma) and hgh (4.0 ma) operaton, the physcal extent of beam onzaton s greater at the hgher current ma 4.0 ma IWM04_20

30 MD PROPERTIES vs CURRENT: GAS TEMPERATURE.whch results n part from larger cathode voltage and n part from rarefacton produced by gas heatng ma 4.0 ma IWM04_21

31 MD PROPERTIES vs CURRENT: ELECTRON DENSITY The end result s a more tghtly confned plasma at the lower pressure ma 4.0 ma IWM04_22

32 MD PROPERTIES vs CURRENT: T(gas), [e] Peak electron densty and gas temperature scales nearly lnearly wth current densty. Ar, 250 Torr, γ = 0.15 IWM04_23

33 MULTISTAGE DEVICES Multstage MDs are desrable for long gan lengths for lasers. The desgn of such devces requres attenton to thermodynamcs ssues. 600 Torr Ne. IWM04_31 Ref: J. G. Eden

34 EXAMPLES OF 2-STAGE MDs Desgn affects gas heatng, rarefacton; range and nfluence of secondary electrons and dvson of current. IWM04_32

35 DESIGNING MDs AS VISIBLE SOURCES: AGING As MDs age wth use, crtcal dmensons and materal propertes (such as secondary emsson coeffcents) often change. Modelng s valuable n the desgn process to determne the senstvty of optcal propertes to agng related changes n devce parameters. Ref: Mara Crstna Penache, Thess, 2002 APL_0904_31

36 SENSITIVITY TO γ (SECONDARY EMISSION): [e] The electron densty ncreases wth decreasng γ, a counterntutve result lkely produced by more effcent onzaton by the more energetc secondary electrons. γ = 0.05 γ = 0.20 APL_0904_32

37 SENSITIVITY TO γ (SECONDARY EMISSION): VOLTAGE, [e] Voltage and peak electron densty ncreases wth decreasng γ to counter smaller flux of beam electrons whch onze effcently. Power ncreases when holdng current constant. Ar, 250 Torr, 2 ma APL_0904_33

38 SENSITIVITY TO γ : VISIBLE EMISSION Vsble emsson ncreases as γ decreases, n part reflectng ncrease n power. Dstrbuton of emsson also shfts to beng more domnated by beam electrons. Ar, 250 Torr, 2 ma APL_0904_34

39 SENSITIVITY TO CRITICAL DIMENSIONS: [e] Straght Devce-to-devce varaton n fabrcaton or eroson/wear durng operaton my change crtcal dmensons. How senstve are operatng characterstcs? Contrast straght and tapered delectrcs. Peak electron densty s hgher and more dstrbuted n straght MD. Ar, 250 Torr, 2 ma APL_0904_35 Tapered

40 SENSITIVITY TO CRITICAL DIMENSIONS: VISIBLE EMISSION Straght Tapered Magntude of vsble emsson s senstve to loss n crtcal dmenson. Dstrbuton s less senstve. Robust desgns are possble whch are tolerant to eroson and loss of crtcal dmenson. Ar, 250 Torr, 2 ma APL_0904_36

41 Straght SENSITIVITY TO CRITICAL DIMENSIONS : AXIAL FLOW Speed of (downward) axal flow produced by cataphoress s > 50% hgher n the less tapered MD. Tapered Hgher current densty, larger E/N, larger on-axs plasma densty all contrbute. Ar, 250 Torr, 2 ma IWM04_24

42 MD AS A RADICAL SOURCE: He/O 2 Large current denstes and ntrnscally hgh gas flow makes MDs deal for reactant generators. Demonstrate wth electronegatve He/O 2 mxture. Hgher collsonalty produces larger operatng voltages, larger electrc felds. IWM04_25 He/O 2 =90/10, 125 Torr, 2 ma

43 MD SUSTAINED IN He/O 2 : ELECTRON SOURCES S(beam) T e S(bulk) Larger voltage enables effcency beam onzaton deep nto plasma. Volumetrc attachment produces dstnct regons of postve and negatve bulk sources IWM04_26 He/O 2 =90/10, 125 Torr, 2 ma

44 MD SUSTAINED IN He/O 2 : ELECTRON, ION DENSITIES [e] [N + ] [N - ] Negatve ons are domnated by O 2 - at pressures of 100s Torr. IWM04_27 He/O 2 =90/10, 125 Torr, 2 ma

45 MD SUSTAINED IN He/O 2 : RADICAL, EXCITED STATE DENSITIES [O] [O 2 ( 1 )] [O 3 ] The range of O atoms s lmted by recombnaton and ozone formaton. O 2 ( 1 ) and O 3 are fnal products, havng longer ranges. Cataphoress nduced flow preferentally ejects reactants downward. IWM04_28 He/O 2 =90/10, 125 Torr, 2 ma

46 MD SUSTAINED IN He/O 2 : FLOW PROPERTIES T(gas) [He] [O 2 ] In spte of Frank-Condon heatng, gas temperatures are lower (for a gve current) than n argon due to hgher thermal conductvty of He. IWM04_29 He/O 2 =90/10, 125 Torr, 2 ma

47 MD SUSTAINED IN He/O 2 : FLOW PROPERTIES T(gas) [He] [O 2 ] Optmzaton of MDs as radcal sources wll requre careful attenton to flow propertes to maxmze delvery of reactants. IWM04_30 He/O 2 =90/10, 125 Torr, 2 ma

48 PYRAMIDAL MICRODISCHARGE DEVICES S MDs wth 10s µm pyramdal cavtes dsplay nonequlbrum behavor: Townsend to negatve glow transtons. Small sze also mples electrostatc nonequlbrum. Delectrc Slcon Cathode Plasma Anode S.-J. Park, et al., J. Sel. Topcs Quant. Electron 8, 387 (2002); Appl. Phys. Lett. 78, 419 (2001). IWM04_05

49 MODEL GEOMETRY: S PYRAMID MICRODISCHARGE Investgatons of a cylndrcally symmetrc S pyramd mcrodscharge were performed. GEC03_03

50 BASE CASE: Ne, 600 Torr, 50 µm DIAMETER Optmum operaton produces large enough charge densty to warp electrc potental nto cathode well. In spte of large T e, onzaton s domnated by beam electrons Ne, 600 Torr, 50 µm, 200 V, 1 MΩ GEC03_04

51 BASE CASE: Ne, 600 Torr 50 µm DIAMETER There s essentally no regon of quasneutralty or whch s postve column-lke. Monomer and dmer ons are segregated. Excted state denstes > cm -3 rval macroscopc devces Ne, 600 Torr, 50 µm, 200 V, 1 MΩ GEC03_05

52 TRANSITION TO NEGATIVE-GLOW BEHAVIOR Although geometry precludes true hollow cathode behavor, negatve glow behavor sets n a lower pressures. Characterze negatve glow by S[Ne 2+ ] / (S[Ne + ] + S[Ne 2+ ] ) GEC03_06 Ne, 50 µm dameter, 200 V, 1 MΩ

53 SCALING WITH PRESSURE: PLASMA PROPERTIES Over a range of pressures that V(appled) and R(ballast) can be constant, confnement at hgher pressures produces hgher peak plasma denstes. [e] x cm Torr [2.1 x cm -3 ] 650 Torr [3.9 x cm -3 ] 750 Torr [5.6 x cm -3 ] GEC03_08 Ne, 50 µm dameter, 200V, 1 MΩ

54 SCALING CONSIDERATIONS: CATHODE FALL THICKNESS In MDs, the cathode fall thckness may be commensurate wth cavty sze. Current densty s therefore crtcal to scalng. Low j (and [e]) may result n cathode fall not beng conformal to cathode V, 1 MΩ [e]= 4.9 x cm V, 1.75 MΩ [e]= 5.3 x cm -3 GEC03_06 Ne, 50 µm dameter, 600 Torr

55 SCALING WITH SIZE: pd, BALLAST = CONSTANT Scalng whle mantanng pd, V(appled) and R(ballast) constant results n a reduced j and [e] n the larger devce. The plasma s not conformal to the cathode. GEC03_10 Ne, -200 V, 1 MΩ

56 SCALING WITH SIZE: pd, j = CONSTANT Scalng whle mantanng pd and j constant produces smlar plasma denstes and conformalty to the cathode. 400 Torr 600 Torr 1000 Torr GEC03_11 Ne, -200 V

57 CONCLUDING REMARKS MDs (even n a dc mode) are dynamc enttes wth strong couplng between electron and on transport, gas dynamcs and chemcal processes. Subtle changes n geometry, physcal parameters (e.g., secondary emsson coeffcent) can have profound mpact on operatng characterstcs. There are sgnfcant dfferences n pd scalng between devces wth L > Debye lengths (or cathode fall) and L < λ, d. As MDs age wth use, crtcal dmensons and materal propertes (such as secondary emsson coeffcents) often change. Modelng s valuable n the desgn process to determne the senstvty of operatng characterstcs to agng related changes n devce parameters. IWM04_33