ECE507 - Plasma Physics and Applications

Transcription

1 ECE57 - Plasma Phsis and Appliations Leture 4 Prof. Jorge Roa and Dr. Fernando Tomasel Department of Eletrial and Computer Engineering

2 Constant, uniform Let s align with the -ais, so = k. Then we an write F = ( = = i j. The differential euations of motions are d dt d dt d dt m m (3 (1 ( Taking the time deriatie of (1 and using ( we obtain d dt m This is the diff e for a harmoni osillator with angular freuen = /m (lotron or Larmor freuen ECE 57 Leture 4

3 3 Constant, uniform (3 ( (1 ] Re[ ( ( t i t i e i e A similar euation is found for. The solution of these euations an be written as We drop the Re we are dealing with real uantities / ( tan 1 Integration onstants and are / out of phase, we hae irular motion in a plane perpendiular to. Integrating one more we obtain (3' (' (1' ( ( t e e e e i i t i i t i / is alled Larmor radius, or gro-radius Find these euations b ourself! ECE 57 Leture 4

4 Constant, uniform Aeraging the motion during an orbit we find the euation for the trajetor of the guiding enter g g g i e e t i So in the ase of a onstant, uniform magneti field harged partiles spiral about the magneti field lines. Note that positie ions and eletrons rotate in opposite diretions the upper sign on the preeding euations orresponds to positiel harged partiles. The diretion of rotation of both negatie and positie partiles is suh that redues the ambient magneti field plasmas are diamagneti! The Larmor freuen and radius depend on the mass of the partiles. For the same absolute alue of harge, ions will hae larger orbits and lower freuenies. i ECE 57 Leture 4 4

5 Constant, uniform Negatiel harged partile moing in a region of onstant, uniform. The magneti field faes into the page. For a hdrogen plasma immersed in a 1T magneti field, e = 8 GH and i = 15. MH A low energ beam is injeted aross a magneti field in a hamber with argon at low pressure. Note the dark gap between the athode and beam onset. In this sheath region the eletrons still hae insuffiient energ for light eitation. ECE 57 Leture 4 5

6 Constant, uniform The ion and eletron Larmor radii and freuenies proide spae- and time-sales in a magnetied plasma. Phenomena that our on spae-sales muh smaller than the gro-radius, or on time-sales muh shorter than one Larmor period an be desribed using euations for an unmagnetied plasma. For large spae-sales and long time-sales, gro motion is essential to the desription of the plasma behaior. In some plasmas, the eletrons ma be magnetied, but the ions ma not. Homework: Look through artiles in Phsial Reiew Letters, Phsis of Plasmas, Plasma Phsis, Plasma Soures Siene and Tehnolog or in other journals oer reent ears and find at least one artile eah about laborator, solar or terrestrial, and astrophsial plasmas immersed in magneti fields. Ealuate eletron and ion gro-radii and Debe radius. Compare to sstem sies for eah ase. Calulate number of partiles in a Debe sphere. Ealuate Larmor freuenies and ompare to the timesale eolution of the oerall plasma. Whih of these are reall plasmas? Whih of these are magnetied or unmagnetied? ECE 57 Leture 4 6

7 7 Constant, uniform and E (3 ( ( (1 ( E m dt d E m dt d E m dt d Let s again align with the -ais, so = k. From the fore law F = (E + the differential euations of motions are Taking the time deriatie of E and replaing in E 1 we obtain E m dt d E m dt d ECE 57 Leture 4

8 8 Constant, uniform and E (3 ' ( ' ' (1 ' ' ( ( t m E e i E e E t i t i These euations are similar to those we found before for onstant, but not uite the same. Looks like a transformation ould help. Noting that (E / = i E / j E /, we will rather anale = - (E /. The solutions for are ' / ' ( tan ' ' ' 1 Integration onstants t m E E g So the guiding enter is moing with eloit in the referene frame moing with eloit (E /, and is moing with eloit with respet to the laborator. Note that the drift is independent of, m, and! ECE 57 Leture 4

9 E drift Sine the drift eloit is independent of the harateristis of the harged partiles, the whole plasma will drift together aross the eletri and magneti field lines. Larger Larmor radius here M.75 m in 75 se E.88 m in 88 se m M/m = 3 ECE 57 Leture 4 Smaller Larmor radius here 9

10 Uniform E and : drift and eletri mirror E E ECE 57 Leture 4 1

11 Constant, uniform and a fore F It is simple to generalie to the ase of an other simple fore. We an simple replae the eletri fore E with a general fore F. The guiding enter will now moe with eloit F = (F / or, in the ase of grait, F = m(g /. Although somewhat similar, note that in this ase the drift eloit does depend on m and. Conseuentl, the presene of grait will result into a net urrent densit in the plasma. The graitational drift is horiontal, not ertial! g ECE 57 Leture 4 11

12 Constant, nonuniform How muh an we tell about the moement of harged in nonuniform magneti fields without knowing the eat form of (,,? Assuming that the ariation of the magneti field within the Larmor radius is small, we an Talor epand g ( g Larger Larmor radius here Smaller Larmor radius here and then replae into Es (1 and (, page 1 F ( e i( t i( t g e e i Show it! ECE 57 Leture 4 1

13 Constant, nonuniform Now remembering that we are interested on the real part of these eponentials, and taking the initial phase eual to ero, we aerage in a gration to obtain _ F so the guiding enter drift eloit for perpendiular gradients an be written as Show it! What happens with F? grad 1 F W 3 Note that this drift eloit, like in the ase of graitational drift, depends on the sign of the harged partile, and so it results in a net urrent and a olumetri eletri field. ECE 57 Leture 4 13

14 Cured : Curature drift What is the magneti field is ured? As partiles moe along the line fields, the will feel a entrifugal fore gien b F m R // ˆ r m // R R Using the euations defined before, we an diretl dedue the urature drift ur 1 F m // R R W // R R Note that the onstant, ured magneti field does not satisf Mawell s euations, so the gradient drift needs to be added. ECE 57 Leture 4 14

15 Curature drift - Complete For the magneti field to hae ero url in all diretions perpendiular to, the magneti field strength must fall off as R 1 [ in lindrial oordinates ( ( r ] R r r The total drift (urature + gradient an then be written as ur grad m // R m m // 3 R Show it! For an isotropi, Mawellian plasma the aerage ured-field drift an be written as ur grad 1 3 T W// W 3 Show it! ECE 57 Leture 4 15

16 Other drifts ECE 57 Leture 4 16

17 A summar of guiding enter motion General fore F : Gradient drift : Curature drift : 1 W W F E Eletri field : E m Graitational field : g F grad ur // g 3 R R Cured field in auum: grad ur m 3 // ECE 57 Leture 4 17

18 Eample: Sputtering and reatie sputtering In onept, sputtering and reatie sputtering are simple proesses Metal sputtered from a target is deposited onto the substrate. If the metal is sputtered in the presene of a reatie gas, it will readil form a ompound deposit. DC or pulsed-d power offers the most straightforward and ost effetie option for suh a proess Substrate Metalli or dieletri oating Metal Target (athode (+ (- Power Suppl Sputtering gas (Argon Reatie gas (Ogen, Nitrogen, et ECE 57 Leture 4 18

19 Issues with glow disharge sputtering soures High ion urrent densities (> 1 ma/m, neessar to ahiee aeptable deposition rates, fore to operate the disharge with a high oltage (~ -5 kv. Howeer, the sputtering effiien is relatiel low at these energies, and dereases with inreasing energ. Disharge is maintained b seondar eletron emission from the athode. Pressures must be high enough (>3 mtorr so the seondar eletrons are not immediatel lost to the walls. These pressures, howeer, are higher than optimum for deposition of sputtered atoms onto the substrates (sputtered atoms are sattered b argon atoms ECE 57 Leture 4 19

20 A solution: planar magnetron disharges Magnetron flange mount aking plate Aluminum Deposit Al Al Aluminum Target Ar+ Ar+ Magneti trapping field Rae Trak Al Argon In Substrate Front View Side View ECE 57 Leture 4

21 Magnetron disharge Map of the magneti field measured aboe the surfae of the target. The magnetron is lindriall smmetri. The solid line is a ross setion along a radius of the intensit of the radiation emitted b the plasma (-8 nm. -D image of the plasma seen with a narrow pass filter entered at nm (Al I 3s ( 1 S3p - 3s ( 1 S4s. ECE 57 Leture 4 1

22 Tpial high-speed end-on piture of a miroar. The gate width is 1 ns, and the dela from the beginning of the urrent pulse is 35 ns. The ar is used to injet a stream of eletrons that eidene the E drift, resembling the use of des in the stud of fluid motion ECE 57 Leture 4

23 A different iew of the ar. The image is the result of appling a transformation that straightens the enterline of the eth trak (indiated b the solid line. Cross setional iew of the luminous streak along the enterline. ECE 57 Leture 4 3

24 Eposure: 1 ns Cross setions of the streak for different delas (indiated in ns. Note that the intensit profile does not hange appreiabl with the dela. The etent of the disturbane at the earliest dela at whih we were able to auire images (17 ns indiates that the perturbation introdued b the ar traels with a minimum speed of approimatel m/s. [Tomasel et al., Plasma Soures Si. Tehnol. 1, 1 (3]. ECE 57 Leture 4 4