Arthur Sherman - Chemical Vapor Deposition for Microelectronics (779637), страница 9
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= Mean free pathe- ElectronD- DeuteriumT=Tritium--('I')Eo-..<u.cE::::l~'Vitil-- I ---1]::'::104-c:--.:10 15 r - - - - - - - I - t - - - l I _C'-QJ~rLD >l emCcu"'0c:-- --EM~u,cuijjrL~ >1 cm1]~1--0.1-L--L-1010 2·15til.;;~OJ0::.,--------105 L-_---'-~..l...-~u__ISolar corona_'_10 3----- --- 10~--~~~--"'---10 4510 6Temperature, electron· voltsFigure 1: Plasma phenomena displayed for a deuterium plasma. 9where vT is the local velocity of the charged particle normal to the magneticfield line, m is the mass of the charged particle, and q is its charge.
Obviously,the mass of an electron is much smaller than the mass of a heavy ion, so theLarmor radius for electrons will be much smaller than for ions. Therefore, ifwe operate a glow discharge in the presence of a magnetic field, in general theelectrons will be confined by the magnetic field, while the ions will not beaffected. However, it is difficult to create any significant charge separation ina plasma, so confining the electrons has the effect of confining the ions aswell. It is important to note, however, that neutral particles (including freeradicals) will not be influenced by the magnetic field.The Debye length (d) in a plasma is an indication of the distance a strongelectric field can extend from a surface into a plasma.
It is given byd = (kT E:)1/2 ,~ewhere € is the permitivity of free space. For low pressure discharges where necan be quite small, the Debye length can be large and a sheath region along aFundamentals of Plasma-Assisted CVD45surface (where significant charge separation occurs) can extend a considerableway into the plasma.The different regions mentioned earlier (S, T, M, EM and E) are defined interms of these three parameters (A, d and rL)' Table 1 describes each regionand its boundaries.The region of our n e versus T plot in which plasma-assisted CVD reactorsfunction is also shown by the shaded area.
Clearly, this only represents a verysmall region of the total space within which a reactor could operate. In thefuture, operation of CVD reactors in other regions of this plot may lead to CVDfil ms of unique properties.Table 1: Regions in Deuterium PlasmaRegion SRegion TReg; onReg; on~1r Le<E~1r>Region ELdr LdAe , r Ld<Ad1 cm> 1 cm,rLe>1cmCollisions occur before an electroncan gyrate appreciably; all transport properties are scalarA magnetic field will give rise totensorial properties for electronrelated phenomenaAll properties are tensorialThe B field controls the electronsbut charge separation and the resulting E field combine with the B fieldto control the behaviorThe B field is too weak to influencethe plasma motionIt is also of interest to consider a typical plasma used for CVD.
If we havep ~ 250 mTorr, we will likely have T e ~ 20,000oK. Then, the electron meanfree path and the electron-heavy particle collision frequency can be estimated:and we recognize that the collision frequency is much higher than the highestfrequency typically used in a plasma CVD reactor (13.56 MHz).
Therefore,electrons will experience many collision during each applied field cycle.= 1 mmand\)ea<C >e-A-ea(BkT /nm )1/2e eAea10 6 m s-110- 3 m10 9 s-146Chemical Vapor Deposition for Microelectronics2.2.3 Electron Cyclotron Resonance in PlasmasAmong the many phenomena that can occur in a plasma,1! one of themore interesting from the point of view of discharges used for PECVD is thatof electron cyclotron resonance. When a plasma is subjected to an alternatingelectric field in the presence of a perpendicular static magnetic field, the electrons will receive energy from the electric field but will gyrate because of themagnetic field.
Consider the arrangement shown below,/w =eBemeBwhere the magnetic field is normal to the page. Initially, an electron is accelerated to the right by the E field. If we = w, .however, the 8 field will turn theelectron around just in time to again be accelerated by the E field in the opposite direction. Thus, the electron gains energy as E oscillates in both directions(provided there are many oscillations between collisions), and a resonant condition is achieved. Such a resonance will reduce the electric field necessary toin itiate a discharge in a gas,11 as is shown in Figure 2.1001--\-----~----+----~:'1...-.-.-j80~~::::o::::::;;=;::;:;;;n;;¥J;;;;;(?m;;;;im~-c.-~~r_--___i~ 60'X·~--\,------+-----_¥----r-;",e-,~~~i5t;I:b'IO'.&-.-----+--\-----I---~t:--~~~----l~~2010002000Gauss3000B) Magnefic fieldFigure 2: Breakdown field for He + Hg gas as a function of magnetic field fordifferent pressures.
11Fundamentals of Plasma-Assisted CVD47For higher pressures, very little resonance is seen as electron collisionsoccur so frequently that the electron cannot be turned by the magnetic fieldin time to catch the reversing electric field. At lower pressures, there is a strongresonance.The behavior of such a resonant discharge can be described by solving thecontinuum momentum equations for electron velocity, assuming a constantfrequency ve . The force on the electrons is both due to the electric field andthe Lorentz force caused by the magnetic field. The average power input perunit volume to the plasma is found to be tO(7)PIt is useful to compare this power input to a plasma to the power that wouldbe input when no magnetic field is present (we = 0).
Then we can writePPw =0p(8)eThis relation is plotted in Figure 3 for different values of wive. As can be seen,when the frequency of the appl ied field is large cOrTtpared to the coil ision frequency in the plasma, a strong resonance is predicted, in agreement with experimental results.52.L.-_-==:::I:=:=::::=;;;;;;;====--....._ _..L-O l - - - - . L . - - _ L .
. -_ _o234567Figure 3: Power input to plasma in the presence of steady magnetic field. tO48Chemical Vapor Deposition for Microelectronics2.3 REACTOR INFLUENCE ON PLASMA BEHAVIORIn astrophysical studies, one can study plasmas unaffected by sol id surfaces. By way of contrast, laboratory plasmas always interact with such surfaces. Accordingly, if we are to properly understand the behavior of laboratoryplasmas, we must inquire into the nature of the plasma-solid surface interaction.There are several aspects of this interaction that we will touch on.
First,we will review concepts of the DC and AC discharge. Then, the consequencesof using unequal size electrodes will be discussed. For AC discharges, frequencywill also playa role; and finally, the influence of magnetic fields on dischargeswill be considered.2.3.1 DC/AC Glow DischargesA glow discharge in a low pressure gas ("'"'1 Torr) created by a DC appliedvoltage exhibits a nonuniform appearance. A typical discharge is shown in Figure 4.
12 Since the cathode is cold, the discharge is maintained by secondaryelectrons produced there by positive ion impacts. The ions experience a strongelectric field near the cathode, which causes them to accelerate toward it. Thesheath is the region next to the cathode in which charge neutrality is not obeyedand relatively few collisions occur. This encompasses the Aston, Crookes andFaraday dark spaces, and the cathode and negative glow regions. There is anexcess of ions in this region, hence the net positive charge there. The positivecol umn has no net space charge. Therefore, it is the plasma we referred toearlier.
It is of a high electrical conductivity, so a relatively modest electricfield is all that is necessary to conduct the DC current through it. Ions andelectrons in this region can be lost by gas phase recombination, or diffusionto the tube walls. They can be regenerated by electron impact ionization in thepositive column, or the secondary electron emission from the cathode mentioned earlier. A similar but much smaller sheath appears at the anode.There is also a potential difference between the positive column and tubewall. This potential difference is created because the electrons are much moremobile than heavy ions and tend to flow rapidly out toward any boundingsurface.
Since the tube wall is an insulator, they tend to collect there causingthe insulator to assume a negative potential relative to the plasma. This createsan electric field close to the tube wall which hinders further electron flow towards it. A deficit of electrons forms in a sheath close to the surface, and thissheath assumes a net positive charge. Ions in the plasma, however, see the tubewall potential which is negative compared to the plasma and are attractedto it. This is the diffusion to the tube walls mentioned in the previous paragraph, and is often referred to as "ambipolar" diffusion.If the glow discharge of Figure 4 is operated under alternating voltageconditions, we observe a discharge with two dark spaces. This is in reality aseries of DC discharges of alternating polarity.
Up to about 10kHz, the frequency is low enough so that the discharge lights and extinguishes on eachcycle. There is sufficient time between cycles for most electrons to leave thepositive column and be lost to the tube walls. The loss of electrons extinguishesthe glow discharge.
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