Why plasma processing? (1) UCLA Accurate etching of fine features

The Coburn-Winters experiment UCLA Ion bombardment greatly enhances chemical etching

UCLA Why plasma processing? (2) Plasma enhanced chemical vapor deposition (PECVD) Sputtering Ashing

Low-temperature plasma physics UCLA Plasmas are collisional At least 3 species: ions, electrons, neutrals Always boundaries and sheaths Many effects not present in hot plasmas; e.g. dissociation of molecules electron attachment to form negative ions charged particulates (dust) interaction with surface layers

The nature of sheaths UCLA

The sheath’s E-field accelerates the ions and makes them go straight UCLA

The Debye length and quasineutrality UCLA Poisson eqn. Gradient scale length L DefineThen The LHS cannot be very large, so n i ~ n e unless L ~ D

Sheaths are very thin UCLA numerically, Let Then Debye sheaths are approximately 5 D thick

The Child-Langmuir Law UCLA When the potential of an electrode is very negative, the sheath drop is so large that n e can be neglected near the electrode. The sheath thickness then follows a simple law. ions and electrons ions only quasi-neutral +  +++  d  V 3/4

Presheath and Bohm criterion UCLA For a sheath to form, the ions entering the sheath must have a minimum velocity of c s = (KT e /M) 1/2, or E = ½KTe. This means that there must be a presheath where ions are accelerated. Presheaths are hard to calculate, so we assume a sheath edge at x = x s.

Log (V) vs. x (exact calculation) UCLA The Child-Langmuir slope is not followed unless V is very large.

Applying a voltage UCLA The sheath barrier for electrons at the wall or large electrode must be about 5 KT e to make ion and electron currents equal. If two walls are at different potentials, the more negative one will have a larger sheath and smaller electron current. The plasma follows the potential of the most positive electrode. It must always be more positive than the walls. If the voltages oscillate, the electron current will flow alternately to one or the other electrode.

Neutral collisions UCLA Ions and electrons make “billiard ball” collisions with neutral atoms, so the i-n and e-n cross sections are about the same. The e-n collision rate is where the average is over the electrons’ Maxwellian distribution An atom has a radius of about cm (= 1 Ǻ or 0.1 nm), so the cross section is about cm 2. A hydrogen atom has a  of 0.88 Ǻ. Particles diffuse by random walk.

Resonant charge exchange UCLA HOWEVER, ions and atoms of the same species have much larger cross sections because of charge exchange. Suppose a fast ion encounters a slow neutral. An electron can simply jump from the neutral to the ion, making a slow ion and a fast neutral. The ion appears to have suffered a large collision even if the energy exchange is very small, so the cross section is very large. Charge exchange cross sections, e.g. Ar+ - Ar, can be 100 times larger (~ cm 2 ).

Momentum transfer collisions in Argon UCLA << Ramsauer minimum

Collision frequencies UCLA

Argon ionization UCLA

Ionization cross sections UCLA

Charge exchange cross sections UCLA J.W. Sheldon, Phys. Rev. Lett. 8, 64 (1962) Argon Xenon

Charged-particle (Coulomb) collisions UCLA

Coulomb collisions with and w/o a B-field No B-field In “weak” B-field Together, these cause a 90  scatter a factor ln  times more often than a single 90  scatter.

“Spitzer” resistivity UCLA These are for 90  deflections in multiple collisions. The Coulomb logarithm ln  can be approximated by 10. Electrons driven through a plasma by an E-field are slowed down by collisions with ions, resulting in this resistivity: Density cancels out and plasma resistivity is independent of n.

When are electron-ion collisions important? UCLA Electron-neutral collisions: Electron-ion collisions: (ln  ~ 10) Hence, For 3 mTorr and T e = 3 eV, n crit  2  /cm 3 Then

Mobility and Diffusion ( || to B or B = 0) UCLA u is the drift velocity due to an E-field, and  is the mobility Here u is the drift velocity in a pressure gradient, and D is the diffusion coefficient The fluxes to the walls are: Quasineutrality requires  i =  e An E-field will set up to retard the electrons and accelerate the ions. This is not in the sheath; it is in the collisional body of the plasma. Result:

Diffusion and mobility perpendicular to B UCLA Cyclotron frequency Larmor radius Diffusion and mobility across B is slowed down by a factor ~  c 2 / 2, which can be large for electrons but is usually negligibly small for ions.

The Simon Short Circuit Effect (1) UCLA In a magnetic field, ambipolarity does not have to be obeyed in either the || or the  direction. More electrons will flow to the endplates, and more ions to the sidewalls. Only the total fluxes have to be equal.

The Simon Short Circuit Effect (2) UCLA The sheath drop at the endplates can vary with radius, allowing a few more electrons to leave at large r than at the center. Electrons appear to have moved radially outwards, although they are lost axially. The ambipolar field is not observed. The electron density tends to be Maxwellian even in the r direction.

Particle balance in gas discharges UCLA Ions diffuse out normally at the Bohm rate, and electrons follow by the short circuit effect. The g’s are geometric factors (r, L, etc.) Ion-electron pairs are replenished by ionization. Here V is the volume, and the is the ionization rate. Equating input and output, we see that the plasma density n cancels out, leaving only a relation between pressure and electron temperature.

T e rises as pressure decreases UCLA

Power balance in plasma sources UCLA The energy leaving the plasma is the sum of three terms. This is the energy carried out by each ion leaving the plasma through the sheath. This is the energy carried out by each electron leaving the plasma, including the perpendicular part. W c is the energy lost by line radiation and used in ionization. It is the function E c (T e ), which is the energy required to make an ion-electron pair (next slide). The density produced at given RF power absorbed is W tot times the loss rate of ions through the wall sheaths.

The Vahedi curve UCLA This includes all losses in inelastic collisions Argon