PS510A - Measurement of Electron Temperature of Argon Plasma Assignment

Assignment Task

1: Consider an argon plasma with an electron temperature of 3.0 eV sputtering silicon which is at a potential of -600 V with respect to the plasma. Suppose the Ar+ density at the sheath edge is 1011 cm-3. Take the mass density of silicon as 2.3 × 103 kg/m3 and the atomic mass of silicon as 28. u.

1.1 Calculate the Bohm speed of the Ar+ ion. (Recall uB = p eTe/mi .)

1.2 Justify the expression for the sputtering rate, Rs, namely,

1.3 Given that for 600 eV Ar+ ions γs = 0.52 calculate the sputtering rate of silicon by such ions. Give your answer in ˚A/min.

2: A plasma that uses CF4 at its feed-gas contains is a widely used source of F atoms for the etching of silicon - it is preferred over F2 feed-gas as this leaves a pitted surface. CF4 itself is a stable gas and it is the dissociated products F, CF3 and CF2 which are of interest in etching.

On active surfaces, of which silicon is an example, CF3 and CF2 typically dissociatively adsorb, releasing a C atom and three, or two, F atoms that each form a bond to the silicon surface. While CF3 and CF2 deliver enchants to the surface, they also deliver C atoms, which can form a protective layer on the surface that inhibits the etch reaction. Similarly, CF3 and CF2 can dissociatively or non-dissociatively adsorb on an SiFx, resulting in a buildup of carbon or polymer film on the silicon surface. It is unlikely that the film will be removed from the surface in the absence of ion bombardment except as CF4(g), so that consequently the flux of CFx radicals (x < 4> of F atoms on the silicon surface requires, xΓCFx + ΓF = 4ΓCF4 + 4 + ΓSiF4. And the conservation of C atoms requires, ΓCF4 = ΓCFx

Consider now a surface model for pure chemical silicon etch (no ion bombardment) in a CF4 discharge. Let n1 and n2 be the gas-phase densities of CFx radicals and F atoms near the surface, respectively, and let θ1 and θ2 be the fractions of the SiF3 surface covered with CF4 and SiF4, respectively. Let Ka1 and Ka2 be the adsorption rate constants for CFx radicals and F atoms, respectively, and let Kd1 and Kd2 be the desorption rate constants for CF4(g) and SiF4(g), respectively. Assume Langmuir kinetics with adsorption of CFx and F on the SiF3 surface only.

2.1 In the steady state, give the two conservation equations for carbon and fluorine on the surface. HINT: Recal Eqs. 6.10 & 6.11 from the module notes.

2.2 Solve these to obtain the surface coverages θ1 and θ2. Hint: The manipulation can be somewhat simplified if you solve for the quantities (1−θ1−θ2) and θ2 from the expression for C and substitute those expressions into the expression for F. Then solve for θ1 and substitute that expression into the expression for C. You are required to show.

2.3 Find an expression for the etch rate for silicon (ESi = ΓSiF4 /nSiF3 ) normalized to the F density, n2, for the case of n = 3 (i.e. for CF3) and for Kd2/Ka1 >> n1, n2. Hint: You are looking for ESi/n2 = n ′ 0Ka2(Ka2/Ka1− n1/n2)/4nSiF3.

2.3 Plot the normalized etch rate per incident F atom (in units of ˚A/min·cm3 .) as a function of n2/n1 for Ka1 = Ka2 = 4 × 10−14 cm3 · s −1, n ′ 0 = 7 × 1014 cm−2 , Kd1 = Kd2 = 1012 s −1 and nSiF3 = 5 × 1022 cm−3.

This PS510A – Engineering has been solved by our PHD Experts at My Uni Paper.