Uniformity Of Etching In Parallel Plate Plasma Reactors

J. Electrochem. Soc., Vol. 136, No. 1, January 1989 9 The Electrochemical Society, Inc.creases and as n ew gas formulations yielding faster etchrates are developed. Nonuniform etching necessitatesover-etching which can result in substrate damage and/orrapid mask undercut owing to loading. Both p h e n o m e n aadversely affect device yields. In the case of deep trenches,etching must be uniform for the trench capacitors to havea tight capacitance distribution (18). Etch nonuniformityma y be the result of gradients in etchant concentration, inion b o m b a r d m e n t flux and/or energy, or in wafer surfacetemperature. Nagy (16) and Selwyn (17) found etchant concentration gradients at the boundary where two surfaceswith different reactivity met. Such concentration gradients are thought to be responsible for the often-observed"bullseye" clearing pattern, in which the etch rate decreases monotonically from the wafer periphery to its center (19). Although several studies on uniformity of etchinghave appeared in the literature, no systematic studycoupling both theory and experiment has been presented.Recently, a transport and reaction model of a singlewafer parallel plate plasma reactor was formulated (20).The oxygen plasma etching polymer was chosen as amodel experimental system. Good qualitative agreementwas obtained between the model predictions and measured etch rates as a function of pressure, power, and flowrate.In the present work, an extension of the previous modelis presented. Given the surface reaction kinetics, the twodimensional model is capable of predicting both etch uniformity and anisotropy. The present paper emphasizes theuniformity aspect. An experimental te c h n i q u e based onspatially resolved optical emission spectroscopy was developed to obtain a three-dimensional mapping of theetchant concentration profiles. Although spatially resolved OES has been used extensively to map the plasmaemission along planes parallel to the discharge electrodes(21), studies of emission profiles along the wafer radius arescarce. Such profiles were obtained in an oxygen discharge in both an e m p t y reactor (no reactive film) and aloaded reactor (with a reactive film covering part of thesubstrate electrode). The radial emission profiles werethen converted to etchant species concentration profiles.The experimental results were compared with the mathematical model predictions. The effect of power, pressure,flow rate, and reactive film radius on the etch uniformitywas studied.189face, large radial concentration gradients may develop, especially at the boundary between the wafer and the surrounding electrode. Since the etching rate is usually afunction of the local etchant concentration, the result isetching nonuniformity. Transport and reaction principleswere used to analyze the reactant concentration distribution.G a s f l o w d i s t r i b u t i o n . - - G a s flow resembles the threedimensional, axisymmetric stagnation point flow (22). Assuming constant gas physical properties and negligiblev o l u m e change during reaction, the m o m e n t u m equationscan be decoupled from the mass and heat transfer equations. Invoking the co n t i n u u m approximation which isvalid for pressure above about 0.25 torr (for typical reactordimensions), the Navier-Stokes equations and the continuity equation read (see List of Symbols for meaning ofsymbols)OUU-- orW OU10PL O p Orv(O2UI OU\ O r 2 r Or 0ww0rU-- OrL 0 10P-pL O oUIs v --1 02U r 2 L 2 0 2] ---\Or 2UUr Or1 oW-- -- ---- orrL 0 l -- L 2 042 ]0[1][2][3]w h er e z/L is a dimensionless axial coordinate. Theboundary conditions areU 0atz - L for all r[4]W 0atz - L for all r[5]W -Wwatz Lforallr[6]where Ww is the uniform gas velocity at the entrance to thereactor. By settingu rf'( )-2s[7]Model FormulationThe model was developed for a radially symmetric single-wafer parallel plate plasma reactor shown schematically in Fig. 1. Feed gas enters uniformly through theupper porous wall electrode. Etching products and unreacted feed gas are p u m p e d radially outwards. The waferwas assumed to be in good thermal and electrical contactwith the substrate grounded electrode. Hence the wafersurface temperature was assumed constant. Gas temperature variations were also neglected. The primary focus ofthis work was on the concentration distribution of theetchant species and its effect on etching uniformity. Inparticular, due to etchant consumption on the wafer sur-Gas inT2LGlowI/'////// ,RF PowerrGas out. . . . . . / //////////////iSheathw -w 0[8]the continuity equation is automatically satisfied. Here f(0is a function of only a n d f ' ( 0 df/d . Inserting Eq. [7] and[8] into Eq. [1] and [2] and eliminating the pressure P, resuitsf"' 2Rwff" 0[9]Hence the flow Eq. [1]-[3] have been reduced to a fourthorder ordinary differential equation. The pertinent boundary conditions aref'(- 1) f ( - 1 ) 0[10]f(i) i[ii]The wall Reynolds n u m b e r is defined as Rw W,vL/2v.After solving Eq. [9] subject to boundary conditions Eq.[10] and [11] to obtain f( ) and f ' ( 0 , the radial and axial velocity components can be obtained by using Eq. [7] and [8],respectively. In general, Eq. [9] must be solved by numerical techniques. An approximate analytic solution can beobtained, however, for values of the wall Reynolds number sufficiently less than unity. Such a solution may beuseful since for typical parameter values Rw 1. By usingregular perturbation techniques (23), the following approximate solution was obtainedW rWaferr r,,00,JFig. 1. Schematic of the single-wafer parallel plate etching reactorstudied.3 4 -32 i 3-ii7 2i- 19)J[12]

190J. Electrochem. Soc., Vol. 136, No. 1, January 1989 9 The Electrochemical Society, Inc.W -Ww 3-1 3 1 4-39 Rw-1- 1 219The third term on the right-hand side of Eq. [15] represents etchant elimination by v o l u m e reactions. A typicalex am p l e is etchant recombination according to 1)][13]Kv160A A MFor values of Rw 1, Eq. [12] reduces to---rU 8L1-[14]Hence, under the condition Rw 1, the radial velocityprofile is parabolic and symmetric with respect to theplane z 0. Since a wide range of flow rates (values of Rw)were examined in the present investigation, numerical solution of Eq. [9] was performed to obtain the gas velocityprofiles. These profiles were then used in the convectivediffusion equation to describe etchant transport and reaction.Etchant transport and reaction.--The model was applied to a diatomic gas A2 which upon dissociation in theplasma produces atomic etchant species A. Examples include the O5 and C12 plasmas. Emphasis was placed on theoperating regime of typical single-wafer reactors ( 1 torr,13.56 MHz). Un d er such conditions, the glow is usuallysustained by bulk ionization. Therefore, secondary electron emission was neglected. In addition, above the iontransit frequency [ 3 MHz, Ref. (12)], ions respond to anaverage sheath voltage. Therefore, a time-averaged modelof the sheath may be used to obtain the ion b o m b a r d m e n tflux and energy (24). Some modulation may occur in theelectron energy distribution at 13.56 MHz (25), which inturn will modulate the etchant production rate by electronimpact dissociation. However, the etchant losses occur ona time scale m u c h longer than that of etchant production.Hence a time-independent etchant concentration shouldbe established. The steady-state etchant species mass balance then readsOrOzr- r \Or/ Oz2 j 2kpneC2 - Rv[15]The second term on the right-hand side of Eq. [15] represents etchant production by electron impact dissociationof parent moleculeskp-- 2 A eA2 e[R1]The production rate constant, kp, depends on the electronenergy distribution function and the cross section for thereaction. For a Maxwellian electron distribution functionr-- 3The electron energy varies with position, especially alongthe axial direction. Electrons pick up energy from the oscillating sheaths resulting in higher electron energy at thesheath/glow boundaries. A spatially-averaged value of k,was used in this work. This is not expected to significantlyaffect the radial etchant concentration profiles, especiallyfor a small interelectrode gap.Two forms of the electron density profile were examined. Uniform electron density (he rand the profilecorresponding to a diffusion-controlled discharge in a cylindrical container (26)(z)ne (r, z) neoJo 2.405 r cos\r2/2-L[17]where J0 is the zeroth order Bessel function of the firstkind.[R2]where M is a third body needed to conserve both energyand m o m e n t u m during recombination. Volume recombination is especially important at higher pressures. The pertinent reaction rate can be expressed as Rv KvC 2CM. Surface reactions enter in the boundary conditions describedbelow0C -0atr 0,-L -z -L[18]-0atr r ,-L- z- L[19]OrOC,Or0cl-D, -WwCI kcC Oz0C1D -- OzkaC,atz L, 0- r- r2atz -L,r r -r2aC,9 D1 Rtat z -L,0 - r - Ozrl[20][21][22]Equation [18] is a symmetry condition and Eq. [19] is a simplified exit boundary condition. Equation [20] accounts forboth etchant convection away from and etchant recombination on the upper electrode surface. A first-order recombination reaction has been assumed (27). Equation [21] describes surface recombination on the part of the lowerelectrode surrounding the wafer. The surface recombination rate may be written as the product of the etchant fluxstriking the surface (1/4 v C1) and the wall recombinationcoefficient w. The corresponding reaction rate constant isthen ki 1/4 VlWi with i a, c. Equation [22] describes etching on the wafer surface. Recombination was neglectedcompared to etching on the wafer surface. The surface reaction kinetics is co m p l ex and very little understood, especially the effect of ion bombardment. Ions may create "active" sites on the surface where reaction of neutrals canproceed faster and/or ions may "clear" the surface by sputtering adsorbed species or polymeric films and exposing"fresh" surface sites for further reaction to occur (28, 29).For modeling purposes, the following simplified kineticm o d el was used based on the surface "damage" mechanism (30)kdA2§ S --- S*[R3]kn-- P[R4]k A S* P[R5]A Se-e--* A2 MIn Eq. [R3] positive ions (mainly molecular ions A2§ bombard the surface and create "d am ag ed " surface sites S*.Etchant A can react on both undamaged and damaged surface sites (Eq. JR4] and [R5], respectively), perhaps fasteron the latter, to produce P. Sputtering of the surface by ionb o m b a r d m e n t has been neglected, but it can be easily accounted for. The total etch rate iskd( I knC, at (k C1) ( kde I k C1/[23]where the reaction rate of [R3] has been assumed proportional to the ion flux I and the average ion energy e . Reactions [R4] and [R5] have been assumed first-order in etchant concentration C1. The degree of anisotropy is defined

d. Electrochem. Soc., Vol. 136, No. 1, January 1989 9 The Electrochemical Society, Inc.as the ratio of the ion-assisted reaction rate [R5] to the totalreaction rate Rt. Thenkdl e An -cp,knr2-k rzalp -D1% -PC 2 C t -- C 1 -RgTg[25]C iThe etchant mass balance Eq. [15] was nondimensionalized by usingC 1ne01 - -zO -CtT -LneandS -r2[26]The dimensionless equation isPe A [ r- 1 - 2 f( ) - a] Da (1 - 0x)0 - f31012(1 - O0[27]The dimensionless boundary conditions areCq0i0 -0ate 0,1D1[24]kdI e k C For large ion flux and/or energy or for slow chemical etching reaction (small k0, the degree of anisotropy approaches unity, i.e., highly anisotropic etching results. Oneobserves from Eq. [23] that for large ion to etchant fluxes(large t /C1), the rate is simply k C,, i.e., the rate is limitedby the etchant supply. In the absence of ion b o m b a r d m e n t(I 0), Eq. [23] reduces to Rt knC1, i.e., only chemical(isotropic) etching occurs.At sufficiently high gas flow rates, the etching reactionproduct concentration in the plasma will be low. Assuming that A is the only important etchant, and that the majorc o m p o n e n t s in the plasma are A and A2, Eq. [15] suffices todetermine the etchant concentration distribution. The parent molecule concentration can then be found as-1 - -18-191kdnekT uRknCtkcrzVxWcr2D - 4 D i :g - -kar2DxuR ( k T J M 2 ) 112 I * -- (% 2Pe)0 001A-- %0 0 A 001 dP 01 la t e 1at - 18e *I * 010- 1 - 1[29][30])O 1 - Iat - 1[31]In Eq. [27]1 or3.64 J0(2.405 ) cos (7r/2 )0r [32a][32b]depending on the electron density profile used. Other dimensionless quantities in Eq. [27] arerzA --Pe-Wwr2L2DI2kpner22Da - -Dx[ 1 -Q- - -[33]2"rrDlr2KvCt2r22DI[34]Functions f ( 0 and f ' ( 0 were found by solving Eq. (9). Further, in Eq. [29]-[31][35]I neUR[36],The Peclet number, Pc, shows the relative importance ofconvection as compared to diffusion. The Damk6hlernumber, Da, shows the relative significance of etchant production as compared to diffusion. For large values of Da,the etchant is produced faster than it can diffuse, resultingin nonuniform concentration profiles. Dimensionlessgrouping 131is analogous to Da

etching must be uniform for the trench capacitors to have a tight capacitance distribution (18). Etch nonuniformity may be the result of gradients in etchant concentration, in ion bombardment flux and/or energy, or in wafer surface temperature. Nagy (16) and Selwyn (17) found etchant con-