Analysis of Nonuniformities in the Plasma Etching of Silicon with CF4/02 Alan S. Kao and Harvey G. Stenger, Jr. Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015 ABSTRACT Experimental and modeling work has been performed to examine the effects of reactor pressure, etchant gas flow rate, and wafer location on the uniformity of plasma etching silicon using CF4/O2 in a parallel-plate-radial flow reactor. In- trawafer etch rates were measured at 12 points across a 3 in. wafer at pressures between 125 and 200 mtorr, 70~ and gas residence times between 1.28 and 2.14s. Depending on the operating conditions, an edge-to-center decrease in etch rate of 5-25% was observed. A combined reactor/reaction model is able to predict this degree of nonuniformity. Uniformity was improved by increasing the reactor pressure and decreasing the flow rate of the etchant gas. Etch uniformity was also found to be a function of wafer location within the reactor. Data are presented which show the influences of process pa- rameters on both etch rate magnitude and uniformity. Intrawafer nonuniform etching in plasma and reactive ion etching systems is a major problem in current IC pro- cessing technology. The result of intrawafer nonuniformi- ties is a direct decrease in circuit yields or overdesign to compensate for etch rate variations. In particular, the plasma etching of silicon, silicon dioxide, and aluminum in a parallel plate radial flow system often displays an edge-to-center decrease in etch rate, a phenomenon some- times referred to as the "bullseye effect" (1, 2). Clearly, the inability to etch consistent circuits on each chip of a wafer will continue unless the causes of the bullseye effect are better understood and corrections are made. Several papers have been published which discuss the problem of etch nonuniformities. Stenger et al. (1) studied the interwafer nonuniformities of NF3 etching silicon in a radial flow reactor. The etch rates for this system were found to be more uniform at lower flow rates holding pres- sure, feed gas composition, and temperature constant. Since they evaluated etch rates by measuring the decrease in wafer mass after etching, intrawafer nonuniformities could not be examined. Dalvie et al. (3) have developed a model of CF4 etching silicon in a radial flow reactor. Their model assumes uniformly distributed silicon on the lower electrode, low CF4 dissociation rates, and radially constant electron density. The effects of pressure, flow rate, and dis- charge power on etch rate were simulated. They found that average etch rates increased as the flow rate decreased or the reactor pressure increased. The primary effect of in- creasing the discharge power in their model was to in- crease the average electron density, which resulted in higher etch rates. Their model also predicted intrawafer as well as interwafer etch nonuniformities; however, no ex- perimental data were offered for comparison. Alkire and Economou (4) examined the nonuniform stripping of photoresist with 02 in a barrel reactor, which is a common application of barrel etchers. The transport of etching spe- cies to the wafer in barrel reactors relies predominantly on diffusion, with little convective influences. This results in a depletion of the etching species across the wafer, thus causing nonuniform etching. Again, only model results were given with no experimental data. Experimental work has been published by Nagy (2) and Peccoud et al. (5). Nagy presented an experimental investigation of reactive ion etch nonuniformities. He attributed the decrease in etch rate from edge to center to an intensified production of the reactant species over the wafer. Peccoud et al. also observed the bullseye effect when etching aluminum with CC14 in a parallel plate reactor, which they minimized ex- perimentally by increasing the RF frequency. This paper presents the results of a series of experiments aimed at quantifying the dependencies of etch uniformity on process parameters. Data are presented showing the ef- fects of reactor pressure, etchant gas flow rate, and wafer location on the intrawafer etch profile uniformity. These data were taken from a parallel-plate radial-flow plasma etching reactor (RFPER). A quantitative model is also de- veloped which helps explain several trends in the data. Experimental The data presented were obtained using a Plasma- Therm (P.T.) PK-2440 RFPER similar to that used in our previous work (1). A schematic diagram of the RFPER is shown in Fig. 1. A radio frequency (RF) generator (P.T. Model HFS-3000D) feeds a 13.56 MHz signal to the upper electrode while the lower electrode is grounded. A match- ing network (P.T. Model AMNS-3000E) is used to match the impedance of the plasma process to that of the RF gen- erator. Both electrodes are 55.9 cm diam, the exit port is 5.8 cm diam, and an electrode spacing of 5.7 cm was used for our experimental work. A heat exchanger (P.T. Model HES-1), controlled by a temperature regulator (P.T. Model TR-1), is used to control the lower electrode temperature. The upper electrode is not heated. The etchant gas used was a commercially available mix- ture of 4% O= in CF4 (Matheson Gas). CF4 is an etchant gas commonly used for etching semiconductors and metals (6, 7) and O2 is added to improve etch rate (8). The gas en- ters the reactor at the outer edge of the electrode through a perforated tube and flows axisymmetrically toward the exit port in the center. Three inch diameter silicon wafers were placed on the lower electrode in various configura- tions. Prior to etching the wafers, a 5000A layer of thermal silicon dioxide was grown on the <100> face. The wafers were subsequently patterned using Baker PR-1 positive photoresist and the exposed SiO2 was wet etched with HF to leave 20% of the surface area as bare silicon. The resist was then removed with acetone, leaving the other 80% of the wafer surface as silicon dioxide. The wafers were pat- rf power supply hot glyc, to vacuum pump Fig. 1. Schematic diagram of the radial flow plasma etching reactor for etch rate measurements. 954 J. Electrochem. Soc., Vol. 137, No. 3, March 1990 (cid:14)9 The Electrochemical Society, Inc.
`
` Ex.1006 p.1
`
`

`
`J. Electrochem. Sac., Vol. 137, No. 3, March 1990 (cid:14)9 The Electrochemical Society, Inc. 955 Fig. 2. Silicon dioxide mask pattern used to define regions to be etched. terned to allow measurement of etch depths continuously across the wafer. Figure 2 diagrams the etched pattern. Etch depths were measured at various stages of the ex- perimental process: (i) before etching, to measure the ini- tial SiO2 film thickness, (ii) immediately after etching, to measure the amount of SiO2 and silicon that was removed, and (iii) after stripping off the oxide layer with HF, to de- termine the amount of silicon etching that had occurred. The etch depths were measured using a Sloan Dektak sur- face profile measuring system. Etch rates were calculated as etch depth of silicon divided by etch time. The flow of the etchant gas is regulated by a mass flow controller unit (MKS Instruments Model 254), which is ca- pable of providing constant flow rates up to 100 sccm. The pressure in the reactor chamber is maintained by a pres- 2900 sure monitor (P.T. Model PRM-1) and a process valve con- 2800 troller (P.T. Model PVC-3). This pressure control system can maintain pressures from 50-1000 mtorr at an inlet flow ~ 2700 of 100 sccm. %'2eoo The base operating conditions were a reactor pressure of 150 mtorr, an electrode temperature of 70~ and an etch- ~ 2~00 ant gas flow rate of 100 sccm. Heat transfer rates are ade- z400 quate in this reactor configuration (10) to allow the as- sumption of isothermality for the electrode, the gas neutral 23oo species, and the wafer. Etch times were 15 min and an RF ,.15 power of 750W (0.31 W/cm 2 or 0.054 W/cm 3) was used. To in- crease the reproducibility of the results, the reactor system was conditioned before each set of experiments by etching E 1.10 2 a series of bare silicon wafers as a blank run. The chamber ~ was thoroughly purged several times with nitrogen before ~ ~.o5 feeding with CFJQ. Experimental Results Radial etch profiles were measured from the point closest to the reactor exit (point A) to the point closest to the reactor entrance (point B) for several wafer configura- tions. The data are plotted in.two ways: (i) average abso- lute etch rate at any position across the wafer, and (ii) etch rates normalized to the minimum etch rate over the wafer, to indicate the degree of nonuniformity across each wafer. The etch rates in Fig. 3-6 were measured at twelve loca- tions across the wafer diameter. Smooth curve etch pro- files were determined by a second-order regression and are plotted on each figure to help visualize the data trends. In all of these experiments, the amount of SiO2 etching that occurred was negligible compared to the amount of silicon removed. The first series of experiments involved the etching of a single wafer at a time. The wafer was placed in the center radial location (see insert in Fig. 3) and etched using the base case conditions and gas flow rates of 60, 80, and 100 sccm. The resulting etch rate profiles are shown in Fig. 3. The etch rate was highest at the point closest to the reactor exit (point A) in all cases. The data plotted on the normal- ized scale in Fig. 3 show that etching becomes more uni- form with decreasing flow rate. The relative difference be- tween the highest and lowest etch rate across each wafer dropped from 15 to 3% as the flow rate was decreased from 100 to 60 sccm. The absolute etch rate scale in Fig. 3 shows that the average etch rate decreases from 2790 to 2480 A/min with decreasing flow rate. The effects of varying the reactor pressure from 125 to 150 to 200 mtorr at constant flow rate and temperature are shown in Fig. 4. As pressure is increased, the uniformity of the etching improves; the relative difference between each wafer's highest and lowest etch rate went from 15 down to 5% as the pressure was increased from 125 to 200 retort. The average absolute etch rate increases from 2450 to 2600 A/rain with increasing pressure from 125 to 200 mtorr. Figure 5 shows the effect of wafer location on the intra- wafer etch profile. In separate runs, individual wafers were etched in each of the three positions shown as inserts on Fig. 5. The reaction conditions were those of the base case (100 sccm, 150 mtorr, 70~ and 750W). The etch nonuni- formity is similar for the three wafers; all three show a steady increase in etch rate in the direction of the flow. The average etch rate of the wafers decreased from 2690 to 2480 to 2290 A/min for the outer-, center-, and inner-placed wa- fers, respectively. Loading the reactor with three wafers at once (see insert of Fig. 6) resulted in an almost uniform etch profile for the wafer closest to the reactor entrance (Fig. 6). The relative difference in etch rate across the wafer was only 3%. The wafer at the inner position displayed a nonuniform etch rate profile similar to that obtained in the experiment with only one wafer at the inner position. However, the relative difference in etch rate across the inner-placed wafer in- creased to 25% from the 11% difference obtained when the wafer was etched alone in the inner position. A "loading ef- fect" (10, 1]) is observed in Fig. 6 since the average etch direction of flow I I I ~k (cid:12)9 flow = 100 sccm (cid:12)9 flow = 80 sccm (cid:12)9 flow = 60 sccm (cid:12)9 (cid:12)9 (cid:12)9 o (cid:12)9 (cid:12)9 1.00 ' - - - " -' ' " -1,0 -0.5 0.0 0.5 1.0 Normalized Position Fig. 3. Effects of flow rote on etch rate and etch uniformity. Pressure = 150 mtorr, temperature = 70~ RF power = 750W. Data points are measured values, and curves are second-order polynomials fit to the date.
`
` Ex.1006 p.2
`
`

`
`956 J. Electrochem. Soc., Vol. 137, No. 3, March 1990 (cid:14)9 The Electrochemical Society, Inc. A 2800 ~- direction of flow B A "Q--direction offlow 2300 2700 E 2600 | 2500 2400 2300 1.15 ~ 1.10 Z1.05 1.00 6 orrj 125 retortS(cid:12)9 I , I i I Ae=~== (cid:12)9 P = 125 mtorr (cid:12)9 (cid:12)9 (cid:12)9 &(cid:12)9 (cid:12)9 -1.0 -0.5 0.0 0.5 1.0 Normalized Position Fig. 4. Effects of reactor pressure on etch rate and etch uniformity. Flow rate = 100 sccm, temperature = 70~ RF power = 750W. Data points are measured values and curves are second-order polynomials fit to the data. 22OO E 2100 | 2000 19o0 1800 1700 1.25 ._(cid:127)1.20 E ~1.15 z1.10 1.05 1.00 inner (cid:12)9 @ (cid:12)9 && (cid:12)9 ~(cid:12)9 [ , I I ~(cid:12)9 (cid:12)9 inner ring (cid:12)9 outer dng~ -1.0 --0,5 0.0 0.5 1.0 Normalized Position Fig. 6. Effects of wafer loading on etch rate and etch uniformity. Pressure = 150 mtorr, flow rate = 100 sccm, temperature = 70~ RF power = 750W. Data points are measured values, and curves are sec- ond-order polynomials fit to the data. rate of these wafers (1900-2000 AJmin) is significantly lower than that of a single wafer run at the same conditions (2480 A/min). Discussion The observed nonuniformities in etch rate provide a good test for any quantitative model which attempts to ex- plain the concentration profiles within a plasma reactor. Modeling the plasma etching process is an interesting problem because of the complexities of the plasma sys- tem. An accurate model for predicting the concentration profile of any species within the reactor must account for changes in concentration due to diffusion, convection, and chemical reaction. In the past, there have been several models describing the plasma etching process. Models for radial flow reactors have been presented for CF4 by Dalvie et al. (3), SF6 by Kline (12), SF6/O2 by Anderson et al. (13), and NF3 by Stenger et aL (1). Kushner (14) developed a general model using a parallel plate configuration for the etching of Si and SiO2 in CnFm/H2 and C,Fm/Q plasmas. Lii et aL (15) combined an analog circuit model to predict the electron 3100 ~2900 ~2700 2500 Z 2300 2100 1.15 E1.10 .~ z 1.05 1.00 -1.0 A ~ direction of flow B -0.5 0.0 0.5 1.0 Normalized Position Fig. 5. Effects of wafer position on etch rate and etch uniformity. Pressure = 150 mtorr, flow rate = 100 sccm, temperature = 70~ RF power = 750W. Data points are measured values, and curves are sec- ond-order polynomials fit to the data. energy and electron density with a kinetic model for SF6 etching silicon. Edelson and Flamm (16) simulated CF4 etching silicon using a cylindrical plug flow configuration and Alkire and Economou (4) presented a model for the nonuniform stripping of photoresist with 02 in a barrel re- actor. While some of these papers have discussed the prob- lem of intrawafer nonuniform etching, little experimental data have been published and compared to the derived models. Model Development In contrast to the more complex models that have been presented by others (3, 13, 16, 17), the model presented here takes a simplified approach to the plasma etching sys- tem. Although we recognize the complexity of plasma etching, it is expected that much can be learned from a simplified model that explains a majority of the observa- tions. Therefore our objective is to present a model which helps to explain experimental data without introducing unnecessary complexity. The model will assume that plasma etching occurs via three lumped reaction steps: (i) dissociation of etchant gas molecules by electron bombardment (or chemical reaction with free radicals) (18); followed by (ii) a surface reaction between the substrate atoms and the reactive etching spe- cies produced in the plasma, and (iii) chemically reactive species (free radicals) recombining to form nonreactive species through loss reactions. The surface reaction may be further broken down to adsorption of the etching spe- cies, surface reaction, and desorption of the resulting vola- tile molecules into the plasma. Of equal importance to these reaction steps are the diffu- sion and convection of species within the reactor. There- fore, the concentration of the etching species at any loca- tion in the reactor is governed by: (i) generation by electron dissociation and chemical reaction of etchant gas molecules, (ii) losses due to reaction with the substrate material, (iii) losses due to free radical reactions, (iv) diffu- sion into and from other regions, and (v) convective influ- ences due to gas flow from the reactor entrance to exit. It is assumed here that the etching species are predomi- nantly generated in the plasma when collisions between electrons and the etchant gas molecules produce reactive ions and free radicals. In the present system, electron col- lisions with CF4 molecules most probably produce CF3 and F radicals. It is also known that the reaction CF4 + e- --* CF2 + 2F (18) occurs appreciably; however, our method would determine, as in our previous work (1), that the reaction rate constant found from the experimental data would be a product of the dissociation rate constant and the stoichiometric coefficient of the fluorine produced
`
` Ex.1006 p.3
`
`

`
`J. Electrochem. Soc., Vo1.!137, No. 3, March 1990 (cid:14)9 The Electrochemical Society, Inc. 957 in the dissociation rate. It can also be expected that the dis- sociation reaction is directly related to the concentration of electrons and their energy distribution (which is de- pendent on the power supplied to the electrode and the re- actor pressure) (19) and the fluorinated species concentra- tion. Although Plumb and Ryan (18) show that F radicals can also be formed by oxygen reactions, we are at much lower O2 concentrations than in their work [4% here vs. 25% in (18)]. We therefore ignore the contribution of oxy- gen on the generation of F radicals. The surface reaction between fluorine atoms and silicon has been studied in depth by Flamm et al. (17, 20). In their mechanism, the exposed silicon surface is perfluorinated with adsorbed fluorine, followed by SiF2 molecules desorbing due to further collisions of the substrate with fluorine atoms. The desorbed SiF2 perfluorinates rapidly in the plasma to form stable SiF4. As a result of the etching reaction, there is a decrease in fluorine concentration in re- gions close to the silicon surface. This creates a concentra- tion gradient, causing fluorine atoms in nonetching re- gions of the reactor to diffuse toward the wafer. Recombination or loss reactions (producing F2, C2F6, COF, F20, or reproducing CF4) are numerous (18). To de- velop a detailed model which includes each reaction would require increased computational difficulties with little difference in the final results. For the present model, it is assumed that the amount of F consumed by loss reac- tions is first order in F and first order in gas density, since nearly all gas phase species can react with fluorine radicals to form a nonreactive species. Designating k*~ to be the rate constant for the disso- ciation of CF~, k~ to be the rate constant for the surface etching reaction, and k~ to be the loss reaction rate con- stant, the rate of reaction in the gas phase (positive for ap- pearance and negative for disappearance) of each major component can be written P Fluorine: rr = +k*dCcF4C~ - -- k~cfas~ -- klCF-R~ [la] CF4: rCF4 = -- k*aCcF4%- [lb] 1 Silicon: rsi = + ~ keCFasi [lc] 4 Replacing k*dc~- with kd, the component continuity equations for CF4 and F are CF4: vr aCCF4 = Dcr4-CF4 { l r ~r k(r OCCF41Or / 1 ~2CcF 4 ~2CcF4~ - + -- kdCcF4 [2a] + r2 002 az 2 J F: {10(,0c t Pr ~-r = DF-CF4 ~ ~ ~-r] r 2 00 ~ 0z 2 J P + kdCcf4 - klcf-~ [2b] In Eq. [2a-b] the gas is assumed to be primarily composed of CF4 species. Both component balances must be solved simultaneously since the generation of F is dependent on the concentration of CF4. It is assumed here that the con- centration of electrons is only a function of the power sup- plied to the electrodes, independent of location, and that the effects of pressure and gas flow rate on electron con- centration are negligible. In previous work for this reactor configuration (1), the concentration of reacting species was shown to be only slightly dependent on z. The etching rates, pressures, and dimensions are similar in this work; therefore, the concen- trations and their derivatives can be replaced by the aver- age across the reactor thickness _1 fh Ci=2 -~ h cidz [3] Assuming that the derivatives of concentration with re- spect to r and 0 are independent of z, these derivatives can be removed from the integrals in Eq. [2a-b]. Substituting the definition of Eq. [3] and [2a-b] and integrating gives aC-cr4 {10 / 1 a2~'cF4 Vr = DCF4_CF4 (r 0CcF4 ~- ar r~r\ 0~'--/ r 2 aO 2 I(OCcF4t I(OCcF41 1 kdCcF4 [4a] 2h\ az /~-h ~\ az /~=-hJ acF {1 a (rae~ 1 l ae~ Vr- = DF-CF4 + --- ar -r ~r \ ~r / r2 002 + -- - + kdUCF4 -- klC-F~ [4b] 2h\az/~=h ~\aZ/z= hJ It is assumed the derivatives with respect to z are not func- tions ofz except at the surface of the wafer. Where there is exposed silicon, there will be a flux of fluorine atoms as they adsorb onto the wafer surface and subsequently react. This flux is represented by DFCF4(C~CFI =S(r,O)k~-~r [5] \ aZ/z~_ h where the function S(r, 0) is equal to the fraction of the wa- fer's silicon exposed to the plasma at the surface of the wafer and zero everywhere else. The mask pattern used is assumed to be uniform and has line spacings which are much less than the electrode spacing. Therefore, instead of devising a complex function for describing the position of the lines being etched on the wafer, we have chosen to use the function S to indicate where the flow of F atoms nor- mal to the electrode mostly occurs. The SiO2 mask used experimentally covered 80% of the wafer surface. By set- ting S = 0.2 over the entire wafer, we imply that etching oc- curring over the available silicon area, which is 20% of the total wafer area, can be approximated by simulating etch- ing over the entire wafer surface area at 20% of the actual etch rate. Since the z dependence of concentrations has been re- moved, it can be assumed that at all values ofz other than where there is etchable material, the flux in the z direction is zero is zero D /OCr\ (aCcF4t F-CF 4 |--~ = DCF4_CF 4 : 0 [6] \aZ/z=h \ Oz /z-(cid:127) Substituting Eq. [5] and [6] as well as the relationship v~ = vorJr from the overall continuity equation into Eq. [4a-b] r Or [1 a (r3CCF4 ~ -Dcr~-cF4 r~r\ ar / 1 O2gCF4~ +- -- kaCcF4 [7a] r 2 002 J P + kdCcF4 -- klC--F-R~ [7b] In dimensionless form, these equations become PeCF4 0CcF4_ 1 O / OCcF4\ 1 02CCF4 BiaCc~4 [8a]
`
`Ex.1006 p.4
`
`

`
`958 J. Electrochem. Sac., Vol. 137, No. 3, March 1990 (cid:14)9 The Electrochemical Society, Inc. ~Pecr4 OCv _ 1 0 (~0CF t 06 ~0~\ 0~1 where 1 O2CF 6 2 002 --- - SBi~CF +~/BiaCcF 4 -- Bi]CF [8b] ~ r DCF4.CF 4 Voro Ci = : -, 6 =_ , ~ - -- Pecr4- C0 ro DF_CF 4 DCF4-CF 4 kdro 2 k~ro ~ klro2(P/RT) Bia-D , Bi~- , Bil- CF4-CF 4 2hDF-cF4 DF-CF4 The boundary conditions at the entrance and exit of this system are the Danckwerts boundary conditions, which assume that no reaction occurs after the reactor exit and that the total flux at the entrance of the reactor is equal to the sum of the convective and diffusive fluxes t (o% = :0 1 (OCcr4t Pecr4 \--~]e-1 = CCF4 -- YCF4,0 [9a] [9b] , (0% \~-/~=1 = CF [9C] ~/PecF4 The diffusion of fluorine atoms in the plasma is of pri- mary interest, since they are the etching species. The diffu- sion coefficients can be estimated from the Chapman- Enskog Eq. [21] 2.88 x 104 DF.CF4 -- -- [10] P 1.40 x 104 Dcr~_cr~ - -- [11] P where P is in pascals and DAB is in cm2/s. Model Solutions Equations [8a-b] were solved using the finite element program TWODEPEP published by IMSL (22). The pro- cess parameters used are summarized in Table I. The solu- tion of equations [8a-b] results in a map of CF4 and F con- Table I. Summary of parameters Electrode radius Exit tube radius Wafer radius Reactor volume, half thickness Electrode temperature Reactor pressure Gas flow rate ro 27.95 cm ri 2.9 cm rw 3.81 cm h 2.85 cm T 343 K P 125, 150, and 200 mtorr F 60, 80, and 100 sccm 0 (cid:14)9 -1.0 -0.67 -0.33 0,0 "K-X- 0.065 i 0.33 0.67 Dimensionless Reactor Radius Fig. 7. Contour plot of dimensionless fluorine concentration through- out the reactor. Flow rate = 100 sccm, pressure = 150 mtorr, tempera- ture = 70~ RF power = 750W. centrations throughout the reactor. Etch rates across each wafer are calculated from the product of the fluorine con- centration, the etching reaction rate constant, ke, and the silicon loading density, asi. Plotting the model-generated map of fluorine concentration gives a visual inspection of the expected etch rate profiles. Figure 7 shows a contour plot of the dimensionless F concentration for the case of one wafer being processed at 100 sccm and 150 mtorr. The unknown reaction rate constants, kl, kd, and ke, were varied in each call to TWODEPEP to allow minimizing the error between the observed and the calculated etch rate. The three runs which varied flow rate (data of Fig. 3) were used to determine the set of three constants. Observed etch rates (data points) vs. predicted etch rates (lines) are shown in Fig. 8 for the single-wafer case at three different flow rates. The agreement is good at 60 and 80 sccm flow rates, with a small deviation observed at 100 sccm near the center of the wafer. The rate constants used to calculate the model curves in Fig. 8 are given in Table II. The calculated Peclet and Blot numbers for these best-fit parameters are listed in Table III for the various cases. These constants are not to be con- sidered fundamental rate parameters. Instead, they are fit parameters which give a mechanistic structure to the plasma reactor model. However, it is interesting to com- pare these constants to those reported elsewhere (18). In work by Ryan and Plumb (18) at 500 mtorr and 295 K, con- stants are reported between 10 -'2 and 10 -]6 cm3/s/molecule for various reactions which consume fluorine (e.g., F + CF3 --> CF4). Our value of 1.11 x 10 -16 falls within their range, suggesting it is of a reasonable size. Plumb and Ryan also report a value for the first-order dissociation constant of CF4, kd (which is a product of the Table II. Best fit rate parameters Dissociation ka 0.13s 1 Loss kl 6.67 x 107 cm3/s/gmol or 1.11 x 10 -16 cm3/s/molecule Etching ke 305 cm/s Table III. Dimensionless numbers for best fit parameters P Flow (Pa) (sccm) PeCF4 Bid Bie Bi] 16.6 100 0.422 0.121 24.2 0.176 19.9 60 0.253 0.145 29.0 0.254 19.9 80 0.338 0.145 29.0 0.254 19.9 100 0.422 0.145 29.0 0.254 26.6 100 0.422 0.193 38.7 0.451 2900 2800 %- 'E 2700 2600 2500 2400 2300 ~-- direction of flow B I~ (cid:12)9 II ] 00 sc~ r i i , -1.0 -0.6 -0.2 0.2 0.6 1.0 Position across wefer Fig. 8. Model (curves) vs. data (points) for the effect of flow rate on etch rate. Pressure = 150 mtorr, temperature = 70~ RF power = 750W.
`
` Ex.1006 p.5
`
`

`
`J. Electrochem. Soc., Vol. 137, No. 3, March 1990 (cid:14)9 The Electrochemical Society, Inc. 959 28OO 2700 ~ 2600 2500 2400 2300 A ~ direction of flow B ~00 torr (cid:12)9 (cid:12)9 125 mtorr q i i .0 -0.5 0,0 0.5 1,0 Position ~cross wafer Fig. 9. Model (curves) vs. data (points) for the effect of pressure on etch rate. Flow rate = 100 sccm, temperature = 70~ RF power = 750W. true dissociation constant and the electron concentration), of 20s -~. This is more than two orders of magnitude greater than our value of 0.13s 1. However, this is not discouraging since their results are for experiments conducted at power densities of 3.5 W/cm 3, which is nearly two orders of mag- nitude greater than our power density of 0.054 W/cm 3. Ac- counting for this difference in power makes the agreement reasonable, since the electron concentration is propor- tional to the applied power density (18). The etch rate constant, ke, can be compared to the value from Flamm et al. (20), which was measured for etching Si downstream from a dissociated F2 source. At 70~ ke from (20) has a value of 49 cm/s, which is a factor of six less than that found from our work. Although not a large difference, several factors such as ion bombardment and other etch- ing reactions besides the fluorine-silicon reaction could ac- count for the higher value of the reaction rate parameter. The three rate constants are assumed to be independent of pressure. However, when the model was used to predict the etch rates for the data of Fig. 4 (pressure effect), the model predicts a larger effect of pressure on etch rate than was observed. To overcome this discrepancy, the sensitiv- ity of predicted etch rate on the three parameters was tested. After several cases were reviewed, it was found that making the loss rate constant (kl) proportional to pressure allowed the effects of pressure to be more adequately de- scribed. The loss constant was then determined from the kt at 150 mtorr multiplied by the ratio of the run pressure and 150 mtorr. Model vs. data etch rates are plotted in Fig. 9 for the single-wafer cases of Fig. 4 (125 and 200 mtorr). (The case of 150 mtorr was included in Fig. 8.) The reason for this pressure dependence of kl is unknown and further work is warranted. Wafer location and wafer loading effects were also exam- ined using the model and the rate constants in Table If. 2600 2500 2400 2300 E 2200 21oo 2900 A 4"* direction of flow B 00 (cid:12)9 (cid:12)9 00 inner wafer (cid:12)9 (cid:12)9 (cid:12)9 (cid:12)9 m 2800 2700 2600 outer wafer (cid:12)9 ml 2500 -1.0 -0.5 0.0 0.5 1.0 Position across wafer Fig. 10. Model (curves) vs. data (points) for the effect of wafer loca- tion on etch rote. Flow rate = 100 sccm, pressure = 150 mtarr, tem- perature = 70~ RF power = 750W. 2050 1950 1850 1750 E v 1650 ~ 2250 A ,6- direction of flow (cid:12)9 (cid:12)9 (cid:12)9 outer wafer (cid:12)9 (cid:12)9 mm mm -~ ~ 0 2150 ~ inner wafer 2050 (cid:12)9 1950 (cid:12)9 (cid:12)9 185O 175( , , (cid:12)9 , 00, -1.0 -0.5 0.0 0.5 1.0 Position across wofer Fig. 11. Model (curves) vs. data (points) for the effect of wafer load- ing on etch rote. Flow rate = 100 sccm, pressure = 150 mtorr, tem- perature = 70~ RF power = 750W. Figure 10 shows the comparison of model and data for the single-wafer case at the inner and outer locations. The case for the middle location was shown in Fig. 8. Etch rates for the outer wafer are reasonably predicted by the model with the error between 10 and 100 A/min. However, the model significantly overpredicts the etch rate for the inner wafer with errors in excess of 300 A/min. It is uncertain what causes this discrepancy; however, at the reactor exit, the existence of plasma or electron nonuniformities could cause unpredictable experimental results. In Fig. 11 a similar effect is seen for the wafer loading re- sults. The model comes close to predicting the etch rates of the outer wafer, but is not accurate for the inner wafer case. As with the single-wafer results, the etch rate in- creases more rapidly at the reactor exit than the model pre- dicts. Again, nonuniformities in the electric field (23) or the flow field at the reactor exit may be causing these anoma- lies. What is encouraging in Fig. 10 is the model's ability to predict a loading effect. With three wafers, the average etch rate is approximately 1950 A/rain, while the single- wafer etch rates were approximately 2500 A/min. The model, without varying the originally determined reaction rate constants, predicts this loading effect. Several observations from this modeling-experimental study give insight into the controlling rates in this plasma etching system. First, from Fig. 3 and 8, it is observed that decreasing flow rate enhances the etch rate. This indicates that longer residence times are allowing a higher genera- tion extent of active (F) species. Thus, the dissociation rate is rate limiting rather than the surface reaction rate. Sec- ondly, from Fig. 4 and 9, it is obsel"ced that higher pres- sures resulted in higher etch rates. This would be expected since dissociation rates will increase with CF4 concentra- tions (Eq. [ta]). However, their increase could not be ac- counted for by the model without increasing the loss rate constant proportionally with pressure. This is unexpected but may indicate a loss mechanism which is more compli- cated than assumed in this study. Thirdly, the location of the wafer had only a small effect on etch uniformity. This is a combination of the dissociation rate limitation, where rate increases from the reactor entrance, and the strong in- fluence of the wafer's presence. However, this effect was poorly predicted by the model at the reactor's entrance, in- dicating nonuniformities in the exiting electric or flow f