Principal Component Analysis of Optical Emission Spectroscopy and Mass Spectrometry: Application to Reactive Ion Etch Process Parameter Estimation Using Neural Networks

We report on a simple technique that characterizes the effect of process parameters (i.e., pressure, RF power, and gas mixture) on the optical emission and mass spectra of CHFJO2 plasma. This technique is sensitive to changes in chamber contamination levels (e.g., formation of Teflon-like thin-film), and appears to be a promising tool for real-time monitoring and control of reactive ion etching. Through principal component analysis, we observe that 99% of the variance in the more than 1100 optical and mass spectra channels are accounted for by the first four principal components of each sensor. Projection of the mass spectrum on its principal components suggests a strong linear relationship with respect to chamber pressure. This representation also shows that the effect of changes in thin-film levels, gas mixture, and RF power on the mass spectrum is complicated, but predictable. To model the nonlinear relationship between these process parameters and the principal component projections, a feedforward, multi-layered neural network is trained and is shown to be able to predict all process parameters from either the mass or the optical spectrum. The projections of the optical emission spectrum on its principal components suggest that optical emission spectroscopy is much more sensitive to changes in RF power than the mass spectrum, as measured by the residual gas analyzer. Model performance can be significantly improved if both the optical and mass spectrum projections are used (so called sensor fusion). Our analysis indicates that accurate estimates of process parameters and chamber conditions can be made with relatively simple neural network models which fuse the principal components of the measured optical emission and mass spectra. In the reactive ion etching (RIE) process, plasma characteristics depend on many parameters; some of these parameter values are set by the tool operator, e.g., chamber pressure, RF power, and gas flow, while others are internal to the condition of the chamber, e.g., thin-film thickness on the chamber walls, or the amount of material etched. Plasma characteristics can be observed using in situ measurements, e.g., via optical emission spectroscopy (OES) or residual gas analysis (RGA). How these measurements can be used to estimate the process parameters is the question that this paper is concerned with. Currently, an etch process is arrived at through experiments which try to find the particular process parameters that result in the desired etch selectivity and profile. These conditions translate into a recipe which typically defines the set-points for gas flow, chamber pressure, RF power, and etching time. But since a chamber is usually stressed under high throughput, the chamber 's internal parameters will vary even though the input parameters (as set by the operator) have not changed. This leads to results that are difficult to reproduce. The situation is further complicated by the fact that an unsuccessful etch may be caused by a mismatch between the process settings and the conditions actually produced by the machine's hardware, which is the case when there is, for example, a malfunctioning mass flow controller. Research on model ing the relationship between process set-points and the desired etch profile (1-3) has greatly improved our understanding of the basic physical and chemical mechanisms in the RIE process. These models typically try to account for the plasma chemical reactions, the ionization and motion in an electric field, and the surface reaction kinetics (4). For monitoring and control application, however, it is unlikely that such models can be readily applied, since the particular reaction rates and cross sections are generally unknown. Another approach has been to track the chamber conditions in situ. The idea here is to monitor the trajectory of one or two channels of an OES or RGA for the "perfect chamber," and then try to track that trajectory during the manufacturing process. Various artificial intelligence tools have been devised that, through rule-based expert systems, can detect significant deviation from the desired trajectory (5). However, we know only of the work of Bolker et al. (6) where an in si tu measurement, the RGA, was correlated to the process set-points. In the present work we use in situ measurements in order to identify how the observed state of the plasma depends on each input process parameter (e.g. pressure, power, and/or mass flow/composition of gas). If it can be shown that the effect of each process parameter on the observed state of the plasma is uniquely identifiable, then discrepencies between the current and desired state of the plasma can be attributed to a particular parameter--facilitating monitoring and diagnosis. Furthermore, the system should be able to alert the operator to conditions that cannot be overcome by manipulation of the input parameters, such as leaks in the chamber, or significant formation of contaminations (e.g., fluorocarbon, Teflon-like film) inside the chamber (7, 8). This report describes our effort for identifying the effects of the process parameters on the in si tu measurements of OES and RGA. Using principal component analysis (PGA), we show that changes in chamber pressure, RF power, gas mixture, and contamination levels result in complex but predictable clustering patterns when the OES and RGA measurements are projected onto their first few principal components. Our results indicate that for the limited set of experiments conducted, nearly all of the information in the OES and RGA measurements can be represented by these principal components. This way of representing the in si tu measurements allows for very efficient modeling, since the characteristics of the plasma can be represented with only a few variables with almost no loss of information. Furthermore, relationships are much easier to visualize due to the significant reduction in dimensionality of the data set. We explored both linear and nonlinear estimators for model ing .the relationship between process parameters and these principal component projections. For the nonlinear estimator, we use a feed-forward, multi-layered neural network. The results reported here suggest that accurate estimates of process set-points and chamber contamination levels can be made with relatively simple neural network models, using the principal components of the OES and RGA measurements. Present address: Department of Brain and Cognitive Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. 2 Present address: IBM Advanced Semiconductor Technology Center, East Fishkill, New York 12533-6531. Experiments In the present work, we are concerned with the following problem: A mixture of CHFjO2 is vertically dissociated and ionized at a certain chamber pressure and RF J. Electrochem. Soc., Vol. 139, No. 3, March 1992 9 The Electrochemical Society, Inc. 907 908 J. Electrochem. Soc., Vol. 139, No. 3, March 1992 9 The Electrochemical Society, Inc. Table I. Experiment numbers and the corresponding process parameter values. Exp. Power Mix Press. Thin Exp. Power Mix Press. Thin no. watts % 02 mTorr film no. watts % 02 mTorr film 1 200 3 25 9.4 37 200 3 50 20.2 2 300 3 25 9.5 38 300 3 50 20.2 3 350 3 25 9.6 39 350 3 50 20.3 4 200 9 25 9.8 40 200 9 50 20.5 5 300 9 25 9.8 41 300 9 50 20.5 6 350 9 25 9.9 42 350 9 50 20.6 7 200 15 25 10.0 43 200 15 50 20.6 8 300 15 25 10.0 44 300 15 50 20.7 9 350 15 25 10.1 45 350 15 50 20.7 10 200 3 50 10.2 46 200 3 75 20.9 11 300 3 50 10.3 47 300 3 75 21.2 12 350 3 50 10.4 48 350 3 75 21.4 13 200 9 50 10.5 49 200 9 75 21.8 14 300 9 50 10.5 50 300 9 75 22.0 15 350 9 50 10.6 51 350 9 75 22.2 16 200 15 50 10.7 52 200 15 75 22.4 17 300 15 50 16.7 53 300 15 75 22.5 18 350 15 50 10.7 54 350 15 75 22.6 19 200 3 75 11.0 55 200 3 50 30.0 20 300 3 75 11.3 56 300 3 50 30.0 21 350 3 75 11.7 57 350 3 50 30.0 22 200 9 75 12.0 58 200 9 50 30.2 23 300 9 75 12.2 59 300 9 50 30.2 24 350 9 75 12.3 60 350 9 50 30.3 25 200 15 75 12.6 61 200 15 50 30.4 26 300 15 75 12.6 62 300 15 50 30.4 27 350 15 75 12.7 63 350 15 50 30.4 28 200 3 25 19.3 64 200 3 75 30.5 29 300 3 25 19.4 65 300 3 75 30.8 30 350 3 25 19.5 66 350 3 75 31.2 31 200 9 25 19.7 67 200 9 75 31.7 32 300 9 25 19.8 68 306 9 75 31.8 33 350 9 25 19.9 69 350 9 75 32.1 34 200 15 25 19.9 70 200 15 75 32.4 35 300 15 25 20.0 71 300 15 75 32.4 36 350 15 25 20.1 72 350 15 75 32.5 p o w e r (no wafe r is p r e s e n t in t he chamber) . F r o m the m e a s u r e d opt ical e m i s s i o n and mass spect ra , t he task is to e s t ima te the value o f t h e s e pa ramete r s , as well as the a m o u n t of Teflon-l ike th in-f i lm (7, 8) p r e s e n t on the surface of t he c h a m b e r ' s in te r io r? Bui ld-up of th is film (here af ter r e fe r red to as thin-fi lm) c h a n g e s the charac te r i s t i cs of t he p lasma, can s ignif icant ly r e d u c e the Si e t ch rate (9-11), and in e x t r e m e cases , can flake off and ser ious ly con t amina t e t he wafer . For the fo l lowing e x p e r i m e n t s , the RIE reactor was a 13.56 MHz f lexible diode, wi th a 40 cm d i ame te r lower e lec t rode and a p o w e r range f rom 0 to 1000 W. C h a m b e r p r e s s u r e was con t ro l l ed by an au tomat i c th ro t t le valve and m e a s u r e d by an M K S Barat ron. The CHFJO2 m i x was det e r m i n e d by se t -poin ts on the M K S mass / f low cont ro l le rs w i th a f low range of 0 to 100 sccm. The opt ical emis s ion of the p l a sm a was ana lyzed us ing a 512 d iode array (150 g roves /mm) E G + G P A R C Mode l 1460, w i th a dual pos i t ion s t e p p e r m o t o r a d j u s t m e n t on the d i f f rac t ion gra t ing tha t a l lowed for v i ewing of emis s ions f rom 240 to 900 nm. D o w n s t r e a m m a s s spec t ra for mas se s 1 to 99 were t aken on an Inf icon Quad rex 200 RGA. Bo th the OES and RGA w e r e in te r faced to an IBM PS/2 Mode l 80 for eff icient data col lec t ion and label ing. An Inf icon IC6000 Quartz Crystal Mic roba lance (QCM), w i th the crysta l m o u n t e d on the wall, was u s e d as an ind ica tor of t he a m o u n t of thin-f i lm in t he c h a m b e r 4 (12). C h a m b e r p r e s su re was c h a n g e d f rom 25 to 75 mTor r by i n c r e m e n t s of 25 mTorr . Gas flow was kep t cons t an t at 100 sccm, and the ratio of CHFJO2 was c h a n g e d f rom Note that because no wafer was present in the chamber, for any given set of process set-points, the plasma's characteristics, and therefore the state of the process, did not vary significantly with respect to time. Although under conditions of high pressure and power one can readily observe thin-film build-up over several minutes, which results in a change in the species present in the optical and mass spectra, these measures remain essentially stationary for a period of a few tens of seconds after the power is applied. We assumed that the relationship between the in situ measurements and the process parameters in stationary. 4 Thin-film growth is reflected in a lowering of the frequency readout of the QCM. Unfortunately, without knowledge of the film density, this readout cannot be converted to an absolute measure of the thin-film thickness. However, as a relative measure, the QCM provides an accurate estimate of the change in thin-film thickness. 97%/3% to 85%/15% by i n c r e m e n t s of 6%. RF p o w e r was set at e i ther 200, 300, or 350 W for each of the above pe rmuta t ions. To in ten t iona l ly and qu ick ly depos i t thin-fi lm, we se t t he i n p u t p a r a m e t e r s at 50 mTorr , 100 s c c m CHF3, and 250 W. The QCM s h o w e d rap id bu i ld -up of thin-f i lm on the c h a m b e r walls, w h i c h was a c c o m p a n i e d by a d rop in VDC. We r e c o r d e d t h e c h a n g e in the QCM's output , and r epea t ed the above set of e x p e r i m e n t s at m e d i u m and h igh levels of thin-fi lm. In Table I w e ' v e l i s ted the e x p e r i m e n t n u m b e r s and the c o r r e s p o n d i n g p roces s p a r a m e t e r values. The R G A and OES m e a s u r e m e n t s w e r e s to red for each p roces s se t -point . We s to red the R G A s p e c t r u m for masses 1 to 99, a n d the s p e c t r u m f rom 251.8 to 562.2 n m for the first 510 ch an n e l s o f opt ical emis s ion (resolut ion of 0.61 nm), and f rom 549.2 to 860.9 for t he s eco n d 510 channels. A total o f 72 e x p e r i m e n t s were p e r f o r m e d (see Table I). Principal Component Analysis Pr inc ipa l c o m p o n e n t analysis enab les r educ t ion of a data set whi le re ta in ing m o s t of its variat ion. The n e w set o f var iab les are cal led the pr inc ipa l c o m p o n e n t s der ived f rom l inear t r a n s f o r m a t i o n s of t he original ones. They are s tat is t ical ly unco r r e l a t ed to each o the r and typical ly a smal l f rac t ion of t h e m (the first several) con ta in the majori ty of the var ia t ion (13). For the p r o b l e m at hand , changes in the p ro ce s s p a r a m e t e r s resul t in ch an g es in the s ta te of t he p lasma, w h i c h is e s t i m a t e d by the 99 var iables of the m e a s u r e d mass s p e c t r u m and the 1020 var iables of the m e a s u r e d opt ical emi s s i o n spec t rum. By visual inspection, it is p e r h a p s poss ib le to cor re la te pa t t e rns in par ts o f t h e s e spec t ra wi th ch an g es in t he p roces s pa ramete r s . But b ecau s e the n u m b e r of r e c o r d e d var iables is so large, it is very difficult , for example , to see t he effect of RF p o w e r on the RGA. F u r t h e r m o r e , bu i ld ing a m o d e l tha t e s t ima te s four p roces s p a r a m e t e r s f rom s o m e 1119 d i f fe ren t variables w o u l d be imprac t ica l for bo th eff ic iency and accuracy cons idera t ions . By e m p l o y i n g pr inc ipa l c o m p o n e n t analysis , we h o p e to f ind a smal l s u b s p a c e s p a n n e d by a set of o r thogona l vectors ( the first few p r i n c i p a l c o m p o n e n t s ) , w h e r e project ions of t he original data can be effect ively s tudied . I f t h e s e J. Electrochem. Soc., Vol. 139, No. 3, March 1992 9 The Electrochemical Society, Inc. 909 few uncor re la ted var iables r ep roduce mos t of the var ia t ion in all of the or iginal var iables , and if these var iables are int e rpre tab le (i.e., have a phys ica l meaning) , t hen the PCs give an al ternate, and m u c h s imple r descr ip t ion of the data than the or iginal variables. Our resul ts demons t r a t e that this is in fact the case for the RIE process descr ibed in the prev ious section. C o m p u t i n g the pr inc ipa l c o m p o n e n t s amoun t s to calcula t ing the e igenvec to r s in descend ing order of the covar iance ma t r ix o f t he var iables in quest ion. Le t y~ = [s~, q~, pi, c~] T, r ep resen t t he process pa rame te r vec to r for e x p e r i m e n t i, where s is the R F power , q is the pe rcen t 02 in the C H F J 02 mix ture , p is the c h a m b e r pressure, and c is the thinfilm con tamina t ion level as measu red by a quar tz crystal m ic roba l ance (QCM). Le t mi =[m h, mi 2 . . . . . mbg] w and oi = [%, %, . . . , %0~0] T, r ep resen t the mass and optical spectra for e x p e r i m e n t i, respect ively . The task is to bui ld a m o d e l which, g iven an obse rva t ion of the state of the process, m~ and o~, p roduces an es t imate of the process ' s i npu t and internal parameters , y~. Our approach is to use pr incipal c o m p o n e n t analysis to find mi and ~ f rom m~ and o~ where the d imens iona l i ty of ~ and 6i is m u c h less than mi and oi, and then bu i ld l inear and non l inear mode ls that descr ibe y, as a func t ion of @i and ~i. The ma t r ix Y = [y~, y ~ , . . . , yT~]T is the set of process setpoints v is i ted in the exper iments . Matr ices M = [m~, m~, . . . . mn] T and O = [oi, o2 . . . . . 072] w are the measu red mass and opt ical emiss ion spect ra for the set of process setpoints Y. Fo r example , O~k is the va lue of the kth OES channel , for the j t h process sett ing, yj. The pr incipal componen t s of the mat r ices M and O can be calcula ted by f inding the e igenvec to r s of their r espec t ive covar iance matrices; Matr ices g and C are the sampled covar iances of M and O, respec t ive ly 1 L Bjk = ~ ~ (Mij Mj)(Mik ~rk) [1] c ~ = : : E ( Q o j ) (o ,~ o~) [2] $ 1 ~_--z-1 w h e r e j , k = 1, 2 , . . . , 9 9 i n E q . [ 1 ] , j , k = 1, 2 , . . . , 1 0 2 0 i n Eq. [2], l = 72 (i.e., the n u m b e r of exper iments ) , and Mj and Oj are def ined as E 1 z = ~ Mij [3] Mj ~i:,