A model for reactive ion etching of PZT thin films

Surface and Coatings Technology 116–119 (1999) 456–460 www.elsevier.nl/locate/surfcoat

A model for reactive ion etching of PZT thin films G. Suchaneck a, *, R. Tews b, G. Gerlach a a Institute for Solid State Electronics, Dresden University of Technology, Mommsenstr. 13, D-10602 Dresden, Germany b SIMEC GmbH&Co. OHG, Postfach 10 09 40, D-01076 Dresden, Germany

Abstract In this work, a simplified model for the discharge kinetics and surface chemistry of r.f. discharges containing CF , CHF and 4 3 Ar gas mixtures suitable for lead zirconate–titanate (PZT ) etch rate simulation is presented. The electron density and the fraction of power dissipation in the discharge bulk, in the sheaths and due to the oscillating sheath boundaries were calculated by an electron kinetics model for given etching parameters. A Maxwellian electron energy distribution was assumed. For a parallel plate etching reactor with a plug gas flow parallel to the electrode surface, the ion energy flux determining the PZT etch rate was calculated. The fraction of power dissipated by ion bombardment was about 80%. A weak dependence of the ion energy flux on gas composition was obtained. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Electron kinetics; Plasma modeling; PZT etching

1. Introduction Lead zirconate–titanate (PZT ) ferroelectric thin films are known for their possible application in non-volatile random access memories as well as dynamic random access memories. The CMOS integration of ferroelectric materials drives the development of dry etching rather than wet etching techniques of this material. Various techniques of PZT reactive ion etching (RIE ) were investigated, for instance using a high density distributed ECR plasma and SF /Cl or HBr/SF [1] and CF /Cl 6 2 6 4 2 or CF Cl chemistries [2], a tri-electrode reactor driven 2 2 by high frequency (13.56 MHz) for ion generation efficiency and low frequency (450 kHz) to control ion energy and a CF chemistry [3], a low frequency planar 4 electrode RIE etcher and CCl F , Ar, SF and oxygen 2 2 6 plasmas [4], diode RIE etchers (13.56 MHz) with CF /Ar [5], CHClFCF [6 ], CCl F [7], Cl and CF 4 3 2 2 2 4 low pressure plasmas [8]. Increasing with r.f. or microwave power, the etch rates were obtained, predominantly determined by ion bombardment [1,3,5,7], but also with some chemical enhancement as shown by comparison with pure argon sputtering [1,2,5] and a strong substrate temperature dependence [1,4]. Lower compared to sili* Corresponding author. Tel.: +49-351-463-5281; fax: +49-351-463-2320. E-mail address: [email protected] (G. Suchaneck)

con and silicon dioxide etch rates [1], unsatisfactory profile angles [3], redeposition of etch products and residue formation [3,5,7], sidewall roughening [4], a different from the bulk composition of PZT sidewall surfaces and doping of this area by low energy ions such as F and Cl [8], radiation and particle bombardment induced damage influencing the P–E hysteresis, fatigue behavior and leakage current [6 ] requires a deeper understanding of the process. In this work, a simplified model for the discharge kinetics and surface chemistry of r.f. discharges containing CF , CHF and Ar gas mixtures for PZT etch rate 4 3 simulation is presented, estimations of vibrational excitation, dissociation, electron attachment and ionization cross-sections of CHF are given, and the ion impact 3 energy determining the PZT etch rate calculated.

2. Electron collision cross-sections Cross-section sets of CF [9–12] and Ar [13] were 4 used. In the case of CHF estimations were made 3 as follows. The momentum transfer cross-section of CF was 4 scaled to a lower kinetic molecule diameter with a factor of 0.9233. Vibrational excitation cross-sections were

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G. Suchaneck et al. / Surface and Coatings Technology 116–119 (1999) 456–460

calculated from: =∑ s , (1) vib nm using the Born–Bethe dipole approximation formula [14] which in the high energy limit E≥7(E −E ) satism n factorily describes the transfer cross-sections of optically allowed transitions in terms of the oscillator strength: s

A

B

e4 f E nm s = , (2) ln nm 16pe2 E(E −E ) E −E 0 m n m n where e is the electron charge, e the dielectric constant, 0 E the energy of the states and f the oscillator strength nm calculated from IR absorption spectra according to: f = nm

4m e c2 e 0 e2

P

2

s(v) dv, (3) 0 where m is the electron mass, c the speed of light, v e the photon wave number and s(v)=a(v)/n the absorption cross-section, a(v) the absorption coefficient, n the number of vibrating bonds per unit volume. Integrated absorptions ∆ a(v) dv were calculated from spectra in Ref. [15] ( Table 1). Fig. 1 compares vibrational excitation cross-sections of CF and CHF with an electron 4 3 swarm experiment fit of CF based on a numerical 4 solution of the Boltzmann equation [11]. Oscillator Table 1 Wave number, integrated absorption and oscillator strength of the CHF and CF vibration modes 3 4 Gas

v (cm−1)

f×106

Vibration mode

CHF 3

507 700 1143 1209 1377 3035 631.3 1276

0.688 1.55 58.3 0.823 19.8 3.33 1.45 140

E C–F def. 3 A1 C–F def. 3 A1 C–F stretch 3 E C–F stretch 3 E C–F rock. 3 A1 C–H stretch C–F asym. bend. C–F asym. str.

CF

4

Fig. 1. Vibrational excitation cross-sections for CF and CHF deter4 3 mined from IR absorption (this work) and using a numerical solution of the Boltzmann equation (BE) [11].

457

strengths of CF IR non-active vibrations were assumed 4 to be equal to the corresponding asymmetric vibrations. A first approximation of electron impact ionization cross-sections at 20, 35 and 70 eV is the additive rule: s =b+∑ n a , (4) i i i i where n is the number of atoms of kind i in the i molecule, a and b are regression coefficients taken from i Ref. [16 ]. The determined values were then expressed as an equation:

A B AB

E E e4 −1 ln s =∑ D , (5) i n 16pe2 E2 I I n 0 n n where D are fitting coefficients which were determined n from photoelectron spectra in Ref. [17]: D =0.84× 1 10−16 cm2, D =1.26×10−16 cm2, D =2.10×10−16 cm2, 2 3 D =1.47×10−16 cm2, D =1.89×10−16 cm2 and 4 5 D =0.42×10−16 cm2 for vertical ionization by trans6 itions to the 6a , 1a , 5e, 4e, 3e+5a , and 4a orbitals 1 2 1 1 with ionization potentials I of 14.8 eV, 15.5 eV, 16.2 eV, n 17.24 eV, 19.84 eV and 24.44 eV, respectively. Eq. (5) describes the cross-section of an optically allowed transition from the ground state to excited states [18]. Fig. 2 shows a comparison of the calculated electron impact ionization cross-sections with values determined for CF in Ref. [19]. Taking into account that the ionization 4 cross-sections of CF determined by various groups 4 scatter within a factor of two [10], the results seems to be very satisfactory. The dissociation of CHF differs from that of CF 3 4 due to a lower CF –H bond energy (4.6 eV ) compared 3 to CF –F (5.6 eV ). Therefore, the extrapolation of 3 CF data [9] was performed by fitting the contribution 4 of dissociation into atomic fluorine near the dissociation threshold to Eq. (5) of optically allowed transitions and shifting it with the same transition coefficient to lower by 1 eV values. Electron attachment usually corresponds to one or more resonance processes peaked at low energy. Thus, a reasonable general representation of the attachment

Fig. 2. Electron impact ionization cross-sections for CF and CHF . 4 3

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G. Suchaneck et al. / Surface and Coatings Technology 116–119 (1999) 456–460

cross-section is given by [20]: s =∑ K Eli exp(−m E ), (6) a i i n where K , l , m are adjustable parameters and n corresi i i ponds to the number of cross-section peaks. Calculations in this work were performed using a broad peak which includes partially the data of CH [21] and the contribu4 tion of CF− generation of CF [22,23], described by 3 4 K =2×10−32 cm2, l =30, m =4. 1 1 1 Fig. 3 shows a summary of estimated CHF electron 3 collision cross-sections.

3. Etch rate simulation There is considerable literature on the simulation of CF containing plasmas for etching of silicon and silicon 4 dioxide [12,24–28]. Sophisticated models were proposed including primary electron impact reactions and up to 36 secondary reactions between the generated species in the gas phase or at wall surfaces [26 ] where at least eight reactions should be taken into account in the case of a CF /O plasma. Despite the fact that ion densities 4 2 are orders of magnitude smaller than the neutral radicals, their contribution to the etching process was estimated by plasma etching modeling to be 50 to 80% [24]. This is a result of large ion mobilities and space charge enhanced ambipolar diffusion. On the other hand, the etch rate of these materials is determined by two rate limiting parameters, the ion energy flux and the fluorine flux (or fluorine density) independent of the type of plasma etch tool type, and can be described by [29]: K J E [1−C (n /n )2] es i i sp CFx F , (7) 1+A (J E /n ) s i i F where E is the ion energy at the wafer, n the density i CF of CF radicals causing polymer formation xon the wafer x surface and thus inhibiting the etch process, n the F density of fluorine atoms as a measure of the etching

R#

species flux, J the ion particle flux and K , C , A are i es sp s constants, C (SiO )=0.13, A (SiO )=3.3×10−3 for sp 2 s 2 ion energy fluxes given in mW/cm2 and fluorine densities given in 1012 cm−3. The term in parenthesis accounts for polymer deposition and can be negative indicating net deposition. High silicon oxide etch rates were achieved at high J E under conditions of negligible i i polymer formation and A J E /n #1, i.e. for a nearly s i i F constant denominator. In the case of PZT etching, fluorine interaction with the surface is inhibited because the vapor pressures of Pb, Zr and Ti fluorides are too low at temperatures 20– 300°C to allow significant vaporization of these fluorides once they are formed by reactions on the surface ( Table 2). Therefore, ion bombardment effects are primarily responsible for the etching which is in confirmation with the literature. Mass spectrometry of volatile species in CF /Cl high density ECR plasmas shows 4 2 that, in agreement with thermodynamic estimations, fluorine containing radicals are reactive with respect to titania and zirconia [2]. This is confirmed by X-ray photoelectron spectroscopy and Auger electron spectroscopy surface analysis, revealing that low pressure CF 4 plasma selectively removed the Ti–O and Zr–O bonds, inducing oxygen vacancies which must be compensated by Ar or Cl admixture selectively breaking relatively weak Pb–O bonds and inducing Pb vacancies by physical sputtering rather than by chemical activity [8]. For an effective combination of physical attack (ion bombardment) and chemical reactivity (attack by fluorine radicals), a threshold energy of 150 to 200 eV is required [2]. The PZT etch rate is dependent on the ion energy and is proportional to the bias voltage squared at high values [1]. Thus, the ion energy flux to the wafer surface will be a reasonable measure of the etch rate. Calculations of the ion energy flux determined by the mean sheath voltage U were performed considering a sh nearly collisionless sheath model [30]. The total power balance is given as: =2en u (e +e +U ), (8) r.f. e B c r 9 sh where n is the mean electron density in the plasma e bulk, u the BOHM velocity: B kT e, u = B m i

P

S

Table 2 Melting temperature, sublimation temperature and standard formation enthalpy of lead, titanium and zirconium fluorides

Fig. 3. Electron collision cross-section for CHF . 3

Fluoride

T (°C ) M

PbF 2 PbF 4 TiF 4 ZrF 4

824 #600

T (°C ) S

H0 (kJ/mol ) f

1292

−664

284 # 600

−931 −1863

G. Suchaneck et al. / Surface and Coatings Technology 116–119 (1999) 456–460

459

m the ion mass, T the mean electron temperature, e i e c and e the energy lost per created electron–ion pair and r due to wall recombination, respectively:

C

1 I e = ∑ mf e + c i izi K −K i=1 iz a

A

3

m

Ji e T k +∑ e k e el j j m i ji=1 i i i

BD

,

I K −K = ∑ mf (k −k ), iz a i izi ai i=1 where mf is the mole fraction of the corresponding gas i in the gas mixture, k the rate constant of elastic el collision, k the rate constant of inelastic collisions j (excitation, dissociation, ionization) with an energy loss of e per collision and K −K the net rate constant of j iz a electron–ion pair creation. A Maxwellian electron energy distribution was assumed for rate constant calculations. Plasma bulk and sheath parameters were matched considering ions entering the sheath with the BOHM velocity: nN [k (e)−k (e)]d=2nu (e), iz a B

(9)

where N is the density of neutral species and k the a electron attachment rate. This simple form of a boundary condition of electronegative low pressure plasma follows from the existence of almost two different CF 4 plasmas: an inner positive–negative ion plasma, and an outer electron–positive ion one [12,31]. The density and the temperature of negative ions determine the BOHM velocity of the positive ions entering the sheath, but they have no influence on the dynamics of the positive ions in the sheath. The BOHM velocity in electronegative gases is smaller than in a plasma without negative ions [32]. Ion energy fluxes calculated as a function of r.f. power, total pressure, CF or CHF and Ar gas flow 4 3 rates were compared with experimental PZT etch rates. Fig. 4(a) illustrates the PZT etch rate with the r.f. power dependence for a CF –Ar gas flow ratio of 4, a 4 total flow rate of 20 sccm and a pressure of 0.01 mbar [5], compared with the experimental data for a CHF –Ar gas flow ratio of 0.25 and a pressure of 3 0.04 mbar in a Plasmalab 80+ (Oxford Plasma Technology) machine. The calculated ion energy fluxes for a frequency of 13.56 MHz, a total pressure of 0.04 mbar, a CF , CHF /Ar flow ratio of 1, an electrode 4 3 diameter of 17 cm and an electrode distance of 4 cm satisfactorily describe the r.f. power dependence. The calculated electron temperatures of the discharges were about 3 eV. The fraction of power dissipated by ion bombardment was about 80%. This simplified model is in agreement with the experimental evidence that the major dissociation process of CF is dissociative ioniza4 tion according to the reaction [5,33]: CF +e−[CF++F+2e−. 4 3

(a)

(b) Fig. 4. Comparison of calculated ion energy fluxes with PZT etch rates in CF /Ar [5] and CHF /Ar gas mixtures: (a) r.f. power dependence; 4 3 (b) dependence on CF –, CHF –Ar gas flow ratio. 4 3

The ion energy flux qualitatively reproduces also the weak PZT etch rate dependence on gas composition [Fig. 4(b)]. Comparing the calculations with experiment, the great oversimplification should be taken into account. For instance, the electron distribution function of a CF discharge may be described rather by a two4 temperature Boltzmann distribution [12,25,28]. In this case, dissociation and ionization are maintained by the high energy tail of the electron distribution function having a much higher electron temperature than the bulk [28]. This means that the estimated ion energy fluxes are at a lower limit. Improving the proposed model, the main advantage of real time decisions in plasma processing is lost.

4. Conclusions The etch rate of PZT thin films was analyzed qualitatively in terms of the ion energy flux to the film surface. Simulations of CF /Ar and CHF /Ar discharges were 4 3 compared with experimental data. Calculations for CF /Ar gas mixtures based on collision cross4 sections were derived from electron swarm data and for

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CHF only crude estimations of electron collision cross3 sections were made. The obtained weak dependence of the ion energy flux to the film surface on gas composition opens the possibility of optimizing the etching process taking into account, for instance, sidewall angles, sidewall roughening, residue formation, etc. Due to some chemical etch rate enhancement compared with pure argon sputtering, the CF or CHF fraction should be at least 20%. 4 3

Acknowledgement This work was supported by the Forschungsgemeinschaft as part of SFB422.

Deutsche

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