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Real dimensional simulation of SiO2 etching in CF4+H2 plasma
Vacuum 65 (2002) 101–108
Real dimensional simulation of SiO2 etching in CF4+H2 plasma R. Knizikevic$ ius* $ st., LT-3006 Kaunas, Lithuania Department of Physics, Kaunas University of Technology, 73, K. Donelaicio Received 3 July 2001; accepted 24 August 2001
Abstract The reactive ion etching of silicon oxide in CF4+H2 plasma is considered. The profiles of etched grooves are calculated as a function of mask dimensions, fluxes of chemically active and non-active plasma components and parameters of ion bombardment. To achieve this goal the chemical composition of CF4+H2 plasma is calculated and the one-dimensional etching of SiO2 in this plasma is considered. The values of phenomenological constants are found by extrapolation from the experimental results. Using the values of phenomenological constants, found by analysis of chemical composition of plasmas and one-dimensional etching, the etched groove profiles at real dimensions are calculated. The influence of hydrogen addition to fluorocarbon plasma on an etched groove profile is considered. Special attention is given to the selectivity of SiO2 etching over Si. The conditions under which etching selectivity is high are found. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: CF4+H2 plasma; SiO2; Reactive ion etching
1. Introduction Silicon integrated circuits are most widespread today. Silicon is easily processed compared to other semiconductor materials (GaAs, InP), and its oxide is used as an insulator. In integrated circuit manufacture, it is required to etch SiO2 selectively over Si. The addition of H2 to a CF4 plasma is used for selective etching of SiO2. It is determined experimentally [1] that, at sufficiently low H2 concentration, a thin fluorocarbon film forms on both Si and SiO2 surfaces during etching, but Si and SiO2 removal continues *Corresponding author. Fax.: +370-7-350737. E-mail address: [email protected] (R. Knizikevi$cius).
despite the existence of such layer. The structure of this film depends on the H2 concentration in the feed gas. Above a critical H2 concentration, the fluorocarbon film becomes more cross-linked, fluorine deficient, and amorphous carbon-like. Formation and subsequent growth of this fluorinated amorphous carbon (a-C : F) film stops etching of both Si and SiO2. In the absence of ion bombardment, the critical concentration at which etching is arrested and a-C : F growth begins is the same for both Si and SiO2. H atoms abstract and replace F atoms both on the surface and in the fluorocarbon film, resulting in the formation of a fluorine-deficient amorphous carbon-like film. In the presence of ion bombardment, this critical H2 concentration is increased (but at different amounts) for Si and SiO2. The film formed on
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$ / Vacuum 65 (2002) 101–108 R. Knizikevicius
SiO2 is more easily sputtered than that formed on Si due to the higher number of CaO bonds. The thickness of the fluorocarbon layer on SiO2 is much smaller than on Si for comparable discharge conditions [2,3]. During Si etching in this plasma, the adsorption of CF2 radicals on the Si surface is enhanced by ion bombardment, i.e. the sticking coefficient of CF2 radicals on the Si surface is increased in the presence of ion bombardment [4]. Meanwhile the fluorocarbon film is thin on the SiO2 surface as adsorbed CFx (xp3) radicals react with surface oxygen to form volatile CO, CO2, and COF2 molecules. These phenomena are used in the selective etching of SiO2 layers on a Si surface. As the SiO2 layer is etched, the underlying Si layer is etched slowly. In this way, the fixed depth grooves and contact holes are formed. The difference in processes occurring at the sidewall and bottom of the microstructure determine the final profile of etched groove. The presence of ion bombardment enables high etching selectivity and straight sidewalls to be achieved [5]. A better understanding of etched groove shape dependence on H2 content in the feed will allow more efficient integrated circuit manufacture. In previous work [6,7], etching through a mask in fluorine-based plasma was considered. However, the values of frequency probabilities used in these models were freely chosen and the profiles of etched grooves were calculated in relative units. In this work, the main reactions occurring in a CF4+H2 plasma are considered and the concentrations of plasma components are calculated by extrapolation from the experimental data. Using the derived composition of the flux of particles from the plasma, one-dimensional etching of SiO2 is investigated. The values of frequency probabilities, obtained from analysis of one-dimensional etching, are used for the calculation of the real dimensions of etched grooves.
2. Modelling of plasma composition In Table 1 the homogeneous reactions, taking place in a CF4+H2 plasma, in a general case, are
presented. In order to reduce the number of frequency probabilities, only the main reactions are included in the model: CF4 þ e-CF3 þ F þ e;
ð1aÞ
H2 þ e-2H þ e;
ð1bÞ
F þ H2 -HF þ H;
ð1cÞ
CF3 þ F þ M-CF4 þ M;
ð1dÞ
CF3 þ H-CF2 þ HF;
ð1eÞ
H þ F þ M-HF þ M;
ð1fÞ
2H þ M-H2 þ M:
ð1gÞ
Reaction rates are characterized by frequency probabilities of dissociation and reaction: G1 ¼ gCF4 þe-CF3 þFþe ½e=N;
ð2aÞ
G2 ¼ gH2 þe-2Hþe ½e=N;
ð2bÞ
R25 ¼ kr;FþH2 -HFþH ;
ð2cÞ
R35 ¼ kr;CF3 þFþM-CF4 þM ½M=N;
ð2dÞ
R36 ¼ kr;CF3 þH-CF2 þHF ;
ð2eÞ
R56 ¼ kr;HþFþM-HFþM ½M=N;
ð2fÞ
R66 ¼ kr;2HþM-H2 þM ½M=N;
ð2gÞ
where gi is the dissociation rate constant, N is the total neutral particle concentration in the plasma, kr;i is the reaction rate constant, and M is a third particle or wall of the reactor. Let us assume that frequency probabilities of dissociation and reaction do not depend on H2 content in the feed. The concentrations of electrons and ions in the plasma are not taken into account, as the degree of ionization of plasma does not exceed (1–2)%. It follows that seven chemical species exist in the plasma: CF4, H2, CF3, CF2, F, H, HF with relative concentrations n1 ¼ ½CF4 =N; n2 ¼ ½H2 =N; n3 ¼ ½CF3 =N; n4 ¼ ½CF2 =N; n5 ¼ ½F=N; n6 ¼ ½H=N; and n7 ¼ ½HF=N; respectively. The following system of rate equations describes the kinetics of chemical composition of a CF4+H2 plasma:
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius Table 1 List of values of enthalpies and free Gibbs energies of reactions, taking place in CF4+H2 plasma Reaction
DH (kcal/mol)
DG (kcal/mol)
CF4 þ e"CF3 þ F þ e CF3 þ e"CF2 þ F þ e CF2 þ e"CF þ F þ e H2 þ e"2H þ e CF4 þ H-CF3 þ HF 2CF3 þ M-C2 F6 þ M 2F þ M-F2 þ M CF3 þ H2 -CHF3 þ H F þ H2 -HF þ H CF3 þ H-CF2 þ HF CF3 þ H þ M-CHF3 þ M 2CF2 þ M-C2 F4 þ M CF2 þ H-CF þ HF CF2 þ H þ M-CHF2 þ M CF þ H-C þ HF CHF3 þ F-CF3 þ HF CHF3 þ F-CF4 þ H H þ F þ M-HF þ M
123.7 104.6 123.3 104.0 6.0 71.6 37.8 0.0 32.0 48.0 104.0 70.0 12.0 56.0 20.0 33.5 22.0 136.0
112.6 94.1 114.6 97.0 15.9 – 29.6 3.8 31.6 34.4 93.2 80.9 13.9 – 20.6 35.4 19.5 128.6
3. Modelling of one-dimensional etching The one-dimensional reactive ion etching (RIE) of a SiO2 substrate in a CF4+H2 plasma is considered. The composition of plasma is calculated from the above model of plasma composition. The main reactions taking place on the surface are the following: 2SiO2 þ 2CF3 -SiF2 þ SiF4 þ 2CO2 ;
ð4aÞ
SiO2 þ 2CF2 -SiF4 þ 2CO:
ð4bÞ
Phenomenological constants k1 and k2 characterize these reaction rates, respectively. The SiF2, SiF4, CO, and CO2 molecules formed leave the surface. A frequency probability of removal of the ith component, oi ; consists of frequency probabilities of sputtering and desorption, oi;s and oi;d : oi ¼ oi;s þ oi;d ¼ Yi I0 =C þ n0 expð Ed;i =kTÞ; ð5Þ
dn1 ¼ I1 G1 n1 þ R35 n3 n5 En1 ; dt dn2 ¼ I2 G2 n2 R25 n2 n5 þ R66 n26 En2 ; dt dn3 ¼ G1 n1 R35 n3 n5 R36 n3 n6 En3 ; dt dn4 ¼ R36 n3 n6 En4 ; dt dn5 ¼ G1 n1 R25 n2 n5 R35 n3 n5 R56 n5 n6 En5 ; dt dn6 ¼ 2G2 n2 þ R25 n2 n5 R36 n3 n6 dt R56 n5 n6 2R66 n26 En6 ; dn7 ¼ R25 n2 n5 þ R36 n3 n6 þ R56 n5 n6 En7 : dt
103
where Y is the sputtering yield, I0 is the ion flux, C is the concentration of surface molecules ðC ¼ 8:901018 m2 Þ; n0 is the frequency of oscillation of molecules in the solid, and Ed is the activation energy of desorption. It follows that four components exist in the adsorbed layer: SiF2, SiF4, CO, and CO2 with relative concentrations c1 ¼ ½SiF2 =C; c2 ¼ ½SiF4 =C; c3 ¼ ½CO=C; and c4 ¼ ½CO2 =C: The following system of rate equations includes rate expressions of different processes [8] and describes the kinetics of components in the adsorbed layer: ! 4 X dc1 ¼ k1 1 ci n2CF3 oc1 ; dt i¼1 ! 4 X dc2 ¼ k1 1 ci n2CF3 dt i¼1 ! 4 X þ k2 1 ci n2CF2 oc2 ; i¼1
ð3Þ
where Ii ¼ Fi =V0 N is the injection rate of ith component of gas mixture, E is the frequency probability of exhaust, Fi is the flow rate of the ith component, and V0 is the volume of the reactor.
! 4 X dc3 ¼ 2k2 1 ci n2CF2 oc3 ; dt i¼1 ! 4 X dc4 ¼ 2k1 1 ci n2CF3 oc4 : dt i¼1
ð6Þ
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius
104
The solutions of the system of linear equations (6) have the following form: ci ðtÞ ¼
4 X
ðAij þ Bij expðlj tÞÞ;
ð7Þ
j¼1
where Aij and Bij are the coefficients, defined from the initial conditions, lj is the solution of the characteristic equation. The stationary surface concentrations of components are equal to c1 ¼
c2 ¼
c3 ¼
c4 ¼
k1 n2CF3
;
ð8aÞ
;
ð8bÞ
2k2 n2CF2 ; þ 3k2 n2CF2 þ o
ð8cÞ
Fig. 1. Schematic presentation of RIE through the mask.
2k1 n2CF3 : 4k1 n2CF3 þ 3k2 n2CF2 þ o
ð8dÞ
has some peculiarities, related to the geometry of the mask. At first, the assumption that the mean free path of particles arriving at the surface is much larger than the feature size was taken into account. This assumption is always fulfilled during etching in the low-pressure plasma. The second assumption is that the angular distribution of particles in the plasma is isotropic. During twodimensional etching, the concentrations of atoms at the surface of an etched groove depends on the position of the arbitrary point Mðx;yÞ (Fig. 1). Let us assume that the concentration of atoms is equal to ni ðx; yÞ ¼ n0;i Yðx; yÞ=p; where n0;i is the relative concentration of the ith plasma component, and Yðx; yÞ is the angle. The groove bottom is subjected to ion bombardment, and the processes of activation of surface molecules and physical sputtering take place there. The sputtering of the SiF2, SiF4, CO and CO2 molecules is characterized by frequency probabilities of sputtering
4k1 n2CF3 þ 3k2 n2CF2 þ o k1 n2CF3 þ k2 n2CF2 4k1 n2CF3 þ 3k2 n2CF2 þ o 4k1 n2CF3
The etching rate is proportional to the removal rate of formed SiF2 and SiF4 molecules. According to Eqs. (8a) and (8b) the etching rate at the steady state regime is equal to Vst ¼
h0 oð2k1 n2CF3 þ k2 n2CF2 Þ
; 4k1 n2CF3 þ 3k2 n2CF2 þ o
ð9Þ
( is the thickness of one monowhere h0 ¼ 3:35 A layer, which was estimated using expression h0 ¼ ðMSiO2 =rSiO2 NA Þ1=3 ; where MSiO2 is the molecular weight of SiO2 ðMSiO2 ¼ 6:009102 kg mol1 Þ; rSiO2 is the density of SiO2 ðrSiO2 ¼ 2650 kg m3 Þ; and NA is Avogadro’s number.
4. Modelling of two-dimensional etching The etching of grooves on a silicon oxide substrate in a CF4+H2 plasma is considered. In the calculation of profiles of etched grooves, the results obtained from previous models of chemical composition of plasma and one-dimensional etching of Si are used. As etching takes place through a mask, the number of atoms, reaching the surface, depends on the position of an arbitrary point M on the surface (Fig. 1). Two-dimensional etching
oi;s ¼ Yi I0 f ðaÞ=C; 0:5
ð10Þ
where f ðaÞ ¼ cos a is the sputtering yield dependence on the incident ion angle a measured from the surface normal [9]. The non-activated SiO2 molecules on the sidewall react more slowly with CF2 and CF3 radicals, and the values of phenom-
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius
enological constants k1 and k2 are assumed to be ten times lower. Eq. (6) describes the kinetics of the surface concentrations of the components. The etching rate V is proportional to the removal rate of the SiF2 and SiF4 molecules which are formed: V ¼ h0 oðc1 þ c2 Þ:
ð11Þ
Knowing the surface concentrations of components from the solutions of Eq. (6), the etching rate as a function of coordinate and time is obtained. The point Mðx; y; tÞ after time interval Dt will take position M 0 ðx þ Dx; y þ Dy; t þ Dt), where Dx ¼ Vnx Dt and Dy ¼ Vny Dt; nx and ny are the components of the surface normal ~ n (Fig. 1). In this way, the groove profile as a function of time is obtained.
5. Results and discussion 5.1. Chemical composition of plasma The experimental results presented in Fig. 2 [10] are used in the model in order to calculate the chemical composition of a plasma. It was observed that the maximum concentration of HF molecules is achieved for 31% H2 in a plasma of a CF4+H2 gas mixture. Let us assume that the temperature of
Relative concentration
1.0
HF
0.8
0.6
H2
0.4
0.0 0
10
20
30
40
50
the plasma T ¼ 500 K, the total neutral particle concentration with the discharge off is N ¼ 1:931022 m3 ; and the total gas injection rate I ¼ 5:47 s1 : The total gas injection rate was estimated using expression I ¼ F=ðV0 NÞ where the flow rate is measured in molecules s1. The plasma composition is calculated using Eq. (3). Experimental [10] and theoretical dependences of the relative concentration of H2 and HF molecules in the plasma on H2 content in the feed are shown in Fig. 2. The following values of frequency probabilities of dissociation and reaction were found by extrapolation from experimental results: G1 ¼ 3:7 s1 ; G2 ¼ 2:0 s1 ; R25 ¼ 1:0104 s1 ; R35 ¼ 100 s1 ; R36 ¼ 2:0104 s1 ; R56 ¼ 1:0104 s1 ; R66 ¼ 100 s1 : The chemical composition of the plasma as a function of H2 content in the feed, using Eq. (3), is presented in Fig. 3. The concentration of HF molecules with increase of H2 content in the feed increases at first due to the reactions of H atoms with F atoms and CF3 radicals (Eqs. (1e) and (1f)). As the concentration of HF molecules approaches the maximum value, almost all F atoms and CF3 radicals have reacted (Fig. 3). With further increase in H2 content in the feed the concentration of HF molecules starts to decrease in proportion to the amount of injected CF4 molecules. In a CF4+H2 plasma, H atoms react with CFx (xp3) radicals. At a H2 content in the plasma X25%, the concentration of CF2 radicals is about 10 times higher than that of CF3 (Fig. 3) or CF radicals [11,12]. This indicates that an intensive reaction of H atoms with CF3 radicals takes place in the plasma. The conversion coefficient of the ith component of the gas mixture indicates a part of molecules converted to reaction products and is equal to Zi ¼ 1 Eni =Ii :
0.2
60
70
80
H2 content in the feed, %
Fig. 2. Experimental [10] (points) and theoretical (curves) dependences of the relative concentrations of H2 and HF molecules on H2 content in the feed.
105
ð12Þ
The dependences of the conversion coefficients of CF4 and H2 molecules on H2 content in the feed are presented in Fig. 4. It is seen that, at low H2 content in the feed (o30%), all H2 molecules are converted. The increase of conversion coefficient of CF4 molecules at low H2 content in the feed is related to the dissociation reaction (Eq. (1a)) and to subsequent reaction of H atoms with CF3
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius
106 100
0.35 0.30
CF4
H2
0.25
60
V, µm/min
Concentration, %
80
HF 40
CF2
F 0
H
CF3
20
40
0.15 0.10
20
0
0.20
60
80
0.05 0.00
100
H2 content in the feed, %
40
60
80
100
Fig. 5. Experimental [13] (points) and theoretical (curve) dependences of SiO2 etching rate on H2 content in the feed.
5
100
H2
80
4
Concentration, %
Conversion coefficient, %
20
H2 content in the feed, %
Fig. 3. The dependences of the concentrations of CF4+H2 plasma components on H2 content in the feed.
60
CF4
40
20
3
CO CO2
2
SiF4 1
0
0
0
20
40
60
80
100
H2 content in the feed, %
Fig. 4. The dependences of the conversion coefficients of CF4 and H2 molecules on H2 content in the feed.
radicals (Eq. (1e)). At higher H2 content fixed amounts of CF4 and H2 molecules are converted. 5.2. One-dimensional etching The experimental results presented in Fig. 5 (points) [13] are used in the model in order to calculate SiO2 etching rates. Let us assume that the SiO2 etching rate in the absence of H2 in the feed is equal to a value measured during experiment [14]. In the calculation of etching rates the results obtained from the previous modelling of plasma composition (Fig. 3) are used. Experimental and theoretical SiO2 etching rate dependences on H2
0
SiF2
0
20
40
60
80
100
H2 content in the feed, %
Fig. 6. The dependences of the concentrations of adsorbed layer components on H2 content in the feed.
content in the feed, calculated using Eq. (9), are shown in Fig. 5. The following values of phenomenological constants and frequency probability of desorption are determined: k1 ¼ 19 s1 ; k2 ¼ 14 s1 ; o ¼ 10 s1 : The dependences of the concentrations of adsorbed layer components on H2 content in the feed are shown in Fig. 6. It is seen that the concentrations of adsorbed layer components are low. The dependences of concentrations of CO2 and SiF2 molecules are similar to the dependence of concentration of CF3 radicals in the plasma. This is influenced by the same reaction of CF3 radicals with SiO2 molecules (Eq. (4a)). The
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius x, µm
-0.1 -0.4
-0.3
-0.2
-0.1
0.0 0.0
107
0.1
0.2
0.3
-0.4
-0.3
-0.2
-0.1
0.0 0.0
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7
y, µm
x, µm
-0.1
0.4
0.2
0.3
0.4
3
1 2
0.7
y, µm
0.8
Fig. 7. The evolution of groove profile during RIE. Mask width 0.5 mm, mask height 0.1 mm, and etching time 40 min. The groove profile is shown every 8 min.
0.1
0.8
Fig. 8. The etched groove profiles during RIE at different values of H2 content in the feed: (1) 20%, (2) 30%, and (3) 50%. Mask width 0.5 mm, mask height 0.1 mm, and etching time 40 min.
maxima of the concentrations of CO and SiF4 molecules are achieved at the maximum concentration of CF2 radicals in the plasma.
1.2
1.0
The chemical composition of plasma and the values of phenomenological constants, found by analysis of one-dimensional etching, are used for the calculation of real etched groove profiles. As the dependence of etching rate of SiO2 on H2 content in the feed was calculated for biased substrate, no additional processes in the groove bottom are included. The evolution of groove profile during RIE is shown in Fig. 7. It is seen that the etching rate in the vertical direction is almost constant. This is influenced by the low concentration of molecules in the adsorbed layer. Moreover, under present conditions, the etched groove has sloping sidewalls. The values of phenomenological constants and frequency probability of desorption, found by analysis of onedimensional etching were used for the calculation of etched groove profiles, except for the sidewall, where these values were assumed to be 10 times lower. The etched groove profiles at different values of H2 content in the feed are shown in Fig. 8. The depth of etched grooves at low H2 content in the feed (o30%) shows a negligible variation. For
Aspect ratio
5.3. Two-dimensional etching
0.8
0.6
0.4
0.2
0.0
0
20
40
60
80
100
H2 content in the feed, %
Fig. 9. The dependence of the aspect ratio on H2 content in the feed. Mask width 0.5 mm, mask height 0.1 mm, and etching time 40 min.
applying a CF4+H2 plasma for reactive ion etching of two-dimensional structures in SiO2, the main parameters that describe the shape of the etched groove: aspect ratio ðymax =2xmax Þ and etching anisotropy (ymax =d; where d is the lateral undercutting) must be determined. The dependence of aspect ratio on H2 content in the feed is shown in Fig. 9. The aspect ratio of etched grooves in region of (0–30)% H2 content shows a negligible variation. This phenomenon is used for selective SiO2 etching over Si. The etching anisotropy in region of (0–80)% H2 content is equal to 10.5.
108
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius
6. Conclusions 1. The aspect ratio of etched grooves in region of (0–30)% H2 content shows a negligible variation. 2. At low H2 content in the feed (o30%) all H2 molecules are converted to reaction products. This is influenced by dissociation and subsequent reaction of H atoms with CF3 radicals. 3. During one-dimensional etching of SiO2 the concentrations of adsorbed layer components are low. References [1] Marra DC, Aydil ES. J Vac Sci Technol A 1997;15:2508– 17. [2] Zhang Y, Oehrlein GS, Bell FH. J Vac Sci Technol A 1996;14:2127–37.
[3] Rueger NR, Beulens JJ, Schaepkens M, Doemling MF, Mirza JM, Standeart TEFM, Oehrlein GS. J Vac Sci Technol A 1997;15:1881–9. [4] Inayoshi M, Ito M, Hori M, Goto T, Hiramatsu M. J Vac Sci Technol A 1998;16:233–8. [5] Oehrlein GS, Kurogi Y. Materials Science & Engineering R Reports 1998;24:153–84. [6] Knizikevi$cius R, Galdikas A, Grigonis A, Pranevi&cius L, $ Vacuum 1996;47:1473–7. Rutku´nien’e Z. [7] Galdikas A, Grigonis A, Knizikevi$cius R, Pranevi$cius L, Vosylius J. Mater Sci 1997;4:14–25. [8] Lieberman MA, Lichtenberg AJ. Principles of plasma discharges and materials processing. New York: Wiley, 1994. p. 572. [9] Ono K, Tuda M. Jpn J Appl Phys 1997;36:4854–65. [10] Truesdale EA, Smolinsky G. J Appl Phys 1979;50:6594–9. [11] Hikosaka Y, Sugai H. Jpn J Appl Phys 1993;32:3040–4. [12] Maruyama K, Ohkouchi K, Goto T. Jpn J Appl Phys 1996;35:4088–95. [13] Coburn JW, Kay E. Solid State Technol 1979;22: 117–24. [14] d’Agostino R, Cramarossa F, De Benedictis S, Ferraro G. J Appl Phys 1981;52:1259–65.
Real dimensional simulation of SiO2 etching in CF4+H2 plasma R. Knizikevic$ ius* $ st., LT-3006 Kaunas, Lithuania Department of Physics, Kaunas University of Technology, 73, K. Donelaicio Received 3 July 2001; accepted 24 August 2001
Abstract The reactive ion etching of silicon oxide in CF4+H2 plasma is considered. The profiles of etched grooves are calculated as a function of mask dimensions, fluxes of chemically active and non-active plasma components and parameters of ion bombardment. To achieve this goal the chemical composition of CF4+H2 plasma is calculated and the one-dimensional etching of SiO2 in this plasma is considered. The values of phenomenological constants are found by extrapolation from the experimental results. Using the values of phenomenological constants, found by analysis of chemical composition of plasmas and one-dimensional etching, the etched groove profiles at real dimensions are calculated. The influence of hydrogen addition to fluorocarbon plasma on an etched groove profile is considered. Special attention is given to the selectivity of SiO2 etching over Si. The conditions under which etching selectivity is high are found. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: CF4+H2 plasma; SiO2; Reactive ion etching
1. Introduction Silicon integrated circuits are most widespread today. Silicon is easily processed compared to other semiconductor materials (GaAs, InP), and its oxide is used as an insulator. In integrated circuit manufacture, it is required to etch SiO2 selectively over Si. The addition of H2 to a CF4 plasma is used for selective etching of SiO2. It is determined experimentally [1] that, at sufficiently low H2 concentration, a thin fluorocarbon film forms on both Si and SiO2 surfaces during etching, but Si and SiO2 removal continues *Corresponding author. Fax.: +370-7-350737. E-mail address: [email protected] (R. Knizikevi$cius).
despite the existence of such layer. The structure of this film depends on the H2 concentration in the feed gas. Above a critical H2 concentration, the fluorocarbon film becomes more cross-linked, fluorine deficient, and amorphous carbon-like. Formation and subsequent growth of this fluorinated amorphous carbon (a-C : F) film stops etching of both Si and SiO2. In the absence of ion bombardment, the critical concentration at which etching is arrested and a-C : F growth begins is the same for both Si and SiO2. H atoms abstract and replace F atoms both on the surface and in the fluorocarbon film, resulting in the formation of a fluorine-deficient amorphous carbon-like film. In the presence of ion bombardment, this critical H2 concentration is increased (but at different amounts) for Si and SiO2. The film formed on
0042-207X/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 1 ) 0 0 4 1 3 - 4
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$ / Vacuum 65 (2002) 101–108 R. Knizikevicius
SiO2 is more easily sputtered than that formed on Si due to the higher number of CaO bonds. The thickness of the fluorocarbon layer on SiO2 is much smaller than on Si for comparable discharge conditions [2,3]. During Si etching in this plasma, the adsorption of CF2 radicals on the Si surface is enhanced by ion bombardment, i.e. the sticking coefficient of CF2 radicals on the Si surface is increased in the presence of ion bombardment [4]. Meanwhile the fluorocarbon film is thin on the SiO2 surface as adsorbed CFx (xp3) radicals react with surface oxygen to form volatile CO, CO2, and COF2 molecules. These phenomena are used in the selective etching of SiO2 layers on a Si surface. As the SiO2 layer is etched, the underlying Si layer is etched slowly. In this way, the fixed depth grooves and contact holes are formed. The difference in processes occurring at the sidewall and bottom of the microstructure determine the final profile of etched groove. The presence of ion bombardment enables high etching selectivity and straight sidewalls to be achieved [5]. A better understanding of etched groove shape dependence on H2 content in the feed will allow more efficient integrated circuit manufacture. In previous work [6,7], etching through a mask in fluorine-based plasma was considered. However, the values of frequency probabilities used in these models were freely chosen and the profiles of etched grooves were calculated in relative units. In this work, the main reactions occurring in a CF4+H2 plasma are considered and the concentrations of plasma components are calculated by extrapolation from the experimental data. Using the derived composition of the flux of particles from the plasma, one-dimensional etching of SiO2 is investigated. The values of frequency probabilities, obtained from analysis of one-dimensional etching, are used for the calculation of the real dimensions of etched grooves.
2. Modelling of plasma composition In Table 1 the homogeneous reactions, taking place in a CF4+H2 plasma, in a general case, are
presented. In order to reduce the number of frequency probabilities, only the main reactions are included in the model: CF4 þ e-CF3 þ F þ e;
ð1aÞ
H2 þ e-2H þ e;
ð1bÞ
F þ H2 -HF þ H;
ð1cÞ
CF3 þ F þ M-CF4 þ M;
ð1dÞ
CF3 þ H-CF2 þ HF;
ð1eÞ
H þ F þ M-HF þ M;
ð1fÞ
2H þ M-H2 þ M:
ð1gÞ
Reaction rates are characterized by frequency probabilities of dissociation and reaction: G1 ¼ gCF4 þe-CF3 þFþe ½e=N;
ð2aÞ
G2 ¼ gH2 þe-2Hþe ½e=N;
ð2bÞ
R25 ¼ kr;FþH2 -HFþH ;
ð2cÞ
R35 ¼ kr;CF3 þFþM-CF4 þM ½M=N;
ð2dÞ
R36 ¼ kr;CF3 þH-CF2 þHF ;
ð2eÞ
R56 ¼ kr;HþFþM-HFþM ½M=N;
ð2fÞ
R66 ¼ kr;2HþM-H2 þM ½M=N;
ð2gÞ
where gi is the dissociation rate constant, N is the total neutral particle concentration in the plasma, kr;i is the reaction rate constant, and M is a third particle or wall of the reactor. Let us assume that frequency probabilities of dissociation and reaction do not depend on H2 content in the feed. The concentrations of electrons and ions in the plasma are not taken into account, as the degree of ionization of plasma does not exceed (1–2)%. It follows that seven chemical species exist in the plasma: CF4, H2, CF3, CF2, F, H, HF with relative concentrations n1 ¼ ½CF4 =N; n2 ¼ ½H2 =N; n3 ¼ ½CF3 =N; n4 ¼ ½CF2 =N; n5 ¼ ½F=N; n6 ¼ ½H=N; and n7 ¼ ½HF=N; respectively. The following system of rate equations describes the kinetics of chemical composition of a CF4+H2 plasma:
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius Table 1 List of values of enthalpies and free Gibbs energies of reactions, taking place in CF4+H2 plasma Reaction
DH (kcal/mol)
DG (kcal/mol)
CF4 þ e"CF3 þ F þ e CF3 þ e"CF2 þ F þ e CF2 þ e"CF þ F þ e H2 þ e"2H þ e CF4 þ H-CF3 þ HF 2CF3 þ M-C2 F6 þ M 2F þ M-F2 þ M CF3 þ H2 -CHF3 þ H F þ H2 -HF þ H CF3 þ H-CF2 þ HF CF3 þ H þ M-CHF3 þ M 2CF2 þ M-C2 F4 þ M CF2 þ H-CF þ HF CF2 þ H þ M-CHF2 þ M CF þ H-C þ HF CHF3 þ F-CF3 þ HF CHF3 þ F-CF4 þ H H þ F þ M-HF þ M
123.7 104.6 123.3 104.0 6.0 71.6 37.8 0.0 32.0 48.0 104.0 70.0 12.0 56.0 20.0 33.5 22.0 136.0
112.6 94.1 114.6 97.0 15.9 – 29.6 3.8 31.6 34.4 93.2 80.9 13.9 – 20.6 35.4 19.5 128.6
3. Modelling of one-dimensional etching The one-dimensional reactive ion etching (RIE) of a SiO2 substrate in a CF4+H2 plasma is considered. The composition of plasma is calculated from the above model of plasma composition. The main reactions taking place on the surface are the following: 2SiO2 þ 2CF3 -SiF2 þ SiF4 þ 2CO2 ;
ð4aÞ
SiO2 þ 2CF2 -SiF4 þ 2CO:
ð4bÞ
Phenomenological constants k1 and k2 characterize these reaction rates, respectively. The SiF2, SiF4, CO, and CO2 molecules formed leave the surface. A frequency probability of removal of the ith component, oi ; consists of frequency probabilities of sputtering and desorption, oi;s and oi;d : oi ¼ oi;s þ oi;d ¼ Yi I0 =C þ n0 expð Ed;i =kTÞ; ð5Þ
dn1 ¼ I1 G1 n1 þ R35 n3 n5 En1 ; dt dn2 ¼ I2 G2 n2 R25 n2 n5 þ R66 n26 En2 ; dt dn3 ¼ G1 n1 R35 n3 n5 R36 n3 n6 En3 ; dt dn4 ¼ R36 n3 n6 En4 ; dt dn5 ¼ G1 n1 R25 n2 n5 R35 n3 n5 R56 n5 n6 En5 ; dt dn6 ¼ 2G2 n2 þ R25 n2 n5 R36 n3 n6 dt R56 n5 n6 2R66 n26 En6 ; dn7 ¼ R25 n2 n5 þ R36 n3 n6 þ R56 n5 n6 En7 : dt
103
where Y is the sputtering yield, I0 is the ion flux, C is the concentration of surface molecules ðC ¼ 8:901018 m2 Þ; n0 is the frequency of oscillation of molecules in the solid, and Ed is the activation energy of desorption. It follows that four components exist in the adsorbed layer: SiF2, SiF4, CO, and CO2 with relative concentrations c1 ¼ ½SiF2 =C; c2 ¼ ½SiF4 =C; c3 ¼ ½CO=C; and c4 ¼ ½CO2 =C: The following system of rate equations includes rate expressions of different processes [8] and describes the kinetics of components in the adsorbed layer: ! 4 X dc1 ¼ k1 1 ci n2CF3 oc1 ; dt i¼1 ! 4 X dc2 ¼ k1 1 ci n2CF3 dt i¼1 ! 4 X þ k2 1 ci n2CF2 oc2 ; i¼1
ð3Þ
where Ii ¼ Fi =V0 N is the injection rate of ith component of gas mixture, E is the frequency probability of exhaust, Fi is the flow rate of the ith component, and V0 is the volume of the reactor.
! 4 X dc3 ¼ 2k2 1 ci n2CF2 oc3 ; dt i¼1 ! 4 X dc4 ¼ 2k1 1 ci n2CF3 oc4 : dt i¼1
ð6Þ
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius
104
The solutions of the system of linear equations (6) have the following form: ci ðtÞ ¼
4 X
ðAij þ Bij expðlj tÞÞ;
ð7Þ
j¼1
where Aij and Bij are the coefficients, defined from the initial conditions, lj is the solution of the characteristic equation. The stationary surface concentrations of components are equal to c1 ¼
c2 ¼
c3 ¼
c4 ¼
k1 n2CF3
;
ð8aÞ
;
ð8bÞ
2k2 n2CF2 ; þ 3k2 n2CF2 þ o
ð8cÞ
Fig. 1. Schematic presentation of RIE through the mask.
2k1 n2CF3 : 4k1 n2CF3 þ 3k2 n2CF2 þ o
ð8dÞ
has some peculiarities, related to the geometry of the mask. At first, the assumption that the mean free path of particles arriving at the surface is much larger than the feature size was taken into account. This assumption is always fulfilled during etching in the low-pressure plasma. The second assumption is that the angular distribution of particles in the plasma is isotropic. During twodimensional etching, the concentrations of atoms at the surface of an etched groove depends on the position of the arbitrary point Mðx;yÞ (Fig. 1). Let us assume that the concentration of atoms is equal to ni ðx; yÞ ¼ n0;i Yðx; yÞ=p; where n0;i is the relative concentration of the ith plasma component, and Yðx; yÞ is the angle. The groove bottom is subjected to ion bombardment, and the processes of activation of surface molecules and physical sputtering take place there. The sputtering of the SiF2, SiF4, CO and CO2 molecules is characterized by frequency probabilities of sputtering
4k1 n2CF3 þ 3k2 n2CF2 þ o k1 n2CF3 þ k2 n2CF2 4k1 n2CF3 þ 3k2 n2CF2 þ o 4k1 n2CF3
The etching rate is proportional to the removal rate of formed SiF2 and SiF4 molecules. According to Eqs. (8a) and (8b) the etching rate at the steady state regime is equal to Vst ¼
h0 oð2k1 n2CF3 þ k2 n2CF2 Þ
; 4k1 n2CF3 þ 3k2 n2CF2 þ o
ð9Þ
( is the thickness of one monowhere h0 ¼ 3:35 A layer, which was estimated using expression h0 ¼ ðMSiO2 =rSiO2 NA Þ1=3 ; where MSiO2 is the molecular weight of SiO2 ðMSiO2 ¼ 6:009102 kg mol1 Þ; rSiO2 is the density of SiO2 ðrSiO2 ¼ 2650 kg m3 Þ; and NA is Avogadro’s number.
4. Modelling of two-dimensional etching The etching of grooves on a silicon oxide substrate in a CF4+H2 plasma is considered. In the calculation of profiles of etched grooves, the results obtained from previous models of chemical composition of plasma and one-dimensional etching of Si are used. As etching takes place through a mask, the number of atoms, reaching the surface, depends on the position of an arbitrary point M on the surface (Fig. 1). Two-dimensional etching
oi;s ¼ Yi I0 f ðaÞ=C; 0:5
ð10Þ
where f ðaÞ ¼ cos a is the sputtering yield dependence on the incident ion angle a measured from the surface normal [9]. The non-activated SiO2 molecules on the sidewall react more slowly with CF2 and CF3 radicals, and the values of phenom-
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius
enological constants k1 and k2 are assumed to be ten times lower. Eq. (6) describes the kinetics of the surface concentrations of the components. The etching rate V is proportional to the removal rate of the SiF2 and SiF4 molecules which are formed: V ¼ h0 oðc1 þ c2 Þ:
ð11Þ
Knowing the surface concentrations of components from the solutions of Eq. (6), the etching rate as a function of coordinate and time is obtained. The point Mðx; y; tÞ after time interval Dt will take position M 0 ðx þ Dx; y þ Dy; t þ Dt), where Dx ¼ Vnx Dt and Dy ¼ Vny Dt; nx and ny are the components of the surface normal ~ n (Fig. 1). In this way, the groove profile as a function of time is obtained.
5. Results and discussion 5.1. Chemical composition of plasma The experimental results presented in Fig. 2 [10] are used in the model in order to calculate the chemical composition of a plasma. It was observed that the maximum concentration of HF molecules is achieved for 31% H2 in a plasma of a CF4+H2 gas mixture. Let us assume that the temperature of
Relative concentration
1.0
HF
0.8
0.6
H2
0.4
0.0 0
10
20
30
40
50
the plasma T ¼ 500 K, the total neutral particle concentration with the discharge off is N ¼ 1:931022 m3 ; and the total gas injection rate I ¼ 5:47 s1 : The total gas injection rate was estimated using expression I ¼ F=ðV0 NÞ where the flow rate is measured in molecules s1. The plasma composition is calculated using Eq. (3). Experimental [10] and theoretical dependences of the relative concentration of H2 and HF molecules in the plasma on H2 content in the feed are shown in Fig. 2. The following values of frequency probabilities of dissociation and reaction were found by extrapolation from experimental results: G1 ¼ 3:7 s1 ; G2 ¼ 2:0 s1 ; R25 ¼ 1:0104 s1 ; R35 ¼ 100 s1 ; R36 ¼ 2:0104 s1 ; R56 ¼ 1:0104 s1 ; R66 ¼ 100 s1 : The chemical composition of the plasma as a function of H2 content in the feed, using Eq. (3), is presented in Fig. 3. The concentration of HF molecules with increase of H2 content in the feed increases at first due to the reactions of H atoms with F atoms and CF3 radicals (Eqs. (1e) and (1f)). As the concentration of HF molecules approaches the maximum value, almost all F atoms and CF3 radicals have reacted (Fig. 3). With further increase in H2 content in the feed the concentration of HF molecules starts to decrease in proportion to the amount of injected CF4 molecules. In a CF4+H2 plasma, H atoms react with CFx (xp3) radicals. At a H2 content in the plasma X25%, the concentration of CF2 radicals is about 10 times higher than that of CF3 (Fig. 3) or CF radicals [11,12]. This indicates that an intensive reaction of H atoms with CF3 radicals takes place in the plasma. The conversion coefficient of the ith component of the gas mixture indicates a part of molecules converted to reaction products and is equal to Zi ¼ 1 Eni =Ii :
0.2
60
70
80
H2 content in the feed, %
Fig. 2. Experimental [10] (points) and theoretical (curves) dependences of the relative concentrations of H2 and HF molecules on H2 content in the feed.
105
ð12Þ
The dependences of the conversion coefficients of CF4 and H2 molecules on H2 content in the feed are presented in Fig. 4. It is seen that, at low H2 content in the feed (o30%), all H2 molecules are converted. The increase of conversion coefficient of CF4 molecules at low H2 content in the feed is related to the dissociation reaction (Eq. (1a)) and to subsequent reaction of H atoms with CF3
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius
106 100
0.35 0.30
CF4
H2
0.25
60
V, µm/min
Concentration, %
80
HF 40
CF2
F 0
H
CF3
20
40
0.15 0.10
20
0
0.20
60
80
0.05 0.00
100
H2 content in the feed, %
40
60
80
100
Fig. 5. Experimental [13] (points) and theoretical (curve) dependences of SiO2 etching rate on H2 content in the feed.
5
100
H2
80
4
Concentration, %
Conversion coefficient, %
20
H2 content in the feed, %
Fig. 3. The dependences of the concentrations of CF4+H2 plasma components on H2 content in the feed.
60
CF4
40
20
3
CO CO2
2
SiF4 1
0
0
0
20
40
60
80
100
H2 content in the feed, %
Fig. 4. The dependences of the conversion coefficients of CF4 and H2 molecules on H2 content in the feed.
radicals (Eq. (1e)). At higher H2 content fixed amounts of CF4 and H2 molecules are converted. 5.2. One-dimensional etching The experimental results presented in Fig. 5 (points) [13] are used in the model in order to calculate SiO2 etching rates. Let us assume that the SiO2 etching rate in the absence of H2 in the feed is equal to a value measured during experiment [14]. In the calculation of etching rates the results obtained from the previous modelling of plasma composition (Fig. 3) are used. Experimental and theoretical SiO2 etching rate dependences on H2
0
SiF2
0
20
40
60
80
100
H2 content in the feed, %
Fig. 6. The dependences of the concentrations of adsorbed layer components on H2 content in the feed.
content in the feed, calculated using Eq. (9), are shown in Fig. 5. The following values of phenomenological constants and frequency probability of desorption are determined: k1 ¼ 19 s1 ; k2 ¼ 14 s1 ; o ¼ 10 s1 : The dependences of the concentrations of adsorbed layer components on H2 content in the feed are shown in Fig. 6. It is seen that the concentrations of adsorbed layer components are low. The dependences of concentrations of CO2 and SiF2 molecules are similar to the dependence of concentration of CF3 radicals in the plasma. This is influenced by the same reaction of CF3 radicals with SiO2 molecules (Eq. (4a)). The
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius x, µm
-0.1 -0.4
-0.3
-0.2
-0.1
0.0 0.0
107
0.1
0.2
0.3
-0.4
-0.3
-0.2
-0.1
0.0 0.0
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7
y, µm
x, µm
-0.1
0.4
0.2
0.3
0.4
3
1 2
0.7
y, µm
0.8
Fig. 7. The evolution of groove profile during RIE. Mask width 0.5 mm, mask height 0.1 mm, and etching time 40 min. The groove profile is shown every 8 min.
0.1
0.8
Fig. 8. The etched groove profiles during RIE at different values of H2 content in the feed: (1) 20%, (2) 30%, and (3) 50%. Mask width 0.5 mm, mask height 0.1 mm, and etching time 40 min.
maxima of the concentrations of CO and SiF4 molecules are achieved at the maximum concentration of CF2 radicals in the plasma.
1.2
1.0
The chemical composition of plasma and the values of phenomenological constants, found by analysis of one-dimensional etching, are used for the calculation of real etched groove profiles. As the dependence of etching rate of SiO2 on H2 content in the feed was calculated for biased substrate, no additional processes in the groove bottom are included. The evolution of groove profile during RIE is shown in Fig. 7. It is seen that the etching rate in the vertical direction is almost constant. This is influenced by the low concentration of molecules in the adsorbed layer. Moreover, under present conditions, the etched groove has sloping sidewalls. The values of phenomenological constants and frequency probability of desorption, found by analysis of onedimensional etching were used for the calculation of etched groove profiles, except for the sidewall, where these values were assumed to be 10 times lower. The etched groove profiles at different values of H2 content in the feed are shown in Fig. 8. The depth of etched grooves at low H2 content in the feed (o30%) shows a negligible variation. For
Aspect ratio
5.3. Two-dimensional etching
0.8
0.6
0.4
0.2
0.0
0
20
40
60
80
100
H2 content in the feed, %
Fig. 9. The dependence of the aspect ratio on H2 content in the feed. Mask width 0.5 mm, mask height 0.1 mm, and etching time 40 min.
applying a CF4+H2 plasma for reactive ion etching of two-dimensional structures in SiO2, the main parameters that describe the shape of the etched groove: aspect ratio ðymax =2xmax Þ and etching anisotropy (ymax =d; where d is the lateral undercutting) must be determined. The dependence of aspect ratio on H2 content in the feed is shown in Fig. 9. The aspect ratio of etched grooves in region of (0–30)% H2 content shows a negligible variation. This phenomenon is used for selective SiO2 etching over Si. The etching anisotropy in region of (0–80)% H2 content is equal to 10.5.
108
$ / Vacuum 65 (2002) 101–108 R. Knizikevicius
6. Conclusions 1. The aspect ratio of etched grooves in region of (0–30)% H2 content shows a negligible variation. 2. At low H2 content in the feed (o30%) all H2 molecules are converted to reaction products. This is influenced by dissociation and subsequent reaction of H atoms with CF3 radicals. 3. During one-dimensional etching of SiO2 the concentrations of adsorbed layer components are low. References [1] Marra DC, Aydil ES. J Vac Sci Technol A 1997;15:2508– 17. [2] Zhang Y, Oehrlein GS, Bell FH. J Vac Sci Technol A 1996;14:2127–37.
[3] Rueger NR, Beulens JJ, Schaepkens M, Doemling MF, Mirza JM, Standeart TEFM, Oehrlein GS. J Vac Sci Technol A 1997;15:1881–9. [4] Inayoshi M, Ito M, Hori M, Goto T, Hiramatsu M. J Vac Sci Technol A 1998;16:233–8. [5] Oehrlein GS, Kurogi Y. Materials Science & Engineering R Reports 1998;24:153–84. [6] Knizikevi$cius R, Galdikas A, Grigonis A, Pranevi&cius L, $ Vacuum 1996;47:1473–7. Rutku´nien’e Z. [7] Galdikas A, Grigonis A, Knizikevi$cius R, Pranevi$cius L, Vosylius J. Mater Sci 1997;4:14–25. [8] Lieberman MA, Lichtenberg AJ. Principles of plasma discharges and materials processing. New York: Wiley, 1994. p. 572. [9] Ono K, Tuda M. Jpn J Appl Phys 1997;36:4854–65. [10] Truesdale EA, Smolinsky G. J Appl Phys 1979;50:6594–9. [11] Hikosaka Y, Sugai H. Jpn J Appl Phys 1993;32:3040–4. [12] Maruyama K, Ohkouchi K, Goto T. Jpn J Appl Phys 1996;35:4088–95. [13] Coburn JW, Kay E. Solid State Technol 1979;22: 117–24. [14] d’Agostino R, Cramarossa F, De Benedictis S, Ferraro G. J Appl Phys 1981;52:1259–65.