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Physicochemical model for reactive sputtering of hot target
Accepted Manuscript Physicochemical model for reactive sputtering of hot target
Viktor I. Shapovalov, Vitaliy V. Karzin, Anastasia S. Bondarenko
PII: DOI: Reference:
S0375-9601(16)31847-3 http://dx.doi.org/10.1016/j.physleta.2016.11.028 PLA 24200
To appear in:
Physics Letters A
Received date: Revised date: Accepted date:
19 June 2016 3 November 2016 22 November 2016
Please cite this article in press as: V.I. Shapovalov et al., Physicochemical model for reactive sputtering of hot target, Phys. Lett. A (2017), http://dx.doi.org/10.1016/j.physleta.2016.11.028
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights • • • •
When model is applied for a cold target, hysteresis width is proportional to the ion current density. Two types of processes of hot target sputtering are possible, depending on the current density: with and without the hysteresis. Sputtering process is dominant at current densities less than 50 A/m2 and evaporation can be neglected. For current densities over 50 A/m2 the hysteresis width reaches its maximum and the role of evaporation increases.
PHYSICOCHEMICAL MODEL FOR REACTIVE SPUTTERING OF HOT TARGET Viktor I. Shapovalov, Vitaliy V. Karzin, Anastasia S. Bondarenko Department of Physical Electronics and Technology, St. Petersburg Electrotechnical University, 197376, 5 Prof. Popov St., St. Petersburg, Russia Abstract A physicochemical model for reactive magnetron sputtering of a metal target is described in this paper. The target temperature in the model is defined as a function of the ion current density. Synthesis of the coating occurs due to the surface chemical reaction. The law of mass action, the Langmuir isotherm and the Arrhenius equation for non-isothermal conditions were used for mathematical description of the reaction. The model takes into consideration thermal electron emission and evaporation of the target surface. The system of eight algebraic equations, describing the model, was solved for the tantalum target sputtered in the oxygen environment. It was established that the hysteresis effect disappears with the increase of the ion current density. Keywords: model, reactive sputtering, hot target, oxide, evaporation Corresponding author. E-mail address: [email protected] (V.I. Shapovalov). 1. Introduction Reactive magnetron sputtering technology is one of the most common methods used for the deposition of binary compounds (oxides, nitrides, carbides etc.) [1–6]. During this process a metal target is usually sputtered in the environment of argon and a reactive gas (oxygen, nitrogen etc.). The chemical composition of the film mainly depends on the reactive gas flow and the power density at the target. Usage of a magnetron with a hot target opens up new possibilities for reactive sputtering [7–9], since the magnetron construction is made in a way that the temperature of the target can be raised up to its melting point [10,11]. One of characteristic features of the reactive sputtering process, discovered in the 1980s [12,13] is the hysteresis effect. This effect is observed during the experimental measurements of the reactive gas partial pressure p vs. reactive gas flow Q0 (fig. 1). With the increase of Q0 from 0 to A the partial pressure p does not change noticeably. This range stands for the “metal” operating mode of the target. The target switches to the “compound” mode in A (A ĺ ȼ transition). In this mode, the partial pressure p is proportional to Q0. With the decrease of Q0 the reverse change of the target operating mode (C ĺ D transition) occurs at a smaller Q0 value. The dashed line in fig. 1 represents a negative slope curve that connects two transition points [14].
1
p
B C D
A
0 Q0 Fig. 1. Qualitative image of the hysteresis effect during the reactive sputtering process.
For the effective application of the reactive sputtering technology, it is necessary to establish its general characteristics and figure out the relations between the dependent and independent variables. Such research can be carried out both experimentally and by simulations. All notorious models for the reactive sputtering process that do not consider the target heating effect [15– 17] are based on two basic assumptions: •
two processes occur on the discharge-excited target surface: the formation of a thin
layer of the metal/reactive gas compound and the sputtering of this compound by the argon ions; •
the deposition of both metal and compound particles sputtered from the target and a
chemical reaction occur on the substrate and on the surface of the vacuum chamber. Different from the models that describe the coating formation as a chemisorption result [16,17], the physicochemical model offered in [18,19] correctly describes the process. This model attributes the synthesis of the coating to the chemical reaction. The law of mass action, the Langmuir isotherm and the Arrhenius equation for non-isothermal conditions were used for mathematical description of the reaction. This paper represents the physicochemical model in general. The influence of the target heating on the sputtering process is taken into consideration. 2. Model The metal (M) target is sputtered in an Ar + X2 environment, where X2 is a chemically active gas. Any stationary state of the process is provided by non-isothermal conditions, since the substrate and the surface of the vacuum chamber have constant temperatures Ts and Tw, respectfully. The target temperature Tt depends on the ion current density j+. Furthermore: •
the discharge current density represents a summation:
j = (1 + γ) j+ + jT ,
(1)
where Ȗ is the ion-induced electron emission coefficient; jT is the thermal electron emission current density (Richardson's law); • the MmXn appears on all of the surfaces as a result of a chemical reaction:
2
M+
k (Ti ) n 1 X2 ↔ M m X n , i = t, s, w , 2m m
(2)
where k(Ti) is the reaction rate coefficient (Arrhenius equation) for the i-surface, that defines the flow of MmXn molecules with the current density Jch(Ti) on the i-surface. The reaction (2) happens due to the physical adsorption of the X2 molecules, which is described by the Langmuir isotherm. As a result, the consumption of the X2 gas occurs on the target, substrate and the vacuum chamber surfaces (fig. 2) and is denoted as the flow Qi, (i = t, s, w); Qt
JCt j+
Target Qt
Substrate Qs Q0 Wall Qw
JMt
șt
1 – șt Target Tt
Pump Qp
Fig. 2. Flows on all surfaces
j+
Fig. 3. Flows on surface of target
• the target surface is sputtered by the argon ions and evaporated according to the HertzKnudsen law, hence the metal JMt and the compound JCt flux rates can be expressed as (fig. 3)
J Mt ( j+ ) = J Msp ( j+ ) + J Mev[Tt ( j+ )] ;
(3)
J Ct ( j+ ) = J Csp ( j+ ) + J Cev [Tt ( j+ )].
(4)
The first addends in the right part of equations (3) and (4) describe the sputtered particles, the second ones describe the evaporated particles; • the temperature influence on the parameters of the sputtering process (such as the sputter yield and the ion-induced electron emission coefficient) and the self-sputtering effect are neglected. Using the law of mass action the way it was done in [18] and taking into consideration (1)– (4) a system of eight algebraic equations for one reactive gas was obtained. These equations describe 1) the balance on the surfaces of • the target (fig. 3): J ch [Tt ( j + )] − J Ct ( j + ) = 0 ;
(5)
• the substrate and the vacuum chamber surface (fig. 4): J ch (Ti ) − J Mi ( j+ ) + J Ci ( j+ ) = 0, i = s, w ;
(6)
3
JCi
1 – și
Qi
JMi
și Substrate (wall)
Fig. 4. Flows on surface substrate (i = s) and wall (i = w).
2) the reactive gas flow on all of the three internal surfaces of the vacuum chamber:
Qi =
n J ch (Ti ) Ai , i = t, s, w ; 2
(7)
3) the reactive gas evacuated through the pumping system:
Qp = c0 pSp ;
(8)
4) the balance of the reactive gas flows:
Q0 = Qt + Qs + Qw + Qp .
(9)
The following parameters were used in (5)–(9): JMi(j+) and JCi(j+) are the flux rates of the metal M and the compound MmXn, respectively, sputtered from the target and deposited on the isurface; c0 = 2.5·1025, Pa–1m–3 is a coefficient converting the flow Qp from [Pa · m3/s] to [s–1]; Sp is the system pumping speed; ɪ is the reactive gas partial pressure. The system of algebraic equations (5)–(9) contains two independent variables: the reactive gas flow and the ion current density. The unknown variables are the partial pressure of the reactive gas X2, the gas flows Qt, Qs, Qw and Qɪ and the fraction of each of the three surfaces covered with the MmXn compound. 3. Simulations The system of equations (5)–(9) was numerically solved for the magnetron with a tantalum target sputtered in the Ar + O2 environment. In this case, the reaction (2) can be described as: k (Ti ) 5 1 Ta + O 2 ↔ Ta 2O 5 , i = t, s, w . 4 2
(10)
The values of the parameters for the task are presented in table 1. The power density dependence of the target temperature was obtained by a numerical solution of a thermal task for a round 1 mm-thick tantalum plate, set 1 mm away from the water-cooled plate and attached to that plate in six spots. Using this dependence and the experimental current-voltage characteristics of the magnetron, the relation connecting the target temperature [K] and the ion current density [A/m2] was determined:
4
Tt ( j+ ) ≈ 293 + 1517(1 − e−0.00438 j+ ) .
(11)
Table 1 Parameters of the model for the reactive sputtering of Ta target in the Ar+O2 environment Parameter
SM
SC
ijM , eV
ij C, eV
ȖM
ȖC
Value
0.600
0.024
4.500
5.150
0.082
0.050
Parameter
BM
Value
17260
Parameter
Ea, 10 J
Value
–20
7.400
AM, 9.2
18
k0, 1033 m–2s–1
AC
BC
Į0
Qph, kal/mol
Nph, 10 mí2
15
20000
1.0
10000
8.260
1.100
Sp, m3/s
At m2
Aw , m2
As , m2
Tw K
Ts, K
0.008
0.002
0.029
0.001
300
600
Denotations. SM, SC are the sputter yields; ijM, ijC the work functions of electrons; ȖM, ȖC the ioninduced electron emission coefficients; AM, BM, AC, BC the approximation parameters for the equilibrium vapor pressure in the Arrhenius equation; Į0 the condensation coefficient of oxygen atoms on tantalum surface; Qph the heat of physical adsorption of oxygen on tantalum surface; Nph the concentration of adsorption sites of oxygen molecules on tantalum surface; k0, Ea the rate coefficient and the activation energy of the chemical reaction (10) for the Arrhenius equation (determined in [18]). Subscript symbols M and C stand for Ta and Ta2O5.
Equations (5)–(9) were solved with a consideration of (10) and (11) in the ion current density range from 0 to 200 A/m2 and the oxygen partial pressure range from 0 to 20 mTorr. As a result, it was established that two types of processes are possible, depending on the current density: the common process with a hysteresis effect and the hysteresis-free process. Fig. 5 shows the
20
20
15
15
15
10 5
a
0 0
4
8
12
p, mTorr
20 p, mTorr
p, mTorr
p = f(Q0) plots for the current density range revealing the verge between those two processes.
10 5 b
0 0
10 5 0
c
5
10 15 0 5 10 15 20 Q0, sccm Fig. 5. Oxygen pressure vs. oxygen flow for j+ (A/m2): a – 160 (1060); b – 165 (1075); c – 170 (1090). Target temperature values in Kelvins calculated using (11) are shown in parentheses.
The plots presented in fig. 6 show this verge most prominently. White dots in fig. 6, a show the current density dependence of the oxygen flows in A and C (fig. 1). Fig. 6, a shows that at a critical ion current density j0 = 167 A/m2 these two values become equal and the hysteresis width comes to 0 (fig. 6, b).
5
8
3
4
1 2
2 j0 0
ǻQ0, sccm
Q0, sccm
6
40
80
120
160
2
1
a
b 200
0 40 80 120 160 200 j+, A/m2 Fig. 6. Current density dependences of: a – the oxygen flow values standing for the transition of the operating mode of the cold target (black dots and dashed lines) and the hot target (white dots): 1 – metal to oxide mode transition, 2 – oxide to metal mode transition; b –the hysteresis width.
This feature discovered during the modeling of the reactive sputtering process for the hot tantalum target is not characteristic for the cold target. The simulation results shown as black dots and dashed lines in fig. 6 prove that. The special case of the model was used to obtain these dependences. For this case the following assumptions were made in equations (1)–(4): jT = 0, J Mev [Tt ( j+ )] = 0 , J Cev [Tt ( j+ )] = 0 and Tt = 500 K = const. As it is seen in fig. 6, a, the oxygen
flow values related to the transition of the operating mode of the target are proportional to the ion current density. Analogical dependence is also characteristic for the hysteresis width (fig. 6, b). 3
ǻQ0, sccm
2
1
0
40
80
120 160 200 j+, A/m2 Fig. 7. The hysteresis width obtained using the model for the hot target: solid line – full model; dots – neglecting the thermal emission effect; dashed line – neglecting the evaporation effect.
Further simulations, presented in fig. 7, allowed us to establish that evaporation is the main physical mechanism that initiates the hysteresis elimination during the reactive sputtering process. The thermal emission effect insignificantly decreases the current density value at which the hysteresis width becomes equal 0.
6
4. Conclusions The described physicochemical model of the hot target reactive magnetron sputtering makes it possible to analyze the process. For the tantalum target, sputtering process in Ar + O2 environment was shown:
•
In a particular case, when model is applied for a cold target, hysteresis width is proportional to the ion current density;
•
Two types of processes of hot target sputtering are possible, depending on the current density: with and without the hysteresis. Furthermore
9 For current densities less than 50 A/m2 the hysteresis width is proportional to the ion current density. This means that sputtering process is dominant at low current densities and evaporation can be neglected;
9 For current densities over 50 A/m2 the hysteresis width reaches its maximum, changing in a non-linear way, and at 167 A/m2 becomes equal to zero. This effect is connected solely to the increasing role of evaporation, which becomes more meaningful than sputtering at current densities over 170 A/m2. Acknowledgments The authors thank Russian Science Foundation for their support on the study (grant 15-1900076). References [1] P. Raman, A. Shchelkanov I., J. McLain, et al, High power pulsed magnetron sputtering: A method to increase deposition rate, J. Vac. Sci. Technol. A. 33 (2015) 031304 (10 pages), http://dx.doi.org/10.1116/1.4916108. [2] V.S. Levitskii, V.I. Shapovalov, A.E. Komlev, et al, Raman Spectroscopy of Copper Oxide Films Deposited by Reactive Magnetron Sputtering, Techn. Phys. Lett. 41 (2015) 1094– 1096, doi: 10.1134/S106378501511022X. [3] Feng J.Q., Chen, J.F. Optical properties and zinc nitride thin films prepared using magnetron
reactive
sputtering,
Advanced
Mater.
Res.
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(2014)
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doi:
10.4028/www.scientific.net/AMR.940.11. [4] N. Jiang, D.G. Georgiev, A.H. Jayatissa The effects of the pressure and the oxygen content of the sputtering gas on the structure and the properties of zinc oxynitride thin films deposited by reactive sputtering of zinc, Semicond. Sci. Technol. 28 (2013) 025009, doi: 10.1088/02681242/28/2/025009. [5] W.D. Sproul, D. J. Christie, D. C. Carter, Control of reactive sputtering processes. Review, Thin Solid Films. 491 . (2005) 1–17, http://dx.doi.org/10.1016/j.tsf.2005.05.022.
7
[6] A.E. Lapshin, V.V. Karzin, V.I. Shapovalov, et al, X-ray Phase Analysis of Copper Oxides Films Obtained by DC Reactive Magnetron Sputtering, Glass Phys. Chem. 42 (2016) 116– 117, doi: 10.1134/S1087659616010065. [7] A. Billard, D. Mercs, F. Perry, et al, Influence of the target temperature on a reactive sputtering
process,
Sur.
Coat.
Technol.
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(1999)
721–726,
http://dx.doi.org/10.1016/S0257-8972(99)00261-3. [8] J. TesaĜ, J. Martan, J. Rezek, On surface temperatures during high power pulsed magnetron sputtering using a hot target, Sur. Coat. Technol. 2011. V. 206. P. 1155–1159, http://dx.doi.org/10.1016/j.surfcoat.2011.08.005. [9] J. Musil, V. Satava, P. Baroch, High-rate reactive deposition of transparent SiO2 films containing low amount of Zr from molten magnetron target, Thin Solid Films. (2010) V. 519. P. 775–777, http://dx.doi.org/10.1016/j.tsf.2010.09.009. [10] M. Laurikaitis, J. Cyviene, J. Dudonis, Deposition of Zr–ZrOx and Y–YxOy films by reactive magnetron sputtering, Vacuum. 78 (2005) 395–399, doi:10.1016/j.vacuum.2005.01.056. [11] A.E. Lapshin, V.S. Levitskii, V.I. Shapovalov et al, Composition and Structure of Copper Oxide Films Synthesized by Reactive Magnetron Sputtering with a Hot Target, Glass Phys. Chem. 42 (2016) 359–362, doi: 10.1134/S108765961604009X [12] S. Maniv, W.D. Westwood, Surface oxidation kinetics of sputtering targets, Surf. Sci. 100 (1980) 108–118, doi:10.1016/0039-6028(80)90447-1. [13] E. Särhammar, K. Strijckmans, T. Nyberg et al, A study of the process pressure influence in reactive sputtering aiming at hysteresis elimination, Sur. Coat. Technol. 232 (2013) 357– 361, http://dx.doi.org/10.1016/j.surfcoat.2013.05.035. [14] A.F. Hmiel, Partial pressure control of reactivly sputtered titanium nitride, J. Vac. Sci. Technol. A, 3 (1985) 592–595, http://dx.doi.org/10.1116/1.572957. [15] H. Eltoukhy, B.R. Natarajan, J.E. Green et al, Mechanism of reactive sputtering of Indium III: A general phenomenological model for reactive sputtering, Thin Solid Films. 69 (1980) 229–235, doi:10.1016/0040-6090(80)90039-5. [16] S. Berg, H.O. Blom, T. Larsson et al, Modeling of reactive sputtering of compound materials, J. Vac. Sci. Technol. 5 (1987) 202–207, http://dx.doi.org/10.1116/1.574104. [17] E. Särhammar, T. Nyberg, S. Berg, Applying «the upgraded Berg model» to predict hysteresis
free
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sputtering,
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doi:10.1016/j.surfcoat.2015.07.054 [18] A.A. Barybin, V.I. Shapovalov, Nonisothermal chemical model of reactive sputtering, J. Appl. Phys. 101 (2007) 054905 (10 pages), doi: 10.1063/1.2435795.
8
[19] A.A. Barybin, A.V. Zavyalov, V.I. Shapovalov, A Nonisothermal Physicochemical Model of Synthesis of Oxyinitrides by Reactive Sputtering Techniques, Glass Phys. Chem. 38 (4) (2012) 396–401, doi: 10.1134/S1087659612040049.
9
Viktor I. Shapovalov, Vitaliy V. Karzin, Anastasia S. Bondarenko
PII: DOI: Reference:
S0375-9601(16)31847-3 http://dx.doi.org/10.1016/j.physleta.2016.11.028 PLA 24200
To appear in:
Physics Letters A
Received date: Revised date: Accepted date:
19 June 2016 3 November 2016 22 November 2016
Please cite this article in press as: V.I. Shapovalov et al., Physicochemical model for reactive sputtering of hot target, Phys. Lett. A (2017), http://dx.doi.org/10.1016/j.physleta.2016.11.028
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights • • • •
When model is applied for a cold target, hysteresis width is proportional to the ion current density. Two types of processes of hot target sputtering are possible, depending on the current density: with and without the hysteresis. Sputtering process is dominant at current densities less than 50 A/m2 and evaporation can be neglected. For current densities over 50 A/m2 the hysteresis width reaches its maximum and the role of evaporation increases.
PHYSICOCHEMICAL MODEL FOR REACTIVE SPUTTERING OF HOT TARGET Viktor I. Shapovalov, Vitaliy V. Karzin, Anastasia S. Bondarenko Department of Physical Electronics and Technology, St. Petersburg Electrotechnical University, 197376, 5 Prof. Popov St., St. Petersburg, Russia Abstract A physicochemical model for reactive magnetron sputtering of a metal target is described in this paper. The target temperature in the model is defined as a function of the ion current density. Synthesis of the coating occurs due to the surface chemical reaction. The law of mass action, the Langmuir isotherm and the Arrhenius equation for non-isothermal conditions were used for mathematical description of the reaction. The model takes into consideration thermal electron emission and evaporation of the target surface. The system of eight algebraic equations, describing the model, was solved for the tantalum target sputtered in the oxygen environment. It was established that the hysteresis effect disappears with the increase of the ion current density. Keywords: model, reactive sputtering, hot target, oxide, evaporation Corresponding author. E-mail address: [email protected] (V.I. Shapovalov). 1. Introduction Reactive magnetron sputtering technology is one of the most common methods used for the deposition of binary compounds (oxides, nitrides, carbides etc.) [1–6]. During this process a metal target is usually sputtered in the environment of argon and a reactive gas (oxygen, nitrogen etc.). The chemical composition of the film mainly depends on the reactive gas flow and the power density at the target. Usage of a magnetron with a hot target opens up new possibilities for reactive sputtering [7–9], since the magnetron construction is made in a way that the temperature of the target can be raised up to its melting point [10,11]. One of characteristic features of the reactive sputtering process, discovered in the 1980s [12,13] is the hysteresis effect. This effect is observed during the experimental measurements of the reactive gas partial pressure p vs. reactive gas flow Q0 (fig. 1). With the increase of Q0 from 0 to A the partial pressure p does not change noticeably. This range stands for the “metal” operating mode of the target. The target switches to the “compound” mode in A (A ĺ ȼ transition). In this mode, the partial pressure p is proportional to Q0. With the decrease of Q0 the reverse change of the target operating mode (C ĺ D transition) occurs at a smaller Q0 value. The dashed line in fig. 1 represents a negative slope curve that connects two transition points [14].
1
p
B C D
A
0 Q0 Fig. 1. Qualitative image of the hysteresis effect during the reactive sputtering process.
For the effective application of the reactive sputtering technology, it is necessary to establish its general characteristics and figure out the relations between the dependent and independent variables. Such research can be carried out both experimentally and by simulations. All notorious models for the reactive sputtering process that do not consider the target heating effect [15– 17] are based on two basic assumptions: •
two processes occur on the discharge-excited target surface: the formation of a thin
layer of the metal/reactive gas compound and the sputtering of this compound by the argon ions; •
the deposition of both metal and compound particles sputtered from the target and a
chemical reaction occur on the substrate and on the surface of the vacuum chamber. Different from the models that describe the coating formation as a chemisorption result [16,17], the physicochemical model offered in [18,19] correctly describes the process. This model attributes the synthesis of the coating to the chemical reaction. The law of mass action, the Langmuir isotherm and the Arrhenius equation for non-isothermal conditions were used for mathematical description of the reaction. This paper represents the physicochemical model in general. The influence of the target heating on the sputtering process is taken into consideration. 2. Model The metal (M) target is sputtered in an Ar + X2 environment, where X2 is a chemically active gas. Any stationary state of the process is provided by non-isothermal conditions, since the substrate and the surface of the vacuum chamber have constant temperatures Ts and Tw, respectfully. The target temperature Tt depends on the ion current density j+. Furthermore: •
the discharge current density represents a summation:
j = (1 + γ) j+ + jT ,
(1)
where Ȗ is the ion-induced electron emission coefficient; jT is the thermal electron emission current density (Richardson's law); • the MmXn appears on all of the surfaces as a result of a chemical reaction:
2
M+
k (Ti ) n 1 X2 ↔ M m X n , i = t, s, w , 2m m
(2)
where k(Ti) is the reaction rate coefficient (Arrhenius equation) for the i-surface, that defines the flow of MmXn molecules with the current density Jch(Ti) on the i-surface. The reaction (2) happens due to the physical adsorption of the X2 molecules, which is described by the Langmuir isotherm. As a result, the consumption of the X2 gas occurs on the target, substrate and the vacuum chamber surfaces (fig. 2) and is denoted as the flow Qi, (i = t, s, w); Qt
JCt j+
Target Qt
Substrate Qs Q0 Wall Qw
JMt
șt
1 – șt Target Tt
Pump Qp
Fig. 2. Flows on all surfaces
j+
Fig. 3. Flows on surface of target
• the target surface is sputtered by the argon ions and evaporated according to the HertzKnudsen law, hence the metal JMt and the compound JCt flux rates can be expressed as (fig. 3)
J Mt ( j+ ) = J Msp ( j+ ) + J Mev[Tt ( j+ )] ;
(3)
J Ct ( j+ ) = J Csp ( j+ ) + J Cev [Tt ( j+ )].
(4)
The first addends in the right part of equations (3) and (4) describe the sputtered particles, the second ones describe the evaporated particles; • the temperature influence on the parameters of the sputtering process (such as the sputter yield and the ion-induced electron emission coefficient) and the self-sputtering effect are neglected. Using the law of mass action the way it was done in [18] and taking into consideration (1)– (4) a system of eight algebraic equations for one reactive gas was obtained. These equations describe 1) the balance on the surfaces of • the target (fig. 3): J ch [Tt ( j + )] − J Ct ( j + ) = 0 ;
(5)
• the substrate and the vacuum chamber surface (fig. 4): J ch (Ti ) − J Mi ( j+ ) + J Ci ( j+ ) = 0, i = s, w ;
(6)
3
JCi
1 – și
Qi
JMi
și Substrate (wall)
Fig. 4. Flows on surface substrate (i = s) and wall (i = w).
2) the reactive gas flow on all of the three internal surfaces of the vacuum chamber:
Qi =
n J ch (Ti ) Ai , i = t, s, w ; 2
(7)
3) the reactive gas evacuated through the pumping system:
Qp = c0 pSp ;
(8)
4) the balance of the reactive gas flows:
Q0 = Qt + Qs + Qw + Qp .
(9)
The following parameters were used in (5)–(9): JMi(j+) and JCi(j+) are the flux rates of the metal M and the compound MmXn, respectively, sputtered from the target and deposited on the isurface; c0 = 2.5·1025, Pa–1m–3 is a coefficient converting the flow Qp from [Pa · m3/s] to [s–1]; Sp is the system pumping speed; ɪ is the reactive gas partial pressure. The system of algebraic equations (5)–(9) contains two independent variables: the reactive gas flow and the ion current density. The unknown variables are the partial pressure of the reactive gas X2, the gas flows Qt, Qs, Qw and Qɪ and the fraction of each of the three surfaces covered with the MmXn compound. 3. Simulations The system of equations (5)–(9) was numerically solved for the magnetron with a tantalum target sputtered in the Ar + O2 environment. In this case, the reaction (2) can be described as: k (Ti ) 5 1 Ta + O 2 ↔ Ta 2O 5 , i = t, s, w . 4 2
(10)
The values of the parameters for the task are presented in table 1. The power density dependence of the target temperature was obtained by a numerical solution of a thermal task for a round 1 mm-thick tantalum plate, set 1 mm away from the water-cooled plate and attached to that plate in six spots. Using this dependence and the experimental current-voltage characteristics of the magnetron, the relation connecting the target temperature [K] and the ion current density [A/m2] was determined:
4
Tt ( j+ ) ≈ 293 + 1517(1 − e−0.00438 j+ ) .
(11)
Table 1 Parameters of the model for the reactive sputtering of Ta target in the Ar+O2 environment Parameter
SM
SC
ijM , eV
ij C, eV
ȖM
ȖC
Value
0.600
0.024
4.500
5.150
0.082
0.050
Parameter
BM
Value
17260
Parameter
Ea, 10 J
Value
–20
7.400
AM, 9.2
18
k0, 1033 m–2s–1
AC
BC
Į0
Qph, kal/mol
Nph, 10 mí2
15
20000
1.0
10000
8.260
1.100
Sp, m3/s
At m2
Aw , m2
As , m2
Tw K
Ts, K
0.008
0.002
0.029
0.001
300
600
Denotations. SM, SC are the sputter yields; ijM, ijC the work functions of electrons; ȖM, ȖC the ioninduced electron emission coefficients; AM, BM, AC, BC the approximation parameters for the equilibrium vapor pressure in the Arrhenius equation; Į0 the condensation coefficient of oxygen atoms on tantalum surface; Qph the heat of physical adsorption of oxygen on tantalum surface; Nph the concentration of adsorption sites of oxygen molecules on tantalum surface; k0, Ea the rate coefficient and the activation energy of the chemical reaction (10) for the Arrhenius equation (determined in [18]). Subscript symbols M and C stand for Ta and Ta2O5.
Equations (5)–(9) were solved with a consideration of (10) and (11) in the ion current density range from 0 to 200 A/m2 and the oxygen partial pressure range from 0 to 20 mTorr. As a result, it was established that two types of processes are possible, depending on the current density: the common process with a hysteresis effect and the hysteresis-free process. Fig. 5 shows the
20
20
15
15
15
10 5
a
0 0
4
8
12
p, mTorr
20 p, mTorr
p, mTorr
p = f(Q0) plots for the current density range revealing the verge between those two processes.
10 5 b
0 0
10 5 0
c
5
10 15 0 5 10 15 20 Q0, sccm Fig. 5. Oxygen pressure vs. oxygen flow for j+ (A/m2): a – 160 (1060); b – 165 (1075); c – 170 (1090). Target temperature values in Kelvins calculated using (11) are shown in parentheses.
The plots presented in fig. 6 show this verge most prominently. White dots in fig. 6, a show the current density dependence of the oxygen flows in A and C (fig. 1). Fig. 6, a shows that at a critical ion current density j0 = 167 A/m2 these two values become equal and the hysteresis width comes to 0 (fig. 6, b).
5
8
3
4
1 2
2 j0 0
ǻQ0, sccm
Q0, sccm
6
40
80
120
160
2
1
a
b 200
0 40 80 120 160 200 j+, A/m2 Fig. 6. Current density dependences of: a – the oxygen flow values standing for the transition of the operating mode of the cold target (black dots and dashed lines) and the hot target (white dots): 1 – metal to oxide mode transition, 2 – oxide to metal mode transition; b –the hysteresis width.
This feature discovered during the modeling of the reactive sputtering process for the hot tantalum target is not characteristic for the cold target. The simulation results shown as black dots and dashed lines in fig. 6 prove that. The special case of the model was used to obtain these dependences. For this case the following assumptions were made in equations (1)–(4): jT = 0, J Mev [Tt ( j+ )] = 0 , J Cev [Tt ( j+ )] = 0 and Tt = 500 K = const. As it is seen in fig. 6, a, the oxygen
flow values related to the transition of the operating mode of the target are proportional to the ion current density. Analogical dependence is also characteristic for the hysteresis width (fig. 6, b). 3
ǻQ0, sccm
2
1
0
40
80
120 160 200 j+, A/m2 Fig. 7. The hysteresis width obtained using the model for the hot target: solid line – full model; dots – neglecting the thermal emission effect; dashed line – neglecting the evaporation effect.
Further simulations, presented in fig. 7, allowed us to establish that evaporation is the main physical mechanism that initiates the hysteresis elimination during the reactive sputtering process. The thermal emission effect insignificantly decreases the current density value at which the hysteresis width becomes equal 0.
6
4. Conclusions The described physicochemical model of the hot target reactive magnetron sputtering makes it possible to analyze the process. For the tantalum target, sputtering process in Ar + O2 environment was shown:
•
In a particular case, when model is applied for a cold target, hysteresis width is proportional to the ion current density;
•
Two types of processes of hot target sputtering are possible, depending on the current density: with and without the hysteresis. Furthermore
9 For current densities less than 50 A/m2 the hysteresis width is proportional to the ion current density. This means that sputtering process is dominant at low current densities and evaporation can be neglected;
9 For current densities over 50 A/m2 the hysteresis width reaches its maximum, changing in a non-linear way, and at 167 A/m2 becomes equal to zero. This effect is connected solely to the increasing role of evaporation, which becomes more meaningful than sputtering at current densities over 170 A/m2. Acknowledgments The authors thank Russian Science Foundation for their support on the study (grant 15-1900076). References [1] P. Raman, A. Shchelkanov I., J. McLain, et al, High power pulsed magnetron sputtering: A method to increase deposition rate, J. Vac. Sci. Technol. A. 33 (2015) 031304 (10 pages), http://dx.doi.org/10.1116/1.4916108. [2] V.S. Levitskii, V.I. Shapovalov, A.E. Komlev, et al, Raman Spectroscopy of Copper Oxide Films Deposited by Reactive Magnetron Sputtering, Techn. Phys. Lett. 41 (2015) 1094– 1096, doi: 10.1134/S106378501511022X. [3] Feng J.Q., Chen, J.F. Optical properties and zinc nitride thin films prepared using magnetron
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[6] A.E. Lapshin, V.V. Karzin, V.I. Shapovalov, et al, X-ray Phase Analysis of Copper Oxides Films Obtained by DC Reactive Magnetron Sputtering, Glass Phys. Chem. 42 (2016) 116– 117, doi: 10.1134/S1087659616010065. [7] A. Billard, D. Mercs, F. Perry, et al, Influence of the target temperature on a reactive sputtering
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