ISSN 10637842, Technical Physics, 2015, Vol. 60, No. 2, pp. 283–291. © Pleiades Publishing, Ltd., 2015. Original Russian Text © A.V. Rogov, Yu.V. Kapustin, Yu.V. Martynenko, 2015, published in Zhurnal Tekhnicheskoi Fiziki, 2015, Vol. 85, No. 2, pp. 126–134.
ELECTROPHYSICS, ELECTRON AND ION BEAMS, PHYSICS OF ACCELERATORS
Factors Determining the Efficiency of Magnetron Sputtering. Optimization Criteria A. V. Rogov*a, Yu. V. Kapustina, and Yu. V. Martynenkoa,b a b
National Research Centre Kurchatov Institute, Moscow, 123182 Russia National Research Nuclear University MEPhI, Moscow, 115409 Russia *email: alex
[email protected] Received June 27, 2014
Abstract—We report on the results of experimental study of the dependence of sputtering energy efficiency Kw in a dc planar magnetron sputtering setup on the discharge power, working gas pressure, magnetic field, cathode erosion depth, and the structure of the gas puffing system and anode. We propose that this parameter be used for comparing the degree of perfection of the magnetron design irrespective of the magnetron size and structural features. The results of measurements of Kw in sputtering of Al, Ti, Cr, Cu, Zn, Zr, Nb, Mo, Ag, In, Sn, Ta, W, Pt, and Au are considered. The optimization criterion is worked out for the magnetic system of the magnetron, which ensures the minimal working pressure and the maximal sputtering rate for the cathode. The results are analyzed theoretically. DOI: 10.1134/S1063784215020206
INTRODUCTION Magnetron sputtering systems (MSSs) are distin guished by a high energy efficiency ζ of the sputtering process as compared to other systems based on ion beam sputtering. This parameter is defined as [1] ζ = m s / ( j i U i ),
(1)
where ms is the mass sputtered per unit time from unit area of the target, ji is the ion current density on the surface of the material being sputtered, and Ui is the voltage accelerating ions. This parameter is conve nient for comparing the efficiency of sputtering sys tems with different ways of formation of a sputtering ion beam. However, it is difficult to use this parameter in analysis of the effect of structural features and oper ation regimes of MSSs on its efficiency because the values of current density of sputtering ions at different points of the sputtering zone differ by several orders of magnitude, and the sputtering regime changes upon cathode disintegration. In this study, we analyze the energy efficiency of such systems using the integrated energy efficiency factor Kw defined as K w = Δm/ ( tW ),
(2)
where Δm is the total mass of the sputtered material of the cathode (mg), t is the sputtering time (min), and W is the average integrated power of the magnetron dis charge (W). Such a choice of dimensions is convenient for measurement of a given parameter. In contrast to ζ, Kw can easily be measured and can be used for analyz ing the effect of various factors on the efficiency of a sputterer.
In designing new magnetrons, the question arises about the effect of parameters such as the method of working gas puffing into the sputtering zone and the structure of the anode on the sputtering efficiency. Since the structural features of magnetrons are patent ing objects and are often trade secrets, the obtaining of comprehensive information on the functional features and perfection of underlying engineering solutions for industrial magnetrons is difficult at present. This com plicates the development of new magnetron systems and the choice of a specific MSS model. In this study, we analyze the complex of factors that determine the efficiency of sputtering in a dc magne tron. The results are analyzed theoretically. We believe that our results will facilitate further development of the magnetron sputtering technique and technology. 1. EXPERIMENTAL SETUP The experiments were carried out on a vacuum sputtering apparatus with an oilfree evacuation sys tem. All results were obtained on planar magnetrons with a disk cathode and the magnetic system with per manent magnets operating in the dc regime. For the maximal cathode thickness (or the thickness of the cathode insertion in the case of indirect cooling sys tem), we use the limiting value for which the initiation and stable operation of the cathode discharge is ensured for a voltage less than 650 V and an argon pressure lower than 8 mTorr. We used the following magnetrons. (i) An original magnetron (minimagnetron) with a cathode diameter of 25 mm, the magnetic system con
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Kw, mg/(W min) 0.16 2 0.15 4 3 0.14 1 0.13 0.12
0
20
40
60
80
100
120 W, W
Fig. 1. Dependence of sputtering efficiency Kw of a copper cathode on the magnetron discharge power at pressure PAr = 4.5 × 10–3 Torr; 1—experimental curve; 2—Kw(W) dependence calculated by formula (17) for α = 6.5 and γ = 0.7; 3—Kw(W) dependence calculated by formula (17) for α = 6.5 and γ = 1; 4—Kw(W) dependence for I(mA) = U(V)—300.
sisting of SmCo magnets (the periphery annular mag net ∅25 × ∅15 × 5 mm, and the central cylindrical magnet ∅10 × 10 mm), an indirect cathode cooling system, an insulated builtin anode, and gas puffing into the sputtering zone. The maximal thickness of the cathode insertion is 2 mm. (ii) The same magnetron with the magnetic system consisting of NdFeB magnets (the periphery annular magnet ∅25 × ∅18 × 5 mm and the central cylindrical magnet ∅10 × 10 mm); the maximal thickness of cath ode insertion is 4.5 mm. (iii) Commercial ONIX2 magnetron (Angstrom Sciences, USA) [2] with a cathode diameter of 50 mm, am indirect cooling system, and a builtin earthed anode; the maximal thickness of the cathode insertion is 9.6 mm, external gas puffing. Together with the ONIX2 magnetron, we used a GS 10/800 (Analog & Digitale Leitungselektronik, Germany) technological power supply (PS) with the stabilization regime in power, voltage, or discharge cur rent and with a maximal power of 1 kW. For minimag netrons, we used an original PS with a maximal output power of 250 W and with the same stabilization regimes. The sputtering rate was measured by the Qpod quartz crystal monitor [3]. The energy efficiency factor Kw was determined by weighing the cathodes of the magnetrons on the CAUW 220D analytic balance. The mass of the sput tered material was determined as the difference between the initial and final masses of the cathode. As regards the Ar pressure and the average current density of sputtering ions at the cathode, the sputter ing regimes used in our experiments correspond to operation regimes of commercial sputterers widely used in vacuum sputtering.
2. EXPERIMENTAL RESULTS 2.1. Dependence of Kw on the Magnetron Discharge Power It is well known that the dependence of the sputter ing rate (and, accordingly, the rate of deposition of the sputtered material on the substrate) on the magnetron discharge power is close to linear [4–7]. In modern power supplies, the stability of the sputtering rate is ensured by the output power stabilization regime. However, the exact dependence of the cathode sput tering rate in a dc magnetron discharge on its power and the requirements to the stabilization accuracy have not been analyzed comprehensively as yet. Figure 1 shows the results of measurements of the dependence of Kw on the discharge power on the min imagnetron (NdFeB) by weighing the cathode before and after sputtering for Cu and corresponding approx imating curves. In addition, we measured on the same magnetron the rate of deposition of the coating for a fixed pressure and the component concentration in the gas in the vacuum chamber. The materials sub jected to sputtering were Cu and Mo. To eliminate the effect of erosion on the results of measurements, we used cathodes without initial degradation. The argon pressure was PAr = 4.5 × 10–3 Torr. The quartz monitor of deposition rate was arranged coaxially with the magnetron cathode at a distance of 50 mm from it. The coating deposition rate for the fixed pressure and the component concentration of the gas in the vacuum chamber is directly proportional to the cathode sput tering rate. Therefore, the ratio deposition rate Vd to discharge power W is directly proportional to Kw. This allows us to refine the form of the Kw(W) dependence. The results of measurements of this quantity for Cu and Mo are presented in Fig. 2, which shows that the sputtering efficiency Kw weakly depends on the dis charge power both for Cu and for Mo and slightly decreases in the range of high powers. The increase in the deposition rate with W in the range of low energies is due to poor conditions of film formation for small fluxes of the deposited material. Thus, both methods of measurements yielded sim ilar results. However, the use of the quartz monitor makes it possible to considerably improve the accuracy of measurements and to reduce the measuring time as compared to the method with weighing. The deviation of Kw from its mean value does not exceed ±5%; there fore, in practical applications, we can assume that in the entire working range of the input power to the dis charge, Kw is independent of the magnetron discharge power. 2.2. Dependence of Kw on the Working Gas Pressure In the formation of especially pure coatings or for a considerable distance between the substrate and the magnetron, deposition should be carried out at work ing gas pressures extremely low for the magnetron TECHNICAL PHYSICS
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0.205
0.088
0.200
0.086
0.195 0.084
Cu
0.082 0.080
0.190 0.185
0
20
40
60 80 W, W
100
Kw, mg/(W min) 0.15
0.210 Vd /W(Cu), Å/(s W)
Vd /W(Mo), Å/(s W)
0.090
0.180 120
Fig. 2. Power dependence of the ratio of deposition rate Vd (A/s) to discharge power W (W) for sputtering of Cu and Mo.
used in experiments. It is known that the effect of increase in the argon pressure during sputtering is analogous to the effect of an increase in the magnetic field strength [1]. On the other hand, an increase in the magnetic field to above approximately 0.08 T does not yield a positive effect [8]. However, deeper analysis of the effect of these parameters on the magnetron dis charge is of interest in our opinion. Figure 3 shows the results of measurement of the dependence of Kw on the argon pressure for the minimagnetron with the SmCo magnetic system for Cu sputtering. The thickness of the cathode insertion is 0.6 mm, and discharge power is W = 100 W. At pressures from 1.8 to 4 mTorr, the magnetron in question exhibits an increase in Kw with pressure P. In this pressure range, the discharge regime is tran sient from the glow discharge to the magnetron dis charge. The former type of the discharge is observed for pressures below the initiation threshold for the magnetron discharge and is characterized by a weak bulk glow in the cathode region of the magnetic trap and by currents of about 1 mA for the maximal voltage of the power supply. In this case, sputtering of the cathode is practically not observed. With increasing working pressure, the degree of ionization in the cath ode region increases, the discharge is localized near the cathode, and, correspondingly, its sputtering is intensified. The difference between the maximal and minimal values of Kw amounts to 17%. In the pressure range 4–10 mTorr, the value of Kw can be treated as constant (deviation is less than 3%). This region corresponds to the magnetron discharge. From the form of the dependence of Kw on PAr, the range of working pressures corresponding to the true magnetron discharge in the given magnetron can be established more exactly. An insignificant decrease in Kw at pressures exceed ing 7 mTorr can be explained by the effect of backward scattering and reverse diffusion of the sputtered mate rial to the cathode of the magnetron being sputtered. TECHNICAL PHYSICS
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0.14
0.13
0.12 1
2
3
4
5
6
7
8
9 10 11 PAr, mTorr
Fig. 3. Dependence of Kw on the argon pressure.
Thus, the effect of PAr on Kw should be taken into account for pressures close to the minimal working pressure of the magnetron. 2.3. Effect of the Structure of the Gas Puffing System on the Sputtering Efficiency We analyzed the effect of the method of gas puffing on the sputtering efficiency. In the magnetron with an insulated anode used in our experiments, gas was sup plied directly to the sputtering region through the annular gap between the anode and the cathode being sputtered. The control experiment was performed with the puffing of the working gas into the vacuum cham ber at a distance of about 350 mm from the magnetron. The argon pressure in the magnetron discharge region differs substantially in these two cases. To verify this assumption, we selected the working pressure in the case of gas puffing at a large distance from the magne tron, which ensured the coincidence of the I–V curve with that obtained for the gas puffing in the cathode region. The experiment was performed on the mini magnetron with the SmCo magnetic system. The material being sputtered was Cu. The results are shown in Fig. 4. The results of measurements of the I–V character istics at different pressures were used for constructing the dependence of the discharge voltage on pressure for a fixed discharge current (I = 100 mA) for both methods of gas puffing. This dependence is shown in Fig. 5. It can be seen from Fig. 5 that for the magnetron used in our experiments, the coincidence of the I–V curves was observed upon an increase of pressure by a factor of 1.3 in the entire range of working pressures. Since this parameter depends only on the structural features of the gas puffing system, it can be referred to as the gas efficiency factor. It can also be used for esti mating the engineering perfection of the gas puffing system in the comparison of different magnetron sput
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terers. Since the energy efficiency of sputtering in the range of minimal working pressures (see Fig. 3) strongly depends on pressure, this parameter is impor tant for operation of the sputtering system in the low pressure range. Thus, gas puffing directly to the depo sition zone considerably improves the MSS efficiency and the conditions of transportation of sputtered material from the magnetron to the substrate, which noticeably affects the quality of coating. As applied to the magnetron used here (see Fig. 3), the increase in Kw due to the use of builtin gas puffing system in the range of minimal pressures can be as large as 7%.
I, mA 250 1 200 2 150 100 50 0 300
330
360
390
420
450
480 U, V
Fig. 4. Current–voltage characteristic of the discharge: 1—gas puffing through the magnetron, PAr = 5 mTorr; 2—external gas puffing, PAr = 7 mTorr.
Ud, V 480 460 1 440 420
2
400 380 2
3
4
5
6
7
8
9 10 11 PAr, mTorr
Fig. 5. Pressure dependence of the discharge voltage for a fixed discharge current: 1—external gas puffing, 2—gas puffing through the magnetron.
0.17 1
0.16 0.15 0.14 0.13
2 1
2
The dependence of Kw on the cathode thickness was measured on the ONIX2 magnetron and the minimagnetron with Cu sputtering. The thickness of the cathodes was chosen close to the maximal thick ness for the given magnetrons and was 9 and 4.5 mm, respectively. The discharge power was 600 and 100 W, respectively. Sputtering was carried out in the dis charge power stabilization regime. The working pres sure was approximately 4 mTorr. The duration of a sput tering cycle in both cases was the same (T = 30 min). After each sputtering cycle, a layer of material with a thickness larger than the maximal erosion depth was removed from the cathode on the side of the erosion zone on a lathe because the next experiment was car ried out on a planar cathode without destruction. The resultant dependence of Kw on cathode thickness h was shown in Fig. 6. For both magnetrons, we observed a decrease in the value of Kw in the range of cathode thicknesses close to the maximal value. The difference between the maxi mal and minimum values of Kw for the minimagnetron and for the ONIX2 magnetron was 13 and 10%, respectively. 2.5. Dependence of Kw on the Magnetic Field at the Cathode Surface
Kw, mg/(W min) 0.18
0.12 0
2.4. Dependence of Kw on the Cathode Thickness
3
4
5
6
7
8
9 10 h, mm
Fig. 6. Dependence of Kw in thickness h of the Cu cathode: 1—minimagnetron; 2—ONIX2.
To determine the dependence of Kw on the mag netic field, we can use the above dependences of this parameter on the cathode thickness (see Fig. 6). The dependence of the magnetic field at the surface of the cathode on its thickness was measured experimen tally using TPU02 magnetometer. We measured the maximal value of magnetic field |B| at the cathode sur face as a function of cathode thickness h. The results of measurements are shown in Fig. 7. Using the data represented in Figs. 6 and 7, we con structed the dependence of Kw on |B|, which is shown in Fig. 8. It can be seen from this figure that the value of Kw increases when the maximal value of the magnetic field increases to |B| ≈ 140 mT. In the range 140– 240 mT, this parameter is stabilized. Upon a further TECHNICAL PHYSICS
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increase in the magnetic field, the value of Kw decreases smoothly. 2.6. Dependence of Kw on the Cathode Erosion Depth The results of analysis of the dependence of Kw on the cathode erosion depth for sputtering of Cu in the minimagnetron and in the ONIX2 magnetron are shown in Fig. 9. The increase in the sputtering efficiency for a small erosion depth is due to an increase in the cathode area subjected to ion bombardment and an increase in the magnetic field with erosion depth. The crater in the cathode caused by sputtering is filled with the plasma (we can assume that the thickness of the dark cathode space remains unchanged). Ions leaving the emission boundary of the plasma bombard the cathode along the normal to its surface. With increasing erosion depth, the increasingly large portion of evaporated material is redeposited at the opposite walls of the cra ter. This explains the decrease in the sputtering effi ciency for a large depth of the erosion zone. Since the angular distribution of sputtered atoms depends on the composition and structure of the material being evap orated [9], the position of the extremum also depends on these parameters. For the minimagnetron and for the ONIX2 mag netron used in our experiments, the variation of Kw upon degradation of the cathode was 10 and 40%, respectively. The ratio of maximal cathode erosion depth her to its mean diameter Dk for the magnetrons used in our experiments was the same (her/Dk ≈ 0.18). In our opin ion, the absolute value of the erosion depth in the cathode and the design of the magnetic system are determining factors in this case. 2.7. Effect of the Design and Shape of the Anode on the Sputtering Efficiency The experiments were performed on the minimag netron with the SmCo magnetic system. We studied the dependence of the I–V characteristic on the diam eter of the orifice in the annular anode located with the minimal gap above the surface of the cathode being sputtered coaxially with it. The cathode material was copper. The argon pressure was PAr = 4 mTorr. The results of measurements are represented in Fig. 10, which shows that the optimal diameter of the orifice in the anode is 22 mm for the magnetron used in experi ments. For unbalanced magnetic systems, like in our case, the optimal diameter of the anode orifice is equal to the diameter of the zone bounded in the plane of the anode electrode by the field line passing at the maxi mal distance from the cathode and intersecting its sur face twice. The same magnetic field line bounds the region of the magnetic trap of the magnetron dis charge. The magnetic field distribution was calculated TECHNICAL PHYSICS
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|B|, mT 400 300
1
200 2 100 0
0
2
4
6
8
10
12 h, mm
Fig. 7. Dependence of the maximal magnetic field |B| on the cathode thickness: 1—minimagnetron (NdFeB); 2— ONIX2.
Kw, mg/(W min) 0.18 1
0.17 0.16 0.15 2
0.14 0.13 0.12 0
40
80
120 160 200 240 280 320 |B|, mT
Fig. 8. Dependence of Kw on the maximal magnetron field |B| at the cathode surface: 1—minimagnetron; 2—ONIX2.
Kw, mg/(W min) 0.14 1 2
0.12
0.10
0.08 0
1
2
3
4
5
6
7
8 9 her, mm
Fig. 9. Dependence of sputtering efficiency Kw on the cathode erosion depth: 1—minimagnetron; 2—ONIX2.
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I, mA 250 15
1
200 3
150 2
100
10
50 0 300
330
360
390
420
450
480 U, V h, mm
Fig. 10. Current–voltage characteristic of the discharge for various diameters of the aperture in the annular anode: 1—20, 2—22, and 3—24 mm.
5
using the FEMM 4.2 program. The results of calcula tion are shown in Fig. 11. The magnetic field distribution indicates that the optimal value of the diameter of the anode diaphragm depends on the cathode thickness (distance from its surface to the magnetic system). The rated value of the optimal anode orifice diameter at a height of 3 mm (the thickness of the cathode insertion is 2 mm) is approximately 20 mm, which is close to the value of the optimal diameter of the anode (22 mm) obtained experimentally. Such a geometry of the anode elec trode ensures the outflow of electrons leaving the mag netic trap zone due to the drift across the magnetic field. In this case, the thermal load on the substrate during deposition is reduced, which improves the quality of coatings. A decrease in the orifice diameter relative to the optimal value leads to the departure of electrons from the magnetic trap to the anode along magnetic field lines, which deteriorates the magnetron discharge parameters.
0
N
S
S
N
0
5
10
15
r, mm Fig. 11. Magnetic system and magnetic field distribution in the minimagnetron (NdFeB).
Ud
2.8. Dependence of Kw on the Material Being Sputtered The sputtering coefficient for the metal surface bombarded by ions strongly depends on the composi tion of the material being sputtered and on the energy of bombarding ions. To estimate the mean energy of sputtering ions in the magnetron discharge, we used the experimentally measured spectrum of sputtering ions in the magnetron, which was obtained in the dc sputtering of a Ti cathode by argon ions [10] and is shown in Fig. 12. The spectrum is normalized, Ud
∫ P ( E ) dE = 1. 0
The mean energy of bombarding ions is
(3)
E av =
∫ EP ( E ) dE.
(4)
0
The calculations using the dependence represented in Fig. 12 give the value (5) E av ≈ 0.6U d . The proportionality factor between the average energy of ions and the discharge voltage was used for calculating the average energy of bombarding ions for all materials under study. The table contains the values of Kw obtained for 15 elements in analysis of technological experiments per formed during the last several years. The sputtering was carried out for various initial thicknesses and ero sions of the cathodes; for this reason, these data are qualitative by nature. For each element, sputtering coefficient YAr was calculated using the TRIM98 pro TECHNICAL PHYSICS
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I, mA 270
0.04 180
3
0.03 0.02
90
0.01
2 0
0
20
40
60
80 100 120 140 160 180 E, eV
A = K w / ( MY Ar ), where M is the atomic mass of the element under investigation and YAr is the sputtering coefficient. All measurements were taken on the minimagne tron with a cathode diameter of 25 mm and with the SmCo magnetic system at pressure PAr ≈ 4 × 10–3 Torr. The data presented in the table show that the value of A for all materials under investigation is constant with accuracy sufficient for applications. The mean value of this parameter is (1.5 ± 0.5) × 10–3. The error in determining the value of A can be reduced by taking all measurements for the same thickness and the same degree of cathode degradation. This makes it possible to use parameter A for calculating the energy effi ciency of sputtering Kw for different cathode materials by measuring its value for the given magnetron on one of these materials.
340 360
380 400
420
440 460 U, V
Fig. 13. Current–voltage characteristics of a minimagne tron for the optimal diameter of anode orifice: 1—experi mental I–V curve; 2—calculation by formula (6'); 3—cal culation by formula (7).
Fig. 12. Energy spectrum of Ar ions for sputtering of the Ti cathode. Discharge voltage is Ud = 225 V.
gram for the average energy of argon ions. The table also contains the values of parameter
1 320
3. ANALYSIS OF RESULTS The results obtained in this study can be explained using the current–voltage characteristic typical of magnetrons. Figure 13 shows such a characteristic recorded on the minimagnetron with the anode having the optimal orifice diameter. For magnetrons, the power approximation of the I–V characteristic is often used [4] in the form α
I∼U , (6) where α ~ 5–7. For our magnetron with the optimal anode diameter, we obtain 6.3
(6') I ( mA ) = ( U ( V )/185 ) . Our measurements show that the I–V characteris tic in the region of the magnetron discharge proper is correctly approximated by the linear dependence I = k ( U – ΔU ), (7) where ΔU = 330 ± 30 V and k ≈ 0.5–3.5 mA/V. Quan tity ΔU weakly depends on the magnetic field, while the value of k decreases with increasing magnetic field. The existence of the minimal voltage ΔU for which the
Measured values of Kw for various metals Element
Al
Ti
Cr
Cu
Zn
Kw, mg/(W min) U p, V Eav, eV YAr, atoms/ion TRIM M, amu A × 103
0.024 412 243 0.49
0.029 370 218 0.35
0.065 407 240 0.87
0.13 310 183 1.17
27.0 1.81
47.9 1.73
52.0 1.44
63.6 1.74
Zr
Mo
Ag
In
Sn
Ta
W
Pt
Au
0.33 0.058 0.054 539 361 373 318 213 220 3.80 0.42 0.46
0.083 325 192 0.58
0.33 430 254 1.74
0.19 384 226 1.23
0.20 367 217 0.91
0.11 366 216 0.57
0.12 415 245 0.68
0.27 400 236 1.09
0.41 455 269 1.67
65.4 1.33
95.4 1.50
108 1.76
115 1.34
119 1.85
181 1.07
184 1.04
195 1.27
197 1.25
91.2 1.51
Nb
92.9 1.26
Up is the mean voltage of the magnetron discharge over sputtering time; Eav is the average energy of bombarding ions, Y is the sputtering factor, and M is the relative atomic mass of the element. TECHNICAL PHYSICS
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ions, multiplied by atomic mass M of the cathode material: (12) dm/dt = IY ( E ef )M. In magnetrons, current I to the cathode strongly depends on discharge voltage U. Using simple approx imation (6), we obtain the discharge power
Ys, atom/ion 1.8 2 1.2
W ∝ JU = k 1 U 0.6
3
J = k2 W and the discharge voltage
1
1+α
,
(13)
α/ ( 1 + α )
,
1/ ( 1 + α )
0.6 Ei, keV
(14) U∝W . The sputtering coefficient in the energy range 200– 500 eV is given by
Fig. 14. Dependence of the sputtering factor for Cu on the energy of bombarding ions: 1—data from [12]; 2— approximation by Y = 3.75E; and 3—Y = 2.4E0.7.
(15) Y ∝ ( E ef ) ∝ ( U ) ∝ ( W ) , where γ ≈ 1/2. The cathode sputtering rate dm/dt depends on the discharge power as
0
0.1
0.2
0.3
0.4
0.5
magnetron discharge is initiated can be associated with the minimal jump in the cathode voltage Uk (Uk ≈ 0.6U, where U is the discharge voltage), for which the electron drift velocity is sufficient for the beginning of ionization of the working gas. Indeed, the drift velocity is given by V D = E/B = U k / ( dB ), (8) where E = Uk/d is the electric field strength in the region of the cathode potential drop of width d. This gives the minimal voltage Uk, min required for ioniza tion: 1/2
(9) ΔU = U k, min /0.7 = 2 ( I/m e ) / ( Bd ), where I is the ionization potential for the working gas (I = 15.7 eV for argon). For B = 0.1 T and d = 1.5 mm, we have ΔU ≈ 300 eV. According to [11], the width d of the cathode drop is determined by the Larmor radius for electrons, ρ = (2meU/e)1/2/B (me and e are the elec tron mass and charge, respectively) and by the elec tron path length relative to ionization of the working gas atoms, λ = 1/(nσ) (n is the concentration of atoms of the working gas and σ is the cross section of ioniza tion of the working gas atoms by electron impacts): 1/d = 1/ρ + 1/λ, (10) d = ρ/ ( 1 + ρ/λ ). For ρ/λ Ⰶ 1, we obtain 1/2
3/2
ΔU = ( 8I/m e B ) ( 1 – 8nσ ( I/e ) B ). (11) This expression shows that ΔU decreases with increas ing magnetic field B and working gas concentration n, which is in conformity with the measured I–V charac teristics. For the magnetron used in our experiments with the optimal anode diameter, we have I(mA) = 2(U(V) – 325) (Fig. 13). The cathode sputtering rate dm/dt in the magne tron is equal to the product of ion current I to the cath ode and coefficient Y(Eef) of cathode sputtering by
γ
γ
γ/ ( 1 + α )
( α + γ )/ ( α + 1 )
dm/dt ∝ W , and the sputtering efficiency factor is given by
(16)
( γ – 1 )/ ( 1 + α )
K w = ( dm/dt )/W ∝ W . (17) In view of the weak dependence of voltage on power, the dependence of Kw on W is also very weak. Coefficient A also exhibits a weak dependence on the power: – 1/ ( 1 + α )
A∝W . (18) For copper used in our experiments, the depen dence of the factor of sputtering by argon ions on the energy is shown in Fig. 14 [12]. The same figure shows the approximations Y = 3.75E for E < 200 eV and Y = 2.4E 0.7 for E > 200 eV. For our magnetron with α = 6.5 and γ = 0.7, factor Kw ~ W–0.04. For low energies of ions, when γ = 1 and dh/dt ∝ P, we have Kw = const. This is in good agree ment with the experimental dependence (see Fig. 1). In this case, coefficient A ∝ W–0.13. Thus, the dependence of the cathode erosion rate in the magnetron on the discharge power is close to linear in view of the strong dependence of the current on the discharge voltage, and factor Kw is almost inde pendent of the discharge power. If we use approximation (7) for the I–V characteris tic, for W Ⰶ 2kΔU2, the discharge voltage can be repre sented by the following function of discharge power W: U ≈ ΔU + W/ ( 2kΔU ), (19) and the sputtering efficiency factor in the magnetron is given by γ–1
2
K w ∝ ΔU [ 1 – ( 1 – γ )W/ ( 2kΔU ) ]. (20) Thus, for W < [2/(1 – γ)]kΔU2, the Kw(U) depen dence is a weakly decreasing function. This decrease is the weaker, the larger the values of k and ΔU. For ΔU ≈ 325 V and k ≈ (0.5–3.5) × 10–3 A/V, we have 2
[ 2/ ( 1 – γ ) ]kΔU ≈ 100 W. TECHNICAL PHYSICS
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FACTORS DETERMINING THE EFFICIENCY
As can be seen from Fig. 1, expression (20) is also a correct approximation of the dependence of Kw on dis charge power W. In our case, for discharge power W < 100 W, sputtering efficiency Kw can be treated as con stant. CONCLUSIONS Analysis of magnetron sputtering efficiency Kw revealed that this parameter is convenient for experi mental investigations of the effect of various factors on the sputtering efficiency in magnetron sputtering sys tems. This parameter is almost independent of the magnetron discharge power (the deviation from the mean value is less than ±5%). A change in the cathode erosion depth during cath ode operation produces the strongest effect on the energy efficiency of sputtering (up to 40%). This dependence has a clearly manifested maximum and is determined by the structure of the magnetic system of the magnetron. This is manifested especially strongly in the optimization of the magnetron magnetic system in accordance with the criterion ensuring the maximal cathode thickness. The next important factor is the argon pressure in the course of sputtering (up to 17%). The pressure produces the strongest effect on the operation in the range of minimal pressures for a given magnetron. The cathode thickness also affects the value of Kw (up to 10%). This is due to the fact that in the same magnetic system, the values of the magnetic field at the cathode surface and the configurations of the mag netic trap are different depending on this parameter. It should be noted that in the case of an annular inso lated anode, the optimal diameter of the orifice in the anode ensuring the maximal efficiency of sputtering also depends on this parameter. The design of the gas puffing system also influences the sputtering efficiency significantly. For example, when the working gas is fed directly into the magnetic trap zone, the gain in the energy efficiency is up to 7% as compared to external gas puffing. The distance between the anode and cathode for an annular insulated anode does not appreciably affect Kw. The magnetic field also produces a strong effect on the energy efficiency of sputtering. In the range of val ues 240 mT ≥ |B| ≥ 140 mT, the value of Kw almost remains unchanged. For a lower magnetic field, a sharp decrease in this parameter is observed. For strong magnetic fields, this parameter also decreases, but more smoothly. The results of measurements of the value of Kw for different metals can be used for estimating the sputter ing efficiency of any magnetron sputtering system. For this purpose, it is sufficient to measure this parameter for one of the materials given in the table. The propor tionality factor equal to the ratio of the measured and TECHNICAL PHYSICS
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tabulated value, which takes into account the struc tural differences of magnetrons, can be used for other materials given in the table. Parameter A = Kw/(MY) (M is the mass of the ele ment in question and Y is the factor of sputtering by the working gas for energy 0.6Up) is almost indepen dent of the sputtering regime and the cathode mate rial. Thus, as applied to a given magnetron, it can be used for calculating the energy efficiency of sputtering Kw for any cathode material if we know its value for one of the other materials. From the theoretical point of view, it is the strong dependence of current on the voltage in the magne tron discharge that ensures an almost linear depen dence of the cathode erosion rate on the discharge power, and sputtering efficiency Kw makes it almost independent of the discharge power. When the cathode without initial degradation is used, the value of Kw depends only on the material being sputtered and on the efficiency of electron con finement in the magnetic trap (i.e., the degree of its perfection). Its value is determined by the structural features of the magnetron, is independent of the size of the cathode being sputtered, and can easily be mea sured. Thus, this parameter can be used for comparing magnetrons with allowance for the required operation conditions for choosing the best system. REFERENCES 1. B. S. Danilin, Application of LowTemperature Plasma for ThinFilm Deposition (Energoatomizdat, Moscow, 1989). 2. http://www.angstromsciences.com 3. http://www.inficon.com 4. P. V. Kashtanov, B. M. Smirnov, and R. Khipper, Phys. Usp. 50, 455 (2007). 5. JinHyo Booa, Min Jae Jungb, Heon Kyu Parkb, Kyung Hoon Namb, and Jeon G. Han, Surf. Coat. Technol. 188–189, 721 (2004). 6. W. M. Posadowski, Thin Solid Films 392, 201 (2001). 7. Li Gou, Changsong Qi, Junguo Ran, and Changqiong Zheng, Thin Solid Films 345, 42 (1999). 8. J. Goree and T. E. Sheridan, Appl. Phis. Lett. 59, 1052 (1991). 9. Yu. V. Martynenko, A. V. Rogov, and V. I. Shul’ga, Tech. Phys. 57, 439 (2012). 10. D. Czekaj, E. K. Hollman, V. A. Volpias, A. G. Zaytsev, A. Chernakova, and B. Goranchev, Bulg. J. Phys. 18, 63 (1991). 11. V. T. Barchenko, Yu. A. Bystrov, and E. A. Kolgin, Ion– Plasma Technologies in Electronic Industry (Energoat omizdat, St. Petersburg, 2001). 12. W. Eckstein, C. GarciaRosales, J. Roth, and W. Otten berger, Sputtering Data (MaxPlanckInstitut fur Plas maphysik, 1993), IPP 9/82.
Translated by N. Wadhwa