Measuring the Ion Current to the Substrate During Deposition of Thin Films by Hollow Cathode Plasma Jet

WDS'07 Proceedings of Contributed Papers, Part II, 212 217, 2007. ISBN 978-80-7378-024-1 MATFYZPRESS Measuring the Ion Current to the Substrate During Deposition of Thin Films by Hollow Cathode Plasma Jet P. Virostko and M. Tichý Charles University in Prague, Faculty of Mathematics and Physics, Czech Republic. Z. Hubička, M. Čada, and P. Adámek Institute of Physics of the Academy of Sciences of the Czech Republic, v.v.i., Prague, Czech Republic. Abstract. Measurements of positive ion flux to the substrate during deposition of thin films by hollow cathode plasma jet are presented. Different methods of obtaining negative bias of substrate and measuring the resulting ion flux are compared and discussed pulsed DC bias, RF bias, and pulse-modulated RF bias of substrate. For determination of current and voltage waveforms on the substrate when the RF bias is applied, an electric circuit model of power feed line to the substrate is presented. Introduction A knowledge of plasma parameters and parameters describing an interaction of plasma with a substrate during deposition of thin films contributes to better understanding of deposition processes as well as to the reproducibility of deposited films. An important parameter that describes the plasmasubstrate interaction is a positive ion flux to the substrate. A bombardment of substrate with positive ions is often used to modify properties of deposited films. To enhance the bombardment, the substrate is negatively biased with respect to the bulk plasma potential by applying an external voltage to the substrate. For conducting substrate and deposited film, a DC voltage is used. For substrate from dielectric material or for dielectric deposited film, the negative DC bias is created by applying radiofrequency (RF) voltage to the substrate through a blocking capacitor. To obtain the ion current for the RF bias, it is necessary to determine RF current and voltage waveforms directly on the substrate, but RF current and voltage probes cannot be placed directly onto the substrate in the vacuum chamber. We present an electric circuit model of the power feed line to the substrate for determination of RF current and voltage waveforms on the substrate from RF current and voltage waveforms measured outside of the reactor chamber. We used a shielded feed line to the substrate, which we modeled as a coaxial transmission line with a capacitance on its end accounting for a parasitic capacitance between the substrate and a grounded reactor. The model is more realistic than for example a circuit model of an RF power feed line by Spiliopoulos et al. [1996], where the feed line was characterized as an inductor, thus neglecting the length of the feed line in comparison with the wavelength of RF voltage waveform. On the other hand, our model is simpler than a general two-port circuit model and a procedure to determine the impedance between the measuring point and the RF electrode proposed by Sobolewski [1992]. The ion current to the substrate was determined from the RF current waveform on the substrate according to Sobolewski [1998] as the current at time t 0 when the simultaneously measured RF voltage on the substrate reached its minimum. The ion current measured using this method for continuous RF bias was compared to the ion current measured for pulsed DC bias, and for pulse-modulated RF bias using the method of Braithwaite et al. [1996]. In this case, the ion current is determined from discharging of a blocking capacitor when the RF voltage is turned off. The ion current was measured in the hollow cathode plasma jet deposition system [Bárdoš et al., 1993; Hubička et al., 2003] for different substrate bias and discharge conditions. Experimental setup A schematic view of the hollow cathode plasma jet system for thin film depositions can be seen in Fig. 1. The main part of the deposition system is a nozzle made of material to be sputtered. The nozzle is connected to a power generator. A working gas flows through the nozzle and an intensive hollow cathode 212

Figure 1. The experimental setup of the hollow cathode plasma jet deposition system. Figure 2. A schematic view of power feed line to the substrate for RF bias. RF GEN pulse-modulated RF generator, MATCH matching unit, R 0 auxiliary resistor, C blocking capacitor, U RF, I RF RF voltage and current sensors, Z c shunt circuit, U s,1 oscilloscopic probe, Z l, l l coaxial transmission line, C p parasitic capacitance between the substrate and the grounded reactor. discharge is ignited at the nozzle outlet. The discharge is carried out into a grounded continuously pumped UHV reactor and a plasma jet is formed. Downstream from the nozzle a substrate is placed, on which a thin film is deposited. A DC mode of discharge excitation was used, with titanium nozzle, and argon as the working gas. The flow rate of argon was Q Ar = 138 sccm and the pressure in the reactor was held at p = 2.7 Pa. Discharge currents were set in the range I D = 0.1 0.6 A, corresponding to power P D = 20 120 W absorbed in the discharge. A planar substrate of circular cross-section with diameter d s = 40 mm was placed 34 mm downstream from the nozzle, coaxially with the nozzle. A cylindrical Langmuir probe with diameter d p = 380 µm and length l p = 3.5 mm was used to determine the plasma parameters. The probe was placed 18 mm downstream from the nozzle, 20 mm from the joint axis of the nozzle and the substrate. The substrate was connected either to a pulsed DC source through a resistor R, or to a pulse-modulated RF (frequency 13.56 MHz) generator through a blocking capacitor C (see Fig. 1). In case of pulsed DC bias, the substrate voltage was square-modulated with repetition frequency 35 khz. The substrate was held on negative voltage U DC,S in the active part of modulation cycle, and it was grounded in the off-time. The pulsed DC voltage was used because of possibility to measure the ion current also for thin dielectric deposited layers. A schematic view of electrical circuit used for RF bias of the substrate can be seen in Fig. 2. An RF generator was connected through a matching unit to a capacitor C, on which a negative DC bias was induced due to non-linear properties of sheath around the substrate. The RF voltage and current waveforms U RF (t), I RF (t) were measured by a calibrated voltage sensor and a Rogowski coil. A tunable shunt circuit [Sobolewski, 1992] was used to compensate an influence of parasitic capacitance C p between the substrate and the grounded reactor. The impedance Ẑc 1 of the shunt was set to minimize the 1 The hat indicates a complex quantity. 213

measured RF current amplitude I RF when the RF voltage was applied to the substrate without burning discharge. The voltage sensor, the Rogowski coil, and the shunt circuit were placed outside of the reactor chamber as close as possible to a vacuum feedthrough for the power feed line to the substrate. The power feed line in the reactor between the feedthrough and the substrate was shielded. An oscilloscopic probe was mounted on the feed line before the feedthrough to measure a decay of substrate voltage U s1 (t) after the RF bias was turned off in the modulation cycle. The repetition frequency of the modulation cycle was 200 Hz (period 5 ms) and the active part of RF bias was 1 ms. Methods of determination of ion current to the substrate The ion current to the substrate was obtained directly from the voltage drop on the resistor R in the active part of modulation cycle for the pulsed DC bias of substrate. When the RF voltage through a blocking capacitor C was used, the DC bias of substrate U DC,S was determined as the time averaged value of voltage U s1 (t). First method to obtain the ion current to the substrate for the RF bias was the method by Braithwaite et al. [1996] that requires pulse-modulation of the RF voltage. They have shown that the ion current I i can be determined from the slope of U s1 (t) voltage decrease, when the RF voltage is turned off, as: I i = C du s1 dt. (1) A blocking capacitor with the capacitance C = 23.5 nf was used so that the time of discharging from the DC bias U DC,S to the plasma potential V pl was τ = 0.2 3.5 ms for all discharge and bias conditions. The ion current was determined according to Eq. (1) from the first 100 µs after the RF voltage was turned off, where the decay of U s1 (t) was linear. Second method to determine the ion current for the RF bias was a method by Sobolewski [1998], in which the ion current is determined as the current to the substrate I s (t) at time t 0 when the simultaneously measured RF voltage on the substrate U s (t) reaches its minimum. The advantage of this method is that it does not require the RF voltage to be switched off. A following electric circuit model was used to determine the RF voltage and current waveforms on the substrate U s (t), I s (t) from the waveforms U RF (t), I RF (t) measured on the feed line outside of the reactor chamber. The power feed line between the measuring point and the substrate was considered as a lossless homogeneous coaxial transmission line of length l l and characteristic impedance Ẑl, with a capacitance C p on its end accounting for parasitic capacitance between the substrate and the reactor (see Fig. 2). Complex amplitudes of Fourier components of voltage and current waveforms Û(x), Î(x) in a transmission line are described by equations: Û(x) = ˆV 1 exp ( ˆγx) + ˆV 2 exp (ˆγx), Î(x) = ˆV 1 exp ( ˆγx) ˆV 2 exp (ˆγx), (2) where x is the position along the transmission line, ˆV 1 and ˆV 2 are the amplitudes of forward and backward wave in the line, and ˆγ is the wave propagation constant. For a lossless homogeneous transmission line, is real and frequency independent, and ˆγ is imaginary and linearly dependent on frequency. We chose x = 0 at the position of measurement of U RF (t) and I RF (t). The Eqs. (2) can be for x = 0 rewritten to: Û(0) = ÛRF = ˆV 1 + ˆV 2, Î(0) = ÎRF ÛRF Ẑ c = ˆV 1 ˆV 2. (3) A current drawn by the shunt circuit ÛRF has to be included in Eq. (3). The Fourier amplitudes of Ẑ c voltage and current waveforms at the substrate, which is at the position x = l l, are described by: Û s = Û(l l) = ˆV 1 exp ( ˆγl l ) + ˆV 2 exp (ˆγl l ), Î s = Î(l l) Ûs Ẑ p = ˆV 1 exp ( ˆγl l ) ˆV 2 exp (ˆγl l ) Ûs Ẑ p, (4) where Ẑp is the parasitic impedance represented by the capacitor C p ; the current drawn by this parasitic impedance Ûs Ẑ p is included in Eq. (4). Assuming the shunt impedance Ẑc, the parameters of the transmission line Ẑl, ˆγl l, and the parasitic capacitance C p are known, the U s (t) and I s (t) waveforms can be determined as follows. The Fourier components ÛRF, ÎRF are computed from the measured waveforms U s (t), I s (t) for the base frequency (13.56 MHz) and its harmonics. Then the amplitudes ˆV 1, ˆV2 are determined according to Eq. (3) and the Fourier components of waveforms on the substrate Ûs, Îs are 214

a) b) Figure 3. a) RF voltage and current waveforms U RF (t), I RF (t), measured on the power feed line for discharge current I D = 0.6 A and DC bias U DC,S = 110 V; b) RF voltage and current waveforms U s (t), I s (t) on the substrate determined from U RF (t), I RF (t) using the presented electric circuit model. At time t 0, when the voltage U s reaches its minimum, the ion current to the substrate I i is determined from I s. computed from Eq. (4). Finally, the waveforms U s (t) and I s (t) are obtained by inverse Fourier transform from Ûs, Îs for the base frequency and its harmonics. The impedance of shunt Ẑc was measured by an impedance meter for the base frequency and its harmonics. To determine Ẑl, ˆγl l and C p, the following equation for change of complex impedance along the transmission line of length l l was used: Ẑ RF = ÛRF Î RF = Ẑs + Ẑl tanh (ˆγl l ) 1 + Ẑs tanh (ˆγl l ), (5) where ẐRF is the measured complex impedance at x = 0 and Ẑs is the impedance at x = l l. The impedance ẐRF was measured at 13.56 MHz without burning discharge for three different impedances Ẑ s for bare substrate, for substrate and capacitance C 1 connected between the substrate and the grounded substrate support, and for substrate and another capacitance C 2 connected. The impedance Ẑ s was represented by a capacitance C p, by a capacitance C p + C 1, and by a capacitance C p + C 2 respectively. By simultaneously solving Eq. (5) for the three pairs of measured and end impedances ẐRF and Ẑs, the parameters Ẑl, ˆγl l and C p are obtained. Results and discussion The determined model parameters were: C p = 12 pf, = 107 Ω, and ˆγl l = n 0.437j, where n is the number of harmonic and j is the imaginary unit. An example of measured RF voltage and current waveforms U RF (t), I RF (t) and calculated waveforms at the substrate U s (t), I s (t) is in Fig. 3. The depicted waveforms were measured for the hollow cathode discharge current I D = 0.6 A and DC bias of substrate U DC,S = 110 V. A dependence of positive ion flux to the substrate j i on the DC bias U DC,s measured for the discharge current I D = 600 ma is depicted in Fig. 4 and a dependence of the ion flux on the discharge current I D measured for the bias U DC,s = 100 V is depicted in Fig. 5. The ion flux determined for RF bias from the current I s at time t 0 is in Figs. 4a, 5a, and the ion flux determined for pulsed DC bias and for pulsemodulated RF bias from discharging of blocking capacitor is in Figs. 4b, 5b. The ion fluxes determined for DC bias and pulse-modulated RF bias correspond well in the range U DC,s = 80 V 0 V (see Fig. 4b). In this range, the ion flux reached an approximately constant value, which is in agreement with the theory for saturated ion current to a planar Langmuir probe. Below the value U DC,s = 80 V, there was a step-like change of ion flux to a higher value for the pulsed DC bias, but not for the pulse-modulated RF bias. This difference was also observed for different discharge currents I D at U DC,s = 100 V (see Fig. 5b). Thus the rise of the measured current is caused by a process dependent on the energy of ions impinging on the substrate and not by the discharge itself. Further investigation is needed to assess the effect in more detail. However, we can conclude that the ion flux is determined unambiguously by these two methods for U DC,s from 80 V to 0 V. The ion flux determined in the RF bias was several times higher than for pulsed DC bias and pulsemodulated method for RF bias (compare Figs. 4a, 5a with Figs. 4b, 5b). One possible explanation for this is an influence of the RF voltage on the plasma (e.g. by an additional ionization around the RF biased substrate). In the Fig. 6, plasma parameters measured simultaneously with the ion fluxes by the 215

a) b) Figure 4. The ion flux to the substrate j i for the discharge current I D = 600 ma and different DC bias of substrate U DC,s. a) ion flux determined for RF bias from the current I s at time t 0 ; b) ion flux determined for pulsed DC bias and for pulse-modulated RF bias from discharging of blocking capacitor. a) b) Figure 5. The ion flux to the substrate j i for the DC bias U DC,s = 100 V and different discharge current I D. a) ion flux determined for RF bias from the current I s at time t 0 ; b) ion flux determined for pulsed DC bias and for pulse-modulated RF bias from discharging of blocking capacitor. a) b) c) Figure 6. Plasma parameters measured in the bulk plasma simultaneously with the ion fluxes depicted in Fig. 5. Squares for pulsed DC bias in the active pulse; circles for RF bias; triangles for pulse-modulated RF bias at time τ = 100 µs after the end of active pulse. a) electron density n e ; b) electron temperature T e ; c) plasma potential V pl. Langmuir probe in the bulk plasma are depicted. The plasma parameters were measured in the middle of active pulse for pulsed DC bias, for the RF bias, and at time τ = 100 µs after the end of active pulse for the pulse-modulated RF bias, when the ion current was calculated in this method. It can be seen that the RF bias influenced the bulk plasma parameters of the continuously burning DC discharge. When compared between the RF bias present on the substrate and the off-time after the RF pulse, the electron density, electron temperature, and plasma potential increased when the RF bias was on. The higher charged particle density and electron temperature mean higher ion current to the substrate. However, the electron density and electron temperature were also higher for the pulsed DC bias but the ion flux is several times lower for the DC bias than for the RF bias. Another source of error might be the procedure to determine the ion flux for the RF bias. The calculated waveforms on the substrate U s (t), I s (t) (Fig. 3b) are comparable to waveforms measured by Gahan and Hopkins [2007] for an RF electrode in an inductively coupled low-temperature plasma. They used a more complex general two-port network method by Sobolewski [1992] to describe the power feed line 216

and parasitics between the point of measurement and the electrode surface. However, when determining the ion flux from the current and voltage waveforms on the substrate I s (t), U s (t), the waveforms I RF (t), U RF (t) have to be measured very precisely. Test calculations showed that the precision of measurement of current amplitude I RF and of the phase between the current and voltage φ RF at the fundamental frequency have the main influence on the resulting ion flux. The relative error of current and voltage amplitude for 13.56 MHz was determined to be 10 %, and the error of measurement of the phase between the current and voltage was determined to be less than 5 for 13.56 MHz. When the amplitudes and the phase of the measured waveforms were varied in the range of determined errors, the ion flux changed significantly it was between 0.5 to 1.5 times of original value. In this way, the relative error of ion flux measurement for the continuous RF bias method was estimated to be 50 %. The ion current to the substrate is also assumed to be constant in time in the method. This assumption is valid for ion plasma frequency ω i ω the angular frequency of the RF voltage. In our case, the ion plasma frequency calculated for argon ions for the highest charged particle density was ω i = 3.6 10 7 rad s 1, which is already comparable to the angular frequency of the RF voltage ω = 8.5 10 7 rad s 1. The frequency dependence of the method was comprehensively discussed by Sobolewski [2001]. He showed that for ω i ω the ion current and the ion density in the sheath are changing in time and the ion current determined from I s (t) at time t 0 is different from the average ion current. For similar low-temperature plasma, he observed that the RF method yielded the ion flux up to two times higher than the pulsed DC method when the ion plasma frequency was close to the angular frequency of the RF bias. The effect of several times higher ion flux determined by the RF method can therefore be explained partly by the heating of plasma when the RF is on, partly by the inaccuracy of ion flux determination, and partly due to ion plasma frequency being already comparable with the driving frequency, which yield higher values of ion flux as was shown by Sobolewski [2001]. Conclusion Measurements of positive ion flux to the substrate during deposition of thin films by hollow cathode plasma jet are presented. Different methods of obtaining negative bias of substrate and measuring the resulting ion flux are compared. For determination of the current and voltage waveforms on the substrate when the RF bias is applied, an electrical model of power feed line to the substrate is presented. Ion flux determined for RF bias according to Sobolewski [1998] is much higher than the ion flux determined for the same conditions for pulsed DC bias and for pulse-modulated RF bias determined from discharging of a blocking capacitor. This can be partly attributed to the additional ionization and heating of plasma around the substrate by the RF voltage, which can be seen from Langmuir probe measurements. Other contribution to the higher ion flux determined for the RF bias can be a relatively high inaccuracy of the RF bias method, and the fact that the ion flux is not constant during one period of RF voltage, because the ion plasma frequency is comparable to the angular frequency of RF voltage. Acknowledgments. This work was supported by project KAN400720701 of the Academy of Sciences of the Czech Republic and by grant GACR 202/06/0776 of the Czech Science Foundation. References Bárdoš, L., S. Berg, and H. Baránková, Radio-frequency plasma-jet applied to coating of internal walls of narrow tubes, J. Vac. Sci. Technol. A, 11, 1486 1490, 1993. Braithwaite, N. S. J., J. P. Booth, and G. Cunge, A novel electrostatic probe method for ion flux measurements, Plasma Sources Sci. T., 5, 677 684, 1996. Gahan, D. and M. B. Hopkins, Electrical characterization of a capacitive rf plasma sheath, Rev. Sci. Instrum., 78, 016102, 2007. Hubička, Z., M. Čada, I. Jakubec, J. Bludská, Z. Málková, B. Trunda, P. Ptáček, J. Přidal, and L. Jastrabík, Investigation of the RF plasma jet system for deposition of LiCoO x thin films, Surf. Coat. Tech., 174, 632 637, 2003. Sobolewski, M. A., Electrical characterization of radio-frequency discharges in the Gaseous Electronics Conference Reference Cell, J. Vac. Sci. Technol. A, 10, 3550 3562, 1992. Sobolewski, M. A., Measuring the ion current in electrical discharges using radio-frequency current and voltage measurements, Appl. Phys. Lett., 72, 1146 1148, 1998. Sobolewski, M. A., Measuring the ion current in high-density plasmas using radio-frequency current and voltage measurements, J. Appl. Phys., 90, 2660 2671, 2001. Spiliopoulos, N., D. Mataras, and D. E. Rapakoulias, Power dissipation and impedance measurements in radiofrequency discharges, J. Vac. Sci. Technol. A, 14, 2757 2765, 1996. 217