Retarding Field Analyzer for Ion Energy Distribution Measurement Through a Radio-Frequency or Pulsed Biased Sheath

Full Paper Retarding Field Analyzer for Ion Energy Distribution Measurement Through a Radio-Frequency or Pulsed Biased Sheath David Gahan,* Borislav Dolinaj, Chanel Hayden, Michael B. Hopkins A compact, floating retarding field energy analyzer for measurement of ion energy distributions impacting an electrode through a radio-frequency or pulsed bias sheath in a plasma discharge is presented. The analyzer is designed to sit on the electrode surface, in place of the substrate, and wide-band low pass filters allow it to float at the electrode potential. This avoids the need for modification of the electrode. The capabilities of the analyzer are demonstrated through ion energy distribution and electron energy distribution measurements at the electrode surface in an inductively coupled plasma reactor. For a sinusoidal radio-frequency driving signal applied to the electrode the analyzer is shown to resolve ions with different mass. When the radio-frequency power to the plasma pulsed the analyzer is used to resolve the ion energy distributions at different times in the pulse. The high energy tail of the electron energy distribution reaching the electrode surface is also measured. A comparison with a Langmuir probe shows exceptional agreement in the energy region where both devices overlap. Introduction The ion energy distribution (IED) and ion flux impacting a substrate during a plasma process are important parameters for determining the process outcome. The knowledge of the flux and energy of the ions is essential for process design. Apart from the IED, a knowledge of the discharge electron energy distribution function (EEDF) is also desirable since sheath models attempting to predict IED s and ion fluxes are strongly dependent on the form of the EEDF. Retarding field energy analyzers (RFEA s) have been used to measure IEDs at grounded [1 13] and driven electrodes [14 20] in rf discharges in recent decades. The RFEA has been D. Gahan, C. Hayden, M. B. Hopkins National Centre for Plasma Science and Technology, Dublin City University, Glasnevin, Dublin 9, Ireland D. Gahan, B. Dolinaj, M. B. Hopkins Impedans Ltd., Invent Centre, Dublin City University, Glasnevin, Dublin 9, Ireland E-mail: david.gahan@dcu.ie employed mostly at grounded surfaces as this simplifies the RFEA data acquisition electronics. Measurements made at rf driven electrodes are more difficult but have been achieved using techniques that allow the RFEA (and measurement electronics) to float at rf bias potential. The list of references [1 20] is by no means all inclusive but along with the references therein should serve as a useful overview of the important contributions and advances made by precedent researchers. Here, a floating RFEA design is presented for use at either a grounded or rf driven electrode in a plasma discharge. The RFEA is designed to sit on the electrode surface, in place of the substrate, and signal cabling is taken out through a reactor side port. This prevents the need for modification to the reactor configuration. The analyzer is not limited to the measurement of the time averaged IED. It is also possible to obtain the time averaged EEDF [3,21] reaching the analyzer by reversing the polarity of the different grid potentials. Time resolved IEDs in a pulsed discharge have also been made [22] using a quadrupole mass energy analyzer, gated at selected times relative to the discharge pulse. In the following sections a set of measurements are presented to show the usefulness of this floating RFEA ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim DOI: 10.1002/ppap.200931607 S643

D. Gahan, B. Dolinaj, C. Hayden, M. B. Hopkins design including (i) time averaged IED, through a radio-frequency (rf) driven sheath, with two ion species, (ii) time averaged EEDF and (iii) time resolved IED in a pulsed rf sheath. Compensated Langmuir probe measurements made in the vicinity of the RFEA are used to make comparisons where possible. Experimental Part Schematics of the experimental setup and the RFEA design are given in Figure 1. The plasma source consists of a cylindrical quartz tube (100 mm outer diameter, 150 mm long) in which the discharge was ignited. Power was coupled inductively, at 13.56 MHz, through a two turn antenna which encompasses the quartz tube. The plasma then expanded into a larger cylindrical stainless steel chamber (420 mm diameter, 290 mm long). The larger region was Figure 1. (a) Schematic of the experimental apparatus and (b) schematic of the RFEA design. closed at the end opposite the sourcewith a stainless steelend-plate where the electrode was mounted. The larger chamber contained numerous ports through which the plasma volume was easily accessed with electrical probes. The electrode was a 60 mm diameter aluminium disc mounted on a PTFE holder. The RFEA was mounted on the surface of this electrode. A wide band amplifier supplied a rf potential to the electrode, througha 0.47 pf blocking capacitor to achieve capacitive coupling. Experiments were conducted using argon and argonhelium gas mixtures. For some experiments the electrode was grounded. Current and voltage probes were mounted on the power lead of the rf biased electrode to monitor rf voltage and current waveforms at the electrode/rfea surface. [23] It was important to note at this point that the variable frequency rf bias source was not matched to the electrode-plasma impedance. The bias voltage was used to modify the electrode sheath without significantly changing the bulk plasma parameters (since no significant power was delivered to the plasma via the electrode). The benefit of this was that IED s can be compared at different bias potentials and frequencies with essentially constant plasma parameters at the sheath edge. Details of the RFEA [24] are sketched in Figure 1(b). The entrance orifice faced the plasma and allowed a sample of the ions arriving through the sheath into the RFEA for analysis. The analyzer had a cylindrical shape with a plasma facing front face of 60 mm diameter (equal to the electrode diameter) and an overall height of 3 mm. The analyzer was electrically connected to the electrode and floated at the same potential. Only one ion entrance orifice was depicted in the drawing for clarity but in reality an array of 800 mm holes, over an area of 1 cm 2, was used to maintain a measurable ion flux to the analyzer. A grid, G 1 (all grids had 18 mm holes and 50% transmission and were made from nickel), covered the plasma facing orifices from the back side, to reduce the sampling area open to the plasma, minimizing disturbance to the sheath electric field. A second grid, G 2, was used to discriminate ions, or electrons, with different energies. A potential sweep from the dc potential of G 1 (corresponding to zero retarding potential) covering the entire range of energies that the ions or electrons may have was used. At each bias step in the sweep only ions or electrons with sufficient energy to overcome the potential barrier could pass G 2 and reached the collector plate, C, which terminated the analyzer. A third grid, G 3, was biased negatively (or positively) with respect to the potential of G 1, to repel the unwanted charged species that entered the analyzer. C was biased negatively (or positively), with respect to G 3 to draw the charged species that pass G 3 towards it and to reflect any secondary electrons that were emitted from C. For each bias step applied to the discriminator the corresponding ion current to the collector was recorded. Importantly, G 2,G 3 and C were allowed to float at the electrode/ analyzer rf potential, when rf biased, to accurately measure the IED. The rf potential was capacitively coupled from the electrode/ analyzer surface (both are in electrical contact) to each grid and collector through the relatively large capacitance between them and the analyzer body. Low pass filters with high input impedance at the frequencies of interest, placed between each grid and collector and the RFEA electronics, ensured that the grids/collector maintained the electrode rf potential. These high input impedance S644 ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim DOI: 10.1002/ppap.200931607

Retarding Field Analyzer for Ion Energy Distribution... filters also prevented loading of the rf electrode and had high attenuation at the output preventing any rf voltage drop across the RFEA electronics. Results and Discussion IED at a rf Biased Electrode When ions cross a sheath driven with a rf potential variation their energies may be modulated if the ion transit time t i t i ¼ 3sðm i =2eV s Þ 1=2 (1) where m i is the ion mass, s the time averages sheath width and V s is the time averaged sheath potential, across the sheath is not significantly longer than the rf period (t rf ), in which case the ions would only respond to the time averaged sheath potential. IEDs (for a single ion species) modulated in a sinusoidal rf sheath have the well known saddle shaped structure with two peaks corresponding to the maximum and minimum sheath potential, as seen by the ions. The separation of these two peaks, with respect to the peak-to-peak rf sheath potential, is largely determined by the ratio t i /t rf (or the product vt i, where t rf ¼ 2p=v). The peak energy separation DE of the IED is defined for all values of vt i by Sobolewski et al. [25] as " DE ¼ ev pk pk 1 þ 2:25 # 2 1=2 2p vt i ; (2) where v is the bias frequency in radians. Figure 2 (top) shows a series of IEDs measured with the electrode (on which the RFEA is mounted) rf biased with 100 V pk pk at 5 MHz. The discharge is driven with rf powers between 300 and 700 W (13.56 MHz) at a pressure of 2.25 mtorr in a helium:argon gas mixture of 10:1. Two sets of peaks are clearly visible, one for the argon ions (largest in magnitude) and one for the helium ions. Two sets of peaks are seen because the two positive ion species present have different masses (40 atomic mass units (amu) for argon and 4 amu for helium). This results in two ion species having different transit times (Equation (1)) across the sheath and from Equation (2) it can be seen that this causes different DEs. The helium ions, having the lighter mass, have a greater energy spread than the argon ions. As the source power is increased the energy separation for each set of peaks increases. However, the rate of increase of DE for the helium ions is less than that for argon. The ratio of the transit times for the two ions t helium /t argon is equal to the ratio of the square root of their masses pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffi m helium m argon 0:32, determined from Equation (1). Using Langmuir probe measurements of the plasma Figure 2. IEDs in a helium-argon discharge as a function of discharge power (top) and the function described by Equation (2) showing the variation in DE for both ion species (bottom). parameters the transit time for the ions was calculated for the various power settings. Figure 2 (bottom) shows the function described by Equation (2) and the calculated vt i region for both ions. The different variations in DE are now easily understood, even though the ratio of the transit times is fixed. DE for argon is varying along a rapidly increasing region of the curve while DE for helium is varying along a region which is beginning to level off. Time Resolved IED through a Pulsed Plasma Sheath The RFEA can also be used to time resolve the IED arriving at the electrode through the sheath when the rf power to the discharge is pulsed. For this measurement the RFEA is operated at a grounded electrode. Therefore, the ion energy ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plasma-polymers.org S645

D. Gahan, B. Dolinaj, C. Hayden, M. B. Hopkins at any point of time is equivalent to the plasma potential at that time. The rf generator is pulsed with a period of 1 ms and a duty cycle of 50% i.e., the discharge power is on for 500 ms and off for the same length. The pulsing of the rf power modulates the time averaged plasma plasma potential (at the pulse frequency) and consequently the IED reaching the electrode. It is worth noting that the rf component of the plasma potential at 13.56 MHz does not affect the IED as it is small in amplitude (5Vpk pk), and has a period much shorter than the ion transit times, and so the discharge is similar to a pulsed dc discharge. The RFEA electronics are synchronized to a reference pulsed waveform taken from the rf generator. For a set discriminator potential the current to the collector is recorded at specified times during the pulse cycle enabling an IED measurement at any time during this cycle. Figure 3 shows IEDs recorded at ten evenly spaced times through one full cycle of the pulsed rf power. The 0 s position is the beginning of the on-time. The flux and mean energy of the ions increases as the pulse advances up to the end of the ontime. At the transition from on-time to off-time the IED has a double peaked structure. The high energy ions were created during the end of the on-time and the low energy ions were created at the beginning of the off-time. As the cycle advances further the mean energy and flux of the ions decreases steadily. This shows that the discharge does not completely extinguish at any point over the 500 ms offtime, often referred to as the afterglow. The time resolved RFEA is thus a useful and relatively inexpensive diagnostic for use in pulsed discharge applications e.g., reactive magnetron sputtering, where modulating the applied power has been shown to produce greater control over the processing plasma properties. [26] EEDF at a Grounded Electrode The electron energy distribution f ð"þ, at a cylindrical Langmuir probe can be written in the well known form rffiffiffiffiffiffi f ð"þ p ffiffi ¼ d2 I e 2me 2e " dv 2 e 2 ; (3) S m e where e is the electron energy, d 2 I/dV 2 the second derivative of the probe current voltage characteristic, m e the electron mass, e the electronic charge and S is the p probe area. The distribution in this form, f ð"þ= ffiffi ", is known as the electron energy probability function (EEPF). To make a direct comparison of the EEDF from probe and RFEA the EEDF from the RFEA must be determined in the same form as that given by the Langmuir probe. The electron current as a function of the retarding potential of the sheath (the sheath potential is generally a repelling potential for electrons) combined with the retarding potential applied to the RFEA discriminating grid is written as I e ðvþ ¼ A rffiffiffiffiffiffiffi T n 2e" ee exp ev r (4) m e kt e where n e is the electron density, A the total orifice area through which electrons enter the RFEA, T the combined transmission of the three grids through which the electrons must pass before being detected, " ¼ð 1 2 m eu 2 Þ=e is the average electron energy in ev and V r ¼ V p V d is the total electron retarding potential defined as the difference between the plasma potential V p (where the electrons originate) and the retarding potential applied to the discriminating grid V d. Differentiating with respect to V r gives di e ¼ en rffiffiffiffiffiffiffi ea 2e" 1 exp ev r : (5) dv r T m e kt e kt e Assuming a Maxwellian energy distribution defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 pffiffi ev f ð"þd" ¼ n e pðkt e Þ 3 " exp d": (6) kt e and substituting into (5) gives f ð"þ p ffiffi ¼ di rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e T 2m e " dv r A e 3 ; (7) p"kt e Figure 3. Time resolved IEDs at a grounded electrode in a pulsed rf argon discharge. where T ¼ 8 accounts for the loss in current due the three RFEA grid layers each with 50% transmission, A ¼ 1.9 10 5 m 2 the current collection area, kt e is the electron temperature of the EEDF reaching the RFEA. Only the high energy tail of the EEDF is detected by the RFEA due S646 ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim DOI: 10.1002/ppap.200931607

Retarding Field Analyzer for Ion Energy Distribution... to the positive sheath in front of the analyzer surface. This high energy tail of the distribution can be fitted with a Maxwellian distribution so the above assumption of a Maxwellian distribution is valid. Thus, a direct comparison can be made between the EEDF determined from the Langmuir probe using Equation (4) and that determined from the RFEA using Equation (7). A comparison is shown in Figure 4. Good qualitative and quantitative agreement is found between both sets of data. The Langmuir probe resolves the two temperature shapes of the EEDF while the RFEA resolves only the high energy tail of the distribution in the present experimental set-up. Here, the RFEA allows the EEDF to be extended over a higher energy range since the ion current does not have to be subtracted from the RFEA electron current signal as is the case for the Langmuir probe. The purpose of the measurement shown in Figure 3 is to highlight the ability of the RFEA to accurately resolve the tail of the EEDF, in the bulk plasma, at the electrode surface. At the lowest pressure a two temperature distribution is clearly visible while at the highest pressure the distribution has become almost Maxwellian. The reasons for the departure of the EEPF from Maxwellain equilibrium are discussed extensively in the literature by Godyak. [27,28] The higher energy tail present at lower pressures tends to be due to electrons that gain energy through stochastic processes, from interaction with the skin layer [27,28] electric fields in inductive discharges. As the pressure is increased the EEPF has been shown to become more Maxwellian (see Figure 10 in reference [29] for example), as seen here, due to stronger electron electron collisions. Conclusion A compact, floating RFEA design is presented that may be installed retrospectively without the need for any modification to the plasma reactor. Specially designed low pass rf filters allow the RFEA to float at the electrode potential (on which it is mouted). The design has been shown to be capable of a variety of measurements including the time averaged IED through a rf biased sheath with two ion species, time resolved energy distributions in a pulsed rf sheath, and the EEDF reaching the RFEA at a grounded electrode. These measurements show the versatility of the RFEA as a discharge diagnostic and, importantly, it measures particle properties at a surface which is paramount to many processing applications. Received: September 15, 2008; Accepted: May 4, 2009; DOI: 10.1002/ppap.200931607 Keywords: electron energy distribution; ion energy distribution; retarding field energy analyzer; rf plasma Figure 4. Comparison of EEDF measured with the Langmuir probe and the RFEA for (a)2.25 mtorr, (b) 4.5 mtorr and (c) 7.5 mtorr [1] J. W. Coburn, E. Kay, J. Appl. Phys. 1972, 43, 4965. [2] K. Kohler, J. W. Coburn, D. E. Horne, E. Kay, J. H. Keller, J. Appl. Phys. 1985, 57, 59. [3] S. G. Ingram, N. St, J. Braithwaite, J. Phys. D 1988, 21, 1496. [4] A. D. Kuypers, H. J. Hopman, J. Appl. Phys. 1988, 63, 1894. [5] J. W. Coburn, Thin Solid Films 1989, 171, 65. [6] A. D. Kuypers, H. J. Hopman, J. Appl. Phys. 1990, 67, 1229. [7] S. G. Ingram, N. S. J. Braithwaite, J. Appl. Phys. 1990, 68, 5519. [8] W. M. Holber, J. Forster, J. Vac. Sci. Technol., A 1990, 8, 3720. [9] J. Janes, C. Huth, Appl. Phys. Lett. 1992, 61, 261. [10] J. Janes, C. Huth, J. Vac. Sci. Technol., A 1992, 10, 3086. ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plasma-polymers.org S647

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