Control of Ion Energy Distributions on Plasma Electrodes

Control of Ion Energy Distributions on Plasma Electrodes P. Diomede, D. J. Economou and V. M. Donnelly Plasma Processing Laboratory, University of Houston DOE Plasma Science Center Teleseminar, February 8, 2013 1

Outline Introduction/Motivation 3 Methods to control IEDs on plasma electrodes PIC MCC simulations and comparisons with experiments Model for rapid calculation of IED and comparisons with experiments Conclusions 2

Introduction / Motivation Control of the energy of ions bombarding a substrate is important for both plasma etching and PECVD. The ion energy must be high enough to drive anisotropic etching, but not too high to induce substrate damage and/or loss of selectivity. As device dimensions keep shrinking, requirements on selectivity and substrate damage become ever more stringent. In addition, the ion bombardment energy is critical for controlling film microstructure and properties in PECVD. Such requirements impose strict limits not only on the mean ion energy but also on the ion energy distribution (IED). 3

IED on an electrode biased with sinusoidal RF voltage τ τ i rf = 3sω M ( ) 2π 2eV s 1/ 2 τ i /τ rf <<1 wide (bimodal) IED τ i /τ rf >>1 narrow (single peaked) IED τ i = ion transit time through sheath τ rf = period of the rf sheath E field =2π/ω 4

IED for Sinusoidal Sheath Voltage IEDs on the grounded electrode of a 13.56 MHz Ar CCP at 75 mtorr. Peak separation is reduced for heavier ions. Single peak is centered at the DC sheath voltage. Impurity ions are used to avoid charge transfer collisions. 1 IEDs on the grounded electrode of an Ar CCP at 50 mtorr. A single peak is obtained at high enough frequencies. 2 1. J. Coburn and E. Kay, J. Appl. Phys., 43, 4965 (1972). 2. K. Kohler et al., J. Appl. Phys., 58, 3350 (1985). 5

Three principal ways to control IEDs 1. Plasma is generated by independent source power. Apply judicious bias voltage waveform on the substrate electrode immersed in the plasma. The substrate bias has minor effects on the plasma chemistry. The energy of ions is determined by the substrate voltage. The voltage appearing on the face of the substrate is at a constant negative value (V front ), except for small excursions to positive values to neutralize the charge. M. A. Wank, R. A. C. M. M. van Swaaij, P. Kudlacek, M. C. M. van de Sanden, and M. Zeman, J. Appl. Phys. 108, 103304 (2010) 6

Effect of non sinusoidal bias waveforms on IEDs Computational investigation by Agarwal and Kushner using an ICP reactor scale model. This voltage waveform on the substrate is positive during α=10% of the cycle. 15 mtorr Ar/c C 4 F 8 =75/25 gas mixture. 500 MHz TVW frequency A. Agarwal and M. J. Kushner, J. Vac. Sci. Technol. A 23, 1440 (2005) 7

Three principal ways to control IEDs 2. Produce the plasma with customized voltage waveforms. The Electrical Asymmetry Effect The Electrical Asymmetry Effect (EAE) provides a new method to control the ion energy distribution (IED) on plasma electrodes. Importantly, the ion flux can also be controlled, independently of the ion energy. V ( t) = U cos(2π f t + θ ) + U cos(2πf 2 A voltage of the form 1 1 2 is applied to an electrode of a capacitively coupled plasma (CCP) reactor, with f 2 =2f 1. The DC bias (thus the ion energy) can be varied simply by changing the phase θ 1. 1 t ) Adding higher harmonics enhances the EAE, but implementation becomes cumbersome. A DC bias can be imposed even on a geometrically symmetric system (equal electrode areas). 8

Control of ion energy distributions using the electrical asymmetry effect Measured ion energy distribution functions in a geometrically and electrically asymmetric discharge at the powered (left) and grounded (right) electrode (Argon, 1 Pa, d = 4 cm, U 1 = U 2 = 100 V, f 1 = 13.56 MHz, f 2 = 27.12 MHz). V ( t) = U cos(2π f1t + θ1) + U 2 cos(2πf 2 1 t ) U. Czarnetzki, J. Schulze, E. Schüngel and Z. Donkó, PSST, 20, 024010 (2011) 9

Independent Control of Ion Flux and Ion Energy V ( t) = U cos(2π f1t + θ1) + U 2 cos(2πf 2 1 t Mean ion energy and ion flux as a function of θ 1 in an argon CCP discharge. 7.5 mtorr, U 1 =U 2 =100 V, f 1 =13.56, f 2 = 2f 1. As the phase shift θ 1 is varied, ion energy varies but ion flux remains almost constant. ) U. Czarnetzki, J. Schulze, E. Schüngel and Z. Donkó, PSST, 20, 024010 (2011) 10

Gaussian Voltage Pulses Gaussian voltage pulses (repetition frequency of 13.56 MHz) of the form 2 V( t ) = V0exp[ a( t t 0 ) ] τ = 2 ln 2/ a V 0 = voltage amplitude t 0 = time of pulse max, τ = FWHM IED depends on FWHM ( τ) of applied voltage T. Lafleur and J. P. Booth, J. Phys. D: Appl. Phys., 45, 395203 (2012) 11

Three principal ways to control IEDs 3. Apply synchronous bias on boundary electrode during afterglow of pulsed plasma Boundary Electrode Boundary Voltage Plasma Power Bias ON Plasma ON OFF Substrate For a grounded conductive substrate, the sheath voltage is equal to the plasma potential. 12

T e (ev) 4.0 ON OFF 3.5 3.0 2.5 2.0 1.5 T e and V p during a pulse Time resolved Langmuir probe measurements V p (V) 16 14 12 10 8 6 1.0 0.5 0.0 0 10 20 30 40 50 60 70 80 90 100 time (µs) 4 2 0 0 10 20 30 40 50 60 70 80 90 100 time (µs) T e is hardly affected by the application of the DC bias, while V p is raised. The spread in the energy of ions entering the sheath scales with T e. 1 1. K. U. Riemann, Phys. Fluids 24 2163 (1981) 13 13

IEDs in pulsed Ar ICP with synchronous DC bias voltage applied to the boundary electrode Time-Averaged Ion Energy Distribution 0.05 0.04 0.03 0.02 Ar press. (mtorr): 7 0.01 14 50 28 0.00 0 4 8 12 16 20 24 28 32 Energy (ev) Separation of the peaks can be tuned by DC bias value and pressure. Narrow IED can be achieved in the afterglow. Full width at half maximum (FWHM) of the IED ranges from 1.7 to 2.4 ev. H. Shin, W. Zhu, L. Xu, D. J. Economou and V. M. Donnelly, PSST, 20 055001 (2011). 14

IEDs in pulsed Ar ICP with different synchronous DC bias voltages applied to the boundary electrode DC Bias applied continuously on the BE. Peak at high energy is shifted by the energy of the applied dc bias for positive biases. Low energy peak not detected by the measurements which discriminate lowenergy ions having a broad angular distribution. M. D. Logue, H. Shin, W. Zhu, L. Xu, V. M. Donnelly, D. J. Economou and M. J. Kushner, PSST, 21 065009 (2012) 15

PIC MCC Simulations Simulation of pulsed plasma with synchronous boundary voltage. Comparison with experimental data. 16

Simulation of Pulsed CCP Reactor with DC Bias in Afterglow Pulsed plasma is sustained in capacitively coupled plasma (CCP) reactor. 50 V DC bias is applied on the upper (boundary) electrode in the afterglow to modify the IED on the lower (substrate) electrode. 17

Application of DC Bias in the Afterglow of a Pulsed Plasma After plasma power turn off (afterglow), T e and V p decay rapidly. Apply synchronously tailored positive bias voltage V dc during specified time window in the afterglow. Bias raises plasma potential, modifying the IED on the wafer. 18

PIC simulation of Ar CCP: IED without Bias Ar plasma, V RF = 300 V, ν RF = 13.56 MHz, p = 10 mtorr, d = 6 cm 10 khz pulse frequency 50% duty ratio 1.2 IED for continuous wave (cw) plasma w/o bias 1.2 IED for pulsed plasma (10 khz, 50% duty cycle) w/o bias 1.0 1.0 Normalized IED 0.8 0.6 0.4 Normalized IED 0.8 0.6 0.4 0.2 0.2 0.0 0 50 100 150 200 Ion energy (ev) Bimodal distribution centered around 1/2 V RF. Tail to the left of the main peak due to ionneutral collisions. Multiple secondary peaks given by ions created by CE collisions. 0.0 0 50 100 150 200 Ion energy (ev) Bimodal IED is retained, originating from the power ON fraction of the cycle New peak appears at very low energies due to ions bombarding the substrate during the afterglow. 19

IEDs with Staircase DC Bias Applied in Afterglow Afterglow starts at time t = 50 µs. Additional peaks appear in the IED. Peak location can be controlled by the value of the applied bias voltage. 20

IEDs with Staircase DC Bias Applied in Afterglow (2) Peak strength can be controlled by the duration of the respective DC bias voltage. The relative strength of the other two peaks can be controlled by the duty ratio. P. Diomede, V. M. Donnelly and D. J. Economou, J. Appl. Phys., 109, 083302 (2011) 21

EEPF and Electron Density Evolution 3 n e (10 15 m -3 ) 2 1 0 0 10 20 30 40 50 60 70 80 90 100 Time (µs) In the afterglow of pulsed CCP, apply 50 V DC during t = 70 85 µs, followed by 300 V DC during t = 85 100 µs. EEPF is temporarily heated when the bias is applied but the electron density evolution is hardly affected. 22

Comparison of PIC Simulation with Experimental Data 0.03 50-98µs 60-98µs 70-98µs 80-98µs t = 48 µs t = 38 µs 4.4x10 11 4.0x10 11 3.6x10 11 3.2x10 11 simulation IEDF 0.02 0.01 t = 28 µs t = 18 µs Ion flux (a.u.) 2.8x10 11 2.4x10 11 2.0x10 11 1.6x10 11 1.2x10 11 8.0x10 10 4.0x10 10 0.00 0 2 4 6 8 101214161820222426283032 Energy (ev) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 IEDs predicted by the PIC simulation of the afterglow (right) compared to data # (left). The low energy peak of the data is due to the active glow (not simulated by PIC). 0.0 Energy (ev) T e (ev) 3.0 2.5 2.0 1.5 1.0 0.5 0.0 30 40 50 60 70 80 90 100 Time (µs) Electron temperature in the afterglow predicted by PIC (line), compared to data # (points). Pulsed Ar plasma, 10 KHz modulation, 20% duty, 14 mtorr, 120 W average power, 24.4 V DC bias applied in afterglow during time windows shown above. # H. Shin, W. Zhu, L. Xu, D. J. Economou and V. M. Donnelly, PSST, 20 055001 (2011). 23

Simulation of Pulsed H 2 CCP Reactor with DC Bias in Afterglow The Bari hybrid model for H 2 CCPs Neutral species: fluid model for H atoms and H 2 (v = 0, 14). Plasma kinetics: PIC/MCC applied to electrons and four ionic species (H 3+, H 2+, H +, H ). 24

Application of DC Bias in the Afterglow of a Pulsed Plasma After plasma power turn off (afterglow), T e and V p decay rapidly. Apply synchronously tailored positive bias voltage V dc during specified time window in the afterglow. Bias raises plasma potential, modifying the IED on the wafer. 25

1.2x10 15 Number densities and electron KE Evolution H + 3 mid plane of the discharge (x = 3 cm) number density (m -3 ) 1.0x10 15 8.0x10 14 6.0x10 14 4.0x10 14 2.0x10 14 Electron KE (ev) 0.0 0 10 20 30 40 50 60 70 80 90 100 6 time (µs) 5 4 3 2 1 e - H - H + 2 H + 0 0 10 20 30 40 50 60 70 80 90 100 time (µs) RF ON RF OFF DC ON Plasma ON (t=0 µs): increase approaching quasi steady state values ~ 20 µs. Plasma OFF (t=50 µs): decay throughout the afterglow. H 2+ ions disappear after 5 µs into the afterglow. Plasma ON (t=0 µs): rapidly rise to a peak early, quasi steady state ~ 10 µs. Plasma OFF (t=50 µs): plummet during the first few µs and decay at a much slower rate later in the afterglow. DC bias ON (t=70 µs): temporary heating. Hydrogen plasma V RF = 300 V, ν RF = 13.56 MHz, p = 50 mtorr d = 6 cm, 10 khz pulse, 50% duty ratio 26

IEDs for continuous wave (cw) plasma w/o bias (1) Normalized IED 1.0 0.8 0.6 0.4 0.2 simulation H + 3 Normalized IED 1.0 0.8 0.6 0.4 0.2 simulation H + 0.0 0 50 100 150 Ion energy (ev) 0.0 0 50 100 150 Ion energy (ev) experiment H 3 + Bimodal structure and tail towards lower energies due to ion neutral collisions. The H + IED bimodal structure has a wider energy spread, due to the lower mass of H +. Predicted bimodal distribution, with a more intense peak at lower energy, is close to the experimental IED for H 3+. Experiments: D. O Connell et al. Phys. Plasmas 14, 103510 (2007) H 2, V RF = 300 V, ν RF = 13.56 MHz, 50 mtorr, 6 cm 27

IEDs for continuous wave (cw) plasma w/o bias (2) H 2+ IED exhibits multiple peaks, explained by symmetric charge exchange collisions during the sheath collapse. Ions thus created experience only a fraction of amplitude of the oscillating sheath voltage. Computed H 2+ IED is in good agreement with experimental results. The energy dependence of the acceptance angle of the ion optics contributes to an artificial distortion of the IED in the low energy region. Normalized IED 1.0 simulation H 2 + 0.8 0.6 0.4 0.2 0.0 0 50 100 150 Ion energy (ev) experiment H 2 + H 2, V RF = 300 V, ν RF = 13.56 MHz, 50 mtorr, 6 cm Experiments: D. O Connell et al. Phys. Plasmas 14, 103510 (2007) 28

Computed IEDs for pulsed plasma with 50 V DC bias in the afterglow 1.0 H + 3 1.0 Normalized IED 0.8 0.6 0.4 0.2 Normalized IED 0.8 0.6 0.4 0.2 H + 2 0.0 0 50 100 150 Ion energy (ev) 0.0 0 50 100 150 Ion energy (ev) Normalized IED 1.0 0.8 0.6 0.4 0.2 H + Additional peaks appear in the H 3 + and H + IEDs. Peak location can be controlled by the value of the applied bias voltage. H 2+ disappear in the afterglow due to the rapid decay of T e. 0.0 0 50 100 150 Ion energy (ev) H 2, V RF = 300 V, ν RF = 13.56 MHz, 50 mtorr, 6 cm 10 khz pulse, 50% duty ratio 29

Model for Rapid Calculation of IED on Electrode in Contact with Plasma Bulk Plasma (n 0, T e ) Sheath Electrode (Target) Blocking capacitor, C b Applied rf, V rf Assumptions: Bulk n 0 and T e are not influenced by rf bias. Sheath is collisionless. Ion flux at sheath edge is time independent. 30

Semi-analytic Model Schematic of the sheath region 1. Electrode immersed in semi infinite plasma of given electron (ion) density and electron Electrode Sheath Pre-sheath Plasma (bulk) x I d I e I i n 0, T e temperature. 2. Electron, ion and displacement currents flow through the sheath. 3. Non linear sheath capacitance C s is calculated from the electric field at the electrode, E. C s E = ε0a V s V=V S V=V 1 V=0 2nkT e(v V ) V ε kt V 1 e s 1 s 1 2 E = [exp( ) + 2 ] / 0 e 1 A. Metze, D. W. Ernie, H. J. Oskam, J. Appl. Phys., 60, 3081 (1986). P. Miller and M. Riley, J. Appl. Phys., 82, 3689 (1997). T. Panagopoulos and D. Economou, J. Appl. Phys., 85, 3435 (1999). 31

Equivalent Circuit Model V rf C b I T V T V P C T Subscripts T and G refer to target and ground electrodes, respectively. d d C b (Vrf V T ) + C T (VP V T ) + IT = dt dt d d C T (VP V T ) + CG VP + IT + IG = 0 dt dt 0 I G C G dv dt d V = d ( V V τ T i p ) Ions respond to a damped potential V d Voltage V rf is applied through blocking capacitor, C b. Given n 0, T e, V rf and C b, calculate V T, V p, and V d. A. Metze et al., J. Appl. Phys., 60, 3081 (1986). 32

Ion Energy Distribution V d (ωt) 0 y+dy y 0 Support (y,y+dy) π dy 2π ωt f( y) f( y) = = 1 1 2π # of points in 0< ωt< 2 π dvd such that Vd ( ωt) = y d( ωt) IED V = V ( ωt) = " damped " sheath voltage d d Sample damped sheath potential waveform y = V t t = V y 1 d( ω ) ω d ( ) y = ion energy 1 f( y) = 2π # of points in 0< ωt< 2 π such that V ( ωt) = y d dv 1 d dy ( y) P. Diomede, M. Nikolaou, D. J. Economou, Plasma Sources Sci. Technol., 20, 045011 (2011). E. Kawamura, V. Vahedi, M.A. Lieberman, C.K. Birdsall, Plasma Sources Sci. Technol., 8, R45 (1999). 33

Comparison of Semi analytic Model with Experimental Data (1): Pulsed Argon Plasma with DC bias in the afterglow 1.2 1.0 experiment 1.2 1.0 model Normalized IED 0.8 0.6 0.4 Normalized IED 0.8 0.6 0.4 0.2 0.2 0.0 0.0 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Ion energy (ev) Ion energy (ev) IEDs predicted by the semi analytic model (right) compared to data # (left). V p (V) 20 15 10 5 Plasma potential w/o DC bias predicted by the semi analytic model (line), compared to data # (points). Pulsed Ar plasma, 10 KHz modulation, 20% duty, 14 mtorr, 120 W average power, 24.4 V DC bias applied in afterglow during t b = 45 95 µs. 0 0 20 40 60 80 100 Time (µs) # H. Shin, W. Zhu, L. Xu, D. J. Economou and V. M. Donnelly, PSST, 20 055001 (2011). 34

Comparison of Semi analytic Model with Experimental Data (2): Helicon plasma with bias voltage waveform on the substrate Experimental Target voltage, 500 khz, n e = 2.6 10 16 m 3, T e = 3eV X. V. Qin, Y. H. Ting, and A. E. Wendt, PSST 19 065014 (2010). Target voltage in the semi analytic model 0 (a) -100-200 -300 0 (b) -100 Voltage (V) -200-300 0 (c) -100-200 -300 0 (d) -100-200 -300 0 1 2 3 4 5 Time (µs) The simulated voltage waveforms are quite representative of the measured waveforms except for the ringing. 35

Comparison of Semi analytic Model with Experimental Data (2): Helicon plasma with bias voltage waveform on the substrate Experimental Ar + IEDs X. V. Qin, Y. H. Ting, and A. E. Wendt, PSST 19 065014 (2010). Normalized IED IEDs from the semi analytic model 1.0 0.8 (a) 0.6 0.4 0.2 0.0 1.0 0.8 (b) 0.6 0.4 0.2 0.0 1.0 0.8 (c) 0.6 0.4 0.2 0.0 1.0 (d) 0.8 0.6 0.4 0.2 0.0 0 100 200 300 400 Ion energy (ev) Predicted peak locations and heights of the IED are in agreement with the measurements. The FWHM of the experimental peaks is larger, because of the ringing of the applied voltage waveforms. 36

Comparison of Semi analytic Model with Experimental Data (3): ETP with bias voltage waveform on a dielectric substrate The substrate bias has minor effects on the plasma chemistry. The energy of ions is determined by the substrate voltage. The voltage appearing on the face of the substrate is at a constant negative value (V front ), except for small excursions to positive values to neutralize the charge. M. A. Wank, R. A. C. M. M. van Swaaij, P. Kudlacek, M. C. M. van de Sanden, and M. Zeman, J. Appl. Phys. 108, 103304 (2010) 37

Comparison of Semi analytic Model with Experimental Data (3): ETP with bias voltage waveform on a dielectric substrate Electrode downstream of expanding thermal hydrogen plasma (H 3+ ). Biased through blocking capacitor, C b = 166 pf. V p ~0.2 V, T e = 0.15 ev, p = 18 Pa, n e = 2 x 10 10 cm 3 Voltage applied to blocking cap. Voltage of substrate electrode. Top figs.: Kudlacek et al. # Bottom figs.: Semi analytic model prediction. C B = 1.66 nf, A G /A T =25 The energy peaks location and the voltage waveform on substrate electrode are predicted. # P. Kudlacek, R. F. Rumphorst and M.C.M. van de Sanden, J. Appl. Phys., 106, 073303 (2009). 38

Comparison of Semi analytic Model with Experimental Data (4): Control of IEDs using the electrical asymmetry effect Measured ion energy distribution functions in a geometrically and electrically asymmetric dual frequency discharge at the powered (left) and grounded (right) electrode (Argon, 1 Pa, d = 4 cm, U 1 = U 2 = 100 V, f 1 = 13.56 MHz, f 2 = 27.12 MHz). V ( t) = U cos(2π f1t + θ1) + U 2 cos(2πf 2 1 t ) U. Czarnetzki, J. Schulze, E. Schüngel and Z. Donkó, PSST 20, 024010 (2011) 39

Electrical Asymmetry Effect: Semi Analytic Model Prediction powered electrode 0.08 0.06 0.04 0.02 IED (a.u.) grounded electrode 0.20 0.16 0.12 0.08 0.04 IED (a.u.) 0 20 40 60 80 100 120 140 160 Ion energy (ev) 0.00 0 15 30 r ees) 45 60 θ 75 1(deg 90 0 10 20 30 40 50 Ion energy (ev) 60 75 90 0 15 30 45 0.00 θ 1(deg r ees) C b = 0.7 pf, A G = 2 A T, T e = 3 ev, n 0 = 2 x 10 15 m 3, M = 40 amu (Ar + ), f 1 = 13.56 MHz, f 2 = 27.12 MHz, U 1 = U 2 = 100 V, instrumental broadening 2 ev. 40

Concluding Remarks Several methodologies can be implemented to tailor the ion energy distribution on plasma electrodes. PIC MCC and hybrid simulations of a pulsed plasma with synchronous DC bias applied in the afterglow, showed that it is possible to tailor IEDs to have distinct energy peaks with controlled energies and fraction of ions under each peak. Simulations were in good agreement with measurements. Although PIC simulation provides detailed information (e.g., IAD in addition to IED), fast execution of semi analytic model is advantageous for initial screening of tailored voltage waveforms. Models/simulations in synergy with experiments are critical to understand and predict the behavior of plasmas and to unravel new strategies for tailoring IEDs. 41

Acknowledgements Prof. M. Nikolaou, University of Houston Dr. H. Shin, University of Houston, currently at Lam Research Corp. W. Zhu, University of Houston Prof. S. Longo, University of Bari and CNR/IMIP, Italy Prof. M. Capitelli, University of Bari and CNR/IMIP, Italy Financial Support: DoE Plasma Science Center NSF 42