COMPUTATIONAL INVESTIGATION OF DUAL-FREQUENCY POWER TRANSFER IN CAPACITIVELY COUPLED PLASMAS* Yiting Zhang and Mark J.

1. COMPUTATIONAL INVESTIGATION OF DUAL-FREQUENCY POWER TRANSFER IN CAPACITIVELY COUPLED PLASMAS* YitingZhangand Mark J. Kushner Department of Electrical and Computer Engineering, University of Michigan, Ann Arbor, 48109 (yitingz@umich.edu, mjkush@umich.edu) Sang Ki Nam and SaravanapriyanSriranman Lam Research Corp., Fremont, CA 94538 (SangKi.Nam@lamresearch.com, Saravanapriyan.Sriraman@lamresearch.com) June 17, 2013 * Work supported by Semiconductor Research Cooperation, National Science Foundation and the DOE Office of Fusion Energy Sciences.

2. University of Michigan Institute for Plasma Science & Engr. AGENDA • Dual frequency Capacitively Coupled Plasma (CCPs) and Ion Energy Angular Distributions (IEADs) • Description of the model • IEADs and plasma properties for dual-frequency Ar plasma • Voltage control vs. power control • Ratio of dual frequencies • Phase shift • Concluding remarks ICOPS_2013

3. University of Michigan Institute for Plasma Science & Engr. DUAL FREQUENCY CCP SOURCES • Dual frequency capacitively coupled discharges (CCPs) are widely used for etching and deposition in the microelectronics industry. • High frequencies produce higher electron densities at moderate sheath voltage and higher ion fluxes with moderate ion energies. • Low frequencies contribute to the quasi-independent control of the ion flux and energy. • Coupling between the dual frequencies may interfere with independent control of plasma density, ion energy and produce non-uniformities. • LAMRC 2300 Flex dielectric etch tool  A. Perret, Appl. Phys.Lett 86 (2005) ICOPS_2013

4. University of Michigan Institute for Plasma Science & Engr. ION ENERGY AND ANGULAR DISTRIBUTIONS (IEAD) • Control of the ion energy and angular distribution (IEAD) incident onto the substrate is necessary for improving plasma processes. • A narrow angle, vertically oriented IEAD is necessary for anisotropic processing. • Edge effects which perturb the sheath often produce slanted IEADs. • Ion velocity trajectories measured by LIF (Jacobs et al.) • S.-B. Wang and A.E. Wendt, JAP • B. Jacobs, PhD Dissertation ICOPS_2013

5. University of Michigan Institute for Plasma Science & Engr. CONTROL OF IEADs • As the size of transistors shrink, the critical dimension requirements of semiconductor fabrication become more stringent, and therefore more precise control of IEADs becomes important. • This computational investigation addresses plasma dynamics and control of IEADs onto wafers in dual frequency CCPs. • Controlling the voltage, power and phase difference between dual-frequencies to customize IEADs will be discussed. • SEM of a high aspect ratio profile ICOPS_2013

6. University of Michigan Institute for Plasma Science & Engr. HYBRID PLASMA EQUIPMENT MODEL (HPEM) EETM FKM PCMCM Monte Carlo Simulation f(ε) or Electron Energy Equation Se(r) Continuity, Momentum, Energy, Poisson equation Monte Carlo Module N(r) Es(r) • Electron Energy Transport Module（EETM): • Electron Monte Carlo Simulation provides EEDs of bulk electrons. • Separate MCS used for secondary, sheath accelerated electrons. • Fluid Kinetics Module (FKM): • Heavy particle and electron continuity, momentum, energy and Poisson’s equations. • Plasma Chemistry Monte Carlo Module (PCMCM): • IEADs in bulk, pre-sheath, sheath, and wafers. • Recorded phase, submesh resolution. ICOPS_2013

7. University of Michigan Institute for Plasma Science & Engr. REACTOR GEOMETRY • Capacitively coupled plasma with multi-frequency rf biases on bottom electrode. • 2D, cylindrically symmetric. • Ar plasma: Ar, Ar(1s2,3,4,5), Ar(4p), Ar+, e • Base case conditions: • Ar, 30 mTorr, 1000 sccm • Voltage Control (VC): • 2 MHz, 300 V; 60 MHz, 300 V • Power Control (PC): • 2 MHz, 300 W; 60 MHz, 300 W • (Note: Y:X = 2:1) • Real geometry aspect ratio ICOPS_2013

8. University of Michigan Institute for Plasma Science & Engr. MINMAX ELECTRON DENSITY, TEMPERATURE • VC: 300 V, 2 MHz; 300 V, 60 MHz • PC: 300 W, 2 MHz; 300 W, 60 MHz • HF mainly contributes to ionization, and thus the current generated by HF is larger than the LF current. • With voltage control, larger HF power (2926 W total) generates higher ne. With power control, relatively low HF (51 V) due to higher efficiency of electron heating generates lower electron density. • Uniformity increases with higher ionization. • Ar, 30 mTorr, 1000 sccm ICOPS_2013

9. Ar+ IEAD FROM BULK TO SHEATH University of Michigan Institute for Plasma Science & Engr. MINMAX • VC :300 V, 2 MHz; 300 V, 60 MHz • The lower ne with PC produces a thicker time averaged sheath thickness. • Longer ion transit time in thick sheath makes the IED curve smoother and lower in energy. DC bias -256 V • PC :300 W, 2 MHz, 300 W 60 MHz • IED on wafer DC bias -123 V ICOPS_2013 ICOPS_2013

10. University of Michigan Institute for Plasma Science & Engr. MINMAX HIGH FREQUENCY VOLTAGE • The plasma impedance changes little, total power increases with VHF2. • With higher HF voltage, plasma density increases significantly. • Higher power correlates with better uniformity. • Ar, 30 mTorr, 1000 sccm ICOPS_2013

11. University of Michigan Institute for Plasma Science & Engr. MINMAX HIGH FREQUENCY VOLTAGE • Changing HF/LF voltage ratio will strongly affect the IEADs. With higher HF, self generated DC bias becomes more negative, and the total IEAD shifts to higher level due to higher sheath potential during anodic LF cycle. • Broadening in high energy peaks due more HF modulation. The energy width is almost independent of HF amplitude. DC bias - 256 V DC bias - 355 V DC bias - 459 V • Ar, 30 mTorr, 1000 sccm ICOPS_2013

12. University of Michigan Institute for Plasma Science & Engr. MINMAX LOW FREQUENCY VOLTAGE • Increasing LF (300 V to 600 V) has little effect on ne and Tesince electron heating scales with 2. • Majority of additional power results in ion acceleration. • Ar, 30 mTorr, 1000 sccm ICOPS_2013

13. University of Michigan Institute for Plasma Science & Engr. MINMAX LOW FREQUENCY VOLTAGE • Increasing LF voltage shapes IED (e.g., ΔE) with little change in plasma properties. • During the cathodic LF cycle, increase in sheath potential accelerates ions to higher energy. • During anodic LF cycle, sheath potential is dominated by HF which is unchanged – and so modulation of IED persists. - 371 V, DC - 307 V, DC - 256 V, DC • Ar, 30 mTorr, 1000 sccm ICOPS_2013

14. HIGH FREQ POWER University of Michigan Institute for Plasma Science & Engr. • With increase in HF power 300 W to 900 W, HF voltage changes by only 30 V. • Amplitude is always small compared to LF, and so width of IEAD does not significantly change. • Increase in ne with power reduces sheath width which then modulates IEAD at HF. • Ar, 30 mTorr, 1000 sccm MINMAX ICOPS_2013

15. LOW FREQ POWER University of Michigan Institute for Plasma Science & Engr. • The plasma density and uniformity change little with LF power. • At low frequency, LF voltage increases nearly linear with power. • The LF power is mainly deposited into sheath – the width of IED increases with LF power. • Ar, 30 mTorr, 1000 sccm MINMAX ICOPS_2013

16. MINMAX IED DEPENDENCE ON ΔPHASE • Energy of HF modulated peaks in IED depend on relative phase between LF and HF. • Shift of energy of peaks depends on value of high frequency due in part to change in sheath thickness. • Ar, 30 mTorr, 1000 sccm ICOPS_2013

17. SHEATH vsΔPHASE 300V 2 MHz 300V 60 MHz • Phase difference between LF and HF modulates sheath potential and electron dynamics during rf period. • The sheath thickness (scales with [e]-1/2 ) is larger in cathodic LF cycle, and so brings about less modulation in high energy peak of IED. • By dynamically controlling phase difference, a smooth time averaged IED can be produce without HF modulation. • Ar, 30 mTorr, 1000 sccm ICOPS_2013

18. University of Michigan Institute for Plasma Science & Engr. CONCLUDING REMARKS • For dual frequency CCPs sustained in Ar plasma, • With higher frequency , the current generated by HF is greater than the LF current. • Increasing HF voltage will increase the plasma density as well as shift the total IEADs to higher energies. • Increasing LF voltage will mainly deposit power within sheath, and therefore extend the IEAD energy width with little change in composition of fluxes. • Changing phase between HF and LF in high density, thin sheath plasma will modify time averaged IEADs significantly. • With knowledge of the relationship between IEADs and settings of dual frequency rf biases, precise customization and control of IEADs can be achieved. ICOPS_2013