Fluid Modeling of Capacitive Plasma Tools

1. Fluid Modeling of Capacitive Plasma Tools FLCC Presentation March 28, 2005 Berkeley, CA David B. Graves, Mark Nierode, and Yassine Kabouzi UC Berkeley FLCC - Plasma

2. Motivation Capacitively-coupled plasma etch tools commonly used, especially in dielectric etch Popular strategy: dual frequency operation to separate control of ion flux and plasma density (high frequency) from ion energy control (low frequency) Overall goal is to develop a 2-D, time-dependent fluid plasma model that can be used for tool design and process control studies Tool-scale model can be coupled to feature scale (e.g. Prof. Chang, UCLA) Fluid model can complement PIC/MC model (Prof. Lieberman, UCB) FLCC - Plasma

3. Today’s Talk • Fluid model of 1-D dual frequency (27 MHz, 2 MHz) Ar discharge. • Fluid model of 2-D single frequency (13.5 MHz) Ar discharge. • Fluid model of non-isothermal, reacting neutral flow in typical industrial capacitive etch tool with split inlet flows. FLCC - Plasma

4. Plasma Model Equations Equations solved via FEMLAB FLCC - Plasma

5. 27 MHz 2 MHz 0.02 m One Dimensional Dual Frequency Results Argon, p = 50 mtorr, 800 V rf @ 27 MHz, , 800 V rf @ 2 MHz applied at left electrode FLCC - Plasma

6. Potential on Powered (Left) Electrode Argon, p = 50 mtorr, 800 V rf @ 27 MHz, , 800 V rf @ 2 MHz applied at left electrode 0.5 FLCC - Plasma

7. Dual Frequency Results: Plasma Density Argon, p = 50 mtorr, 800 V rf @ 27 MHz, , 800 V rf @ 2 MHz applied at left electrode FLCC - Plasma

8. Right Sheath Structure FLCC - Plasma

9. Left Sheath Structure FLCC - Plasma

10. Electron Density in Sheaths: 27 MHz Variation Electron loss at both sheaths Electron loss at right sheath only FLCC - Plasma

11. Electric Field and Plasma Potential: 2 MHz FLCC - Plasma

12. Potentials on Powered Electrode and in Plasma FLCC - Plasma

13. Currents at Powered Electrode FLCC - Plasma

14. Electron Temperature FLCC - Plasma

15. Two-Dimensional, Axisymmetric (r,z) Single Frequency Argon, p = 50 mtorr, 80 V rf @ 13.56 MHz, applied at top electrode Powered electrode Grounded 0.025 m height 0.25 m radius Preliminary 2-D results obtained FLCC - Plasma

16. Period-Averaged Electron Density Argon, p = 50 mtorr, 80 V rf @ 13.56 MHz, applied at top electrode FLCC - Plasma

17. Period-Averaged Electron Temperature Argon, p = 50 mtorr, 80 V rf @ 13.56 MHz, applied at top electrode FLCC - Plasma

18. Period-Averaged Ion Density Argon, p = 50 mtorr, 80 V rf @ 13.56 MHz, applied at top electrode FLCC - Plasma

19. Period-Averaged Plasma Potential FLCC - Plasma

20. Neutral Reacting Flow Model Equations solved via FEMLAB FLCC - Plasma

21. Commercial tools typically feature dual flow configurations to allow for greater process control (e.g. balance fluorocarbon deposition and etching) Investigate the transport of the tuning gas and its effect on reactor chemistry 400/20/9 sccm Ar/c-C4F8/O2 | 0-100 sccm O2 Neutral Flow Configuration Pressure ~ 30 mtorr FLCC - Plasma

22. Mesh and Numerics • 3363 elements, 115106 d.o.f. • All variables use quadratic Lagrangian elements except pressure which is linear • Steady state solution obtained 1-2 hours using iteration script (FEMALB feature; eqns solved iteratively and sequentially) FLCC - Plasma

23. Chemistry Model 1. Simplistic model will assume CF as the ‘depositing’ species and F as the ‘etching’ species 2. Increased O2 flow in the outer annulus leads to increased O2 and O in the outer region 3. Increased O increases rxns 6 & 7 producing F on the same order as rxn 4 FLCC - Plasma

24. Assumed Plasma Density Assume constant Te = 3 Assume radial plasma profile flat except when r > 0.2 FLCC - Plasma

25. Neutral Temperature • Neutral gas heating is proportional to the (assumed) plasma density • ‘Jump’ temperature and ‘slip’ velocity boundary conditions • Temperature profile not affected by outer tuning flow up to 100 sccm O2 FLCC - Plasma

26. Total neutral density Pressure and Temperature Effects • Radial pressure drop is significant ~30% leading to a similar neutral number density profile (n); recall n ~ p/T • Axial pressure gradients are minimal FLCC - Plasma

27. Neutral Species Radial Profiles Qtune = 0 sccm FLCC - Plasma

28. Neutral Species Radial Profiles Qtune = 100 sccm • Note: scale different from previous slide FLCC - Plasma

29. Propose CF/F as model deposition/etch ratio index Varying the outer O2 flow (Qtune) the ratio of CF to F can be modified radially although the overall ratio of CF to F changes too Effects of Altering O2 ‘Tuning’ Gas Flow FLCC - Plasma

30. FEMLAB-based fluid modeling powerful tool to simulate complex, multi-dimensional, reacting plasma tools Tool-scale design/analysis possible Fully transient, coupled neutral-plasma versions can simulate process control Two major limitations to tool-scale fluid models: No feature profile evolution No plasma kinetic information (e.g. EEDF, IEDF, IADF) FLCC plasma project couples fluid modeling (DBG, UCB), feature evolution modeling (JC, UCLA) and PIC/MC modeling (MAL, UCB) Concluding Remarks FLCC - Plasma