200 7. 5. 2

1. Plasma Processing (EECE654) Substitute Lecture Low-Pressure Capacitive RF Discharges 2007. 5. 2 Hyun-Chul Kim* • Many slides in this lecture are based on • Prof. Lieberman’s Presentation Material • (http://www.eecs.berkeley.edu/~lieber/#talks). * mindgame.kim@gmail.com

2. Plasma Reactors for Plasma Processing

3. Plasma Processing for Semiconductor Device Fabrication • Integrated Circuit Cross Section There are up to 10 layers, mostly interconnects (metal + dielectric).

4. Typical Processing Discharges • Capacitive Discharges • (L&L Chap. 11) • Inductive Discharges • (L&L Chap. 12) ions, radicals, electrons, photons • Wave-Heated Discharges • (L&L Chap. 13)

5. Evolution of Etching Discharges 1st Generation 2nd Generation

6. Evolution of Etching Discharges (Cont’d) 3rd Generation

7. Inductive vs. Capacitive RF Discharges • Capacitive Discharges • Inductive Discharges • High plasma density • Independent control of the ion/radical fluxes (through the source power) and the ion-bombarding energy (through the substrate electrode power) • Hardware Simplicity  Low cost • Robust uniformity over large area • Control of dissociation (F-atoms)

8. + + + + – – – – – – – – Dual-Frequency CCP Reactor • Drawbacks of single-frequency (SF) capacitively coupled plasma (CCP) ~ • Low density  Low etch rate • No independent control of ion flux and bombardment energy + + Sheath + + Bulk Plasma Substrate Sheath + Dual-Frequency (DF) CCP → Critical application for dielectric etch ~ ions

9. Electron Heating Mechanisms

10. Discharge Sustainment • Electron generation mechanisms • Electron-impact ionization in the volume • - ionization collisions between electrons and the background gas probabilistic event - - + - • Secondary electron emission (SEE) on a surface • - particle (ions, electrons) impact to a material probabilistic event + + - + • Another emission mechanisms: thermionic emission, photo emission, field emission, explosive emission, and so on.

11. Energy Transfer from External Energy Source to Plasma • (a) Inductively Coupled (or H-Type) Plasma • Sustained by the solenoidal (directed along the plasma boundary) electric field induced by a time-varying magnetic field • Electrodeless • (b, c) Capacitively Coupled (or E-Type) Plasma • Sustained by longitudinal (directed perpendicular to the boundary) electric field • (b) Voltage applied to electrodes in contact with plasma • (c) Electrodes insulated from plasma (electrodeless) [Ref] Y.P. Raizer, Gas Discharge Physics, Springer-Verlag, Berlin (1991)

12. Electron Heating Mechanisms • How is the field energy converted to electron thermal energy? • Ohmic Heating (collisional heating) – capacitive, inductive discharges • Heating by energy gain from the electric field between collisions with neutrals • Dominant in the bulk at high pressure • Stochastic Heating (collisionless heating) – capacitive, inductive discharges • Heating by interaction with oscillating sheaths • Dominant in the sheath at low pressure • Resonant Wave-Particle Interaction Heating- electron cyclotron resonance and helicon discharges

13. Ohmic Heating in RF E-fields • The motion of an electron in Oscillating Fields ( ) • Free oscillations (the motion of a single electron without collisions) - • An electron has a coherent velocity of motion that lags the phase of the electric field force by 90°. → No electron heating on the average. • In the presence of collisions: breaking the phase-coherent motion - • Electron collisions with other particles destroy the phase coherence of the motion (phase randomization), leading to a net transfer of power. • The field does work on overcoming the friction due to collisions of the electron.

14. Stochastic Heating (Collisionless Heating) • A spatially nonuniform electric field by itself might lead to electron heating, even in the absence of interparticle collision, provided that the electrons have thermal velocities sufficient to sample the field inhomogeneity. - In the nonlocal regime, the time-varying field seen by an individual thermal electron is nonperiodic. The electron loses phase coherence with the field, resulting in stochastic interaction with the field and collisionless heating. • Stochastic heating in Capacitive discharges • Stochastic heating mechanism in CCPs - Fermi acceleration* • “Hard wall” model for stochastic heating (after Godyak) - An electron’s interaction with sheath potential barrier is approximated as a test particle colliding elastically with a moving wall. * M.A. Lieberman and V.A. Godyak, IEEE Trans. Plasma Sci. 26, 955 (1998)

15. Fermi Acceleration

16. Stochastic Heating for Homogeneous Model , H

17. Stochastic Heating for Inhomogeneous Model H [Ref] E. Kawamura et al., Phys. Plasmas 13, 053506 (2006)

18. Experimental Evidence for Stochastic Heating

19. Analytic Model for Capacitive Discharges L&L Chap. 11.1

20. + + + + – – – – – – – – Animation from Fluid Simulation Result + + Sheath + Potential + Bulk Plasma Sheath Substrate + X direction ~ Density of : Electron and Ion • 1D RF Voltage-Driven System

21. Chap. 11.1 Homogeneous Model Matrix sheath • This is “unrealistic” model but gives a considerable insight into the qualitative behavior of “real” capacitive discharges.

22. Chap. 11. 1 Homogeneous Model

23. Chap. 11. 1 Homogeneous Model

24. Chap. 11. 1 Homogeneous Model • Spatial potential distribution as a function of rf phase

25. Chap. 11. 1 Homogeneous Model • Analysis of Discharge Equilibrium Production due to ionization = Loss to the walls Power in = Power out • Summary

26. Chap. 11. 1 Inhomogeneous Model Child Law sheath

27. Nonlocal Electron Kinetics

28. EEDF in the local regime ( ) • : Equilibrium with the local electric field • EEDF in the nonlocal regime ( ) • : Non-equilibrium with the local electric field • : Spatially uniform distribution of total energy of electrons Local or NonLocal Election Kinetics Ionization rate Power Distance • At high pressures, the EEDF at a given point depends only on local conditions at that point. Power Ionization rate Distance • At low pressures, the EEDF as a function of total energy does not explicitly depends on the spatial position. • Nonlocal electron kinetics is taken into account in • 1. Kinetic Theory (L&L Chap. 18) (but not in Fluid Theory) • 2. Particle Simulation

29. Nonlocal Electron Kinetics in CCPs (I) • Nonlocal concept was Bernstein and Holstein (1950’s) and has been much developed by Tsendin. Sheath Bulk • The slow electrons with are trapped inside the bulk by the potential well formed by the ambipolar potential. • The accessible volume of the electrons depends on their energies. • The EDF of trapped electrons is a function of the total energy only and does not depend explicitly on the coordinates. The whole available discharge volume contributes to the EDF formation. • The fast electrons with can reach the sheath where the rf field is large and thus much more effectively heated. [Ref] V.I. Kolobov et al., IEEE Trans. Plasma Sci., 23, 503 (1995)

30. Nonlocal Electron Kinetics in CCPs (II) • In the typical condition of low-pressure rf discharges, EEDF is in nonlocal regime.

31. Nonlocal Electron Kinetics in CCPs (III) • Investigation of EEDF shape • Calculation of 1D spatially averaged kinetic model (nonlocal approximation) • hom. field: spatially homogeneous rf field without sheath heating (only Ramsauer effect) •  = 0 : spatially inhomogeneous rf field without stochastic heating • > 0 : spatially inhomogeneous rf field with stochastic heating • As the spatial inhomogeneity of the rf field increases, high-energy electrons are more heated than low-energy electrons and hence EEDF becomes bi-Maxwellian. • Comparison of measured and calculated EDFs for argon at 68.4 mTorr • The concave EDFs can be due to a combination of various effects – the sheath heating, the spatially inhomogenous field, and the Ramsauer effect. Ref: V.A. Godyak et al., Phys. Rev. Lett. 65, 996 (1990) I.D. Kaganovich et al., IEEE Trans. Plasma Sci., 20, 66 (1992) U. Buddemeier, Appl. Phys. Lett. 67, 191 (1995)

32. Nonlocal Electron Kinetics in CCPs (IV) • Investigation of spatial profile of Te from EEDF measurement p = 0.3 Torr p = 0.03 Torr Measured at x = 0.0 (solid), 7.5, 13.4, 19.6, 22.5 mm Measure at x = 0.0 (solid), 13.4, 25, 28.7 mm • The spatially resolved EDF of kinetic energy is found by a simple truncation from the EDF of total energy. [Ref] V.A. Godyak et al., Appl. Phys. Lett. 63, 3138 (1993)

33. Transition in Capacitively Coupled Plasma • V.A. Godyak et al., “Abnormally low electron energy and heating mode transition in a low-pressure argon RF discharge at 13.56 MHz”, Phys. Rev. Lett. 65, 996 (1990). Pressure (Torr) • Godyak’s interpretation: Low-energy group at low pressures is attributed to the combined effect of the stochastic heating and the Ramsauer minimum of argon. • Kaganovich’s interpretation*: the strongly inhomogeneous rf field together with the effects of nonlocality can lead to strong low-energy group, even without accounting for the stochastic heating. (local at high pres. → nonlocal at low pres.) * I.D. Kaganovich and L.D. Tsendin, IEEE Trans. Plasma Sci. 20, 66 (1992).

34. Plasma Conductivity • Ohm’s Law in local regime (where fluid theory is based) • Classical Definition of Conductivity (Maxwellian EEDF) : Collision Freq. for Momentum Transfer • Conductivity for a non-Maxwellian EEDF given by kinetic theory

35. Nonlocal Conductivity • Current Density in the non-local limit for a non-Maxwellian EEDF • (Kinetic Theory) • Under the nonlocality condition, generalized ohm’s law with two effective frequencies can be considered. 1. Shape of EEDF (non-Maxwellian) or Dependence of Collision Freq. on Energy 2. Non-Locality or Collisionless Heating 1 2

36. Plasma Properties • Plasma Resistivity, Plasma Reactance, and Power Density

37. Various Frequencies in SF/DF CCPs • At the discharge center

38. Benchmark of PIC Simulation in CCPs • Our PIC/MCC Simulation Result • Our PIC/MCC simulation result agrees well with Dr. Godyak’s experimental result (Godyak et al, Phys. Rev. Lett. 65, 996 (1990)). [Refs] H.C Kim et al., Jpn. J. Appl. Phys. 44, 1957 (2005); H.C. Kim et al., J. Phys. D: Appl. Phys. 38, R283 (2005)

39. PIC vs. Fluid Models (I) • In PIC simulation result, as the gas pressure decreases, electrons are localized in the discharge center. • Meanwhile, no change in the spatial profile of electron density is found in fluid simulation since the nonlocal electron kinetics is not incorporated in swarm distribution. • The larger plasma potential in fluid simulation result can lead to the overestimation of ion energy on the substrate.

40. PIC vs. Fluid Models (II) • In PIC simulation result, as the gas pressure decreases, the spatial profile of electron temperature changes significantly. (It is associated with the change of the EEDF shape from Druyvesteyn to bi-Maxwellian type under nonlocal conditions.*) • In fluid simulations, the spatial profile of electron temperature does not change much since the shape of swarm EEDF is not so sensitive to the reduced field. * V.A. Godyak and R.B. Piejak, Appl. Phys. Lett. 63, 3137 (1993).

41. PIC vs. Fluid Models (III) • In PIC simulation results, as the gas pressure decreases, the electron power deposition in the bulk changes from positive to negative value. • In fluid simulations, as the gas pressure decreases, the Ohmic heating decreases but the transition from positive to negative power deposition is not observed.

42. Summary for PIC vs. Fluid Models • PIC simulations have been compared with fluid simulations under the gas pressures of 100 mTorr and 50 mTorr. • For two different pressures, the significant difference in the spatial profiles of electron density and electron temperature as well as EEDF transition and negative power deposition was found in PIC simulations but not in fluid simulations. • These discrepancies mean that fluid model is not sufficiently reliable in low-pressure capacitive rf discharges where the effect of the nonlocal electron kinetics is considerable.