List of Figures

1. Figure 1.1 High aspect ratio anisotropic etches, showing the extraordinary capabilities of plasma processing; such etched features are used for device isolation, charge storage capacitors, channel holes, and many other purposes in integrated circuits: trench etch (0.2 m wide by 4 m deep) in single-crystal silicon, circa 2004; set of channel holes (each approximately 0.1 m in diameter by 7.5 m deep) etched into a stacked set of dielectric layers, circa 2023. Source: (a) M. A. Lieberman (Book Author). (b) Courtesy of Lam Research Corporation
2. Figure 1.2 Deposition and pattern transfer in manufacturing an integrated circuit: metal deposition; photoresist deposition; optical exposure through a pattern; photoresist development; anisotropic plasma etch; remaining photoresist removal
3. Figure 1.3 Plasma etching in integrated circuit manufacture: example of isotropic etch; sidewall etching of the resist mask leads to a loss of anisotropy in film etch; illustrating the role of bombarding ions in anisotropic etch; illustrating the role of sidewall passivating films in anisotropic etch
4. Figure 1.4 Experimental demonstration of ion-enhanced plasma etching. Source: Adapted from Coburn and Winters (1979)
5. Figure 1.5 Illustrating ion implantation of an irregular object: in a conventional ion beam implanter, the beam is electrically scanned and the target object is mechanically rotated and tilted to achieve uniform implantation; in plasma-immersion ion implantation (PIII), the target is immersed in a plasma, and ions from the plasma are implanted with a relatively uniform spatial distribution
6. Figure 1.6 Schematic view of a plasma and a discharge
7. Figure 1.7 Energy coupling between electrons and heavy particles in a low-pressure plasma
8. Figure 1.8 Space and laboratory plasmas on a versus diagram (Source: Book (1987)/Naval Research Laboratory); the electron Debye length is defined in Section 2.4
9. Figure 1.9 Densities and energies for various species in a low-pressure capacitive rf discharge
10. Figure 1.10 Electron energy distribution function in a weakly ionized discharge
11. Figure 1.11 The formation of plasma sheaths: initial ion and electron densities and potential; densities, electric field, and potential after the formation of the sheath
12. Figure 1.12 PIC simulation of positive ion sheath formation: - electron phase space, with horizontal scale in meters; electron density ; electric field ; potential ; electron number versus time in seconds; right hand potential versus time
13. Figure 1.13 Typical multi-wafer capacitive rf discharge in plane-parallel geometry, used for anisotropic etching. Source: Lieberman and Gottscho (1994)/with permission of Elsevier
14. Figure 1.14 The physical model of an rf diode. Source: Lieberman and Gottscho (1994)/with permission of Elsevier
15. Figure 1.15 Some modern capacitive discharges are used for etching and deposition; single frequency, dual frequency, and magnetically enhanced
16. Figure 1.16 Some non-capacitive, high-density discharges used for etching and deposition; planar inductive; electron cyclotron resonance; helicon
17. Figure 1.17 A dc planar magnetron discharge, used for thin film deposition
18. Figure 1.18 The central problem of discharge analysis
19. Figure 2.1 Kirchhoff's circuit laws: the total current flowing across a nonuniform one-dimensional discharge is independent of ; the sum of the currents entering a node is zero ( ); the sum of voltages around a loop is zero ()
20. Figure 2.2 PIC simulation of ion loss in a plasma containing ions only: () - ion phase space, showing the ion acceleration trajectories; () number of ion sheets versus , with the steps indicating the loss of a single sheet; () the potential versus during the first 10 s of ion loss
21. Figure 2.3 One-dimensional - phase space, illustrating the derivation of the Boltzmann equation and the change in due to collisions
22. Figure 2.4 The force density due to the pressure gradient
23. Figure 2.5 Calculation of the electron Debye length . A negatively charged sheet is introduced into a plasma containing electrons in thermal equilibrium
24. Figure 3.1 A flux of incident particles collides with a population of target particles in the half-space
25. Figure 3.2 Hard-sphere scattering
26. Figure 3.3 Definition of the differential scattering cross section
27. Figure 3.4 The relation between the scattering angles in () the laboratory system and () the center of mass (CM) system
28. Figure 3.5 Calculation of the differential scattering cross section for small-angle scattering. The center of mass trajectory is practically a straight line
29. Figure 3.6 The processes that lead to large-angle Coulomb scattering: () single large-angle event; () cumulative effect of many small-angle events
30. Figure 3.7 Polarization of an atom by a point charge
31. Figure 3.8 Scattering in the polarization potential, showing () hyperbolic and () captured orbits
32. Figure 3.9 Probability of collision for electrons in and He; the cross section is cm (Brown, 1959/MIT Press)
33. Figure 3.10 Probability of collision for electrons in Ne, Ar, Kr, and Xe, showing the Ramsauer minima for Ar, Kr, and Xe; the cross section is cm (after Brown, 1959)
34. Figure 3.11 Atomic energy levels for the central field model of an atom, showing the dependence of the energy levels on the quantum numbers and ; the energy levels are shown for sodium, without the fine structure (Thorne, 1988/Springer Nature)
35. Figure 3.12 The energy levels of the argon atom, showing () the () configurations and () details of the and configurations, with the two metastable levels shown as heavy solid lines (Edgell, 1961/Interscience Publishers)
36. Figure 3.13 Ionization, excitation, and elastic scattering cross sections for electrons in argon gas (Vahedi, 1993)
37. Figure 3.14 Illustrating the calculation of ion-atom charge transfer
38. Figure 3.15 Experimental values for elastic scattering (), charge transfer (), and the sum of the two mechanisms () for (a) helium, (b) neon, and (c) argon ions in their parent gases (McDaniel et al., 1993/John Wiley & Sons)
39. Figure 3.16 Electron collision rate constants , , and versus in argon gas (Vahedi, 1993)
40. Figure 3.17 Collisional energy loss per electron-ion pair created versus in argon and oxygen. Source: Adapted from Gudmundsson, 2002b.
41. Figure 4.1 Charged particle gyration in a uniform magnetic field; is directed out of the page
42. Figure 4.2 Motion of electrons and ions in uniform crossed and fields
43. Figure 4.3 Plasma oscillations in a slab geometry: () displacement of electron cloud with respect to ion cloud; () calculation of the resulting electric field
44. Figure 4.4 Rf current and electric field amplitudes and phases in the sheath and plasma regions of an rf discharge
45. Figure 4.5 Dispersion versus for electromagnetic and electrostatic electron plasma waves in an unmagnetized plasma
46. Figure 4.6 Calculation of the parallel force due to a magnetic field gradient
47. Figure 4.7 Calculation of the curvature drift due to a magnetic field gradient
48. Figure 4.8 Calculation of the perpendicular gradient drift due to a magnetic field gradient : () the magnetic field lines; () the motion viewed in the - plane
49. Figure 4.9 Dispersion versus for the principal waves in a magnetized plasma with immobile ions for
50. Figure 4.10 Dispersion versus for the principal waves in a magnetized plasma with mobile ions
51. Figure 4.11 The CMA diagram for waves in a magnetized plasma. The cutoffs and resonances are indicated by the lines labeled and , respectively, where denotes the phase velocity and the subscripts label the principal waves. Source: Allis et al., 1963/MIT Press
52. Figure 4.12 A microwave interferometer for plasma density measurement
53. Figure 4.13 Mean electron density versus incident power at the midplane of an rf inductive discharge as measured by a microwave interferometer, compared with ion density as measured by a Langmuir probe. Source: Hopwood et al., 1993b/American Vacuum Society
54. Figure 4.14 Design of () dc or grounded and () floating hairpin resonator probes. Source: Piejak et al. (2005). © IOP Publishing. Reproduced with permission. All rights reserved. https://doi.org/10.1088/0963-0252/14/4/012
55. Figure 4.15 Electron density versus absorbed power in a 10 mTorr argon discharge. Data from 443 MHz cavity resonance (circles), 506 MHz cavity resonance (squares), and Langmuir probe (triangles). Source: Moroney et al., 1989/with permission of AIP Publishing
56. Figure 5.1...