Vacuum Basics: a NEATEC Course Module for Semiconductor Manufacturing

Vacuum Basics: A NEATEC Course Module for Semiconductor Manufacturing

Preface and Disclaimer

This is a special vacuum course made by Plasmetrex for The Northeast Advanced Technological Education Center (NEATEC). The majority of applications of vacuum technology here are for semiconductor manufacturing and related plasma processes. So semiconductor and plasma applications are an important outcome of the provided knowledge.

For additional and deeper knowledge refer to the Advanced Vacuum course.

NEATEC, the publisher, understands that the information in this document is accurate. It has been carefully reviewed for technical accuracy. In the event that technical or typographical errors exist, NEATEC reserves the right to make changes to subsequent editions of this document without prior notice to the holders of this edition. The reader should consult the publisher if errors are suspected. In no event shall the publisher be liable for any damages arising out of or related to this document or the information contained in it.

All rights reserved (including those of translation into other languages) by NEATEC, except content marked by an explicit, differing copyright statement. No part of this document may be reproduced in any form - by photo printing, micro-films, or any other means - nor transmitted or translated into machine language without written permission from the publisher. Registered names, trademarks, etc., used here, even when not specifically marked as such, are not to be considered unprotected by law.

This project is sponsored in part by the National Science Foundation under ATE Grant #1555699. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect those of the National Science Foundation.

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$ 'C2 S '032 % Symbol Unit Value A cm 2 Wafer surface B G Magnetic field C F Capacitance CE F Capacitance of electrode sheath C(W, gap, s, …) F Capacitance (of wall, gap, sheath, …) D m2 / s Diffusion constant d cm Length of bulk plasma G d cm Skin depth E V / m Electrical field Ea eV Activation energy E+ eV Incident ion energy e C Elementary charge F N Electrostatic force FL N Lorentz force f Hz Frequency -1 fRF = ɓRF / 2 p s Generator frequency ΦΛ,0 V Potential at liner surface G N Weight hgap cm Distance between wafer and chuck Iis,L A Ion saturation current at liner lL A Mean conduction current at liner kB J / K Boltzmann constant G ke,i S / m Electrical conductivity L or l (PartIV) cm Electrode gap l cm Plasma length l ~ L cm Effective plasma length Lbulk H Inductance of the bulk

Lcoil H Inductance of the coil mm Mean free path λ+ mm Mean free path of ions G le mm Mean free path of electrons λ D mm Debye length

Symbol Unit Value me kg Electron mass mi kg Ion mass Mr - Relative mass of molecule mt kg Target mass G N - Number of gas particle -3 nreactive cm Concentration of reactants n cm -3 Collision rate -3 n- cm Density of negative ions -3 n+ cm Density of positive ions -3 ne cm Density of electrons -3 nn cm Density of neutrals P Pa (Torr) Pressure G r g / cm 3 Mass density P W Power PRF W RF Power Pbulk W Electron power (bulk power) R nm / min Etch rate RL nm / min Etch rate for layer RM nm / min Etch rate for mask rLe mm Larmor or cyclotron radius R W Resistance Rbulk W Resistance of the bulk RE W Resistance of the electrode sheath Rw W Resistance of the wall sheath S cm Sheath thickness S atom / ion Sputter yield S - Selectivity ε As / Vm Permittivity G ɍ mm 2 Cross section kBTe eV Electron temperature Tgas K ( ¶C) Gas temperature Tn K ( ¶C) Gas (neutrals) temperature

Symbol Unit Value

Tb K ( ¶C) Boiling point Tn K ( ¶C) Gas (neutrals) temperature Ts K ( ¶C) Sublimation temperature TW K ( ¶C) Wafer temperature U V Voltage Ubulk V Voltage of bulk U(gap,bulk,s,bias,…) V Voltage (gap, bulk, sheath, bias, …) Uelectrode V Voltage of electrode sheath Uf V Floating potential Urf V Voltage of generator UP = Û V Peak voltage Usheath V Voltage of sheath UT V Electron temperature Uwall V Voltage of wall sheath Uo eV Binding energy U s-1 Collision rate -1 ueff s Effective collision rate v m / s Mean velocity of reactants ve m / s Velocity of electrons ɓ = 2p f s-1 Circular frequency -1 ɓce s Electron cyclotron frequency -1 ɓp+ s Ion plasma frequency -1 ɓpe s Electron plasma frequency 3 Vchamber cm Chamber volume x - Degree of ionization

Proportional to: ∝ In order off: ∼ Approximate: ≈ SI Units Fundamentals units

Quantity Unit Abbreviation Mass kilogram kg Length meter m Time second s Temperature Kelvin K Electrical current ampere A Amount of substance mole mol

Selected derived units

Quantity Unit Abbreviation Frequency Hertz Hz Force Newton N Energy Joule J = Ws = Nm Power Watt W Electrical charge Coulomb C = As Electric potential Volt V Electrical resistance Ohm ΩG Capacitance Farad F = As/V Inductance Henry H = Vs/A Magnetic flux density Tesla T = 10000 G G Range of parameter for RF discharge

Parameter Range Pressure P 1 - 1000 Pa (10 – 10000 mTorr) Power P 50 - 2000 W Frequency F 50 kHz - 100 MHz Volume V 1 - 200 l Electrode area A 300 - 60000 cm 2 Magnetic field B 0 - 100 G G Plasma density N 10 9 - 10 11 cm -3G Electron temperature Te 1 - 6 V G Ion energy ei 20 - 2000 V -6 -3 Fractional ionization xiz 10 – 10 G Physical constants Quantity Symbol Value Units Speed of light c 299 792 458 m / s (in vacuum) -6 Vacuum permeability Ɇ0 1.26 Ý 10 H / m Vacuum permittivity e0 8.85 Ý 10 -12 As / Vm

Boltzmann constant kB 1.38 Ý 10 -23 Ws / K Elementary charge e 1.60 Ý 10 -19 As

Electron mass me 9.11 Ý 10 -31 kg Atomic mass unit u 1.67 Ý 10 -27 kg G