Multi-Frequency Sheath Dynamics

Transcription

1 Muli-Frequency Sheah Dynamics Seven Shannon, Alex Paerson, Theodoros Panagopoulos, Daniel Hoffman, John Holland, Dennis Grimard (Universiy of Michigan)

2 Purpose of research RF plasmas wih muliple frequency drives show remendous benefi in plasma processing PECVD ools have been using dual source ( + khz) sysems for over a decade for spuering enhancemens in CVD applicaions Curren capaciive sysems use high frequency + low frequency mixing for independen conrol of sheah and bulk plasma characerisics High frequency ionizaion and dissociaion Low frequency ion bombardmen on workpiece Purpose of research Sudy a dual frequency configuraion ha is inended o ailor he sheah only, leaving he bulk ionizaion o a hird independen source Develop a simple analyical model o provide basic undersanding of dual frequency sheahs

3 3 Descripion of mehods of invesigaion Sar wih he simples RF sheah model (marix sheah, oscillaing wih applied RF curren, collisionless) Conrol elecron densiy and DC poenial Deermine RF curren for each frequency ha would generae a V DC bias Tes various curren raios (normalized o single frequency V DC operaion for each See wha happens paricularly, look a wha happens o he ion energies ha are inciden on he powered elecrode, ry differen frequencies Plasma Parameers: n e =1 1 cm -3 V dc = V 15V Ar Plasma 15 gap mm diameer symmeric discharge

4 4 Fix elecron densiy and DC sheah poenial, calculae RF curren for each frequency For each frequency, calculae he curren needed o susain a plasma wih he specified elecron densiy and DC sheah poenial: s en I rf ωa V sheah n s ε Se up he level of curren for each for each frequency wih a mixing weigh x ha defines he fracion o frequency curren: e I low x 8π := V DC ε en e Area I high ( 1 x) 8π := V DC ε en e Area

5 5 Se up he ime dependen sheah poenial based on hese curren values Esablish he ime dependen sheah hickness: I high I low s high := s low := s := s low + s high en e π Area en e π Area s ():= s low + s high + s low sin π + s high sin π Solve for Sheah Poenial DC Componen Fundamenal RF e n e V sheah () := ε s low cos 4 π 3 s low 3 + s low s high + s high s low s high + s high sin πf + high + s low + s low s high sin π s high cos 4 π f high + s low s high cos π π s low s high cos π + π Harmonic Conribuion Frequency Mixing

6 6 Frequency Componens f low f high + e n e 3 ε V s 3 low + s low s high s + high e n e s low + s low s high ε V e n e ε V s low s high + s high e n e s low ε V e n e s high ε V e n e ε V e n e ε V s low s high s low s high

7 7 IEDF calculaion weigh he ampliude of each frequency componen by a facor ωτ (Panagopoulos e al) Esimae he ransi ime of an ion across he sheah: τ i := 3s e m i V dc Weigh each componen by he ransi ime and he frequency of ha componen: e n e V ion () := ε s low cos 4 π 8 π τ i 3 s low 3 + s low s high s high s low s high + s high + + sin π π τ i s high cos 4 π 8 π τ i s low + s low s high + sin ( π ) π τ i s low s high + cos π π τ i π τ π i s low s high cos π π τ i + π τ + π i This gives an ion apparen poenial from which an IEDF can be generaed

8 8 Frequency Componens = f low f high + e n e ε V 3 s low + s low s high + e n e ε V e n e ε V e n e ε V e n e ε V s low + s low s high π τ i s low s high + s high π τ i e n e s low ε V 8π τ i e n e s high ε V 8π τ i s low s high π τ i π τ i s low s high π τ i + π τ i 3 s high

9 9 Sheah Volage and Ion Apparen Volage Comparison Can we ake advanage of his ripple by no using oo high of a frequency? =, = 1356 Volage (V) Volage Ampliude (V) x = 5 Ion Apparen HF Ampliude ~1% of Vdc Time (s) Ion Apparen Sheah Frequency () Sheah Ion Apparen Volage (V) Time (s) Ion Apparen Sheah Volage Ampliude (V) Frequency () Sheah Ion Apparen =, = 6 x = 5 Ion Apparen HF Ampliude ~1% of Vdc

10 1 HF Ripple Ampliude Conrol Using Frequency Mixing Volage (V) Volage Ampliude (V) x = High Frequency dominaes Time (s) Ion Apparen Sheah Frequency () Ion Apparen Sheah Volage (V) Volage Ampliude (V) x = 5 Increase in low frequency conribuion Time (s) Ion Apparen Sheah Frequency () Ion Apparen Sheah Volage (V) Volage Ampliude (V) x = 8 Low Frequency dominaes Time (s) Ion Apparen Sheah Frequency () Ion Apparen Sheah

11 11 IEDF Overlay 13 / Mixing Fracion Consan V dc Waveform Across Sheah 8 6 By Properly Mixing and 13, The IEDF widh can Be conrolled while Mainaining consan Average energy % / 8% 4% / 6% 6% / 4% 8% / % % / % Frequency Mix (13 / ) % / %

12 1 Bulk Plasma Condiion Impac 5% Mixing Case Increasing elecron densiy Increasing DC Poenial

13 13 Increasing frequency on he high side No Difference % 13 % % 13 5% 6 5 5% 13 75% % 7 % 5% 7 5% % 7 75% % 6 % 6 5 5% 6 5% % 6 75%

14 14 Power deposiion o he bulk (ime average elecron power) relaive o oal power as a funcion of frequency Look a a 5 mtorr argon discharge, d = 15, r = 6 P sheah () f := 3 T e V 4 m DC en e Area p Power los o ions in he sheah P bulk () f := 4π V DC ε Aream e T e ν e me d + f m e 1 Time averaged elecron power in bulk 8 Fracion Frequency ()

15 15 Idea for independen conrol of IEDF widh Fracion Frequency () Convenion pick a low frequency o conrol he sheah, pick a high frequency o conrol bulk Wha abou a high frequency bias o drive he bulk and wo low frequencies o drive he bias? Independen conrol of bulk, V dc, and IEDF profile

16 16 Conclusions Simple analyical model of a wo frequency sheah presened and analyzed for a given bulk plasma condiion Sheah dynamics as a funcion of frequency and curren raios shows an abiliy o une IEDF widh by combining low frequency and high frequency (consisen wih PIC modeling resuls of Kim Lee, and Shon (GEC 3, Session CT) as well as O Connell, Turner, and Ellingboe (GEC 4, Poser ES1 41) By selecing wo frequencies wih relaively low bulk power coupling and a hird frequency wih high bulk power coupling, elecron densiy, ime average sheah poenial, and IEDF shape can all be conrolled wih some level of independence

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