1. COMPUTATIONAL INVESTIGATION OF DUAL-FREQUENCY POWER TRANSFER IN CAPACITIVELY COUPLED PLASMAS*
Yiting Zhang and Mark J. Kushner
Department of Electrical and Computer Engineering,
University of Michigan, Ann Arbor, 48109
Sang Ki Nam and Saravanapriyan Sriranman
Lam Research Corp., Fremont, CA 94538
June 17, 2013
* Work supported by Semiconductor Research Cooperation, National Science Foundation and the DOE Office of Fusion Energy Sciences.

2. University of Michigan Institute for Plasma Science & Engr.
AGENDA
Dual frequency Capacitively Coupled Plasma (CCPs) and Ion Energy Angular Distributions (IEADs)
Description of the model
IEADs and plasma properties for dual-frequency Ar plasma
Voltage control vs. power control
Ratio of dual frequencies
Phase shift
Concluding remarks
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013

3. DUAL FREQUENCY CCP SOURCES
Dual frequency capacitively coupled discharges (CCPs) are widely used for etching and deposition in the microelectronics industry.
High frequencies produce higher electron densities at moderate sheath voltage and higher ion fluxes with moderate ion energies.
Low frequencies contribute to the quasi-independent control of the ion flux and energy.
Coupling between the dual frequencies may interfere with independent control of plasma density, ion energy and produce non-uniformities.
LAMRC 2300 Flex dielectric etch tool
 A. Perret, Appl. Phys.Lett 86 (2005)
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013

4. ION ENERGY AND ANGULAR DISTRIBUTIONS (IEAD)
Control of the ion energy and angular distribution (IEAD) incident onto the substrate is necessary for improving plasma processes.
A narrow angle, vertically oriented IEAD is necessary for anisotropic processing.
Edge effects which perturb the sheath often produce slanted IEADs.
Ion velocity trajectories measured by LIF (Jacobs et al.)
S.-B. Wang and A.E. Wendt, JAP
B. Jacobs, PhD Dissertation
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013

5. University of Michigan Institute for Plasma Science & Engr.
CONTROL OF IEADs
As the size of transistors shrink, the critical dimension requirements of semiconductor fabrication become more stringent, and therefore more precise control of IEADs becomes important.
This computational investigation addresses plasma dynamics and control of IEADs onto wafers in dual frequency CCPs.
Controlling the voltage, power and phase difference between dual-frequencies to customize IEADs will be discussed.
SEM of a high aspect ratio profile
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013 5

6. HYBRID PLASMA EQUIPMENT MODEL (HPEM)
EETM
FKM
PCMCM
Monte Carlo Simulation f(ε) or Electron Energy Equation
Se(r)
Continuity, Momentum, Energy, Poisson equation
Monte Carlo Module
N(r)
Es(r)
Electron Energy Transport Module（EETM):
Electron Monte Carlo Simulation provides EEDs of bulk electrons.
Separate MCS used for secondary, sheath accelerated electrons.
Fluid Kinetics Module (FKM):
Heavy particle and electron continuity, momentum, energy and Poisson’s equations.
Plasma Chemistry Monte Carlo Module (PCMCM):
IEADs in bulk, pre-sheath, sheath, and wafers.
Recorded phase, submesh resolution.
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013

7. University of Michigan Institute for Plasma Science & Engr.
REACTOR GEOMETRY
Capacitively coupled plasma with multi-frequency rf biases on bottom electrode.
2D, cylindrically symmetric.
Ar plasma: Ar, Ar(1s2,3,4,5), Ar(4p), Ar+, e
Base case conditions:
Ar, 30 mTorr, 1000 sccm
Voltage Control (VC):
2 MHz, 300 V; 60 MHz, 300 V
Power Control (PC):
2 MHz, 300 W; 60 MHz, 300 W
(Note: Y:X = 2:1)
Real geometry aspect ratio
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013 7

8. ELECTRON DENSITY, TEMPERATURE
VC: 300 V, 2 MHz; 300 V, 60 MHz
PC: 300 W, 2 MHz; 300 W, 60 MHz
HF mainly contributes to ionization, and thus the current generated by HF is larger than the LF current.
With voltage control, larger HF power (2926 W total) generates higher ne. With power control, relatively low HF (51 V) due to higher efficiency of electron heating generates lower electron density.
Uniformity increases with higher ionization.
University of Michigan
Institute for Plasma Science & Engr.
Ar, 30 mTorr, 1000 sccm
ICOPS_2013
MIN MAX 8

9. Ar+ IEAD FROM BULK TO SHEATH
VC :300 V, 2 MHz; 300 V, 60 MHz
The lower ne with PC produces a thicker time averaged sheath thickness.
Longer ion transit time in thick sheath makes the IED curve smoother and lower in energy.
DC bias -256 V
PC :300 W, 2 MHz, 300 W 60 MHz
IED on wafer
DC bias -123 V
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013
ICOPS_2013
MIN MAX 9

10. HIGH FREQUENCY VOLTAGE
The plasma impedance changes little, total power increases with VHF2.
With higher HF voltage, plasma density increases significantly.
Higher power correlates with better uniformity.
Ar, 30 mTorr, 1000 sccm
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013
MIN MAX 10

11. HIGH FREQUENCY VOLTAGE
Changing HF/LF voltage ratio will strongly affect the IEADs. With higher HF, self generated DC bias becomes more negative, and the total IEAD shifts to higher level due to higher sheath potential during anodic LF cycle.
Broadening in high energy peaks due more HF modulation. The energy width is almost independent of HF amplitude.
DC bias
- 256 V
DC bias
- 355 V
DC bias
- 459 V
University of Michigan
Institute for Plasma Science & Engr.
Ar, 30 mTorr, 1000 sccm
ICOPS_2013
MIN MAX 11

12. University of Michigan Institute for Plasma Science & Engr.
LOW FREQUENCY VOLTAGE
Increasing LF (300 V to 600 V) has little effect on ne and Te since electron heating scales with 2.
Majority of additional power results in ion acceleration.
University of Michigan
Institute for Plasma Science & Engr.
Ar, 30 mTorr, 1000 sccm
ICOPS_2013
MIN MAX 12

13. University of Michigan Institute for Plasma Science & Engr.
LOW FREQUENCY VOLTAGE
Increasing LF voltage shapes IED (e.g., ΔE) with little change in plasma properties.
During the cathodic LF cycle, increase in sheath potential accelerates ions to higher energy.
During anodic LF cycle, sheath potential is dominated by HF which is unchanged – and so modulation of IED persists.
- 256 V, DC
- 307 V, DC
- 371 V, DC
Ar, 30 mTorr, 1000 sccm
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013
MIN MAX 13

14. University of Michigan Institute for Plasma Science & Engr.
HIGH FREQ POWER
With increase in HF power 300 W to 900 W, HF voltage changes by only 30 V.
Amplitude is always small compared to LF, and so width of IEAD does not significantly change.
Increase in ne with power reduces sheath width which then modulates IEAD at HF.
Ar, 30 mTorr, 1000 sccm
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013
MIN MAX 14

15. University of Michigan Institute for Plasma Science & Engr.
LOW FREQ POWER
The plasma density and uniformity change little with LF power.
At low frequency, LF voltage increases nearly linear with power.
The LF power is mainly deposited into sheath – the width of IED increases with LF power.
Ar, 30 mTorr, 1000 sccm
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013
MIN MAX 15

16. IED DEPENDENCE ON ΔPHASE
Energy of HF modulated peaks in IED depend on relative phase between LF and HF.
Shift of energy of peaks depends on value of high frequency due in part to change in sheath thickness.
Ar, 30 mTorr, 1000 sccm
ICOPS_2013
MIN MAX

17. SHEATH vs ΔPHASE
300V 2 MHz
300V 60 MHz
Phase difference between LF and HF modulates sheath potential and electron dynamics during rf period.
The sheath thickness (scales with [e]-1/2 ) is larger in cathodic LF cycle, and so brings about less modulation in high energy peak of IED.
By dynamically controlling phase difference, a smooth time averaged IED can be produce without HF modulation.
Ar, 30 mTorr, 1000 sccm
ICOPS_2013

18. University of Michigan Institute for Plasma Science & Engr.
CONCLUDING REMARKS
For dual frequency CCPs sustained in Ar plasma,
With higher frequency , the current generated by HF is greater than the LF current.
Increasing HF voltage will increase the plasma density as well as shift the total IEADs to higher energies.
Increasing LF voltage will mainly deposit power within sheath, and therefore extend the IEAD energy width with little change in composition of fluxes.
Changing phase between HF and LF in high density, thin sheath plasma will modify time averaged IEADs significantly.
With knowledge of the relationship between IEADs and settings of dual frequency rf biases, precise customization and control of IEADs can be achieved.
University of Michigan
Institute for Plasma Science & Engr.
ICOPS_2013