1. CONTROL OF ELECTRON ENERGY DISTRIBUTIONS AND FLUX RATIOS IN PULSED CAPACITIVELY COUPLED PLASMAS*
Sang-Heon Songa) and Mark J. Kushnerb)
a)Department of Nuclear Engineering and Radiological Sciences
University of Michigan, Ann Arbor, MI 48109, USA
b)Department of Electrical Engineering and Computer Science
Oct 2010 AVS
Good afternoon, my name is Sang-Heon Song and my advisor is Prof. Mark Kushner.
The topic of my presentation is “control of electron energy distributions and flux ratios in pulsed capacitively coupled plasmas”.
This work is supported by DOE plasma science center and semiconductor research corporation.
* Work supported by DOE Plasma Science Center and Semiconductor Research Corp.

2. University of Michigan Institute for Plasma Science & Engr.
AGENDA
Motivation for controlling f(e)
Description of the model
Typical Ar pulsed plasma properties
Typical CF4/O2 pulsed plasma properties
f(e) and flux ratios with different
PRF
Duty Cycle
Pressure
Concluding Remarks
Here is the agenda.
We will start with motivation for controlling electron energy distribution function, and briefly describe the model used in this investigation.
Then we will present results in terms of the typical plasma properties for argon and CF4/O2.
The distribution function and flux ratio investigation is approached with varying PRF, duty cycle, and pressure.
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_02

3. CONTROL OF ELECTRON KINETICS- f()
Controlling the generation of reactive species for technological devices benefits from customizing the electron energy (velocity) distribution function.
Need SiH3 radicals*
LCD
Solar Cell
e + SiH4
SiH3 + H + e k
The ability to control electron velocity or energy distribution is ultimately the means to control the generation of reactive species for technological devices.
For example, we need this particular reaction for the amorphous silicon deposition in the LCD or solar cell fabrication.
So we have that rate equation which gives us time rate of change of reactive species.
Those functions have rate coefficients, the rate coefficients come from the electron energy distribution.
So arguably the entire plasma technology is the infrastructure dominated by attempting to control the distribution functions of electrons, ions, and photons.
* Ref: Tatsuya Ohira, Phys. Rev. B 52 (1995)
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_03

4. HYBRID PLASMA EQUIPMENT MODEL (HPEM) Monte Carlo Simulation
Te, S, k
Fluid Kinetics Module
Fluid equations
(continuity, momentum, energy)
Poisson’s equation
Electron
Monte Carlo Simulation
E, Ni, ne, Ti
Fluid Kinetics Module:
Heavy particle and electron continuity, momentum, energy
Poisson’s equation
Electron Monte Carlo Simulation:
Includes secondary electron transport
Captures anomalous electron heating
Includes electron-electron collisions
The model used in this investigation is a two-dimensional fluid hydrodynamics simulation in which the distribution function is solved explicitly by a Monte Carlo simulation.
Fluid equations and Poisson’s equation are integrated in time to obtain a periodic steady state.
The resulting electric fields and ion fluxes to surfaces are transferred to the Monte Carlo simulation where the transport of secondary electrons emitted from surfaces is calculated.
Then the electron impact source functions and sources of secondary electron current resulting from the Monte Carlo simulation are returned to the fluid module.
This process is iterated to convergence.
This particular Monte Carlo simulation uses a particle mesh technique to include electron-electron collisions.
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_04

5. University of Michigan Institute for Plasma Science & Engr.
REACTOR GEOMETRY
2D, cylindrically symmetric
Ar, CF4/O2, 10 – 40 mTorr, 200 sccm
Base conditions
Lower electrode: LF = 10 MHz, 300 W, CW
Upper electrode: HF = 40 MHz, 500 W, Pulsed
Here is the geometry for dual frequency capacitively coupled plasma which will be sustained in argon or CF4/O2 at ten or forty mTorr with the flow rate of 200 sccm.
A low frequency is applied to the lower electrode and a high frequency is applied to the upper electrode, then the high frequency will be pulsed.
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_05

6. University of Michigan Institute for Plasma Science & Engr.
PULSE POWER
Use of pulse power provides a means for controlling f().
Pulsing enables ionization to exceed electron losses during a portion of the period – ionization only needs to equal electron losses averaged over the pulse period.
Pmax
Power(t)
Duty Cycle
Pmin
Time
 = 1/PRF
Pulse power for high frequency.
Duty-cycle = 25%, PRF = 100 kHz, 415 kHz
Average Power = 500 W
So what we would like to do is to investigate the possibilities of using pulse plasmas as a means to customize the distribution functions.
We are going to look at a pulsed capacitively coupled plasma with the duty cycle which is a fraction of the total time of the powers on and a pulse repetition frequency which is how many times per second will repeat this wave form.
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_06

7. Ar
First, for the pure argon case.
SHS_MJK_AVS2010_07

8. University of Michigan Institute for Plasma Science & Engr.
PULSED CCP: Ar, 40 mTorr
Pulsing with a PRF and moderate duty cycle produces nominal intra-cycles changes [e] but does modulate f().
LF = 10 MHz, 300 W
HF = 40 MHz, pulsed 500 W
PRF = 100 kHz, Duty-cycle = 25%
ANIMATION SLIDE-GIF
[e]
VHF 226 V
VLF 106 V
f(e)
MIN
MAX Te
Here is an argon, forty mTorr, three hundred watts of power deposition to the lower electrode at ten mega Hertz and five hundred watts of power deposition to the upper electrode at forty mega Hertz, and the high frequency is pulsed.
We’ve chosen pulse repetition frequency to be high enough that the plasma density does not significantly change over the RF cycle.
And the only thing that does significantly change is the electron energy distribution.
These are electron density and temperature during that pulse period.
And this is the distribution function traced at the edge of the sheath during that pulse cycle.
And this red line is cycle average.
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_08

9. PULSED CCP: Ar, DUTY CYCLE
Excursions of tail are more extreme with lower duty cycle – more likely to reach high thresholds.
ANIMATION SLIDE-GIF
Cycle Average
Duty cycle = 25%
Duty cycle = 50%
VHF 226 V
VLF 106 V
VHF 128 V
VLF 67 V
These are distribution functions with two different duty cycles.
Left one is the cycle average distribution functions for 25% and 50% duty cycle.
And animations are time dependent distribution functions for those duty cycles.
You see that the tail are much above that cycle average during power on cycle, and duty cycle of twenty five percent versus fifty percent.
Therefore the high threshold inelastic processes are more sensitive to that excursion of the distribution function.
LF 10 MHz, pulsed HF 40 MHz
PRF = 100 kHz, Ar 40 mTorr
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_09

10. PULSED CCP: Ar, PRESSURE
Pulsed systems are more sensitive to pressure due to differences in the rates of thermalization in the afterglow.
ANIMATION SLIDE-GIF
Cycle Average
10 mTorr
40 mTorr
VHF 274 V
VLF 146 V
VHF 226 V
VLF 106 V
And these are the distribution functions for two different pressures, 10 mTorr and 40 mTorr.
Since the collision frequency at the higher pressure is so much greater than that at the lower pressures,
one has much more rapid thermalization of the distribution function at the higher pressures
and therefore even on cycle average basis much more decreased tail of the distribution function.
LF 10 MHz, pulsed HF 40 MHz
PRF = 100 kHz
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_10

11. CF4/O2
Now for the CF4 and oxygen gas mixture.
SHS_MJK_AVS2010_11

12. University of Michigan Institute for Plasma Science & Engr.CW
ELECTRON DENSITY
At 415 kHz, the electron density is not significantly modulated by pulsing, so the plasma is quasi-CW.
At 100 kHz, modulation in [e] occurs due to electron losses during the longer inter-pulse period.
The lower PRF is less uniform due to larger bulk electron losses during longer pulse-off cycle.
PRF=415 kHz
PRF=100 kHz
To start with, here is the electron density with different pulse repetition frequency.
At forty mTorr, CF4 eighty percent and oxygen twenty percent mixture with the flow rate of 200 sccm, and the power deposition is the same as the pure argon case.
At lower PRF you can see there is a little more modulation due to electron losses during the longer inter-pulse period.
And also it is less uniform due to larger bulk electron losses during longer pulse-off cycle.
40 mTorr, CF4/O2=80/20, 200 sccm
LF = 10 MHz, 300 W
HF = 40 MHz, 500 W (CW or pulse)
MIN
MAX
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_12
ANIMATION SLIDE-GIF

13. ELECTRON SOURCES BY BULK ELECTRONSCW
ELECTRON SOURCES BY BULK ELECTRONS
The electrons have two groups: bulk low energy electrons and beam-like secondary electrons.
The electron source by bulk electron is negative due to electron attachment and dissociative recombination.
Only at the start of the pulse-on cycle, is there a positive electron source due to the overshoot of E/N.
PRF=415 kHz
PRF=100 kHz
Since this plasma is sustained in electronegative gas mixture, there is dominant electron attachment and dissociative recombination.
In fact, we have two kinds of electrons; one is low energy bulk electrons, and the other is high energy secondary electrons.
So here you see that the electron source by bulk electron is always negative due to attachment and recombination except at the start of the pulse-on cycle where we have the overshoot of E/N.
40 mTorr, CF4/O2=80/20, 200 sccm
LF 300 W, HF 500 W
MIN
MAX
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_13
ANIMATION SLIDE-GIF

14. ELECTRON SOURCES BY BEAM ELECTRONSCW
ELECTRON SOURCES BY BEAM ELECTRONS
The beam electrons result from secondary emission from electrodes and acceleration in sheaths.
The electron source by beam electron is always positive.
The electron source by beam electrons compensates the electron losses and sustains the plasma.
PRF=415 kHz
PRF=100 kHz
Whereas the electron source by beam electrons is always positive.
The secondary electrons emitted from electrodes are accelerated in the sheath, and have sufficiently high energy to ionize feed stock gases.
This positive electron source by beam-like secondary electrons compensates the electron losses by attachment and recombination and sustains the plasma.
40 mTorr, CF4/O2=80/20, 200 sccm
LF = 10 MHz, 300 W
HF = 40 MHz, 500 W (CW or pulse)
MIN
MAX
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_14
ANIMATION SLIDE-GIF

15. TYPICAL f(e): CF4/O2 vs. Ar
Less Maxwellian f(e) with CF4/O2 due to lower e-e collisions.
Enhanced sheath heating with CF4/O2 due to lower plasma density.
Tail of f(e) comes up to compensate for the attachment and recombination that occurs at lower energy.
VHF 226 V
VLF 106 V
VHF 203 V
VLF 168 V
This is the comparison between pure argon and CF4 oxygen mixture, otherwise at the same condition.
During the pulse-on stage, the high-energy electrons are produced by the stochastic heating on the oscillating sheath edge.
The difference is that the distribution function with fluorocarbon is less Maxwellian due to lower e-e collisions.
Another significant difference is that the high energy tail part of the distribution function is much enhanced with fluorocarbon in order to compensate for the electron losses by the attachment that occurs at the lower energy.
ANIMATION SLIDE-GIF
40 mTorr, 200 sccm
LF = 10 MHz, 300 W
HF = 40 MHz, 500 W (25% dc)
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_15

16. University of Michigan Institute for Plasma Science & Engr.
RATIO OF FLUXES: CF4/O2
In etching of dielectrics in fluorocarbon gas mixtures, the polymer layer thickness depends on ratio of fluxes.
Ions – Activation of dielectric etch, sputtering of polymer
CFx radicals – Formation of polymer
O – Etching of polymer
F – Diffusion through polymer, etch of dielectric and polymer
Investigate flux ratios with varying
PRF
Duty cycle
Pressure
Flux Ratios:
Poly = (CF3+CF2+CF+C) / Ions
O = O / Ions
F = F / Ions
Now we are going to talk a little bit more about the fluorocarbon oxygen plasma.
In the fluorocarbon plasma dielectric etching process, there are 4 important species to be taken into account.
Ions activate the etch and sputter polymer, fluorocarbon radicals make the polymer, O radicals remove the polymer, and F atoms diffuse through the polymer, and etch the dielectric and polymer.
So these flux ratios onto wafer are important to control polymer layer thickness.
We would like to investigate these flux ratios with varying PRF, Duty cycle, and pressure.
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_16

17. University of Michigan Institute for Plasma Science & Engr.
f(e): CF4/O2, PRF
Average
PRF = 100 kHz
The time averaged f(e) for pulsing is similar to CW excitation.
Extension of tail of f(e) beyond CW excitation during pulsing produces different excitation and ionization rates, and different mix of fluxes to wafer.
VHF 203 V
VLF 168 V
First we varied PRF.
Left one is the comparison between CW excitation and different PRF.
Although the cycle average distribution functions are similar, enhanced tail above that cycle average produces different excitation and ionization rates, and different mix of fluxes to the wafer.
ANIMATION SLIDE-GIF
40 mTorr, CF4/O2=80/20, 200 sccm
LF = 10 MHz, 300 W
HF = 40 MHz, 500 W (25% dc)
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_17

18. RATIO OF FLUXES: CF4/O2, PRF
Ratios of fluxes are tunable using pulsed excitation.
Polymer layer thickness may be reduced by pulsed excitation because poly to ion flux ratio decreases. CW
100 CW
100
415
415 kHz
100 CW
415
Here is the flux ratios to the wafer as a result of PRF change.
So the flux ratios are tunable using pulsed excitation.
If you increase pulse repetition frequency, you can reduce the ratios even more.
From this result, you may expect that the polymer layer thickness can be reduced by pulse plasma.
F O Poly
40 mTorr, CF4/O2=80/20, 200 sccm, Duty-cycle = 25%
LF = 10 MHz, 300 W
HF = 40 MHz, 500 W
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_18

19. University of Michigan Institute for Plasma Science & Engr.
f(e): CF4/O2, DUTY CYCLE
Control of average f() over with changes in duty cycle is limited if keep power constant.
ANIMATION SLIDE-GIF
Cycle Average
Duty cycle = 25%
Duty cycle = 50%
VHF 203 V
VLF 168 V
VHF 191 V
VLF 168 V
Here we changed the duty cycle of 25% and 50%.
The tail above cycle average during the power-on period is compensated by thermalization during the afterglow.
So the different fraction of power-on and off period may produce different amount of high threshold inelastic processes.
40 mTorr, CF4/O2=80/20, 200 sccm
LF 10 MHz, Pulsed HF 40 MHz, PRF = 100 kHz
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_19

20. RATIO OF FLUXES: CF4/O2, DUTY CYCLE
Flux ratio control is limited if keep power constant.
With smaller duty cycle, polymer flux ratio is more reduced compared to the others. CW
50%
25%
50% CW
25%
25%
50% CW
As a result of varying duty cycle, the flux ratios are changed.
The difference is not as much as by PRF.
But you can notice that the polymer flux ratio is more reduced by decreasing duty cycle while F and O flux ratios are almost same.
So you may expect that the polymer thickness can be reduced by decreasing duty cycle.
F O Poly
LF 10 MHz, Pulsed HF 40 MHz, PRF = 100 kHz
40 mTorr, CF4/O2=80/20, 200 sccm
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_20

21. University of Michigan Institute for Plasma Science & Engr.
f(e): CF4/O2, PRESSURE
Pulsed systems are sensitive to pressure due to differences in the rates of thermalization in the afterglow.
ANIMATION SLIDE-GIF
Cycle Average
10 mTorr
40 mTorr
VHF 233 V
VLF 188 V
VHF 191 V
VLF 168 V
Pressure is another knob that we can use to control the distribution functions.
Pressure controls the rate of diffusion loss in this low pressure capacitively coupled plasma.
Also pressure affects sheath physics particularly anomalous in low pressure, collisional at high pressure, and subsequent transport of electron power significantly affect the distribution function.
Furthermore, the pulsed systems are sensitive to the pressure due to difference in the rates of thermalization in the afterglow.
CF4/O2=80/20, 200 sccm, PRF = 100 kHz
LF 10 MHz, Pulsed HF 40 MHz
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_21

22. RATIO OF FLUXES: CF4/O2, PRESSURE
Flux ratios decrease as pressure decreases.
Polymer layer thickness may be reduced with lower pressure in the pulsed CCP.
P: Pulsed excitation
CW: CW excitation 40 CW
40 mTorr P CW 10 P 10 P CW CW P 40 10
So flux ratios are tunable by pressure, too.
As pressure decreases in pulsed CCP, the flux ratios decrease.
So you may expect the polymer layer thickness can be reduced by decreasing pressure in this pulsed CCP.
<Back Up> This is mostly because of increased ion flux at the lower pressure. As you decrease pressure, the ion density is a little bit reduced, but the Bohm velocity onto the wafer is much more enhanced because electron temperature is increased by stochastic heating at the lower pressure.
How about thinking this way. When you use pulse, flux ratio is reduced. Then if you decrease pressure in that pulsed system, you can reduce the flux ratios even more. P P CW CW
F O Poly
CF4/O2=80/20, 200 sccm
LF = 10 MHz, 300 W
HF = 40 MHz, 500 W
PRF = 100 kHz, Duty-cycle = 25%
University of Michigan
Institute for Plasma Science & Engr.
SHS_MJK_AVS2010_22

23. CONCLUDING REMARKS
Extension of tail of f(e) beyond CW excitation produces different mix of fluxes.
Ratios of fluxes are tunable using pulsed excitation.
Different PRF provide different flux ratios due to different relaxation time during pulse-off cycle.
Duty cycle is another knob to control f(e) and flux ratios, but it is limited if keep power constant
Pressure provide another freedom for customizing f(e) and flux ratios in pulsed CCPs.
In conclusion, we found the possibilities of using pulse plasma as a means to customize the electron energy distribution function and flux ratios onto the wafer.
We have investigated different PRF, duty cycle and pressures.
PRF and duty cycle provide such possibilities due to different inter pulse period.
Also pressure provide another freedom for customizing the distribution function and flux ratios in this pulsed CCP.
Thank you for your attention.
SHS_MJK_AVS2010_23