1. DEVELOPMENT OF ION ENERGY DISTRIBUTIONS THROUGH THE PRE-SHEATH AND SHEATH IN DUAL-FREQUENCY CAPACITIVELY COUPLED PLASMAS*
Yiting Zhanga, Nathaniel Mooreb, Walter Gekelmanb
and Mark J. Kushnera
(a) Department of Electrical and Computer Engineering,
University of Michigan, Ann Arbor, MI 48109 ,
(b) Department of Physics, University of California,
Los Angeles, CA 90095
, )
November 16, 2011
Good morning, my name is Yiting Zhang, today I would like to talk about our computer modeling of the ion energy angular distribution through the presheath and sheath region in a dual frequency ccp . This work is a coordinate work between the COMUTATIONAL PLASMA SCIENCE AND ENGINEERING IN uMICH and the experimental is perfromed BY Low Temperature Plasma Physics Laboratory in UCLA.
* Work supported by National Science Foundation, Semiconductor Research Corp. and the DOE Office of Fusion Energy Science

2. University of Michigan Institute for Plasma Science & Engr.
AGENDA
Introduction to dual frequency capacitively coupled plasma (CCP) sources and Ion Energy Angular Distributions (IEADs)
Description of the model
IEADs and plasma properties for 2 MHz Ar/O2
Uniformity and Edge Effect
O2 Percentage
Pressure
Plasma properties for dual-frequency Ar/O2
Concluding Remarks
First of all, I would like to introduce some backgroud regard to dual frequency CCP and ion energy angular distribution. Then I will talk about our computer modeling and show some results of argon oxygen plasma in different oxygen percentage, pressure and high frequencies.
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_01

3. DUAL FREQUENCY CCP SOURCES
Dual frequency capacitively coupled discharges (CCPs) are widely used for etching and deposition of microelectronic industry.
High driving frequencies produce higher electron densities at moderate sheath voltage and higher ion fluxes with moderate ion energies.
A low frequency contributes 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.
The dual frequency CCPs are widely used in microelectronic industry for etching and deposition propose. The high driving frequencies will enhance the electron densities at moderate sheath voltage and ion flux will increase with moderate ion energies. The low freuncy will contribute the quasi-independent control of the ion flux and energy. When apply both RF frequencies, we should noice that the coupling between the dual frequencies may interfere with independent control of plasma density, ion energy and produce non-uniforities. This picture show a industry standard CCP etch tool.
Tegal 6500 series systems high-density plasma etch tools featuring the HRe–™ capacitively coupled plasma etch reactor and dual-frequency RF power technology. 
 A. Perret, Appl. Phys.Lett 86 (2005)
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_02

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, vertically oriented angular 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.)
The reason we are interested in the ion energy and angular distributions is because control of the IEAD incident onto the substrate will help to improve plasma processes. For example, a narrow vertically oriented angular IEAD is desired for anisotropic processing. By analysis the IEAD along the radius of the wafer we can notice the edge effect which will provide useful information for large wafer process.
S.-B. Wang and A.E. Wendt,
J. Appl. Phys., Vol 88, No.2
B. Jacobs, PhD Dissertation
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_03

5. University of Michigan Institute for Plasma Science & Engr.
IEADs THROUGH SHEATHS
Results from a computational investigation of ion transport through RF sheaths will be discussed.
Investigation addresses the motion of ion species in the RF pre-sheath and sheath as a function of position in the sheath and phase of RF source.
Comparison to experimental results from laser induced fluorescence (LIF) measurements by Low Temperature Plasma Physics Laboratory at UCLA.
Assessment of O2 addition to Ar plasmas, pressure of operation, dual-frequency effects.
So, based on above incitations, The ion properties through sheaths are analyzed and the results from a computational investigation of ion transport through RF sheaths will be discussed today. We investigate the motion of ion species in the RF pre-sheath and sheath as a function of position in the sheath and phase of RF source. The comparison to experimental results from LIF measurements.
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_04

6. HYBRID PLASMA EQUIPMENT MODEL (HPEM)
EMM
EETM
FKM
E(r,θ,z,φ)
B(r,θ,z,φ)
PCMCM
Maxwell Equation
Monte Carlo Simulation f(ε) or Electron Energy Equation
Se(r)
Continuity, Momentum, Energy, Poisson equation
Monte Carlo Module
I,V(coils) E
N(r)
Es(r)
Circuit
Module
Electron Magnetic Module (EMM):
Maxwell’s equations for electromagnetic inductively coupled fields.
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.
The computer model we applied is called hybrid plasma equipment model, in a hybrid code, different physical phenomena are addressed in separate modules, which are iterated to convergence. For IEAD, the electron magnetic module, enlectron energy transport module , fluid kinetics module and plasma chemistry monte carlo module are the majority modules help to find it.
University of Michigan
Institute for Plasma Science & Engr.
M. Kushner, J. Phys.D: Appl. Phys. 42 (2009)
YZHANG_GEC2011_05

7. University of Michigan Institute for Plasma Science & Engr.
REACTOR GEOMETRY
Inductively coupled plasma with multi-frequency capacitively coupled bias on substrate.
2D, cylindrically symmetric.
Base case conditions
ICP Power: 400 kHz, 480 W
Substrate bias: 2 MHz
Pressure: 2mTorr
Ar plasmas:
Ar , Ar*, Ar+, e
Ar/O2 plasmas:
O2 ,O2*, O2+, O, O*,O+, O-
In this study, we choose a industry standard ICp plasma reactor with multi-frequency ccp bias to simplify the ccp reactor (?) and since the reactor is cylindrical geometry, we just consider half of it because of symmetric. The base case condition we set here is ICP with 400khz and 480watt power. Initially we just amply the single 2MHz RF bias to investigate the ion properties under RF bias. And the reason we choose the very low pressure 2mTorr is under the request of LIF measurement .
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_06

8. PULSED LASER-INDUCED FLUORESCENCE (LIF)
A non-invasive optical technique for measuring the ion velocity distribution function.
Ions moving along the direction of laser propagation will have the absorption wavelengths Doppler-shifted from λ0,
Ion velocity parallel to the laser obtained from Δλ=λ0-λL=v//λ0/c
Regards to the LIF measurement, the UCLA group applied a specific wavelength laser to make argon ionization to excited state and the photon will hit the camera’s pixel. By taking 1000s of picture and normalized the pixel intensity at certain position , we can know the dopper shift and thus can calculate the velocity on the direction of the laser propagation.
University of Michigan
Institute for Plasma Science & Engr.
B. Jacobs, PRL 105, (2010)
YZHANG_GEC2011_07

9. University of Michigan Institute for Plasma Science & Engr.
PLASMA PROPERTIES
Majority of power deposition that produces ions comes from inductively coupled coils.
Te is fairly uniform in the reactor due to high thermal conductivity - peaking near coils where E-field is largest.
Small amount of electro- negativity [O2-] /[M+] =0.0175, with ions pooling at the peak of the plasma potential.
The computer modeling results shows that
Ar/O2=80/20, 2mTorr, 50 SCCM
Freq=2 MHz, 500 V
DC Bias=-400 V
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_08 9

10. Ar+ IEAD FROM BULK TO SHEATH
In the bulk plasma and pre-sheath, the IEAD is essentially thermal and broad in angle. Boundaries of the pre-sheath are hard to determine.
In the sheath, ions are accelerated by the E-field in vertical direction and the angular distribution narrows.
Note: Discontinuities with energy increase caused by mesh resolution in collecting statistics.
Ar/O2=80/20, 2mTorr, 50 SCCM
Freq=2 MHz, 500 V
DC Bias=-400 V
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_09

11. University of Michigan Institute for Plasma Science & Engr.
IEAD NEAR EDGE OF WAFER
IEADs are separately collected over wafer middle, edge and chuck regions.
Non-uniformity near the wafer edge and chuck region - IEAD has broader angular distribution.
Focus ring helps improve uniformity.
Maximum energy consistent regardless of wafer radius.
0.5 mm above wafer
Ar/O2=0.8/0.2, 2mTorr, 50 SCCM
Freq=2 MHz VRFM=500 Volt
DC Bias=-400 Volt
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_10

12. University of Michigan Institute for Plasma Science & Engr.
IEAD vs RF PHASE: PRESHEATH
IEADs near presheath boundary are independent of phase, and slowly drifting.
In the pre-sheath, small ion drifts cause the IEAD to slightly change vs phase.
Experimental result shows the same trend.
Phase
B. Jacobs (2010)
Ar/O2 = 0.8/0.2,
0.5 mTorr, 50 SCCM
LF= 600kHz, 425W
HF=2 MHz, 1.5kW
Sheath ~3.6 mm
LIF measured 4.2 mm above wafer
Phase regard to HF
Ar/O2 =0.8/0.2, 2mTorr, 50 SCCM
Freq=2 MHz, 500 V
DC Bias =-400 V
IEAD 4.2 mm above wafer
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_11

13. University of Michigan Institute for Plasma Science & Engr.
IEAD UNDER DIFFERENT RF PHASES
Due to periodic acceleration in sheath, IEAD depends on phase.
During low acceleration phases, IEAD drifts in sheath.
During high acceleration phase, IEAD narrows as perpendicular component of velocity distribution increases.
Phase
B. Jacobs (2010)
Ar/O2 = 0.8/0.2,
0.5 mTorr, 50 SCCM
LF= 600kHz, 425W
HF=2 MHz, 1.5kW
Sheath ~3.6 mm
LIF measured 4.2 mm above wafer
Phase regard to HF
Ar/O2 =0.8/0.2, 2mTorr, 50 SCCM
Freq=2 MHz, 500 V
DC Bias =-400 V
IEAD 0.5 mm above wafer
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_12

14. University of Michigan Institute for Plasma Science & Engr.
IEAD vs PHASES FROM BULK TO SHEATH
Phase
3.3 mm
2.6 mm
1.9 mm
1.2 mm
Ar/O2 =0.8/0.2, 2mTorr, 50 SCCM,Freq=2 MHz, 500 V
DC Bias =-400 V ,IEAD 0.5 mm above wafer
0.5 mm
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_13 14

15. University of Michigan Institute for Plasma Science & Engr.
O2 ADDITION TO Ar
With increasing O2 in Ar/O2, negative ion ( O-) formation decreases fluxes to substrate for fixed power.
Sheath potential only moderately increases - for up to 20% O2, IEADs are only nominally affected since negative ions are limited to core of plasma.
Ar+ IEAD on wafer
2 mTorr, 300 SCCM.
Freq=2 MHz, 300 W.
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_14

16. University of Michigan Institute for Plasma Science & Engr.
IEADs vs PRESSURE
With decreasing pressure and increasing mean free path, trajectories are more ballistic - ions still drift into wafer at low energy during anodic part of cycle.
With higher pressure, lower plasma density increases thickness of sheath . Thicker sheath, more collisions, longer transit time – more distributed ion trajectories through sheath.
Ar+ IEAD on wafer
5/10/20mTorr, 75/150/300 SCCM.
Freq=2 MHz, 500 V
DC Bias =-400 V
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_15 16

17. IEADs vs HIGH FREQUENCY
If high frequency (10 MHz) is close to low frequency (2 MHz), they will interfere each other and contribute to multiple peaks in IEADs.
When high frequency is largely separated from the low frequency (2 MHz) since they changes so fast that ion fail to response, 30 MHz and 60 MHz show similar properties for ion distribution function.
Ar/O2=0.8/0.2, 2mTorr, 50 SCCM
HF = 10/30/60 MHz, 100 V
LF = 2 MHz V
DC BIAS = -100 V, IEAD on wafer
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_16 17

18. DUAL-FREQ IEAD vs PHASES
High frequency produces additional peaks in IEADs compared to single low frequency – structure is phase dependent.
Experiments show similar trend.
B.Jacobs, W.Gekelman, PRL 105, (2010)
Ar/O2=0.8/0.2,
0.5 mTorr, 50 SCCM
LF=600kHz, 425W
HF=2MHz, 1.5kW
Phase refers to HF
Ar/O2=0.8/0.2, 2mTorr, 50 SCCM
HF = 30 MHz, 100 V LF = 2 MHz, 400 V
DC BIAS = -100 V, Phase refers to LF
IEAD 0.5mm above wafer
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_17 18

19. SHEATH vs HIGH FREQUENCY
The sheath and pre-sheath thickness are nearly independent of HF on substrate (for fixed voltage).
Higher frequencies add modulation onto IEADs as a function of phase.
Ar/O2=0.8/0.2, 2mTorr, 50 SCCM
HF = 10/60 MHz, 100 V LF = 2 MHz, 400 V
DC BIAS = -100 V, Phase refers to LF
IEAD 0.5mm above wafer
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_18 19

20. University of Michigan Institute for Plasma Science & Engr.
CONCLUDING REMARKS
In the pre-sheath, IEAD is thermal and broad in angle. When the ion flux is accelerated through the sheath, the distribution increases in energy and narrows in angle.
Multiple peaks in IEADs come from IEADs alternately accelerated by rf field during the whole RF period.
Sheath and Pre-sheath thicknesses are both increased with the pressure. On the other hand, higher pressure bring more collisions and ions reach low energy and broad angular distribution.
Dual Frequency enhance electron and ion densities, provide flexibility of control of ion distribution while adding modulation to IEAD.
University of Michigan
Institute for Plasma Science & Engr.
YZHANG_GEC2011_19