flcc march 28, 2005 flcc - plasma 1 fluid modeling of capacitive plasma tools flcc presentation...

March 28, 2005 FLCC - Plasma

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Fluid Modeling of Capacitive Plasma Tools

FLCC PresentationMarch 28, 2005Berkeley, CA

David B. Graves, Mark Nierode, and Yassine KabouziUC Berkeley


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Motivation• Capacitively-coupled plasma etch tools commonly

used, especially in dielectric etch• Popular strategy: dual frequency operation to separate

control of ion flux and plasma density (high frequency) from ion energy control (low frequency)

• Overall goal is to develop a 2-D, time-dependent fluid plasma model that can be used for tool design and process control studies

• Tool-scale model can be coupled to feature scale (e.g. Prof. Chang, UCLA)

• Fluid model can complement PIC/MC model (Prof. Lieberman, UCB)


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1. Fluid model of 1-D dual frequency (27 MHz, 2 MHz) Ar discharge.

2. Fluid model of 2-D single frequency (13.5 MHz) Ar discharge.

3. Fluid model of non-isothermal, reacting neutral flow in typical industrial capacitive etch tool with split inlet flows.

Today’s Talk


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Plasma Model Equations

( )ee ioniz ioniz e e N

nR k T n n

t

Γ

iiiiiii

ii enZpt

mn MEuuu

eabseeee EPekTnt

ΓEQ

2

3

iiie nZne 2

0

biasVtV )sin(

AJJJdt

dVc die

biasb

EΓ

ene

eee

enee m

enkTn

m

1

eene

eeeee kT

vm

kTnkT

2

5

2

5ΓQ

ii i ioniz

nn R

t

u

Equations solved via FEMLAB


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One Dimensional Dual Frequency Results

Argon, p = 50 mtorr, 800 V rf @ 27 MHz, , 800 V rf @ 2 MHz applied at left electrode

2 MHz

27 MHz

0.02 m


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Potential on Powered (Left) Electrode


0.5


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Dual Frequency Results: Plasma Density



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Right Sheath Structure


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Left Sheath Structure


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Electron Density in Sheaths: 27 MHz Variation

Electron loss at both sheaths

Electron loss at right sheath only


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Electric Field and Plasma Potential: 2 MHz


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Potentials on Powered Electrode and in Plasma


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Currents at Powered Electrode


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Electron Temperature


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Two-Dimensional, Axisymmetric (r,z) Single Frequency

Argon, p = 50 mtorr, 80 V rf @ 13.56 MHz, applied at top electrode

0.25 m radius

0.025 m height

Powered electrode

Grounded

Preliminary 2-D results obtained


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Period-Averaged Electron DensityArgon, p = 50 mtorr, 80 V rf @ 13.56 MHz, applied at top electrode


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Period-Averaged Electron Temperature

Argon, p = 50 mtorr, 80 V rf @ 13.56 MHz, applied at top electrode


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Period-Averaged Ion DensityArgon, p = 50 mtorr, 80 V rf @ 13.56 MHz, applied at top electrode


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Period-Averaged Plasma Potential


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Neutral Reacting Flow Model

nvv EpTCt

TC

v:vqv

nRt

v

npt

Mτvvv

iiii rt

imDv

pM

kT

Equations solved via FEMLAB


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Neutral Flow Configuration

– Commercial tools typically feature dual flow configurations to allow for greater process control

(e.g. balance fluorocarbon deposition and etching)– Investigate the transport of the tuning gas and its effect on

reactor chemistry

400/20/9 sccm Ar/c-C4F8/O2 | 0-100 sccm O2

Pressure ~ 30 mtorr


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Mesh and Numerics

• 3363 elements, 115106 d.o.f.• All variables use quadratic Lagrangian elements

except pressure which is linear• Steady state solution obtained 1-2 hours using

iteration script (FEMALB feature; eqns solved iteratively and sequentially)


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Chemistry ModelREACTIONS

1 Ar + e --> Ar+ + 2e2 c-C4F8 + e --> 2 C2F4 + e3 C2F4 + e --> 2 CF2 + e4 CF2 + e --> CF + F + e5 O2 + e --> 2 O + e6 CF2 + O --> COF + F7 COF + O --> CO2 + F

Assum ed plasm a density , tem peratureNo surface react ions

1. Simplistic model will assume CF as the ‘depositing’ species and F as the ‘etching’ species

2. Increased O2 flow in the outer annulus leads to increased O2 and O in the outer region

3. Increased O increases rxns 6 & 7 producing F on the same order as rxn 4


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Assumed Plasma Density

Assume constant Te = 3

Assume radial plasma profile flat except when r > 0.2


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Neutral Temperature

• Neutral gas heating is proportional to the (assumed) plasma density

• ‘Jump’ temperature and ‘slip’ velocity boundary conditions

• Temperature profile not affected by outer tuning flow up to 100 sccm O2


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Pressure and Temperature Effects

• Radial pressure drop is significant ~30% leading to a similar neutral number density profile (n); recall n ~ p/T

• Axial pressure gradients are minimal

Total neutral density


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Neutral Species Radial ProfilesQtune = 0 sccm


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Neutral Species Radial Profiles

– Note: scale different from previous slide

Qtune = 100 sccm


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Effects of Altering O2 ‘Tuning’ Gas Flow

•Propose CF/F as model deposition/etch ratio index•Varying the outer O2 flow (Qtune) the ratio of CF to F can be modified radially although the overall ratio of CF to F changes too


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Concluding Remarks

• FEMLAB-based fluid modeling powerful tool to simulate complex, multi-dimensional, reacting plasma tools– Tool-scale design/analysis possible

– Fully transient, coupled neutral-plasma versions can simulate process control

• Two major limitations to tool-scale fluid models:– No feature profile evolution

– No plasma kinetic information (e.g. EEDF, IEDF, IADF)

• FLCC plasma project couples fluid modeling (DBG, UCB), feature evolution modeling (JC, UCLA) and PIC/MC modeling (MAL, UCB)

flcc march 28, 2005 flcc - plasma 1 fluid modeling of capacitive plasma tools flcc presentation...

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