SIMULATIONS OF ECR PROCESSING SYSTEMS SUSTAINED …

UNIVERSITY OF ILLINOISOPTICAL AND DISCHARGE PHYSICS

25th IEEE International Conference on Plasma ScienceRaleigh, North Carolina

June 1-4, 1998

IEE98_1

SIMULATIONS OF ECR PROCESSINGSYSTEMS SUSTAINED BY AZIMUTHAL

MICROWAVE TE(0,n) MODES*

* Sponsored by SRC and NSF (ECS94-04133, CTS9412-565)

Ron L. Kinder and Mark J. KushnerDepartment of Electrical & Computer Engineering

University of Illinois, Urbana-Champaigne-mail : [email protected]

[email protected]


AGENDA

• Introduction

• Description of Hybrid Plasma Equiptment Model (HPEM)

• Finite Difference Time Domain Module

• Simulation Device Geometry and Operating Conditions

• Simulation Results ( Power, Ionization Rate, Electron Density Distributions )

• Experimental Validation • Results from Parametric Studies

• Conclusions

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INTRODUCTION

• Due to their ability to produce high degrees of ionization at low gas pressures, ECR sources are being developed for downstream etching and deposition, and the production of radicals for surface treatment.

• One advantage of ECR sources is their ability to provide uniformity over large areas. As industry begins to move toward larger wafers, industrial scaleup of these sources is in progress. LAM currently markets a 200 mm deposition tool (scaling to 300 mm). Hitachi has recently announced a 300 mm etch tool.

• The spatial coupling of microwave radiation to the plasma is a concern due to issues related to process uniformity. Studies suggest that certain waveguide electromagnetic mode fields tend to provide better uniformity over larger areas.

• To investigate these issues, we have developed a FDTD simulation for microwave injection and propagation. The FDTD simulation has been incorporated as a module in the 2-dimensional Hydrid Plasma Equipment Model (HPEM).

• Parametric studies have been performed to determine dependence of ion flux uniformity with varying reactor parameters such as mode of excitation, pressure, and power.

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HYBRID PLASMA EQUIPMENT MODEL

• The base two-dimensional HPEM consists of an electromagnetics module (EMM), an electron energy distribution module (EEDM), and a fluid kinetics simulation (FKS).

• Ion transport was calculated by time integrating the continuity and momentum equations, while electron energy transport was determined by time integrating the electron energy conservation equation.

• Neutral transport was determined by solving the neutral momentum equation.

• An ambipolar approximation was used to solve a Poisson-like equation for the electric potential during early iterations, followed by direct solution of Poisson’s equation.

• Due to the vastly different kinetic time scales for the kinetic reactions compared to convection, such an approximation, allowed for the use of larger time steps, while maintaining stability, during each iteration.

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SCHEMATIC OF 2-D/3-D HYBRID PLASMA EQUIPMENT MODEL

S(r,z)E (r,z)s

v(r,z)

PLASMA CHEMISTRY MONTE CARLO SIMULATION

ETCHPROFILEMODULE

FLUXES

E (r,z, ),

B(r,z, )

Q f

f

ELECTRO-MAGNETICS

MODULE

CIRCUITMODULE

I,V (coils) EQ

S(r,z), T (r,z) (r,z)m

e

FLUID-KINETICS

SIMULATION

HYDRO-DYNAMICSMODULE

ENERGYEQUATIONS

SHEATHMODULE

N(r,z) E (r,z, )s

f(r,z), I (coils), J(r,z, )s f

ELECTRONBEAM

MODULE

ELECTRONMONTE CARLOSIMULATION

ELECTRONENERGY EQN./BOLTZMANN

MODULE

NON-COLLISIONAL

HEATINGLONG MEANFREE PATH(SPUTTER)

SIMPLECIRCUIT

MAGNETO-STATICSMODULE

B(r,z)

= 2-D ONLY

= 2-D and 3-D

EXTERNALCIRCUITMODULE

MESO-SCALE

MODULE

(r,z, )fF

R

(r,z, )fF

V(rf),V(dc)

VPEM: SENSORS, CONTROLLER, ACTUATORS

SURFACECHEMISTRY

MODULE

(r,z, )fF

RFDTD

MICROWAVEMODULE

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DESCRIPTION OF THE FINITE DIFFERENCE TIMEDOMAIN (FDTD) MODEL

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• The FDTD simulation uses an alternating direction implicit (ADI) scheme. Electromagnetic (EM) fields are calculated using a leap-frog scheme for time integration of Maxwell’s equations, with time steps that are 30% of the Courant limit.

• Plasma dynamics are coupled to the EM fields through a tensor form of Ohm’s law which addresses static B-fields.

i - 1 i i + 1

j + 1

j

j - 1

Eθ

Br

Bz

∆ r

∆ z

∇ x E = - ∂B∂t

∇ x Bµ = σ • E + ε ∂E

∂t

2(1/2)-D Alternating Grid:

σ = q ne M -1

M = α −Bz BθB α −Br

−Bz Br α

α = mq (iω + νm)

where,


ABSORBING BOUNDARY CONDITIONS FOR FDTD

• When time domain electromagnetic field equations are solved using finite difference techniques in unbounded space, there must be a method limiting the domain in which the field is computed.

• This is achieved by truncating the mesh and using absorbing boundary conditions at its artificial boundaries to simulate the unbounded surroundings.

• Due to the nature of the 2(1/2)-D alternating direction implicit scheme, boundary conditions using constant gradients for electric and/or magnetic fields cause spurious reflections of the incident waves.

• To remove unwanted reflections, a linearized first order wave equation was imposed as a boundary condition to simulate unbounded surroundings.

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∂Eθn +1

∂z + ∂Eθ

n

∂z = 1c

∂Eθi, j

∂t + 1c

∂Eθi, j−1

∂t

Linearized First Order Wave Equation:


ABSORBING BOUNDARY CONDITIONS FOR FDTD

• When time domain electromagnetic field equations are solved using finite difference techniques in unbounded space, there must be a method limiting the domain in which the field is computed.

• This is achieved by truncating the mesh and using absorbing boundary conditions at its artificial boundaries to simulate the unbounded surroundings.

• Due to the nature of the 2(1/2)-D alternating direction implicit scheme, boundary conditions using constant gradients for electric and/or magnetic fields cause spurious reflections of the incident waves.

• To remove unwanted reflections, a linearized first order wave equation was imposed as a boundary condition to simulate unbounded surroundings.

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∂Eθn +1

∂z + ∂Eθ

n

∂z = 1c

∂Eθi, j

∂t + 1c

∂Eθi, j−1

∂t

Linearized First Order Wave Equation:

Magnetic Coils

WaferPumpPort

Gas Ring

DielectricWindow

• Range of Operating Conditions:

• Gas Pressure Range : 0.5 - 5.0 mTorr • Microwave Power : 500 - 1500 Watts • Flow Rates : 5 - 10 sccm • Microwave Field : Circular TE(0,n) modes (2.45 GHz)

• Microwave Field Modes:

TE 01 TE 02

E H

REACTOR GEOMETRY AND OPERATING CONDITIONS

UNIVERSITY OF ILLINOISOPTICAL AND DISCHARGE PHYSICSIEEE98_8


MAGNETIC FIELD CONFIGURATION

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0

30

Radius (cm)20020

626 626

756 756

519519

847 847

911911

0

20 (a)

0

20

300 Height (cm)

(b)

Schematic representation of magnetic fluxfield lines (arrows) and magnetic fieldintensity, in gauss, (contours) inside an ECRprocessing chamber. ECR resonance, for2.45 GHz, occurs at 875 gauss.

• Schematic representation of themagnetic flux density in thedownstream of the reactorchamber. The magnetic flux ispresented (a) without activation ofthe submagnetic coil and (b) withsubmagnetic coil activation.

•


POWER DEPOSITION: TE(0,1), TE(0,2)• Power deposition occurs predominantly within 3% of the resonance zone (875 G). Although a small amount of power deposition occurs near the bottom coils due to a second resonance region created by the subcoil. • In the TE(0,2) mode the off axis zero results in two separated regions of power deposition. Such power profiles reflect incident electric field profiles.

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• N 2, 500 Watts, 1 mTorr, 10 sccm

0

30 Power

(W / cm 3)

1E+01

1E-03

TE(0,2)TE(0,1)

Radius (cm)20020


IONIZATION RATES: TE(0,1), TE(0,2)

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• Ionization rates follow power deposition profiles and are peaked off-axis.

• There is considerable ionization away from the resonance zone due to enhanced confinement of high energy electrons by static magnetic field lines.

Ionization Rate (cm -3 s-1)

1E+16

1E+14


0

30TE(0,2)TE(0,1)

Radius (cm)20020


ELECTRON DENSITIES: TE(0,1), TE(0,2)

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• Due to the enhanced confinement of electrons by magnetic field lines, densities tend to reflect sources. (Note the local maximum in density by the lower coil.)

• To account for anamolous diffusion of electrons across magnetic fields, a small isotropic correction factor was introduced for electron transport.

Electron Density (cm -3)

1.5E+11

1.0E+10


0

30TE(0,2)TE(0,1)

20020Radius (cm)

Radius (cm)0 5 10510

0

10

20

30

40

Experimental(R. Hidaka et al.)Theoretical

N2, 0.5 mTorr, 3 kW


ION SATURATION CURRENT VALIDATION

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• To validate flux to the substrate trends,control experiments conducted at KyushuUniveristy, Japan (R. Hidakaet al., Jpn. J.Appl. Physc. Vol. 32 (1993), pp. 174) weresimulated.

Microwave Power (kW)

1 20

10

20

Experimental(R. Hidaka et al.)

Theoretical

N2, 0.5 mTorr

• Radial distribution of the ion saturationcurrent density in the case of the TE(0,1)mode shows the ion saturation current isuniform within 5% over and 8 inchdiameter.

0.0

1.0 1016

2.0 1016

3.0 1016

4.0 1016

5.0 1016

6.0 1016

400 500 600 700 800 900 1000 1100

Average Ion Flux to the Substrate

Flu

x (

cm

-2 s

-1)

Microwave power (watts)

TE(0,1)

TE(0,2)


TOTAL ION FLUX TO SUBSTRATE

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0.2

0.4

0.6

0.8

1.0

0

• Flux of ions to the substrate reflects their off-axis production rates, and “tieing” of flux to magnetic field lines.

• These results suggest that ion flux uniformities depend more strongly on ionization locations than heating mechanisms.

Radial Ion Flux Profile for TE(0,1) Mode

Radial Ion Flux Profile for TE(0,2) Mode.

0.2

0.4

0.6

0.8

1.0

0


ELECTRON DENSITY DISTRIBUTION VERSUS PRESSURE

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• As pressure is decreased below 2 mTorr, there is shift in the peak density towards the center of the reactor. Such a result implies that the perpendicular diffusion is enhanced at lower pressures.

Pressure = 0.5 mTorr Pressure = 1.0 mTorr Pressure = 10.0 mTorr

• N2, 750 Watts, 10 sccm, TE(0,1) mode

• For the simulations performed the collision frequency was much smaller than the cyclotron frequency. In this regime, the perpendicular diffusion coefficient goes as the collision frequency; Dperp., ~ νm.

• The parallel diffusion coefficient goes as the inverse of the collision frequency; Dpara., ~ 1 / νm.

Density(cm-3)1E+11

5E+09

Density(cm-3)3E+11

1E+10

Density(cm-3)2E+11

1E+10


TOTAL ION FLUX TO THE SUBSTRATE

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• The ion flux profile, at the substrate, reflects the shift in peak density at lower pressures.

• The magnitude of the average ion flux, above 1 mTorr, follows an inverse pressure dependence.

• At higher pressures, the ion flux profile becomes increasingly uniform due to enhanced cross field diffusion.

Radius (cm)

10

1

0.5

100

Ion Flux to Substrate [5.0E+16/cm 2-s]


0.0

5.0 1015

1.0 1016

1.5 1016

2.0 1016

2.5 1016

3.0 1016

3.5 1016

4.0 1016

0.0

20.0

40.0

60.0

80.0

100.0

0.10 1.0 10 102

Ion Flux and Uniformity to the Substrate

Ave

rage

Flu

x (c

m

-2s-1

) Percent U

niformity (%

)

Pressure (mTorr)

0.0

0.20

0.40

0.60

0.80

1.0

0.10 1.0 10 102

Average Ion Flux x Flux Uniformity

Eff

icie

ncy

Pressure (mTorr)


EFFECTS OF COLLISION FREQUENCYON CROSS FIELD DIFFUSION

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• At pressures below 2 mTorr, the electron temperature increases dramatically due to enhanced power coupling of the incident wave to the plasma. • In the low pressure regime, the high temperature significantly affects the momentum transfer rate coefficient, thereby increasing the collision frequency. At higher pressures the collision frequency depends on the neutral gas density.

• Such results indicate that there exists an optimal pressure for maximizing ion flux and flux uniformity to the substrate.


0.0

2.0

4.0

6.0

8.0

10

0.10 1.0 10 102

Average Electron Temperature

Tem

pera

ture

(eV)

Pressure (mTorr)

0

2 10-7

4 10-7

6 10-7

8 10-7

1 10-6

0

2 1014

4 1014

6 1014

8 1014

1 1015

0.10 1.0 10 102

Momentum Transfer Rate and Gas Density

Ave

rage

Mom

entu

m T

rans

fer

Rat

e C

oeffi

cien

t (cm

-3s-1

)

Neutral G

as Density (cm

-3)

Pressure (mTorr)

TemperatureDependence

PressureDependence


CONCLUSIONS: ECR SOURCE MODELING

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• Simulation of such ECR systems indicate that magnetic field configuration, electromagnetic waveguide modes, and location of resonance strongly influence flux profiles to the substrate.

• Studies suggest that uniform fluxes at the substrate may require a power profile peaked off-axis.

• Lower order TE(0,n) modes tends to produce higher ion fluxes to the substrate, while higher order modes allow for greater uniformity across the substrate.

• At low pressures, < 1 mTorr, plasma dynamics depend highly on electron temperature. Cross field ion diffusion is enhanced by an increased momentum transfer rate coefficient.

• While at higher pressures, the electron temperature falls off due to thermalization and a decreasing efficiency in power coupling between the incident wave and the plasma. This leads to a cross field diffusion that is sensitive to neutral gas densities.

• Studies indicate that there exists an optimal pressure for maximum flux to the substrate and maximum flux uniformity.

SIMULATIONS OF ECR PROCESSING SYSTEMS SUSTAINED …

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