Simulation des Plasmajet-Hochratenätzens von massivem Quarzglas

Transkript

1 Simulation des Plasmajet-Hochratenätzens von massivem Quarzglas 3 cm Johannes Meister, Thomas Arnold 1

2 Outline 1. Plasma Jet Machining (PJM) 2. Motivation 3. Process simulation method Heat flux measurement Heat transfer model Temperature-dependent removal rate 4. Example and application 5. Summary 2

3 PJM: fluorine dry-etching Atmospheric plasma jet source Real Material etchingremoval process Ar, He, O 2, CF 4 Feed gas 2.45 GHz Microwave Microwave shielding Nozzle Plasma jet (ions + e - + neutrals) Shielding gas Plasma jet Plasma jet Waste gases F F Waste gases F F Waste gases F F Waste gases F F OF CO x NF F NOF x F x Gas phase O x N x 2 SiF x F COF reactions x O 2 SiF 4 O 2 SiF 4 Si x O y F z SiF 4 layer Surface reactions SiO SiO 2 2 SiO2 Radical jet (neutrals, e.g. F-atoms) SiO 2 + 4F SiF 4 + O 2 Material removal occurs by different chemical reactions between F-radicals and the surface material 3

4 Dwell time method PJM on a 2 oxidized silicon wafer Model equation Δh ( x,y) r( ) ( ) dxdy = A x x,y y t x, y Brief: Δh = r t Model variables Target removal: Δh Tool function: r Dwell time function: t Model assumptions Long-term stability of the tool Tool is spatial-independent Etching rate is linear 1 cm Basic concept: Plasma source is moved along e.g. meander path over the surface Designated removal is determined by velocity variation 4

5 Motivation Local heating-up effect Etching depth [µm] Groove etching with constant velocities mm/s 7 mm/s 5 mm/s 2 mm/s 1 mm/s y [mm] Global heating-up effect: Moving along a meander path with v = const. R V [mm 3 /min] Volume rate from grooves v [mm/s] -21 Resulting removal y A B x Etching depth [µm] Resulting topology Expected toplogoy Resulting topology Expected topology x [mm] 5

6 Etching process model Etching rate plasma jet Heat flux density plasma jet Heat sink Heat sink Heat sink Heat sink 1. Workpiece geometry (3D Cartesian) and its thermal properties 2. Determination of workpiece heat sinks 3. Determination of jet heat influx 4. Determination of temperature dependent removal rate and coupling with thermal model 5. Implementation of jet motion along the path 6

7 Experimental setup Ar, He, O 2, CF 4 Plasma jet - Gas flows: [O 2 ] 12 sccm [He] 125 sccm [Ar] 2 sccm [CF 4 ] 3 sccm [N 2 ] peripheral 9 sccm ø2 mm N 2 Outlet temperature 15 C - MW GHz: 417 W - Working distance 5 mm Sample - fused silica - ø15 mm, height: 18 mm 7

8 Measurement of heat flux 1. Measurement of surfaces temperatures z IR 2. Solving the transient heat transfer equation using the measured temperature fields as boundary conditions 3. Computing of the heat flux from full temperature field Symmetry ρ C p T t = ( k T ) Advantages (compared to conventional thermo probes): r High spatial and temporal resolution No influence of jet fluid dynamics IR Heat transfer is determined for the material used 8

9 Measurement of heat flux time [s] T top [K] Top temperature [K] time [s] Bottom Ttemperature bottom buttom [K] [K] time [s] r [mm] Q top [W/cm 2 ] r [mm] 3 time [s] r [mm] Q buttom [mw/cm 2 ] Top heat flux [W/cm 2 ] Bottom heat bottom flux [mw/cm 2 ] r [mm]

10 Modeling of heat transfer (FEM) Locally fixed etching in the center of a cylindrical workpiece z Heat flux density plasma jet Symmetry ρ C p T t Heat sink = ( k T ) Heat sink Heat sink r k Boundary condition: heat sink Heat conduction to ambience Natural convection Heat radiation T z = q& ( T ) i = top, bottom side ( cool ) i, Basis function heat influx: Spatial-dependent and temperaturedependent h jet (local heat transfer coefficient) T jet (local average jet temperature) q& jet ( T ) ( r, T ) = h ( r) T ( r) jet jet 1

11 Modeling of heat transfer: Heat sinks Determination of cooling efflux function from measured cooling flux Assumption: cooling depends only on surface temperature Top cooling heat flux Bottom cooling heat flux ( ) ( T ) q& cool top ( ) ( T ) q& cool bottom 11

12 Modeling of heat transfer: Plasma jet Basis function heat influx: Spatial-dependent and temperature-dependent h jet (local heat transfer coefficient) T jet (local average jet temperature) q& jet ( r, T ) = h ( r) T ( r) jet ( T ) jet h jet [mw/(cm 2 K)] Local heat transfer coefficient h jet Q(r= mm) [W/cm 2 ] Heat transfer workpiece center Temperature [K] T jet [K] r [mm] Local average jet temperature T jet r [mm] 12

13 Heat transfer model Temperature [K] Measurement Simulation r = mm r = 1 mm r = 3mm r = 5 mm r = 1 mm r = 2 mm Comparison transient temperature evolution of certain radial positions Verification of heat model by reproducing heating and cooling of the test etching time [s] Extrusion to 3D Cartesian Implementation of jet motion by time dependent boundary condition Temperature [K] Measurement Simulation x [mm] 13

14 Temperature-dependent removal rate ( r, T ) = j ( r) g ( T ) Generalized removal rate model R Arrhenius-Model: Required for computing of j F (r) and g T (T): 1. Multiple groove etchings with different velocities 2. Corresponding temperature profiles F T g T EA ( T ) = exp( ) k B T Etching depth [µm] mm/s 7 mm/s 5 mm/s 2 mm/s 1 mm/s mm/s mm/s -5 5 x [mm] C j F [µm/s] g(t) [1] r [mm] Temperature [K] 14

15 Simulation of the etching process Path: Archimedean spiral with line spacing.45 mm and r = 65 mm From the outside to the center Jet motion: 5 mm/s Machining time: 1 h 38 min Removal profile without temperature dependency Etching depth [u.a.] x [mm] 15

16 Application for topology error compensation Simulation is very time-consuming Embedding into conventional dwell time calculation Computing the dwell times for a desired removal by the conventional method (deconvolution) Enhanced Process simulation with dwell time field Repeat if necessary Determining the dwell times for the corrected topology This method converges very well Topology correction leads in general to a minor temperature field changes that results a very small new topology error Hence, one correction step might be sufficient 16

17 Summary 1. PJM with high-power plasma sources causes thermal induced nonlinear effects 2. A etching model based on a heat transfer model was introduced 3. A workflow for the model s unknown determination was also presented 4. The method predicts the thermal induced topology errors 5. The model can be easily embedded into the conventional dwell time calculation 17

18 Thanks to Dr. Martin Weiser und Dr. Sebastian Vauth from Zeiss SMT Thank you for your kind attention! 18