Neue Prozedur zur Prozesssimulation bei der Plasmajetbearbeitung

Transkript

1 Neue Prozedur zur Prozesssimulation bei der Plasmajetbearbeitung 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. Examples and application 5. Summary 2

3 PJM: fluorine dry-etching Atmospheric plasma jet source Material removal Ar, He, O 2, CF 4 Total: 2.5 slm Feed gas 2.45 GHz Microwave (4 W) Microwave shielding Nozzle Plasma jet (ions + e - + neutrals) Waste gases SiF 4 O 2 SiF 4 SiF 4 Shielding gas N 2 SiO 2 SiO 2 O 2 Plasma jet F F F F F F F F F F F O 2 Waste gases 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 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 High-rate PJM of optical components PJM bridges the gap between ion beam figuring and conventional grinding High removal rate No vacuum necessary Contract-free machining 3 cm Main application: Aspherization of optical components made of fused silica 5

6 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. y A Etching depth [µm] R V [mm 3 /min] Volume rate from grooves v [mm/s] Resulting removal B x Real etching profile Expected profile y [mm] 6

7 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 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] r [mm] r [mm] 3 time [s] Q top [W/cm 2 ] Top heat flux [W/cm 2 ] r [mm] time [s] Q buttom [mw/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 Bottom cooling heat flux Top 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 ( T ) ( r, T ) = h ( r) T ( r) jet jet Local heat transfer coefficient h jet Heat transfer workpiece center Local average jet temperature T jet 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/meander etchings with different velocities 2. Corresponding temperature profiles 5 4 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 -5 5 x [mm] C j F [µm/s] g T [1] r [mm] Temperature [K] 14

15 Simulation of the etching process: Spiral Path: Archimedean spiral with line spacing.45 mm and r = 65 mm Jet motion: 5 mm/s Machining time: 1 h 38 min Sample: fused silica ø15 mm, height: 18 mm Removal profile without temperature dependency -5 simulation etching Etching depth [u.a.] etching depth [µm] x [mm] y[mm] 15

16 Simulation of the etching process: Wedge Wedge: v start = 2 mm/s v end = 1 mm/s Path: Meander with line spacing.5 mm Machining time: 4 min Sample: fused silica ø15 mm, height: 17 mm Etching depth [µm] Simulation Conventional model Real Etching x [mm] 16

17 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 * DTCALC by A. Nickel, IOM Leipzig 17

18 Application for topology error compensation E N S W Target topography: convex asphere (paraboloid) Path: Meander with line spacing.5 mm Machining time: 45 min Sample: fused silica ø1 mm, height: 1 mm Compensated Uncompensated Etching depth [µm] Etching depth [µm] N Target topography Real etching Simulation y [mm] N Target topography Real etching Simulation S y [mm] Etching depth [µm] Etching depth [µm] S W E W Target topography Real etching Simulation x [mm] Target topography Real etching Simulation E x [mm] 18

19 PJM on thin plate: Uncompensated asphere Temperature [K] N W E Dimension: 1 mm x 1 mm x 2.5 mm S -2 S N -2 E W Etching depth [µm] Simulation Target Real etching (thin plate) Real etching (thick disk) y [mm] Etching depth [µm] Simulation Target Real etching (thin plate) Real etching (thick disk) x [mm] 19

20 Summary 1. PJM with high-power plasma sources causes thermal induced nonlinear effects 2. An etching model based on a heat transfer model was introduced 3. The model s unknown can be determined on base of infrared thermography and test etchings 4. The method predicts the thermal induced topology errors and absolute removal 5. The model can be easily embedded into the conventional dwell time calculation 2

21 Thank you for your kind attention! 21