A Tertiary Current Distribution Model with Complex Additive Chemistry and Turbulent Flow

Transcription

1 A Tertiary Current Distribution Model with Complex Additive Chemistry and Turbulent Flow L. A. Gochberg a and J.-C. Sheu b a Novellus Systems, Inc., San Jose, CA, b CFD Research, Corp., Huntsville, AL 1

2 Outline Outline Background Model Description Results Conclusions 2

3 Background Three major categories for electroplating models Primary current models Ohmic voltage drop only in plating bath Secondary current models Primary current with an additional voltage drop at the deposition surface, defined by the electrode kinetics Can also include terminal effect (seed layer voltage drop) Tertiary current models Include multiple coupled physical effects (not always all at once) Electrical current flow (in bath and seed layer) Mass transfer Fluid flow (laminar or turbulent) Additive chemistry Blanket surface deposition (surface chemistry) Heat transfer 3

4 Background A significant amount of modeling work has been done, particularly in electroplating of copper Numerous papers have been published using primary and secondary current models (with and without terminal effects) There have also been models done combining laminar fluid flow with diffusion and simple chemistries (i.e. just a few chemical species and reactions) Some examples can be seen in the works of Hebert and Alkire Several complex additive chemistries in copper plating have been discussed (Kim, MIT Ph.D., 2002, Drews, et. al., 204 th ECS, 2003, and Vereecken et. al., IBM J. Res. & Dev., 2005) At least one of these chemistries was employed in a model which including simple fluid flow (via analytical equations or laminar flow) 4

5 Background There is no known published work involving all the listed physical mechanisms with turbulent flow One possible exception is Dubin, et. al (Future Fab International, Vol. 13 (2002)) They did not specifically claim the ability to do turbulent flow, nor did they provide details about the model Sheu, et. al (204 th ECS Meeting, 2003) showed the following using the commercial software, CFD-ACE+: Demo of 2D, 3D, transient, secondary, and tertiary results Validation examples for several published experimental data sets, but not for a complex additive chemistry Turbulent flow was readily available in this model 5

6 Background Here, we use the same CFD-ACE+ software to present a validation case for the following: Comprehensive tertiary current distribution model with turbulent flow Additive chemistry from G. S. Kim (MIT Ph.D., 2002) Experimental data from J. Reid (available in G. S. Kim thesis) Kim s thesis work is now in the process of being submitted to the ECS Journal 6

7 Model Description CFD-ACE+ (from ESI-CFD, Huntsville, AL) Commercially available, multi-disciplinary, 3D unstructured software package Modules for fluid dynamics, ion transport, and surface chemistry, have been well-developed and validated In particular, special electroplating features include: Coupling of the electrochemical mechanism into surface reaction chemistry Butler-Volmer kinetics for transfer current density Active site competition theory for describing additive chemistry Turbulent diffusivity models at walls for high RPM rotating flow Boundary conditions for secondary and tertiary current models Provisions for seed layer current flow (the terminal effect ) 7

8 Model Description Description of a 14-step additive chemistry (Kim, 2002) No Reactant Product Reaction Types Parameters 1 Cu(II) + θ v +e - Cu(I) ads Reductive k 1, k -1, β 1 Adsorption 2 Cu(I) ads +e - Cu + θ v Reduction k 2, k -2, β 2 3 Cu(II) + SPS ads - SPS ads -Cu(I) ads Reductive k 1, k -1, β 1 θ v +e - Adsorption 4 SPS ads -Cu(I) ads +e - Cu + SPS ads -θ v Reduction k 2, k -2, β 2 5 Cu(II) + Cl ads -θ v +e - Cl ads -Cu(I) ads Reductive Adsorption k 1, k -1, β 1 6 Cl ads -Cu(I) ads +e - Cu + Cl ads -θ v Reduction k 2, k -2, β 2 7 SPS + θ v SPS ads Adsorption k sps1, k sps-1 8 SPS ads + θ v SPS ads -θ v K sps2 9 SPS ads Incorporated + θ v Incorporation i k sps 10 Cl + θ v Cl ads Adsorption k cl1, k cl-1 11 Cl ads + θ v Cl ads -θ v K cl2 12 Cl ads Incorporated + θ v Incorporation i k cl 13 PPG +n θ v PPG ads Adsorption k peg1, k peg-1 14 PPG ads Incorporated +n θ v Incorporation i k peg PPG: Polypropylene glycol (MW = 1200) SPS: bis-(sodium sulfroprophyl) disulfide 8

9 Model Description The model used a 2D axisymmetric geometrical approximation to a 200-mm fountain-type plating cell exit exit contact Seed layer contact shield shield anode anode inlet References: 1) McInerney & Gochberg, 201 st ECS Meeting (2002) 2) Gochberg, 196 th ECS Meeting (1999) 9

10 Model Description Experimental operating conditions Parameter Rotation Speed Flow Rate from center jet H 2 SO 4 Concentration CuSO 4 Concentration HCl Concentration PPG 1200 Concentration SPS Concentration Applied current Seed layer thickness Wafer size Value 100 RPM 8 slm 1.78 M 0.11 M 50 PPM 300 PPM 6 PPM 6 A 50 nm mm diameter 10

11 Results Tertiary current model with k-ε turbulence model Result on left shows a numerical artifact in the model Model on right has an improved mesh quality at the center 1.50 Experiment, time = 0.00 sec Experiment, time = sec Experiment, time = 0.00 sec Experiment, time = sec Experiment, time = sec Experiment, time = sec Experiment, time = sec Experiment, time = sec Tertiary, time = 0.00 sec Tertiary, time = sec Tertiary, time = 0.00 sec Tertiary, time = sec 1.25 Tertiary, time = sec Tertiary, time = sec Tertiary, time = sec Tertiary, time = sec Layer Thickness (micron) Layer Thickness (micron) Radius (m) Radius (m) k-ε models are typically not used in these rotating flows 11

12 Results Tertiary current model with low Reynolds k-ε model Low Re k-ε turbulence model by Chien (1982) No fine mesh resolution in the boundary layer 1.50 Experiment, time = 0.00 sec Experiment, time = sec Experiment, time = sec Experiment, time = sec 1.25 Tertiary, time = 0.00 sec Tertiary, time = sec Tertiary, time = sec Tertiary, time = sec Layer Thickness (micron) Radius (m) 12

13 Results It is known that k-ε type turbulence models suffer from insufficient resolution in the boundary layer There are two common solutions to this issue Make a fine mesh at the boundary Apply a turbulent wall diffusivity correction to the k-ε model Achieving adequate mesh resolution in boundary layers is highly computationally intensive Here, two different wall diffusivity correction methods were tested Rosen and Tragardh (1994) Sherwood (1959) 13

14 Results Tertiary current models were performed with two different turbulent diffusivity corrections 1.50 Experiment, time = 0.00 sec Experiment, time = sec Experiment, time = 0.00 sec Experiment, time = sec Experiment, time = sec Experiment, time = sec Experiment, time = sec Experiment, time = sec CFD Result, time = 0.00 sec CFD Result, time = sec CFD Result, time = 0.00 sec CFD Result, time = sec CFD Result, time = sec CFD Result, time = sec 1.25 CFD Result, time = sec CFD Result, time = sec Layer Thickness (micron) Layer Thickness (micron) Radius (m) Radius (m) Rosen-Tragardh (1995) Sherwood (1959) 14

15 Results Secondary current using an experimental Tafel curve The simple model does a very good job of matching data But, the tertiary model has the capability to predict additive depletion effects which were not evident in these data Layer Thickness (micron) Experiment, time = 0.00 sec Experiment, time = sec Experiment, time = sec Experiment, time = sec Secondary, time = 0.00 sec Secondary, time = sec Secondary, time = sec Secondary, time = sec Radius (m) 15

16 Conclusions A computational electroplating modeling capability was validated with experimental data using a complex additive chemistry and turbulent flow This is believed to be the first time such a model has been presented in the open domain A variety of turbulence models were tested for accuracy in these rotating flow situations The general purpose k-ε turbulence models were not adequate to accurately model the problem With a turbulent diffusivity correction, a low Reynolds number k-ε model matched well with the data Boundary layer mesh refinement was not tested (long run times) 16

17 Conclusions Though the results using a 14-step additive chemistry for copper electroplating (SPS/PPG/Cl) did not exhibit additive depletion effects, the model is capable of predicting such phenomenon Depletion phenomenon will show up with some additive chemistries as well as in systems where the flow can create such effects 17