Simulation of Copper Electrodeposition in Through-Hole Vias

Abstract

Copper electrodeposition processes for filling metallized through-hole (TH) and through-silicon vias (TSV) depend on spatially selective breakdown of a co-adsorbed polyether-chloride adlayer within the recessed surface features. In this work, a co-adsorption-dependent suppression model that has previously captured experimental observations of localized Cu deposition in TSV is used to explore filling of TH features. Simulations of potentiodynamic and galvanostatic TH filling are presented. An appropriate applied potential or current localizes deposition to the middle of the TH. Subsequent deposition proceeds most rapidly in the radial direction leading to sidewall impingement at the via center creating two blind vias. The growth front then evolves primarily toward the two via openings to completely fill the TH in a manner analogous to TSV filling. Applied potentials, or currents, that are overly reducing result in metal ion depletion within the via and void formation. Simulations in larger TH features (i.e., diameter = 85 μm instead of 10 μm) indicate that lateral diffusional gradients within the via can lead to fluctuations between active and passive deposition along the metal/electrolyte interface.

Figure 1.

Schematic of (a) 1-D and (b) 2-D axisymmetric geometries used in the S-NDR model to simulate cyclic voltammetry and through-hole via filling, respectively. Relevant domains and boundaries are indicated with r_i(z, t) and z_i(r, t) defining the spatially and temporally dependent location of the metal/electrolyte interface. For through-hole simulations, once the radial growth of the deposit reaches r_i(0, t) ≤ 0.01R_TH the equations governing the boundary at z = 0 () are changed to those of the electrode ().

Figure 2.

Simulations of cyclic voltammetry at 1 mV/s using a 2-additive (halide-suppressor) S-NDR model for Cu electrodeposition in solution containing 0.88 mol/L CuSO₄ and 0.18 mol/L H₂SO₄ without additives (···) and with 20 μmol/L NaCl and 40 μmol/L polyether suppressor (─). Post experimental iR-correction is for an electrochemical cell with 5 Ω total resistance. The 1-D simulation assumes a fixed boundary layer of 25 μm and electrode area of 0.196 cm² with other parameters from Table I.

Figure 3.

Simulations of potential stepped copper electrodeposition in a through-hole via of aspect ratio 4 at the indicated times. Isocontours of chloride concentration normalized by the bulk concentration are overlaid in the electrolyte domain. The rightmost image shows filling contours at 2 min intervals colorized to indicate local current density at the evolving metal/electrolyte interface. Applied potential steps, relative to the reversible Cu/Cu²⁺ electrode are: −0.12 V to 12 min, −0.14 V to 22 min, −0.16 V to 30 min, and −0.18 V to 40 min; contours at 12 min, 22 min, and 30 min are concurrent with the potential steps. Via radius is 5 μm, via height is 40 μm, and simulated cell radius is 15 μm (full cell domain is not shown). The boundary layer is fixed at 25 μm from the TH field.

Figure 4.

Applied potential (···) program and selected local current density transients (─) for potential-controlled copper electrodeposition in the through-hole via depicted in Fig. 3. Current densities are sampled on the sidewall at mid-height of the via (defined as r = r_i(0, t) until impingement of the sidewall deposits and z = z_i(0, t) thereafter) and on the field at the cell edge (z = z_i(R_c, t)). The applied potential and overpotential are sampled at the via middle. The elapsed time for via closure upon impingement of the sidewall deposits, corresponding to the simulation in Fig. 3 (t = 15 min 32 s), is indicated by the green arrow. Black arrows are used to indicate corresponding axes to line types (solid or dashed).

Figure 5.

Simulations of galvanostatic copper electrodeposition in through-hole vias of an aspect ratio of 2 (upper) and 4 (lower) at the indicated times. Isocontours of chloride concentration normalized by the bulk concentration are overlaid in the electrolyte domain. The rightmost image in each row shows filling contours at 3 min intervals with the lines colorized to indicate local current density values at the evolving metal/electrolyte interface. Via radius is 5 μm and simulated cell radius is 15 μm for both aspect ratios (full cell domain is not shown). The boundary layer (δ) is fixed at 25 μm from the field and applied current density is −2.4 mA/cm² (defined current imposed using projected area πR_c²) for both aspect ratios.

Figure 6.

Selected local current density (─) and potential (···) transients for galvanostatic copper electrodeposition in the (a) AR = 2 and (b) AR = 4 through-hole vias simulated in Fig. 5. Current densities are sampled on the sidewall on the midline of the via (defined as r = r_i(0, t) until impingement of the sidewall deposits and z = z_i(0, t) thereafter and on the field at the cell edge (z = z_i(R_c, t)). Applied potential and overpotential are sampled at the via middle. The elapsed time for via closure upon impingement of the sidewall deposits, corresponding to the simulations in Fig. 5 (t = 12 min 40 s and t = 16 min 57 s), are indicated by the green arrow. Black arrows are used to indicate corresponding axes to line types (solid or dashed).

Figure 7.

Simulations of copper electrodeposition in through-hole vias resulting in void formation under potentiostatic (−0.16 V) and galvanostatic (−9.6 mA/cm²) operating conditions. Isocontours of chloride concentration normalized by the bulk concentration are overlaid in the electrolyte domain. The right hand images show filling contours at 1 min intervals with the lines colorized to show local suppressor coverage at the evolving metal/electrolyte interface. Via radius is 5 μm, aspect ratio is 4, and simulated cell radius is 15 μm for both simulations (full cell domain is not shown). The boundary layer (δ) is fixed at 25 μm from the TH field.

Figure 8.

Simulations of galvanostatic copper electrodeposition in an 85 μm diameter and 150 μm deep through-hole via at −1.5 mA/cm² (defined current imposed using projected area πR_c²) at the indicated times. Isocontours of chloride concentration normalized by the bulk concentration are overlaid in the electrolyte domain. The rightmost image shows filling contours at 20 min intervals with the lines colorized to indicate local current density at the metal/electrolyte interface. The boundary layer is fixed at 6.25 μm from the TH field and simulated cell radius is 127.5 μm (full cell domain is not shown).

Figure 9.

(a) Local current density (─) and potential (···) transients for galvanostatic copper electrodeposition (−1.5 mA/cm²) and (b) magnified growth contours in the through-hole via simulated in Fig. 8. Current densities are sampled on the sidewall on the midline of the via (r = r_i(0, t)) and on the field at the cell edge (z = z_i(R_c, t)). Overpotential and applied potential are sampled at the via middle. The elapsed time for via closure upon impingement of the sidewall deposits, corresponding to the simulation in Fig. 8 (t = 2.75 hr) is indicated by the green arrow. Black arrows are used to indicate corresponding axes to line types (solid or dashed). Contour lines are the same as in Fig. 8, spaced 20 min apart and colorized to indicate local current density.