Numerical Analysis of the Correlation between the Cu+ Ion Concentration and the Current Density

Introduction

  3D chip stacking realize high-density packaging and high-speed performance. High-aspect-ratio through-silicon via(TSV) allow short interconnects and reduced signal delays. This TSV interconnection will be applied to wide I/O memories of the next generation smart phone. Cu electrodeposition in high-aspect-ratio via is one of the key technologies for 3D packaging. Voids or seams formed in the via may causes serious problems in reliability. The formation of the Cu⁺ ion is a crucial intermediate and the Cu⁺ion intermediate is always produced during the electrodeposition process (eq.1 and 2).

  We already reported that 4 μm diameter via of aspect ratio of 7.5 is perfectly filled with the increasing Cu⁺ ion concentration inside the via[1,2]. Additionally, K. Kondo et al. have reported that a large amount of Cu⁺ ion within the confined area of the trench of the trench bottom electrodes and experimentally verified the relation between the Cu⁺ ion and acceleration[3]. In this study, we have calculated the Cu⁺ion concentration shifting at the trench bottom during electrodeposition by using COMSOL Multiphysics.

Numerical Analysis

  The simulation model is shown Fig.1. We have assumed that the electrode surface is only trench bottom. And the reaction equations of Cu²⁺ ion and Cu⁺ ion at trench bottom are shown eq.3 and 4. The reaction kinetic parameters, k₁, k_-1, k₂ and k_-2 have been reported our previous study[2]. The reaction kinetic parameter from Cu²⁺ ion to Cu⁺ ion, k₁ as 8.4×10^-8 m/s, that from Cu⁺ ion to metallic Cu, k₂ as 5.5×10^-5 m/s, that from Cu⁺ ion to metal Cu²⁺, k_-1 as 7.0×10^-6 m/s, that from metallic Cu to Cu⁺ ion, k_-2 as 1.6×10^-8 m/s. Additionally, the diffusion equations in the electrolyte are shown eq.5 and 6. In this simulation model, the reverse current has been applied from 1 to 13 s, and the off-time has been applied from 0 to 1 s and 13 to20 s.

Results and discussion

  We have calculated the Cu⁺ ion concentration shifting at the trench bottom with various trench widths. The calculation results are shown in Fig. 2. From Fig. 2, we have understood that the Cu⁺ ion concentration increase with the reverse current(1s to 13 s) and the off-time(13s to 20 s) with narrowing trench widths.

  Figure 3 shows the result of LSV measurements by using trench-shaped through mask electrode that reported in reference 3. Before measurements, the trench bottom electrode has been dissolved for 12 s with 10 mA/cm² in order to produce Cu⁺ ion at the trench bottom. From Fig. 3, we have understood the current density increase with narrowing trench widths.

Cu(I)Thiolate formation and acceleration effect will be discussed at the meeting.

[1] T. Hayashi et al., J. Electrochem. Soc., 160(6) D256 (2013).

[2] T. Hayashi et al., ECS 224^thMeeting (2013).

[3] K. Kondo et al., ECS Electrochem Lett., 3(4) D3 (2014).