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Chip Scale Review March • April • 2019


Multiscale models for electroplating of TSVs

By M. S. Bharathi, K. H. Khoo, H. Ramanarayan, J. Hongmei, S. Wu, C. A. Joshi, S. S. Quek, D. T. Wu, N. Sridhar


of High Performance Computing]

; L. MingRui

[National University of Singapore

]; K. R. Mangipudi

[Indian Institute of

Technology, Bhubaneshwar]

; J. J. Cheng

[Institute of Materials Research and Engineering]

hrough-silicon vias (TSVs)

used in three-dimensional

i n t e g r a t e d c i r c u i t s

a r e a me a n s of r e a l i z i ng ve r t i c a l

interconnects of stacked silicon wafers

a r c h i t e c t u r e t o a c h i e ve s u p e r i o r

electrical performance at a lower cost.

Nevertheless, as the package size get

smaller, the aspect ratio of the TSVs

increases, which can result in defects

in them during their deposition. These

defects, which include voids, seams,

i mpu r i t ie s a nd g r a i n bou nd a r ie s ,

degrade the electrical and mechanical

performance of the system.

Apa r t f rom t he a spect r at io and

plating conditions, the deposition of

TSVs are heavily inf luenced by the

chemical and transport properties of the

additives used in the plating solution.

A full understanding of these various

factors, and therefore the electroplating

process, can be achieved through an

integration of multiscale modeling and

experimental characterization and tests

of the process. Yang, et. al, coupled

a nu cl e a t ion mod el a t t he m i c r o -

scale along with a current distribution

model to understand the multiscale

behavior of electroplating [1,2]. They

also developed a dynamically-coupled

kinetic Monte Carlo (KMC) model for

surface reactions with a finite volume

model fo r t r a n s po r t a nd chemica l

reactions and a level-set model that

tracks the metal/electrolyte interface

ma c r o s copic a l ly. The s e model i ng

me t hod s , howeve r, do not i nclude

f irst-pr inciple methods essential to

compute the adsorption and transport

properties and the reaction pathways

and activation barriers of the additives.

Here, we present sequential multiscale

modeling tools including first-principle

ca lcu lat ion s a nd a KMC model t o

provide growth guidelines for defect-

f r e e ele c t r oplat i ng of h igh a spe c t

ratio Cu interconnects.

The electrolyte for the electroplating of

copper has multiple additives, which have

varying reactive, adsorption and transport

properties. Apart from the chemical

interactions of the additives in the

electrolyte, the adsorption and transport

properties of the additives determine

their local concentrations and gradients

in the TSV. As the role of additives is to

enhance metallization at the bottom of

the TSV (and suppressing metallization

near the top), it is essential to optimize the

concentration gradients of the additives

in the TSV. Due to the different time and

length scales of these processes during

the electroplating, we employ multiscale

modeling tools to study the process. The

chemistry of the electroplating process,

which includes studying the roles of the

various additives, is carried out using

density functional theory (DFT) and

molecular dynamics (MD) simulations.

The filling of the TSVs by electroplating is

studied at the continuum scale using level-

set methods to track the growth interface.

A KMC model has been developed to

bridge the scales between these two

schemes of studying the electroplating

of copper. These models will study the

electroplating of TSVs as a function of

parameters including the concentrations,

diffusivities, adsorption properties of ions

and additives, applied current density,

and temperature. In this work, we present

the results of our DFT studies on the

mechanisms of the additives and the KMC

model to understand the transport and

adsorption properties of additives during

electroplating of TSVs.

Density functional theory studies

We have studied the mechanism for the

accelerating effect of bis-3-sulfopropyl

disulfide (SPS) and suppressing effect

of polyethylene-glycol (PEG), both of

which are widely used additives in TSV

copper plating. We employ first-principles

DFT calculations to study the energetics

of several adsorptions, dissociation and

displacement reactions that have been

proposed to explain the action of the

additives [3,4]. In our calculations, the

Cu electrode and adsorbate molecules are

modeled at the DFT level and the water

solvent is represented through an implicit

model based on the Poisson-Boltzmann

equation [5]. This model incorporates

the dielectric screening on account of

the permittivity of the solvent and the

electrostatic shielding due to the mobile

ions in the electrolyte. The tuning of the

electrochemical potential is achieved

by charging the system and tracking the

changes to the workfunction [6]. The

free energy of the electron-ion pairs in

electrochemical reactions are evaluated

u si ng t he comput at ional hyd rogen

electrode (CHE) and linear free energy

relationship for electrode potentials

(LFER-EP) [7]. In addition, we have also

tried to include the dispersion forces using

the DFT-D2 scheme to compensate for

deficiencies in GGA xc-functionals [8].

PEG suppressor

In copper deposition f rom a Cu


solution, the basic plating reaction

proceeds via two steps, from Cu





, which is the rate determining step,

and Cu


to Cu, which is much faster.

The plating in the presence of additives

occurs through a large number of possible

interconnected reactions that happen

between the Cu surface, additives and

various ions [3]. The first reaction is the

adsorption of the suppressor PEG at the

outer surface of the via, as PEG diffuses

slowly and adsorbs quickly. In a Cl



containing solution, it was proposed

that PEG grasps the positive Cu ions

to form a complex, which then binds

to the negatively-charged Cl


ions on

the Cu surface [9]. This results in the

formations of a PEG-Cu





on the copper surface that has been

verified by surface-enhanced Raman