Prior to conducting the simulations, the current flow
was analyzed by applying the voltage bias method proposed
in the experimental setup, assuming the structure as a single resistive element. A potential difference was established
by applying 3V to the end of the lower structure
and 0V to the end of the upper structure, which served
as the basis for evaluating the current density distribution
and resistance variation at the bonding interface. Based on
these conditions, FEM-based simulations using the Ansys
Simulation Tool were conducted to analyze the resistance
variations and current density distribution under different
misalignment conditions. Through these simulations, the
current flow paths within the bonding structure were visualized,
and the quantitative changes in resistance as misalignment
increased were evaluated.
Figs. 3 and 4 present the simulation results of the current
density distribution at the bonding interface. Figs. 3
and 4 show the topmost surface of the lower metal line.
The red dashed box indicates the junction area with the
upper metal line. Fig. 3 illustrates the thermal profile and
current density distribution when the misalignment varies
from 0 to 20 mm in a metal interconnect structure with
a line width of 20 mm, while Fig. 4 shows the distribution
for a structure with a 40 mm line width and misalignment ranging from 0 to 40 mm. As shown in Fig.
3, the regions with higher current density exhibit higher
temperatures, indicating that the thermal profile closely
follows the shape of the current density distribution. The
red dashed rectangular regions in each figure indicate the
bonding interface between the upper and lower structures.
The simulation results reveal that, regardless of the line
width, the current density remains low at the central region
of the bonding interface. Additionally, a higher current
density was observed at the metal edges opposite to
the direction of the applied voltage, whereas the edges perpendicular
to the current flow exhibited relatively lower
current density. As the misalignment increased, this nonuniformity
in current density distribution gradually diminished.
Notably, the central region of the bonding interface
maintained consistently low current density regardless
of the misalignment magnitude, whereas the perpendicular
edge regions exhibited an increasing trend in current
density as misalignment became more pronounced.
This suggests that misalignment does not result in a uniform
change in current density across the bonding interface
but rather redistributes the current density, concentrating
it in specific regions. Consequently, even when
composed of identical materials, the resistance may vary
across different regions. If the regions prone to high current
density can be identified and structurally expanded,
the overall resistance of the structure can be reduced,
thereby improving signal transmission efficiency.
An increase in current density indicates a concentration
of current flow in specific regions, implying that structural
changes lead to current path redistribution. However, this
may also induce localized current crowding effects, necessitating
consideration of the resulting electrical property
variations. Therefore, when evaluating the impact of
misalignment on the electrical characteristics of the bonding
interface, it is crucial to recognize that misalignment
not only reduces the total contact area but also redistributes
current flow, altering the electrical equilibrium of
the bonding structure.
Figs. 5(a) and 5(b) present the current density variations
across different regions as a function of increasing misalignment
for metal structures with 20 mm and 40 mm line
widths, respectively. In the simulations, misalignment was
applied by shifting the upper structure to the right, with the
x-axis of each graph representing the degree of misalignment.
The three curves in each graph represent the current
density variations at the Top, Middle, and Bottom regions,
which specifically refer to three distinct positions—upper, central, and lower points, respectively—along the
left edge of the lower metal structure. The Bottom region
is closest to the applied voltage, the Top region is the farthest,
and theMiddle region corresponds to the area where
the most significant variations in current density were observed
in Figs. 3 and 4.
Through simulations, the impact of misalignment in
bonding structures on current density distribution and resistance
was analyzed. In the absence of misalignment,
current density was primarily concentrated in the top and
bottom metal regions, indicating that current flowed efficiently
through these areas. In contrast, the middle region
exhibited relatively low current density, as it contributed
less to the primary current path.
As misalignment increased, noticeable changes in current
density distribution were observed. The top metal region
exhibited a higher current density than the bottom
region, suggesting that current flow was asymmetrically
redistributed due to misalignment. Notably, the middle
metal region, which initially had a low current density, experienced
a sharp increase as misalignment grew. These
findings indicate that as misalignment increases, the regions
of concentrated current shift, leading to localized
increases in current density. This suggests that misalign ment does not merely reduce the effective contact area but
also alters the current flow pattern, concentrating current
in specific regions and modifying the overall signal transmission
characteristics.
Based on this analysis, structural design improvements
should be explored to enhance electrical signal transmission
efficiency despite misalignment. By designing structures
that maximize the effective conduction path, it may
be possible to improve power efficiency through simple
structural modifications rather than complex material
changes.
In conclusion, optimizing the structure to ensure that
the edge of the bonding interface interacts more extensively
with the applied electrical signal can enhance overall
signal transmission efficiency. Such a design approach
could contribute to the optimization of interconnect and
bonding structures in semiconductor devices.
In a 20-mm width structure, the cross-sectional view of the bonding interface. Thermal profile (Temperature) and Current density profile are same.
In a 40-μmm width structure, the cross-sectional view of the bonding interface.
Current density distribution in a bonding metal structure with misalignment (a) 20-μm line width, (b) 40-μm line width.