is not known, we compute the partition function of the right diagram and call
it $Z^{(b)}$. To this end, we first divide the diagram (b) into two parts,
left and right building blocks:

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{{}{}}{}{}\pgfsys@moveto{21.33957pt}{-18.49411pt}\pgfsys@lineto{27.03003pt}{-12.80365pt}\pgfsys@stroke\pgfsys@invoke{
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} {}{{}}{}
{{}{}}{}{}\pgfsys@moveto{145.10925pt}{19.91684pt}\pgfsys@lineto{139.4188pt}{19.91684pt}\pgfsys@stroke\pgfsys@invoke{
} {}{{}}{}
{{}{}}{}{}\pgfsys@moveto{162.18065pt}{-36.98866pt}\pgfsys@lineto{167.87111pt}{-31.2982pt}\pgfsys@stroke\pgfsys@invoke{
} {}{{}}{}
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} {{}}{}{{}}{}
{{}{}}{}{}\pgfsys@moveto{202.01477pt}{8.5359pt}\pgfsys@lineto{196.32431pt}{8.5359pt}\pgfsys@stroke\pgfsys@invoke{
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{}{}{}{}{}}}{}{}\hss}\pgfsys@discardpath\pgfsys@invoke{\lxSVG@closescope
}\pgfsys@endscope\hss}}\lxSVG@closescope\endpgfpicture}}\ .\normalsize$ (279)

We label the topological vertex computation of the left and the right building
blocks respectively as $Z^{{\rm L}}(\mu_{b})$ and $Z^{{\rm R}}(\mu_{b})$,
where the middle edges are associated with Young diagram $\mu_{b}$, and the
partition function is given as a sum of this $\mu_{b}$,

$\displaystyle Z^{(b)}$
$\displaystyle=\sum_{\mu_{b}}\,(-Q_{b})^{|\mu_{b}|}\,Z^{\rm L}(\mu_{b})Z^{\rm
R}(\mu_{b})\ ,$ (280)

where each piece is given by

$\displaystyle Z^{\rm L}(\mu_{b})$
$\displaystyle=\sum_{\nu_{1,2,3}}(-Q)^{|\nu_{1}|+|\nu_{2}|}(-Q_{f}Q^{-1})^{|\nu_{3}|}$
$\displaystyle\hskip
36.98857pt\times\tilde{f}^{-1}_{\nu_{3}}(\mathfrak{q},\mathfrak{t})C_{\nu_{3}\nu_{1}^{t}\text{\o}}(\mathfrak{t},\mathfrak{q})C_{\nu_{2}^{t}\nu_{1}\mu_{b}^{t}}(\mathfrak{q},\mathfrak{t})C_{\nu_{2}\nu_{3}^{t}\text{\o}}(\mathfrak{t},\mathfrak{q})\
,$ (281a) $\displaystyle Z^{\rm R}(\mu_{b})$
$\displaystyle=\sum_{\nu}(-Q_{\tau})^{|\nu|}\tilde{f}_{\nu}^{-1}(\mathfrak{q},\mathfrak{t})C_{\nu\nu^{t}\mu_{b}}(\mathfrak{t},\mathfrak{q})\
.$ (281b)

A little calculation141414See Appendix B for how to compute the partition
function of a vertical periodic strip.  leads that two partition functions are
equivalent up to an (unphysical) extra factor which does not depend on the
Coulomb branch parameters,

$\displaystyle\frac{Z^{(b)}}{Z^{{\rm extra}}}=Z^{(a)}\ ,$ (282)

where

$\displaystyle Z^{{\rm
extra}}=\prod_{k=1}^{\infty}\prod_{i,j=1}^{\infty}\frac{1}{(1-Q^{2}Q_{\tau}^{k-1}\mathfrak{t}^{i}\mathfrak{q}^{j-1})(1-Q^{-2}Q_{\tau}^{k}\mathfrak{t}^{i}\mathfrak{q}^{j-1})}\
.$ (283)

The extra factor $Z^{{\rm extra}}$ typically arises when there are external
parallel 5-branes in a given 5-brane configuration. It follows from (282) that
the physical part of two partition functions $Z^{(a)}$ and $Z^{(b)}$ are the
same. Hence, non-parallel identification leads to a physically equivalent
result compared with the partition function with parallel identification. We
note that such non-parallel identification of external edges in 5-brane webs
of two O5-planes are also discussed in Kim:2021cua  where the partition
functions for KK theories of 6d $SO(8)$ and $SU(3)$ theories on a circle with
a $\mathbb{Z}_{2}$ outer automorphism twist were computed.

##  Appendix B Sum over Young diagrams along a periodic strip

In computing the partition functions for LSTs, we need to sum over Young
diagrams along periodic strips. This involves a successive use of the Cauchy
identities (10)–(13) and leads to Jacobi theta functions, as discussed in
Haghighat:2013gba ; Kim:2021cua .

We encounter products of the Schur functions whose Young diagram indices form
a closed loop. As an example, we consider the following which comes from (21),

$\displaystyle\sum_{\boldsymbol{\nu,\eta}}$
$\displaystyle\left(Q_{\tau}Q_{f}^{-1}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}}\right)^{|\nu_{1}|}\left(Q_{f}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}}\right)^{|\nu_{2}|}\left(\frac{\mathfrak{q}}{\mathfrak{t}}\right)^{\frac{|\eta_{1}|}{2}}\left(\frac{\mathfrak{q}}{\mathfrak{t}}\right)^{\frac{|\eta_{2}|}{2}}$
$\displaystyle\times
s_{\nu_{1}^{t}/\eta_{1}}(\mathfrak{t}^{-\rho}\mathfrak{q}^{-\lambda_{1}})s_{\nu_{2}^{t}/\eta_{1}}(\mathfrak{q}^{-\rho}\mathfrak{t}^{-\lambda_{1}^{t}})s_{\nu_{2}^{t}/\eta_{2}}(\mathfrak{t}^{-\rho}\mathfrak{q}^{-\lambda_{2}})s_{\nu_{1}^{t}/\eta_{2}}(\mathfrak{q}^{-\rho}\mathfrak{t}^{-\lambda_{2}^{t}})\
,$ (284)

which can be decomposed into three parts: the first part is the product of the
factors with the power $|\nu_{i}|$, the second part is the product of the
factors with the power $|\eta_{i}|$, the third part is the product of Schur
functions. Because the $\nu$’s are before the $\eta$’s in the indices of Schur
functions, we first sum over $\nu$’s by the extended Cauchy identities (12)
and (13). We can see that the factor $Q^{|\lambda|}$ does not change before
and after the equal sign, so the first part in the above formula also remains
the same after summation over the $\nu$’s. Then we get some $\mathcal{R}$
factors generated from the extended Cauchy identities and the indices of Schur
functions now change to the form in which $\eta$’s are before $\nu$’s. Then we
sum over the $\eta$’s by the extended Cauchy identities. By the same reasoning
as above, the second part of the above formula does not change and the indices
of Schur functions become the form in which $\nu$’s are before $\eta$’s again.
After repeating another cycle of this process, one finds that (284) is
expressed as

$\displaystyle\prod_{n=1,2}\frac{1}{\mathcal{R}_{\lambda_{2}^{t}\lambda_{1}}(Q_{\tau}^{n}Q_{f}^{-1}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{1}^{t}\lambda_{2}}(Q_{\tau}^{n-1}Q_{f}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{1}^{t}\lambda_{1}}(Q_{\tau}^{n}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{2}^{t}\lambda_{2}}(Q_{\tau}^{n}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})}$
$\displaystyle\times\sum_{\boldsymbol{\nu,\eta}}\left(Q_{\tau}Q_{f}^{-1}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}}\right)^{|\nu_{1}|}\left(Q_{f}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}}\right)^{|\nu_{2}|}\left(\frac{\mathfrak{q}}{\mathfrak{t}}\right)^{\frac{|\eta_{1}|}{2}}\left(\frac{\mathfrak{q}}{\mathfrak{t}}\right)^{\frac{|\eta_{2}|}{2}}$
$\displaystyle\times
s_{\nu_{1}^{t}/\eta_{1}}(Q_{\tau}\mathfrak{t}^{-\rho}\mathfrak{q}^{-\lambda_{1}})s_{\nu_{2}^{t}/\eta_{1}}(Q_{\tau}\mathfrak{q}^{-\rho}\mathfrak{t}^{-\lambda_{1}^{t}})s_{\nu_{2}^{t}/\eta_{2}}(Q_{\tau}\mathfrak{t}^{-\rho}\mathfrak{q}^{-\lambda_{2}})s_{\nu_{1}^{t}/\eta_{2}}(Q_{\tau}\mathfrak{q}^{-\rho}\mathfrak{t}^{-\lambda_{2}^{t}})\
.$ (285)

Note that the arguments of Schur functions are increased by $Q_{\tau}$ with
additional $\mathcal{R}$ functions in the front. If we call this process one
full cycle, then after $m$ full cycles, we have

$\displaystyle\prod_{n=1}^{2m}\frac{1}{\mathcal{R}_{\lambda_{2}^{t}\lambda_{1}}(Q_{\tau}^{n}Q_{f}^{-1}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{1}^{t}\lambda_{2}}(Q_{\tau}^{n-1}Q_{f}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{1}^{t}\lambda_{1}}(Q_{\tau}^{n}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{2}^{t}\lambda_{2}}(Q_{\tau}^{n}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})}$
$\displaystyle\times\sum_{\boldsymbol{\nu,\eta}}\left(Q_{\tau}Q_{f}^{-1}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}}\right)^{|\nu_{1}|}\left(Q_{f}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}}\right)^{|\nu_{2}|}\left(\frac{\mathfrak{q}}{\mathfrak{t}}\right)^{\frac{|\eta_{1}|}{2}}\left(\frac{\mathfrak{q}}{\mathfrak{t}}\right)^{\frac{|\eta_{2}|}{2}}$
$\displaystyle\times
s_{\nu_{1}^{t}/\eta_{1}}(Q_{\tau}^{m}\mathfrak{t}^{-\rho}\mathfrak{q}^{-\lambda_{1}})s_{\nu_{2}^{t}/\eta_{1}}(Q_{\tau}^{m}\mathfrak{q}^{-\rho}\mathfrak{t}^{-\lambda_{1}^{t}})s_{\nu_{2}^{t}/\eta_{2}}(Q_{\tau}^{m}\mathfrak{t}^{-\rho}\mathfrak{q}^{-\lambda_{2}})s_{\nu_{1}^{t}/\eta_{2}}(Q_{\tau}^{m}\mathfrak{q}^{-\rho}\mathfrak{t}^{-\lambda_{2}^{t}})\
.$ (286)

Because $0<Q_{\tau}<1$, in the limit $m\rightarrow\infty$, only when
$\nu_{1}^{t}=\nu_{2}^{t}=\eta_{1}=\eta_{2}$ the contribution is nonzero. So
the above expression becomes

$\displaystyle\bigg{(}\prod_{n=1}^{\infty}\frac{1}{\mathcal{R}_{\lambda_{2}^{t}\lambda_{1}}(Q_{\tau}^{n}Q_{f}^{-1}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{1}^{t}\lambda_{2}}(Q_{\tau}^{n-1}Q_{f}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{1}^{t}\lambda_{1}}(Q_{\tau}^{n}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{2}^{t}\lambda_{2}}(Q_{\tau}^{n}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})}\bigg{)}\sum_{\nu_{1}}Q_{\tau}^{|\nu_{1}|}$
$\displaystyle=$
$\displaystyle\bigg{(}\prod_{n=1}^{\infty}\frac{1}{\mathcal{R}_{\lambda_{2}^{t}\lambda_{1}}(Q_{\tau}^{n}Q_{f}^{-1}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{1}^{t}\lambda_{2}}(Q_{\tau}^{n-1}Q_{f}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{1}^{t}\lambda_{1}}(Q_{\tau}^{n}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\lambda_{2}^{t}\lambda_{2}}(Q_{\tau}^{n}\sqrt{\frac{\mathfrak{t}}{\mathfrak{q}}})}\bigg{)}\prod_{l=1}^{\infty}\frac{1}{1-Q_{\tau}^{l}}\
.$ (287)

Figure 31: A general periodic strip, $y_{i}$ and $z_{i}$ are the exponentiated
vertical positions of the corresponding branes.

More general cases of products of Schur functions whose Young diagram indices
form a closed loop can also be computed via this method. Now we write only the
result of the topological string partition function that corresponds to a
general periodic vertical strip shown in figure 31,

$\displaystyle Z^{\text{strip}}$ $\displaystyle=$
$\displaystyle\prod_{i}\mathfrak{q}^{\frac{||\mu_{i}||^{2}}{2}}\tilde{Z}_{\mu_{i}}(\mathfrak{t},\mathfrak{q})\prod_{j}\mathfrak{t}^{\frac{||\nu_{j}^{t}||^{2}}{2}}\tilde{Z}_{\nu_{j}^{t}}(\mathfrak{q},\mathfrak{t})\bigg{[}\prod_{n=1}^{\infty}\prod_{i<j}\left(\mathcal{R}_{\mu_{i}^{t}\mu_{j}}(Q_{\tau}^{n-1}\frac{y_{i}}{y_{j}}\sqrt{\tfrac{\mathfrak{t}}{\mathfrak{q}}})\mathcal{R}_{\mu_{j}^{t}\mu_{i}}(Q_{\tau}^{n}\frac{y_{j}}{y_{i}}\sqrt{\tfrac{\mathfrak{t}}{\mathfrak{q}}})\right)^{-1}$
$\displaystyle\times\prod_{i}\left(\mathcal{R}_{\mu_{i}^{t}\mu_{i}}(Q_{\tau}^{n}\sqrt{\tfrac{\mathfrak{t}}{\mathfrak{q}}}\right)^{-1}\prod_{i<j}\left(\mathcal{R}_{\nu_{i}^{t}\nu_{j}}(Q_{\tau}^{n-1}\frac{z_{i}}{z_{j}}\sqrt{\tfrac{\mathfrak{q}}{\mathfrak{t}}})\mathcal{R}_{\nu_{j}^{t}\nu_{i}}(Q_{\tau}^{n}\frac{z_{j}}{z_{i}}\sqrt{\tfrac{\mathfrak{q}}{\mathfrak{t}}})\right)^{-1}$
$\displaystyle\times\prod_{i}\left(\mathcal{R}_{\nu_{i}^{t}\nu_{i}}(Q_{\tau}^{n}\sqrt{\tfrac{\mathfrak{q}}{\mathfrak{t}}})\right)^{-1}\prod_{i,j}X_{\mu_{i}^{t}\nu_{j}}(y_{i},z_{j})X_{\nu_{j}^{t}\mu_{i}}(z_{j},y_{i})\bigg{]}\prod_{l=1}^{\infty}\frac{1}{1-Q_{\tau}^{l}}\
,$ (288)

with

$X_{\mu^{t}\nu}(y,z)\equiv\left\\{\begin{array}[]{ll}\mathcal{R}_{\mu^{t}\nu}(Q_{\tau}^{n-1}\frac{y}{z}),&\quad\text{if}\
y<z\\\ \mathcal{R}_{\mu^{t}\nu}(Q_{\tau}^{n}\frac{y}{z}),&\quad\text{if}\
y>z\end{array}\right.\ .$ (289)

##  Appendix C $A$-type little string theory

The $A$-type little string theory has been considered in the literature, e.g.,
Hohenegger:2013ala . For rank-$N$ $A_{M-1}$-type LST with the same set of
Coulomb branch parameters in each gauge node, the web diagram description is
given in figure 32, and the partition function can be obtained by the
topological vertex formalism Hohenegger:2013ala . Here we write their result
as it is,

Figure 32: (a) The web diagram describing $A_{M-1}$-type little string theory.
(b) Its building block.

$\displaystyle Z^{(M,N)}_{\text{pert}}=$
$\displaystyle\bigg{(}\frac{1}{\widehat{\eta}(Q_{U})}\prod_{i,j,k=1}^{\infty}\prod_{r,\ell=1}^{N}\Big{[}\frac{1-Q_{U}^{k-1}Q_{r,r+\ell}Q_{m}^{-1}\mathfrak{t}^{i-\frac{1}{2}}\mathfrak{q}^{j-\frac{1}{2}}}{1-Q_{U}^{k-1}Q_{r,r+\ell}\mathfrak{t}^{i-1}\mathfrak{q}^{j}}$
$\displaystyle\times\frac{1-Q_{U}^{k-1}Q_{r,r+\ell-1}Q_{m}\mathfrak{t}^{i-\frac{1}{2}}\mathfrak{q}^{j-\frac{1}{2}}}{1-Q_{U}^{k-1}Q_{r,r+\ell}\mathfrak{t}^{i}\mathfrak{q}^{j-1}}\Big{]}\bigg{)}^{M}\
,$ (290) $\displaystyle Z^{(M,N)}_{\text{inst}}=$
$\displaystyle\sum_{\alpha^{(i)}_{a}}\Big{(}\prod_{i=1}^{M}Q_{B_{i}}^{|\alpha^{(i)}|}\Big{)}\prod_{i=1}^{M}\prod_{a=1}^{N}\frac{\vartheta_{\alpha^{(i+1)}_{a}\alpha^{(i)}_{a}}(Q_{m})}{\vartheta_{\alpha^{(i)}_{a}\alpha^{(i)}_{a}}(\sqrt{\mathfrak{t}/\mathfrak{q}})}$
$\displaystyle\times\prod_{1\leq a<b\leq
N}\prod_{i=1}^{M}\frac{\vartheta_{\alpha^{(i)}_{a}\alpha^{(i+1)}_{b}}(Q_{ab}Q_{m}^{-1})\vartheta_{\alpha^{(i+1)}_{a}\alpha^{(i)}_{b}}(Q_{ab}Q_{m})}{\vartheta_{\alpha^{(i)}_{a}\alpha^{(i)}_{b}}(Q_{ab}\sqrt{\mathfrak{t}/\mathfrak{q}})\vartheta_{\alpha^{(i)}_{a}\alpha^{(i)}_{b}}(Q_{ab}\sqrt{\mathfrak{q}/\mathfrak{t}})}\
,$ (291)

where $\widehat{\eta}(Q_{U})=\prod_{k=1}^{\infty}(1-Q_{U}^{k})$ and
$Q_{U}=Q_{1}Q_{2}\cdots Q_{N-1}Q_{N}$, $Q_{U}$ is the vertical period,
$Q_{B_{i}}=Q_{b_{i}}Q_{m}$ for $i=1,2,\cdots,M$, $\alpha^{(a)}$ is a set of
$N$ Young diagrams $\\{\alpha^{(a)}_{1},\cdots,\alpha^{(a)}_{N}\\}$ and
$|\alpha^{(a)}|=\sum_{b=1}^{N}|\alpha^{(a)}_{b}|$, and $M+1\equiv 1,N+1\equiv
1$ due to the horizontal and vertical periodicities. Here, $Q_{ab}$ is defined
as

$\displaystyle Q_{ab}=\left\\{\begin{array}[]{ll}Q_{a}Q_{a+1}\cdots
Q_{b-1},&\quad\text{for }a<b\ ,\\\ Q_{U}Q_{ba}^{-1},&\quad\text{for }a>b\ ,\\\
1,&\quad\text{for }a=b\ .\end{array}\right.$ (292)

The $\vartheta$ function is defined as

$\displaystyle\leavevmode\resizebox{422.77661pt}{}{$\vartheta_{\mu\nu}(x|Q_{U})=\prod_{(i,j)\in\mu}\vartheta(x^{-1}\mathfrak{t}^{-\nu^{t}_{j}+i-\frac{1}{2}}\mathfrak{q}^{-\mu_{i}+j-\frac{1}{2}}|Q_{U})\prod_{(i,j)\in\nu}\vartheta(x^{-1}\mathfrak{t}^{\mu^{t}_{j}-i+\frac{1}{2}}\mathfrak{q}^{\nu_{i}-j+\frac{1}{2}}|Q_{U})$},$
(293)

with

$\vartheta(x|Q_{U})=\frac{\theta_{1}(x|Q_{U})}{(-iQ_{U}^{\frac{1}{8}})\prod_{k=1}^{\infty}(1-Q_{U}^{k})}\
,$ (294)

where $\theta_{1}$ is the Jacobi theta function defined in (33).

The $\vartheta$ function can be expressed by the $\varTheta$ function defined
in (32),

$\vartheta_{\mu\nu}(x|Q_{U})=\frac{(-1)^{|\nu|}}{\big{(}\prod_{k=1}^{\infty}(1-Q_{U}^{k})\big{)}^{|\mu|+|\nu|}}\varTheta_{\mu\nu}\Big{(}x\sqrt{\tfrac{\mathfrak{t}}{\mathfrak{q}}}\
\big{|}Q_{U}\Big{)}\varTheta_{\nu\mu}\Big{(}x^{-1}\sqrt{\tfrac{\mathfrak{t}}{\mathfrak{q}}}\
\big{|}Q_{U}\Big{)},$ (295)

which makes it easy to compare (C) with the formula for instanton part of the
partition function of $A$-type LST in section 4.3.

##  Appendix D Characters

Here, we list the characters of symmetry groups that we used in the main text.
The characters of the fundamental weights of $D_{4}$ are given as follows in
an orthonormal basis $\\{B_{1},B_{2},B_{3},B_{4}\\}$:

$\displaystyle\chi_{\bf 1}$ $\displaystyle=\sum_{i=1}^{8}X_{i}^{2},$
$\displaystyle\chi_{\bf 2}$
$\displaystyle=\sum_{i=1}^{8}\sum_{j>i}^{8}X_{i}^{2}X_{j}^{2},$
$\displaystyle\chi_{\text{\bf s}}$
$\displaystyle=\frac{1}{2}\left(\prod_{i=1}^{4}\left(X_{i}+X_{i+4}\right)+\prod_{i=1}^{4}\left(X_{i}-X_{i+4}\right)\right),$
$\displaystyle\chi_{\text{\bf c}}$
$\displaystyle=\frac{1}{2}\left(\prod_{i=1}^{4}\left(X_{i}+X_{i+4}\right)-\prod_{i=1}^{4}\left(X_{i}-X_{i+4}\right)\right),$
(296)

in which
$X_{i}\in\big{\\{}B_{1}^{1/2},\dots,B_{4}^{1/2},B_{1}^{-1/2},\dots,B_{4}^{-1/2}\big{\\}}$.

The characters of the fundamental weights of $D_{5}$ in orthonormal basis
$\\{B_{1},B_{2},B_{3}$, $B_{4},B_{5}\\}$ are given as follows:

$\displaystyle\chi_{\bf 1}$ $\displaystyle=\sum_{i=1}^{10}X_{i}^{2},$
$\displaystyle\chi_{\bf 2}$
$\displaystyle=\sum_{i=1}^{10}\sum_{j>i}^{10}X_{i}^{2}X_{j}^{2},$
$\displaystyle\chi_{\bf 3}$
$\displaystyle=\sum_{i=1}^{10}\sum_{j>i}^{10}\sum_{k>j}^{10}X_{i}^{2}X_{j}^{2}X_{k}^{2},$
$\displaystyle\chi_{\text{\bf s}}$
$\displaystyle=\frac{1}{2}\left(\prod_{i=1}^{5}\left(X_{i}+X_{i+5}\right)+\prod_{i=1}^{5}\left(X_{i}-X_{i+5}\right)\right),$
$\displaystyle\chi_{\text{\bf c}}$
$\displaystyle=\frac{1}{2}\left(\prod_{i=1}^{5}\left(X_{i}+X_{i+5}\right)-\prod_{i=1}^{5}\left(X_{i}-X_{i+5}\right)\right),$
(297)

in which
$X_{i}\in\big{\\{}B_{1}^{1/2},\dots,B_{5}^{1/2},B_{1}^{-1/2},\dots,B_{5}^{-1/2}\big{\\}}$.

The characters of the fundamental weights of $E_{6}$ can be obtained from the
embedding $E_{6}\supset\text{SO}(10)\times\text{U}(1)$ in (260). The Dynkin
diagram and the assignment of the fundamental weights are given as

$E_{6}$ $1$$2$$3$$4$$5$$6$.

The characters $\chi_{i}^{E_{6}}$ of the fundamental weights associated with
the node $i$ of the Dynkin diagram are given as follows,

$\displaystyle\chi_{\bf 1}^{E_{6}}=B_{6}^{-\frac{2}{3}}+\chi_{\bf
s}^{D_{5}}B_{6}^{-\frac{1}{6}}+\chi_{\bf 1}^{D_{5}}B_{6}^{\frac{1}{3}},$
$\displaystyle\chi_{\bf 2}^{E_{6}}=\chi_{\bf
s}^{D_{5}}B_{6}^{-\frac{5}{6}}+(\chi_{\bf 1}^{D_{5}}+\chi_{\bf
3}^{D_{5}})B_{6}^{-\frac{1}{3}}+\chi_{\bf 1}^{D_{5}}\chi_{\bf
s}^{D_{5}}B_{6}^{\frac{1}{6}}+\chi_{\bf 2}^{D_{5}}B_{6}^{\frac{2}{3}},$
$\displaystyle\chi_{\bf 3}^{E_{6}}=\chi_{\bf 3}^{D_{5}}B_{6}^{-1}+\chi_{\bf
2}^{D_{5}}\chi_{\bf c}^{D_{5}}B_{6}^{-\frac{1}{2}}+\chi_{\bf
2}^{D_{5}}+\chi_{\bf 1}^{D_{5}}\chi_{\bf 3}^{D_{5}}+\chi_{\bf
2}^{D_{5}}\chi_{\bf s}^{D_{5}}B_{6}^{\frac{1}{2}}+\chi_{\bf 3}^{D_{5}}B_{6},$
$\displaystyle\chi_{\bf 4}^{E_{6}}=\chi_{\bf
2}^{D_{5}}B_{6}^{-\frac{2}{3}}+\chi_{\bf 1}^{D_{5}}\chi_{\bf
c}^{D_{5}}B_{6}^{-\frac{1}{6}}+(\chi_{\bf 1}^{D_{5}}+\chi_{\bf
3}^{D_{5}})B_{6}^{\frac{1}{3}}+\chi_{\bf c}^{D_{5}}B_{6}^{\frac{5}{6}},$
$\displaystyle\chi_{\bf 5}^{E_{6}}=\chi_{\bf
1}^{D_{5}}B_{6}^{-\frac{1}{3}}+\chi_{\bf
c}^{D_{5}}B_{6}^{\frac{1}{6}}+B_{6}^{\frac{2}{3}},$
$\displaystyle\chi_{\bf{6}}^{E_{6}}=\chi_{\bf
c}^{D_{5}}B_{6}^{-\frac{1}{2}}+1+\chi_{\bf 2}^{D_{5}}+\chi_{\bf
s}^{D_{5}}B_{6}^{\frac{1}{2}},$ (298)

where the $\chi^{D_{5}}$’s are the characters of the fundamental weights of
$D_{5}$ given in (D). In a similar fashion, one can obtain the characters for
the fundamental weights of $E_{7}$ and $E_{8}$ groups.

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# Hermetic chip-scale packaging using Au:Sn eutectic bonding for implantable
devices

Katarzyna M. Szostak1, Meysam Keshavarz2, and Timothy G. Constandinou1,3 1
Next Generation Neural Interfaces (NGNI) Lab, Imperial College London,
Bessemer Building, London SW7 2AZ, UK  2 The Hamlyn Centre, Imperial College,
Bessemer Building, London SW7 2AZ, UK  3 UK Dementia Research Institute,
Imperial College, South Kensington Campus, London SW7 2AZ, UK
<EMAIL_ADDRESS>
###### Abstract

Advancements in miniaturisation and new capabilities of implantable devices
impose a need for the development of compact, hermetic, and CMOS-compatible
micro packaging methods. Gold-tin-based eutectic bonding presents the
potential for achieving low-footprint seals with low permeability to moisture
at process temperatures below 350°C. In this paper, a method for the
deposition of gold-tin eutectic alloy frames via sequential electroplating
from commercially available solutions, with no special fabrication process, is
described in detail. Bond quality was characterised through shear force
measurements, scanning electron microscopy, visual inspection, and immersion
tests. Characterisation of seals geometry, solder thickness, and bonding
process parameters were evaluated, along with toxicity assessment of bonding
layers to the human fibroblast cells. With a successful bond yield of over 70%
and no cytotoxic effect, AuSn eutectic bonding appears as a suitable method
for the protection of integrated circuitry in implantable applications.

Keywords: AuSn, Eutectic, Bonding, Hermeticity, Micropackaging, Encapsulation,
Reliability, Implant

##  1 Introduction

One of the most critical design challenges in the growing sector of
miniaturised, smart implantable devices is providing reliable packaging of a
small footprint and good hermeticity. [1, 2]. Novel implantable devices ever-
expanding capabilities more often include fully wireless communication and on-
node data processing, thus imposing more rigorous requirements for device
packaging [3]. Nowadays, implant packages, aside from ensuring small size,
reliability, and biocompatibility, may additionally require CMOS compatibility
and transparency to the communication signals [4, 5, 6]. Until now, the
majority of implants were packaged by encasing entire systems in metal or
glass cases or by using thick outer coatings, mainly made of medical-grade
silicones [2, 7, 6]. Typically, these solutions either do not provide an
appropriate level of hermeticity or are too large and not fit for wireless
systems with integrated electronics. At the same time, it is not certain
whether standard IC insulation layers alone are sufficient in providing enough
protection against the inherently wet and often corrosive character of the
tissue environment over a long time [8, 9, 10]. Recently, approaches of using
thin, ALD-deposited high-K ceramic materials such as Hafnium Dioxide and
multilayers of Silicon Dioxide with Hafnium Dioxide as a protective coating on
neural implants have emerged [11, 12]. They hold the promise of thin, stable
coatings; however, they would not solve the issue of mechanical stability of
chips stressed by the tissue nor integration difficulty of more advanced
microelectrode designs.

For that reason, the prospect of hermetically enclosing implant electronics at
a wafer- or chip-scale by using narrow seal rings with the addition of in-
silicon feedthroughs is highly desirable [13].

From a myriad of bonding techniques available in electronics and MEMS
packaging, only a few do not require high-temperature processing nor contain
toxic materials while providing good seal hermeticity, thus making them
applicable for implantable devices containing embedded ICs [14, 15]. To list a
few, anodic bonding methods require non-CMOS-compatible high electrostatic
fields, thermocompression, and glass frit bonding use very high temperatures,
while the majority of solders contain copper and silver proven to be cytotoxic
elements. Amongst all packaging methods, eutectic bonding is well-established
and can be performed using relatively relaxed environmental parameters, while
the availability of several different eutectic compositions enables the choice
of the one that would suit the application needs the best. A clear advantage
of metal-based sealing is the tolerance to substrate unevenness and very low
permeability to moisture, superior to even those of silicon or glass [16].

Figure 1: Left: Au-Sn binary phase diagram [17]. Right: most common AuSn
solder deposition methods and their characteristics.

While primarily used for die attach and flip-chip bonding in semiconductor and
optoelectronics packaging, eutectic bonding can be also used for hermetic
sealing [18, 19]. The concept relies on using a single solder frame at the
interface of two substrates protecting circuitry and devices enclosed within.
Since the joint’s thickness and width are in the range of tens of microns or
less, considerable design freedom and reduction in the package size can be
achieved. Out of a number of eutectic compositions existing, the one
particularly interesting for the application in implantable technologies is
gold-tin metallurgy [20, 21]. This is thanks to Au-Sn favourable
characteristics of high joint strength, fluxless processing, reliability, and
moderate liquidus temperature of 278°C.

Although Au-Sn bonding has been already demonstrated for the packaging of MEMS
devices, particularly for RF and inertial applications, in order to utilise
this method more widely and effectively, more studies on bond characteristics
and reliability are needed (Table. 1) [22, 23, 24]. To deliver a good quality
seal, it is of much importance to control the deposition of eutectic
composition correctly, as at precisely 80:20 AuSn ratio by weight (Fig. 1),
the low eutectic temperature of the alloy is paired with desirable properties
of Au5Sn intermetallic phase [25, 26]. There are several possible methods for
depositing gold-tin alloy (Fig. 1), whereas the most popular and cost-
effective approach is electrochemical deposition. This is typically achieved
through alloy plating, which suffers problems of short service life and
solution stability [27]. To overcome that issue, composition plating can be
executed by sequential electroplating, which involves using different chemical
solutions to deposit each component of the eutectic alloy [26].

In this study, the effectiveness of tin-rich sequentially deposited Au-Sn
alloy eutectic bonding is evaluated to determine critical parameters for
achieving high-quality, hermetic seals. The influence of bond geometry, solder
thickness and reflow parameters on bond mechanical properties and hermeticity
are assessed. To establish the preliminary validation of biocompatibility of
the method in implantable applications, the cytotoxicity of plating chemistry
and the alloy itself were assessed by culturing human fibroblast cells on
reflown samples.

Table 1: Selected applications of AuSn solder rings for hermetic sealing. Application: | Details: | Year
---|---|---
| Smart inertial MEMS
---
sensor systems
| \- Chip-to-wafer integration
---
\- AuSn frame: 18 µm height, electroplated
\- Bonding: 300°C, 6 kN force
| 2008
---
[28]
RF MEMS switch |  | \- Wafer-level integration
---
\- AuSn frame: 5 µm height, electroplated
\- Bonding: 310°C
| 2010
---
[29]
| Piezoelectric silicon
---
resonators
| \- Wafer- and array-level integration
---
\- AuSn frame: 4 µm height, electroplated
| 2011
---
[23]
| MEMS microresonators
---
and microbolometers
| \- Chip-level integration
---
\- AuSn frame: 20 µm, electroplated
\- Bonding: 340°C
| 2013
---
[24]
MEMS timing devices |  | \- Wafer-level integration
---
\- AuSn frame: 19 µm, electroplated
\- Bonding: 300°C
| 2013
---
[22]

##  2 Materials and Methods

All experiments were carried out in an academic cleanroom laboratory setting
(Centre for Bio-Inspired Technology Cleanroom, Imperial College London and
London Centre for Nanotechnology Cleanroom, University College London) using
4-inch, double side polished, 525 µm thick (100) silicon wafers of total
thickness variation lesser than 2.3 µm. Substrates were processed in two
batches, separately for lid and base die samples. All mask layers were custom
designed, so that cap wafers sealing rings match with those on the base
wafers. Overall, two sample sizes (4 mm2, 9 mm2), with four widths (30 µm, 60
µm, 90 µm, 150 µm) and three different shapes (circular, rectangular, and
chamfered) of seal rings have been tested. Eutectic stacks heights were
electroplated to the heights of either 10 µm or 15 µm, which corresponds to
Au(6 µm)- Sn(4 µm) and Au(9 µm)-Sn(6 µm) tin-rich compositions, respectively.
The range of tested parameters was based on the previous literature (Tab. 1)
of the subject and project’s constraints regarding the package size, which was
to be kept smaller than 4$\times$4 mm2. Additionally, some of the geometries
contained gold-only rectangular standoffs, placed either inside or outside of
the seal rings (Fig. 2).

Figure 2: A) An overview of process parameters tested in the study B) Reflow
temperature profiles evaluated C) Evaluated seal geometries of the square,
chamfered square, and round frames.

###  2.1 Fabrication of base and lid wafers

A simplified fabrication process flow is depicted in Fig. 3. Processing
commenced with complete RCA clean, after which lid wafers were oxidised with
approximately 320 nm dry thermal silicon oxide and base wafers were coated
with approximately 960 nm PECVD-deposited oxide (Mesc Multiplex 13241 system,
STS, UK). The difference in oxide thickness was chosen, so that base wafers’
oxide thickness corresponds better to those on the BEOL layers used in CMOS
chips. Next, adhesion layers of either Cr or Ti were sputtered (PVD75,
K.Lesker, USA) to the thickness of 20 nm and directly followed by sputter
deposition of 100 nm layer of Au, which would work as a seed layer for later
electrodeposition steps. Subsequently, selected substrates were
photolithographically patterned with 5 µm AZ 15nXT (115 CPS) photoresist to
form an array of square-shaped openings, which were then electroplated with
gold to the height of 5 µm using parameters described in the later steps. This
is to create gold standoffs near the solder lines, which would work as
possible spillage stoppers preventing total solder collapse during bonding.
Then, the photoresist was stripped in heated MICROPOSIT Remover 1165, and
substrates were cleaned in Acetone and Isopropanol baths, followed by DI water
rinse and nitrogen dry.

Until this point, substrates intended for both base and lid of the package
were processed the same. In the next step, lid wafers were
photolithographically patterned with the shapes of seal rings in AZ1518 HS
photoresist followed by differential etching away of previously sputtered
Ti/Au layers and photoresist removal in acetone. In the next step, lid wafers
were again patterned using SPR-220 photoresist to form central square openings
used for the formation of central cavities. These cavities provide space for
the placement of cut copper film pieces (in the future to be replaced by
humidity sensors) used to evaluate bond hermeticity. After removing silicon
dioxide in buffered hydrofluoric acid, cavities were etched down in the Bosch
process to the depth of 200 (Multiplex Pro DRIE, SPTS, UK). Then, lid wafers
were stripped of photoresist, solvent- cleaned, and diced into 4 mm2 and 9 mm2
dies (DAD3230 dicing saw, DISCO Corporation, Japan).

Figure 3: An overview of base (above) and lid (below) wafers fabrication
process flow

After electroplating spillage-stoppers, base wafers were sectioned into four
pieces to separate wafer areas containing designs of different sizes. This was
to avoid electroplating with starkly different local current densities across
the wafer and thus allowing for better control of the deposition process.
Then, base wafer sections underwent another photolithography to pattern
outlines of seal rings. For that, a thicker version of the previously used
photoresist AZ 15nXT (450 CPS) of the thickness of 120% of desired plated
deposit thickness was used. After that, substrates were sequentially
electroplated with gold and tin layers. Once that was achieved, the
photoresist was stripped, and wafers solvent cleaned. Next, samples underwent
selective etching of thin films of adhesion and seed layers in gold, chromium,
and titanium etchants (KI, HClO4:(NH4)2[Ce(NO3)6], HF; respectively) thus
leaving only layers of deposited solder on the silicon dioxide base. Finally,
base wafer sections were diced to singulate dies of sizes corresponding to
those diced from lid wafers, and exact solder heights were measured by contact
profilometry. One set of samples was then annealed in a vacuum oven at 200°C
for four hours.

###  2.2 AuSn Alloy Sequential Electrochemical Deposition

For all described electroplating experiments, custom electrochemical
deposition setup was assembled, which is depicted in Fig. 4. An
electrochemical workstation in a chronopotentiometry mode (Versastat-3-400,
Princeton Applied Research, USA) was employed as a power source. To ensure
better control over plating current, depositions were conducted in a three-
electrode system, using double junction 3.5 KCl-filled silver/silver chloride
(Ag/AgCl) electrode as a reference. Electrical between working electrode
terminal and samples was achieved via custom made spring-loaded contacts. The
thickness of grown deposits was regularly monitored by measuring grown layer
ex-situ using a stylus profilometer(Dektak X, Veeco, USA).

Figure 4: A) Sketch of setup used for electrochemical deposition of Au and Sn
layers; B) Picture of Au-electroplating setup realisation; C) Picture of Sn-
electroplating setup realisation.

For gold electrochemical deposition, a proprietary sulphite based ECF60
(Metalor, UK) gold bath, without additives or grain refiners, was used. This
chemistry was chosen because sulphite-based Au-plating solutions are known to
produce layers of ductile, soft pure gold with good throwing power and are
safer to use than cyanide-based chemistry. Electroplating was carried out
against a 10 cm diameter platinised titanium mesh counter electrode at an
operating temperature of 58°C. The exact plating current density value was
chosen based on the manufacturer’s recommendations and previous literature on
the subject at 3.5 mA/cm2 where the built-in stress of deposited gold layer is
the lowest. To limit the formation of an ion-depleted solution layer in the
cathode vicinity over time, the solution was continuously stirred by immersed
magnetic pellet with a spin speed of 550 rpm/s. Throughout the gold
electroplating process, the counter electrode and samples were kept 5 cm
apart, the distance defined by the geometry of the plating vessel.
Electroplating of tin was performed using proprietary methane sulphonic acid-
based NB Semiplate Sn100 solution (Microchemicals GmbH, Germany), producing
matte tin layers of high purity and low internal stresses. The deposition was
performed using 100 cm2 99.9% tin sheet counter electrode at room temperature.
The plating solution was constantly stirred with 350 rpm/min speed using a
magnetic pellet to disperse hydrogen gas bubbles forming during deposition and
aid the fresh solution’s flow to the sample’s surface. Counter and working
electrodes were kept at a constant distance of 3.5 cm from each other, a gap
defined by the geometry of the plating vessel.

###  2.3 Bonding process

To test the effectiveness of sequential electrodeposition to form eutectic
composition and evaluate bond characteristics, corresponding lid and base dies
were bonded together using a die bonder (Lambda Fineplacer, Finetech,
Germany). In total, 110 sample pairs were processed. All samples were bonded
at least three weeks after the last electroplating step. Shortly before
bonding, sample pairs were briefly cleaned in acetone and isopropanol and
carefully dried with a nitrogen gun to remove any possible dicing-induced
contamination. Several samples were additionally equipped with a small cut out
of copper film placed inside the lid’s cavity to monitor the hermeticity of a
formed seal. Lid and base dies were aligned at complete separation using
bonders’ optical system, brought together to direct contact and subjected to
the force of value ranging from 0 N to 40 N per solder ring. The bonding was
done by applying two different temperature profiles, depending on the tested
batch (orange and blue lines on temperature profile in Fig. 2b). Batch PFR
containing samples pre-reflown in the vacuum oven and batch FR were bonded by
applying 320°C on the sides of both base and lid dies, with the ramp rate of
20 K/s and held at the maximum temperature for 10 min, after which heating was
turned off, and the sample was allowed to return to room temperature without
any external cooling. Samples from batch SR were reflown by applying 200°C to
both base and lid dies, with the ramp rate of 20 K/s for 60 s followed by a
further ramp-up to 320°C bonding temperature where they were held for 5 min.
After that, samples were first actively cooled to 200°C and then allowed to
cool down without any external aids. Once the bonded pairs achieved room
temperature, the force was removed, and samples were removed from the bonder
for characterisation. Throughout the entire bonding process, samples were
observed for the eutectic temperature, premature melting, spillages, and bond
collapse via the side camera (Fig. 5).

Figure 5: Microscope photographs of lid and base chips’ surface as seen before
bonding (left) and after reflow and following shear tests (right). The side
profile of the chip stack as seen during the bonding procedure (centre).
Solder collapse and change in colour appearance of solder are observed.

###  2.4 Post-bonding characterisation

The objectives for an implantable device package are the protection of the
device against an external, humid environment of living and constantly mobile
environment over a long time. Thus, the effectiveness of the bonding approach
was characterised with a focus on shear strength, hermeticity, cell response
to sealing material, and the overall yield of the bonding process. Hermeticity
was qualitatively assessed by evaluating the change in surface oxidation of
copper films as exposed to a wet environment in immersion tests. Of several
leak detection methods available to use as a measure of hermeticity, the
copper test was chosen, because gold-standard methods, such as the helium leak
test, do not offer sufficient resolution for the device’s sub-millimetre
cavity size [30]. In the future, integration of an on-chip humidity sensor
would provide a more quantitative measure of hermeticity [31, 32]. Directly
after bonding, a sample set containing enclosed copper film pieces was placed
in the water for 12 weeks along with the exposed copper control sample. The
liquid was changed weekly. Then, samples were debonded and enclosed copper
pieces evaluated for the change in appearance. The colour change of the copper
film could indicate the progress of oxidation caused by moisture ingress
inside a bonded sample.

The strength of single seal frames was measured by mean of shear tests. The
tests were carried out using force gauge (FH500, Sauter, Germany) fitted with
custom 3D printed holders to which the backside surface of measured samples
was carefully fixed using fast-setting adhesive (Fig. 6). The adhesive layer
was thin enough to prevent it from bleeding into the interface between lid and
base dies. The load was applied with the approximate rate of 0.02 mm/s until
samples debonded at the interface and the maximum measured force was
registered. The shear strength was then calculated by dividing the recorded
force by the total bonded area. Samples were subsequently inspected with an
optical microscope and scanning electron microscope to examine for the extent
of possible spillages and evaluate the fracture mechanism of broken bonds.

Figure 6: Shear test setup.

###  2.5 Cell viability assessment

Selected nine reflown and debonded samples were used as substrates for the
human fibroblast cell viability and cytotoxic assessment. Samples used were
sectioned off wafers before dicing; therefore, they were larger, each
containing several seal rings. This was to evaluate the cytotoxic response of
human fibroblast cell line to the AuSn solder in eutectic composition as
deposited using sequential electroplating from sulphite and methane sulfonic
acid-based gold and tin plating solution chemistries. Biocompatibility was
assessed via analysis of cell morphology as inspected by scanning electron
microscopy. Initially, samples were sterilised by exposing them to UV light
for 20 min followed by washing with PBS three times before adding to the cell
culture medium. Next, cultured human fibroblast cells were employed in cell
experiments to ascertain the cytotoxicity and cellular response to the
fabricated layers. The cell line used in this experiment -fibroblast cell BJ
(ATCC® CRL-2522TM), was purchased from ATCC and cultured in Dulbecco’s
modified Eagle’s medium (DMEM) containing 10% heat-activated fetal bovine
serum with 1% penicillin-streptomycin antibiotics (Pen-strep). Subsequently,
the cells were seeded and cultured on reflown AuSn substrates and placed in
Petri dishes with a seeding density of 750,000 cells/ cm2. The cells were
incubated in the medium for 24, 48, and 72 hours at 37°C and 5% CO2 while they
were examined every 12 h.

##  3 Results

The majority of samples tested exhibited very good mechanical characteristics
of produced joints. Across various geometries and parameters examined, the
overall yield of the bonding process was 73%. Out of the total of 110 sample
pairs processed, 24% have produced seals with mechanical characteristics too
weak to allow to conduct shear strength measurement and debonded upon normal
handling. Within the well-bonded group, 12% of samples exhibited shear
strength values below the minimum as described by MIL-STD-883G military
standard for die-attach calculated per total bond area [33], thus reducing the
total yield of bonding process across the range of parameters tested to
approximately 64%.

Figure 7: Comparison of an oxidation level of copper film immersed for 12
weeks in the water. Left: control sample (exposed to moisture) right: sample
sealed by AuSn frame.

No correlation was observed between the shape of the seal lines and the
resulting measured bond strength. For the frames of the same width, all shapes
(circle, square, chamfered square) exhibited similar ranges of measured shear
strength values. Thus, when mechanical properties are of the foremost
importance, the shape of solder rings are not a relevant parameter. Variations
in seal behaviour were observed for bond frames of different widths, as 150 µm
lines exhibited lower shear strength values compared to thinner 90 µm and 60
µm broad lines of the same height. This could be explained by wider frames
having more significant Au:Sn interface surface area, thus more availability
for premature gold diffusion and the formation of high-temperature
intermetallic compounds. On the other hand, wider frame widths were found more
robust in maintaining the hermeticity of packages. In immersion tests, all 150
µm and the majority (80%) of 90 µm-wide frames kept enclosed copper pieces
intact after 12 weeks in water. Leakages were observed commonly for thinner
frames as a result of a higher probability of misalignment between lid and
base dies. In thinner frames, the appearance of voids has more of a
detrimental impact because of the smaller volume of the solder available for
package protection. All copper pieces enclosed by 30 µm wide AuSn seal frames
showed signs of exposure to water as observed by the copper colour changes
(Fig. 7). From mechanical stability and hermeticity perspective, optimum seal
geometries found out to work the best for the die sizes examined were those of
middle range of widths (60 µm and 90 µm).

A structural parameter that exhibited more influence on the shear strength
values was stack height. Deposited layers were higher than 10 µm to ensure the
proper ratio of gold to tin is maintained. When sequentially electroplating
gold and tin from two separate solutions, two distinct metallic layers of
different grain sizes were achieved. Whereas gold’s layers are deposited to
form smooth layers of small grains and compact microstructure, deposition of
tin from methane sulfonic acid produced films of comparably more developed
morphology. Micro roughness of tin, resulting from its grain size, leads to
difficulties in accurate measurement of the deposited layer, thus controlling
the correct eutectic ratio, especially for thin solder layers. When chosen
eutectic height is tall enough, the grain size measurement error becomes
insignificant, thus allowing for successful Au:Sn proportion deposition. Any
premature Au:Sn intermixing and resultant consumption of metals favouring the
formation of intermetallic compounds different to Au5Sn is minimised with
thicker layers deposited. All samples of as-deposited AuSn heights of 10 µm
and 15 µm achieved eutectic composition, as observed by the presence of a
single uniform metal phase in post-reflow SEM images and in-situ observed
reflow temperature.

Figure 8: Average shear force for samples of different as-plated solder
heights. SL-10 µm total solder on-base die only; SH-15 µm total solder on-base
die only; DL-20 µm total solder on base and lid dies; DL- µm total solder on
base and lid dies.

Four different eutectic height groups were evaluated: SL with 10 µm of as-
plated eutectic height on the base die; SH with 15 µm of as-plated eutectic
height on the base die; DL with 10 µm of as-plated eutectic height on both
base and lid dies (total 20 µm) and DL with 15 µm of as-plated eutectic height
on both base and lip die (total of 30 µm). Additionally, the SL2 group
consisting of dies with 7 µm -high AuSn eutectic on the base die with Cr
adhesion layer was tested (Fig. 8). The latter group yielded the lowest shear
strength values as the chromium layer was proven insufficient to provide an
adequate level of adhesion for grown eutectic. What is more, selective etching
of chromium thin film from the die surface during the last step of processing
led to the premature rapid oxidation of the electroplated tin surface, further
hindering subsequent bonding steps. For that reason, results from group SL2
are not included in the overall statistics of the experiment. For the
remaining samples with Titanium deposited as an adhesion layer, the average
shear force measured was more significant for higher thicknesses of the
deposited solder. For the groups of dies with solder stack present only on one
die, the variation in average shear strength between solder heights of 10 and
15 µm was only 2.71 MPa . Doubling the amount of solder by depositing eutectic
stack on both base and lid wafers led to an average shear strength increase of
1.4 MPa for samples with double-10 µm stacks, and 2.39 MPa for samples with
double-15 µm stacks. It must be noted that when double solder height is
considered, a considerably more extensive excess solder spill-out was observed
for samples of all geometries. Furthermore, all double-height-bonded samples
exhibited different shear fracture modes, mainly breaking at the bond
interface. Considering the increased cost and complexity of double-stacked
samples against only a minor increase in shear strength, it was concluded that
stacks deposited on only one of the package dies were sufficient to provide a
reliable seal.

Figure 9: Measured shear force in relation to pressure applied to the sample
during the bonding procedure.

Analysis of measured shear force against pressure applied onto the seal frames
during the bonding process has shown that with an increase of bonding
pressure, achievable shear strength is on average higher (Fig. 9). This is in
part caused by improved mixing of solder phases during reflow under pressure.
Applying pressure aids in the removal of voids as well as in the improvement
of wetting of solder to the substrate; however, it causes bond line widening
and increases the possibility of solder squeeze out and spillages. Very high
bonding pressures were also found to cause minor shifts in dies alignment when
the surface of the bonder was not perfectly levelled. On the other hand,
minimal or no bonding pressure was found to be a parameter used in 40% of all
samples from the group of the weakest bonds that failed upon regular handling.
Nonetheless, applying low to moderate pressures along with the suitable
adjustments of other bond parameters, such as eutectic height, makes it
feasible to attain shear strengths in the range above 20 MPa, applicable for
intended implantable purposes.

Figure 10: The average shear force between samples reflown with different
temperature profiles, with or without pre-bonding annealing step.

Clear differentiation between the total yield of well-bonded samples can be
observed for dies reflown with different temperature profiles (Fig. 10).
Samples that were heat-treated in a vacuum oven before final reflow
successfully bonded only in 36% cases, while using the same temperature
profile on samples without any prior annealing led to an increase in yield to
78% of well-sealed samples. Typically, pre-reflow annealing is employed to
increase the bondability of as-deposited layers over time by minimising the
rate of diffusion of Au into Sn and the formation of unwanted intermetallics
[34]. However, in our case, annealing negatively impacted bonding process
yield, likely due to increased Ti adhesion layer consumption. Application of
intermediate annealing step at 200°C directly before reflow above eutectic
temperature also had a negative impact on process yield. Thus preferably from
the process yield perspective, reflow at a temperature above eutectic should
occur as soon as possible, with as fast as possible ramp up any without any
prolonged exposure to temperatures above melting temperature of Sn.

Fig. 11 represents SEM pictures of various fracture modes identified after
shear testing. For a large number of samples analysed, the transfer of Ti:Au
thin film bi-layer from the surface of the silicon onto the bond frame was
observed. This indicates the failure occurring at the solidified solder and
adhesion layer interface, pointing out the good mechanical stability and
quality of the bond. The exact location for that type of failure could occur
both at the interface between AuSn and Ti, as well as Ti and SiO2. The high
occurrence rate of this fracture mode may indicate the need for improvements
of the adhesion layer to limit the dissolution of Ti into the solder. Another
type of fracture identified is the one within the solid Si itself, represented
as fragmentary remains of the corresponding sample from the pair attached to
the solder frame. This fracture type was the second most observed and shows
the bond strength surpassing fracture strengths of silicon/silicon oxide die.
The least observed fracture mode was the one occurring within the bulk of the
bond frame bulk itself, usually caused by either the solder imperfections such
as voids or by the wrong composition of the solder and, therefore, phases non-
uniformity.

Figure 11: SEM pictures of fracture modes observed at the debonded interface
of samples following shear testing.

Cell adhesion and morphology were observed by SEM on the surface of reflown
AuSn eutectic after culturing for 1, 2, and 3 days. Representative surfaces
after incubation in the cell culture medium are shown in (Fig. 12). No
cytotoxicity effect on fibroblasts structure could be observed between time
points of 1, 2 and 3 days, with cells consistently exhibiting normal, spindle-
like morphology. Cell density exponentially increased over the course of
incubation time. The continued proliferation of the fibroblast after three
days has created a tissue-like structure on the surface of samples which
suggest the biocompatibility and non-cytotoxicity of the substrates [35, 36].
An untreated area of the samples was considered as a control. Increasing
numbers of fibroblasts attached to the surface and in contact with each other
were observed. The clear preference of cellular attachment on the silicon
oxide compared to the reflown AuSn was noted, with a sparser cellular layer
covering solder lines. Nonetheless, fibroblasts present on the solder frames
remained of healthy morphology, with only a few individual cells exhibiting
round shape. After culturing for more than three days, the density of
fibroblasts coverage was high enough to cover the majority of sample surfaces,
proving no cytotoxic effect of sequentially electroplated AuSn solder.

Figure 12: SEM pictures of reflown chip surface with AuSn solder lines used
for fibroblast cell culturing after 24, 28, and 72 hours of cell culture.

##  4 Conclusions

A method for creating solid and hermetic seals using AuSn alloy sequentially
electroplated from commercially available solutions is presented. Fabrication
of eutectic frames is performed using standard microfabrication methods, and
thanks to the maximum process temperature of 320°C can be applied to
temperature-sensitive devices, such as CMOS microelectronics dies. The use of
electroplating over other methods of alloy deposition allows for a parallel
formation of multiple solder frames with great geometry control, while the
choice of plating sequentially significantly reduces problems of plating
solution stability and shelf life. The wide availability of considerably low
toxicity gold and tin electroplating chemistry makes the process both cost and
time effective. However, because of different Au and Sn layer morphology, it
can be applied only where a thicker solder layer can be tolerated. Bonding
tests with varying parameters of applied temperature, reflow profile, and
frame geometry, along with immersion tests, have shown the possibility of this
method to create an enclosed, mechanically robust hermetic environment. Across
all geometries and process parameters tested, the average measured bonding
strength was over 28 MPa with a bonding success yield of 73%. The dominant
shear fracture observed was at the interface of the adhesion layer, pointing
to the need for improvement under solder metallisation. Nonetheless, even with
only Ti/Au stack underneath, samples have exhibited excellent mechanical
properties. Analysis of average bond shear force between samples having either
single- or double-sided solder rings has shown no need for solder presence on
both base and lid dies. This means that for applications where CMOS dies are
used as a base, there would be no need for on-chip electroplating, as solder
frames on separately processed lid chips would be sufficient to provide a
high-quality seal. Immersion tests conducted for the duration of three months
have shown no signs of moisture penetration in samples sealed with frames of
90 µm and 150 µm width, whereas the majority of thinner 30 µm-wide frames have
exhibited leakage. As a result of cell culture experiments, AuSn reflown
layers have not shown signs of high toxicity to the biological environment. It
would be of future interest to investigate different under-layer metallisation
to further improve the mechanical stability of seals.

Unquestionably one of the most significant trends for the future of
implantable devices is miniaturisation. The designs of novel implantables are
characterised by complicated architectures and expectations of the possibility
of high yield manufacturing. Therefore, the device’s design for
manufacturability, including packaging methodology, should be considered from
the beginning. Presented AuSn-based eutectic sealing can be applied to a
variety of substrate materials and used on a larger scale, such as wafer-
level, thus significantly improving the process throughput.

The presented method appears suitable packaging approach to protect integrated
circuitry in implantable applications or any other application where a device
must be protected from an external operating environment. The possibility to
hermetically seal IC-electronics within an implant, robustly and
straightforwardly, as with using AuSn eutectic, can pave the way to expand the
horizon of implantable devices into the new areas. Such narrow, hermetic seals
do not require any specialised microfabrication approaches, are not toxic, and
provide long-term robustness.

Once combined with the right approach to the challenges of power and data
transmission out of implants [13], correct packaging methodology could enable
future devices to be potentially safer, less invasive, and easier to implant
[37, 38].

The authors would like to thank Matthew Cavuto for the help with the
mechanical design, 3D printing, and assembly of shear testing setup; Dr.
Florent Seichepine for the general advice on processing steps; and Applied
Microengineering Ltd. UK, especially Anna Draisey for process advice and
valuable discussions regarding eutectic bonding.

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