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\begin{document}

\section*{Supplementary Material: Model Parameters}
\begin{table*}[!ht]
\centering
\begin{tabular}{l c c}
Description & Parameter & Value \\
\hline
Grid spacing & $an$ & 1 $A$ \\
Number of energy steps & $NE$ & 7201 $steps$\\
Fermi Energy & $E_f$ & 0.1 $eV$ \\
Effective Density States, Si & $Nc_{Si}$ & 2.8e19 $cm^{-3}$ \\
Effective Density States, Ge & $Nc_{Ge}$ & 1.04e19 $cm^{-3}$ \\
Reference Temperature & $T_p$ & 300 $\unit{K}$ \\
Temperature Difference & $dT$ & 10 $\unit{K}$ \\
\hline
\end{tabular}
\label{t:1}
\caption{Material parameters. Sources: $\dagger$ - \cite{kittel86}}
\end{table*}

\begin{table*}[!ht]
\centering
\begin{tabular}{l c c c}
Part & Material & Effective Mass & Relative Permitivity \\
\hline
Mat 1 (barrier) & Silicon $\Braket{001}$ & 0.91m$_e$ $^{\dagger \dagger}$ & 11.7 $^\dagger$ \\
Mat 2 (well) & Germanium $\Braket{001}$ & 0.95m$_e$ $^{\dagger \dagger}$ & 16.0 $^{\dagger \dagger}$ \\
Contacts & Silicon $\Braket{001}$ & 0.91m$_e$ $^{\dagger \dagger}$ & 11.7 $^\dagger$ \\
\hline
\end{tabular}
\caption{Electronic NEGF material parameters. Sources: $\dagger$ -
  \cite{kittel86},$\dagger\dagger$ - \cite{bulusu08a}}
\label{t:2}
\end{table*}

\begin{table*}[!ht]
\centering
\begin{tabular}{l c c c c c c}
Part & Material & Mass ($\unit{kg}$) & Atoms/basis & $C_o$ ($\unit{J}$)& $d_i$ ($\unit{nm}$) & $d_e$ ($\unit{nm}$)\\
\hline
Mat 1 & Silicon $\Braket{001}$ & 1.69$\cdot 10^{-26}$ & 2 & 49.1$^\dagger$ & 0.543 & 0.235\\
Mat 2 & Germanium $\Braket{001}$ & 4.37$\cdot 10^{-26}$ & 2 & 47.5$^\dagger$ & 0.565 & 0.244\\
Contacts & Silicon $\Braket{001}$ & 1.69$\cdot 10^{-26}$ & 2 & 49.1$^\dagger$ & 0.543 & 0.235\\
\hline
\end{tabular}
\label{t:3}
\caption{Phonon NEGF material parameters. Sources: $\dagger$ - \cite{harrison89}}
\end{table*}

\begin{table*}[!ht]
\centering
\begin{tabular}{l c c c}
Part & Material & Acoustic Def Potential ($\unit{eV}$) & Optical Def Potential ($\unit{eV/m}$)\\
\hline
Mat 1 & Silicon $\Braket{001}$ & 9.0 $^{\dagger}$ & 0.5$\cdot 10^{10}$ $^{\dagger}$ \\
Mat 2 & Germanium $\Braket{001}$ & 9.0 $^{\dagger}$ & 0.79$\cdot 10^{10}$ $^{\dagger}$ \\
\hline
\end{tabular}
\caption{Electronic NEGF scattering deformation potentials for each material. Sources: $\dagger$ -
  \cite{jacoboni83,jacoboni77}}
\label{t:4}
\end{table*}

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