Snowy white herons called egrets are a little exotic in Britain but are common in Mallorca. I cycled past fields in which cattle egrets co-existed with sheep and past a stone cistern hosting lines of egrets round the rim. These sketches were done of birds roosting and hunting in the waters of the nature reserve, spotted by telescope. The larger birds with yellow feet are little egrets, the smaller ones with yellow crests and bills are cattle egrets.
By the time I got round to drawing these birds, I felt I had loosened up a bit. I scribbled only a few lines on the paper, just enough to hold the image so I could go back and throw on a minimum of watercolour washes a few minutes later. The pen and washes work well on the fairly smooth Stillman and Birns watercolour paper. My aim was to work quickly without overworking the picture.
I also spotted a line of about 25 elegant waders, black-winged stilts with long red legs and delicate probing bills.
In loading these drawings, I came across pictures of cattle egrets accompanying horses against a background of tall reeds, drawn while on another cycle ride in Mallorca two years ago with quite different technique.
I had hired a bike and cycled at least a few kilometres every day, usually in the heat of the afternoon when the children had taken refuge in the pool. I wandered the coastal road and lanes around the Albufereta nature reserve, trying to find a way near to the remaining wetland. In these meanderings, I found a small kite and paddle surf shop staffed by enthusiasts, with a fridge stocked with bottles of Galician lager.
On one day, I found a path that wound through dried up ponds to a raised observation point and on another, a track past a farm brought me closer to the remaining marsh from a different direction. The three sketches were each done in an attempt to capture the sparkle of the distant water on a hot day, set against the dry vegetation and distant mountains.
These are all on cold pressed heavy paper: the top two on the Arches carnet de voyage and the lowest one on the smoother Stillman and Birns beta pad. For the first, I drew directly in watercolour whereas in the second I constructed the main shapes first in a waterproof fine marker. Oddly, this allowed me more freedom to use white paper in the composition. In the last drawing, on a different day, I used the fountain pen and then added a minimum of colour with conte crayon and chalk pastel, mobilising the pigment with clean water.
I took the sign-posted path into the Albufereta nature reserve. This led to three bird hides, overlooking dried up ponds, beds baked hard by the sun, strewn with rocks, barren.
But there were movements among the rocks, shapes only clear when viewed by telescope.
These are stone curlews, insect eaters that hide, camouflaged against bare ground, hunkering down on plantigrade feet to merge with the rocks.
These drawings were done with ink and water, then conte crayon and chalk pastel for the few colours, in the Stillman and Birns beta sketch pad.
Albufereta is a small wetland nature reserve surrounded by farmland at the north western corner of Mallorca. In the baking heat, the challenge has been to get close enough to any remaining water to see birds. To make these sketches, I am standing with my back to the coastal road and I think that marsh itself is somewhere concealed between me and the mountains.
I had started a new sketchbook containing cold press, heavy paper made by Stillman and Birn. It takes some getting used to. The grain is fine so the pen scoots over the surface easily. However, I tend to rely on the paper's bite to control the rate at which watercolour unloads from the brush.
The paint dries quickly in this heat, creating hard edges before I have even thought about softening them with water or lifting colour by blotting. I will have to paint in a more planned way, placing layer on layer.
Here, one evening, I looked down from the high bluff made of volcanic rocks that had been forced through the more ancient softer petrified sediments. I had previously drawn these contorted rocks in watercolour and sketched the shapes made by the two rock types in ink and wash.
I approached this using a board covered first in thick, unfixed charcoal, drawing in shapes with fingers and an eraser, reserving the brightness of the light reflecting from the sea. I then worked into this with very wet white acrylic, suspending the charcoal dust and building the contrasting tones. Finally I worked into the wet layers with coloured acrylics, a couple of sticks of chalk pastel and a sharp knife hacking my way back to the paper beneath. I photographed the piece on site.
I set off with the piece on a board in the back of the car. After a while I pulled into a lay-by and looked at it again. In the deepening gloom, I ground more charcoal into the surface and slopped on more white paint, lifting the charcoal but obscuring the colour. I tipped my remaining sepia ink in a streak along the line of the rocks.
I imposed rotational acceleration on wet, slowly drying paint as I drove round twisting lanes up and down hills, catching in the headlights owls, startled into flight by my progress.
I photographed it late that evening, still drying, paint still moving slowly to invade the bastions of ink.
This is the dried form, as it now is, waiting further action.
Early Saturday morning, mid July, I called in at Blacktoft Sands nature reserve. Drizzle alternated with showers. The waters displayed only a scattering of nondescript ducks, and it was mostly pigeons that flew across the reeds or clattered on the roof of the hide.
On the branches of distant shrubs hunched marsh harriers, veiled or revealed by the drifting mists. These, I think, were fledged chicks, joined occasionally by parents. I only saw the adults fly or hunt.
The views were too poor for detailed drawings, and I found it a struggle to capture any sense of these birds on paper that day.
Holy Island is a low rocky outcrop in the coastal mudflats connected twice daily by a causeway revealed by the tides. Arriving, straight away I could hear a low drone. I could not tell whether this was natural or the sound of many motors.
Initially I walked slowly along a long path until I crossed dunes to reach the sea. Then I hurried back and returned with my most powerful telescope. The constant gronking noise came from common seals resting on rocks just out to sea.
At first I was too distant to make out much more than their shapes.
Edging closer by rounding the shoreline, I began to make out the features on their flippers and faces.
I think these were mainly females with their pups. The moved contently, turning and twisting in the sun and slipping in and out of the sea.


Union Bank branches undertake payments of various State Government level Pension to retired State Government employees.
Respective State Authority issue the Pension Payment Orders for State Pension Payment.
For any clarifications/grievances pensioners are free to contact our pension account maintaining branches/Regional Offices under which their branches are functioning.


We are located in central Tucson on North Alvernon Way just one block south of East Speedway Boulevard. We are a short walk from Sun Tran bus stops on route 4 (Speedway) or 11 (Alvernon). The main entrance to the Health & Wellness Center is on the East side of the building.
See the map below for more detailed location information including driving directions to our building.


In 2016, the school applied successfully for National Lottery funding. It was decided to use the funding to provide our pupils with more opportunities to express themselves and have their voices heard. We subsequently commissioned several external providers who would provide these opportunities in a variety of ways. Sessions with a beatboxer, graffiti artist and an animation expert provided creative outlets not normally included within the curriculum. Following these initial sessions we embarked on a longer term project with renowned rapper Andy Testament. Andy worked closely with a range of pupils and classes and ultimately produced CDs containing songs where the lyrics and music were created by the pupils. The lyrics were a reflection of the pupils and their experiences in life. As a school we are committed to listening to our pupils and ensuring what we learn is appropriate for our pupils and what they have experienced.


Unbeatable view from Amtrak Cascades on our way to Sustainable Brands in Vancouver, B.C.
This year was the first PRPOSE attended the Sustainable Brands Conference. It was also the first time the conference was hosted in Vancouver, BC. Which gave us an excuse to take the train — one of the best ways to travel, especially on the West Coast where you hug the water nearly the entire way.
Be clear. Identify the primary purpose of your brand, organization, or business and make it easy for people to understand. "Sustainable" is a big word. What does it mean to you?
Be bold. Don't be afraid of taking a stand. You can't be all things to all people, but you can be the right thing to some people. When you have the opportunity to stand up for those people, do it.
Be open. Good ideas can come from anywhere. They can come from large national businesses like Target or Proctor & Gamble and they can come from a single soy bean farmer.
Be vulnerable. Some of the best interactions were with people outside of the official conference presentations — from fun runs organized by the conference event managers to impromptu happy hours that brought together women in CSR. These were events that were planned with faith that people would show up — and they did. And they loved it.
Be creative. This means entertaining the crazy ideas as well as the well-vetted ideas. It means being open to trying to tackle some of the biggest challenges facing our planet today and never saying "it's too hard" or "it's too big." Remove the word "can't" from your vocabulary.
There were so many examples of all of this playing out over the three days we spent in Vancouver. From the adaptive clothing line for ALL children launched by Target to the visioning sessions where we tackled complex issues facing agriculture in small groups, to the presentations from leaders across the world who were unafraid to challenge our ideas of sustainability and stretch us to think of ways we can learn from each other through creative design that impacts not just our planet, but our social systems, our healthcare, and our economic inequity issues.
The bottom line is simply this. Our environment is about more that climate — it's also about people. Our health, our happiness, our connections with each other, and our ability to thrive. If we are working towards any of those things, we are working on sustainability.


text:
\section{\label{sec:level1}Introduction\\}

The interface of tensile strained germanium ($\varepsilon$-Ge) grown on III-V substrates is currently being considered as the working tunnel-barrier in the channel of future high-performance and low-power consumption tunnel field-effect transistors (TFETs).\cite{Hudait2014,Clavel2015,Nguyen2015} These devices take advantage of band-to-band tunneling of charge carriers between the source and drain, and as a result, can overcome the limit for the subthreshold slope of thermionic devices,\cite{Ionescu11} thereby simultaneously improving the transistor switching speed (performance) and I$_\text{ON}$/I$_\text{OFF}$ current ratio (power efficiency). Concurrently, there is a large research effort dedicated to the integration of optical interconnects on a CMOS compatible platform,\cite{Miller09,Assefa10} allowing for highly efficient ultrafast inter- and intra-chip data communication. The latter requires efficient on-chip light sources, and $\varepsilon$-Ge grown on III-V substrates\cite{Pavarelli13} is being investigated for this purpose due to the tensile strain induced direct band gap of Ge.

The operation of transistor devices depends crucially on the junctions at the border between device materials, and this dependence only becomes stronger as device dimensions continue to shrink.\cite{delAlamo11,Ferain11} From the perspective of optical devices, where electron-hole recombination is required in the active region for light emission, material interfaces also play a dominant role in the device operation\cite{Pavarelli13} by determining the barrier height for electron and hole confinement. Motivated by the technological importance, significant progress has been made in recent decades towards the understanding of solid-state interfaces and the resulting line up of energy bands between materials forming the interface.\cite{Peressi98,Margaritondo12,Agostini13,Brillson16}

In terms of \textit{ab-initio} calculations of band alignments, the lattice-matched isovalent interfaces\cite{Vandewalle87,Vandenberg88,Christensen88,Peressi90,Hybertsen90,Hybertsen91} represent the simplest and most well studied category. Density functional theory (DFT) is typically employed, and idealized, atomically abrupt interfacial structures\cite{Harrison78,Peressi98} are often used. These theoretical works have shown that band alignments for these interfaces are predominantly derived from bulk properties of the adjoining materials.\cite{Vandewalle87,Christensen88} Hence, for isovalent interfaces, the interfacial structure does not have a significant effect.

Band offsets (BOs) across pseudomorphic heterostructures exhibiting heterovalent bonding across the interface have also been studied, both experimentally\cite{Waldrop79,Kraut80,Biasol92,Dahmen93,Volodin14,Pavarelli13} and computationally.\cite{Martin80,Kunc81,Peressi91,Biasol92,Franciosi93,Peressi98,Pavarelli13} As for the isovalent interfaces, a large portion of the computational (atomistic modeling) studies also involve ideal, abrupt interfaces, although some focus has been given to atomic intermixing/diffusion across the interface.\cite{Peressi98} Unlike isovalent junctions, the interfacial structure can have a significant effect on the band offsets of heterovalent interfaces, to the point of inducing \textit{qualitative} modifications to the offsets, e.g. type-I to type-II or vice versa, in interfaces such as $\varepsilon$-Ge/In$_{0.3}$Ga$_{0.7}$As(001),\cite{Pavarelli13} and also for Ge/In$_{x}$Al$_{1-x}$As(001) in certain cases (see results section).

In this paper, the sensitivity of BOs to interface structure in the lattice (mis)matched heterovalent ($\varepsilon$-)Ge/In$_{x}$Al$_{1-x}$As(001) interface is explained by a linear response electrostatic effect\cite{Resta89,Peressi98} which occurs as a result of changes in the position of polarized bonds (IV-III, or IV-V) relative to the abrupt interface. Local changes in the electrostatic potential step across the junction result from the local variations in valence charge density and the latter are in turn induced by variations in the stoichiometry of the interfacial region. Hence, this work extends previous theories of BO-interface structure relations\cite{Resta89,Peressi98} to the technologically important interface ($\varepsilon$-)Ge/In$_{x}$Al$_{1-x}$As(001). By explaining the qualitative changes in the band alignments that can be achieved for the same material interface by only changing the interface structure, this work also contributes to the understanding of how devices can be tailored by the interface.

Lattice mismatching across the interface can also affect the band alignment. When a thin-film is grown pseudomorphically on a substrate with a different lattice constant the thin-film exhibits elastic strain so that it can match the lattice constant of the substrate, below a critical thickness such that stress is not large enough to cause plastic relaxation via e.g. dislocation formation.\cite{ChasonGuduru16} Epitaxial strain can be used to induce a direct bandgap in Ge, useful for silicon-compatible photonics.\cite{LiangBowers10} For strained, heterovalent interfaces such as ($\varepsilon$-)Ge/In$_x$Al$_{1-x}$As the dependence of the band alignment on tensile strain $\varepsilon$, which is varied by the substrate stoichiometry $x$, can be significant due to the reordering of conduction band valleys. Here, we study the band alignment over a range of cation stoichiometry $x$ and show that when combined with modifications of the interface structure (modifications which represent diffusion of group-III atoms into the Ge layer), transitions between type-I and type-II band alignments can be achieved in this interface.

In this work, the variations of valence (VBO) and conduction (CBO) band offsets between Ge and In$_{x}$Al$_{1-x}$As, with respect to interfacial configuration, are investigated using first-principles atomistic simulations---which are detailed in the next section. In Sec.~\ref{results}, we consider a range of systematic structural modifications of the interface. Specifically, we consider (a) the Ge, As, and group-III stoichiometric balance of the mixed interfacial region for fixed substrate stoichiometries, (b) group-III composition of the In$_{x}$Al$_{1-x}$As substrate (for $x$ = 0.0 to 0.25) for fixed interfacial stoichiometries (Sec.~\ref{sec-abrupt-int}), (c) interdiffusion of species across the junction (Sec.~\ref{sec-intdiff}). For interdiffusion, we investigate the relative stability of diffused atoms in either material (Sec.~\ref{sec-Eform}). Finally, in Sec.~\ref{sec-analysis}, we rationalize the results by simple arguments and models based on the linear response electrostatic effect. Based on the results of the simulations and on the linear response analysis, we conclude  (Sec.~\ref{conclusions}) that our simulations provide a picture consistent with existing experimental results. We predict that both type-I and type-II band offsets should be observable for this interface depending on the details of the interface structure.

\section{Computational Methods}
Optimized geometries of bulk and interface models are calculated using DFT within the local density approximation (LDA),\cite{PZ1981,PW1992} along with a plane wave basis set and norm-conserving pseudopotentials\cite{TM1991}, as implemented in the Quantum Espresso software suite.\cite{QE2009} A non-linear core correction is added to the In pseudopotential to treat the core-valence interaction.\cite{LouieFroyenCohen1982} 50 Rydberg kinetic energy cutoff is used for the plane wave basis set. Numerically converged Monkhorst-Pack\cite{MonkhorstPack1976} $k$-point grids
are used for all supercells in this work. The macroscopic average along the $z$ axis (aligned to the (001) direction) of the planar average (parallel to the interfacial plane) of the self-consistent potential\cite{Baldereschi88} [$V$$^{m}$$(z)$] for bulk and interface cells are calculated within DFT.\cite{Giantomassi11} Interface models consist of 24 atomic layers oriented along the (001) direction; 11 monolayers for Ge, 11 monolayers for In$_{x}$Al$_{1-x}$As, and at least 1 mixed monolayer per periodic image of the supercell. Parallel to the interface, interface supercells have dimensions of ($2\times1$) in units of the (110) lattice parameter. The virtual crystal approximation (VCA) is used to approximate the In$_{x}$Al$_{1-x}$As cation alloy for each composition point.

Bulk cells are used to calculate the bulk band edges relative to the respective $V$$^{m}$$(z)$ for each material, and interface cells are used to calculate the potential offset ($dV$, see below) between the slabs. All band offsets correspond to fully relaxed geometries for bulk In$_{x}$Al$_{1-x}$As and interface cells, while for Ge the bulk cells are biaxially strained along the (100) and (010) directions and allowed to relax along (001). Thus, the bulk cells represent biaxially tensile strained Ge grown on an In$_{x}$Al$_{1-x}$As substrate (with AlAs lattice matched to Ge) and the interface models represent the minimum energy bonding configuration between the slabs.

In order to investigate the relative stability of diffused impurities in either Ge or AlAs, large cubic bulk cells with dimensions (3$\times$3$\times$3) in units of the (100) lattice parameter are used to calculate the formation energies\cite{VandewalNeugebauer04,Freysholdt14} of substitutional impurities in bulk Ge and bulk AlAs. \footnote{We do not consider In$_{x}$Al$_{1-x}$As with $x$ $>$ 0 for this purpose due to the inaccurate bond lengths resulting from the VCA approach which would lead to inaccurate impurity-host bonding energies.} These correspond to impurity defects present after growth as a result of diffusion of substrate species during growth of the material on the substrate. Thus, we consider a single Al (As) on a Ge site (Al(As)$_\text{Ge}$) in a 216 atom bulk Ge supercell, and a single Ge on an Al (As) site (Ge$_\text{Al(As)}$) in a 216 atom bulk AlAs cell. The formation energies are calculated as a function of the chemical potential $\mu$$_\alpha$ of each exchanged atom $\alpha$\cite{VandewalNeugebauer04,Freysholdt14} which are related to the bulk elemental phases to establish boundaries on $\mu$$_\alpha$. Thus, the formation energies can be calculated for As-rich and Al-rich conditions, where the range of variation of As and Al chemical potentials corresponds to the heat of formation of AlAs\cite{ZhangNorthrup91}.

Thermodynamically stable configurations correspond to charge neutral interfacial bonding configurations between group-IV and group-III/V atoms\cite{Peressi98,Martin80,Kunc81,BylanderKleinman90} with no electric field building up across either material. In supercell simulations, the lack of a slab dipole is ensured when N$_{IV-V}$ = N$_{IV-III}$, where N$_{IV-V(III)}$ is the number of Ge-V(Ge-III) bonds per simulation cell. This constraint is imposed in all simulations in this work.

Clearly, accurate band offsets require accurate calculations of the bulk band structures, which is precluded in DFT due to the well-known band gap problem.\cite{PerdewLevy82,ShamSchluter85,GodbySchluterSham88} The DFT+$GW$ approach corrects the energy levels using the $GW$ approximation to the electron self-energy\cite{Hedin1965,AryasetGunnars97,HybLouie86} providing sufficiently accurate bulk band structures for evaluating band alignments at semiconductor/oxide interfaces.\cite{Myrta10,Giantomassi11}
In this work, differences of 0.17 eV between the VBO calculated with and without the $GW$ correction are found for the lattice matched Ge/AlAs(001) and for lattice mismatched $\varepsilon$-Ge/In$_{x}$Al$_{1-x}$As(001). For these reasons, all VBOs and CBOs calculated in this work are obtained using the DFT+$GW$ approach. This yields a first-order approximation to the quasiparticle band gaps from which band offsets are derived.\cite{Myrta10,Giantomassi11} Valence and conduction band offsets are computed using
\begin{equation} \label{eq.1}
\Delta E_V = E_{V,Ge} - E_{V,III-V} + \Delta(\delta E_V) + dV \
\end{equation}
\begin{equation} \label{eq.2}
\Delta E_C = E_{C,III-V} - E_{C,Ge} - \Delta(\delta E_C) - dV \
\end{equation}
where $E_{V,Ge}$ ($E_{V,III-V}$) is the valence band maximum of Ge (In$_{x}$Al$_{1-x}$As) relative to $V^{m}$$(z)$ of the bulk cells, $E_{C,Ge}$ ($E_{C,III-V}$) is the DFT conduction band minimum of Ge (In$_{x}$Al$_{1-x}$As) relative to $E_{V,Ge}$ ($E_{V,III-V}$), $\delta$$E_V$ ($\delta$$E_C$) is the \textit{GW} correction to the valence band maximum (conduction band minimum) and $\Delta$($\delta$$E_{V/C}$) represents the difference between the materials in the \textit{GW} correction for the valence/conduction band edge (V/CBE). $dV$ is the offset in $V$$^{m}$$(z)$ across the interface. To obtain $dV$, the entire self-consistent potential was taken, however the change in $V^{m}$$(z)$ across the interface does not significantly involve the exchange-correlation potential, which is flat throughout the interface cell. For unstrained Ge, the conduction band minimum resides at the L point, while for sufficient biaxial strain $\varepsilon$$_{Ge}$ Ge exhibits a direct minimum gap. After relaxing the lattice constants of AlAs and InAs, and assuming a linear variation of the In$_{x}$Al$_{1-x}$As lattice constant with $x$, the corresponding change in cell parameters is applied to the relaxed Ge cell, resulting in $\varepsilon$$_{Ge}$ = 1.76\% when In content $x$ = 0.25. As discussed in the results section, the varying In content affects the ordering of the satellite valleys of both Ge and In, which has important implications for the band offsets.

We note that no spin-orbit coupling (SOC) is included in these calculations. The effect of SOC is to split the heavy hole $p$ states (with $J$ = 1/2 angular momentum) near the top of the valence band. This splitting is 0.30 eV in Ge, and 0.275 eV in AlAs\cite{madelung2004}. As this difference of 0.025 eV is relatively small, we expect a correspondingly small effect on our calculated band offsets, which in this work always correspond to the offset between band extrema. Hence, we consider the gain in accuracy to be insufficient to justify the increased computational load of including relativistic terms, and we omit SOC.

\begin{figure}[t]
\includegraphics[width=1.0\columnwidth]{interface_BOlines}
\caption{\label{fig:interface_BOlines} Atomic structure of the ideal, ordered, As-terminated Ge / In$_{x}$Al$_{1-x}$As interface. Black lines correspond to a schematic representation of the valence and conduction BOs (with and without $GW$ corrections) across the interface. Ge atoms are purple, As atoms are green, and In/Al atoms are blue.}
\end{figure}

\section{Results} \label{results}
\subsection{Abrupt ordered interfaces} \label{sec-abrupt-int}

In this section, we focus on the interface that is atomically abrupt and localized to a single mixed monolayer which resides precisely between the slabs forming the heterojunction. The mixed interfacial monolayer (MIML) consists of either Ge and As atoms, or of Ge and In/Al atoms. This is exemplified by the ordered interface shown in Fig.~\ref{fig:interface_BOlines}. No interdiffusion is considered at this stage. Considering this as a fixed interfacial configuration, the In$_{x}$Al$_{1-x}$ stoichiometry of the substrate is varied from $x$ = 0 to $x$ = 0.25 and the valence and conduction band offsets are tracked in steps of $\Delta$$x$ = 0.05. Varying the In content affects the lattice constant of the substrate which in turn changes the strain state of the Ge slab. As $\varepsilon$$_{Ge}$ increases beyond 1.5\%, the conduction band satellite valleys are reordered in energy and Ge becomes a direct gap material. An analogous statement can be made for the conduction band valleys of In$_x$Al$_{1-x}$As. Our calculations show that for $x$ $\leq$ 0.20, the minimum energy valley in In$_x$Al$_{1-x}$As resides at the X point, while for larger proportions of In, In$_x$Al$_{1-x}$As exhibits a direct minimum gap at $\Gamma$.

In recent experimental works, III-V substrate growth is immediately followed by cooling under an As$_{2}$ overpressure before transfer to a vacuum chamber for Ge growth,\cite{Clavel2015} such that the resulting heterostructure most likely corresponds to Ge grown on an As-terminated In$_{x}$Al$_{1-x}$ slab, rendering an interfacial layer consisting of Ge and As atoms. In other experimental studies, group-III precursors was introduced immediately prior to Ge growth,\cite{Cheng2012} or even coverages of group-III and V atoms on the III-V surface before Ge growth were inferred from the observed surface reconstruction\cite{Maeda1995} with significant III segregation into Ge after Ge growth.\cite{Maeda1999} All of these studies taken together provide an impetus to study both III-terminated and V-terminated In$_{x}$Al$_{1-x}$As interfaced with Ge. As will be shown below, alternative interfacial stoichiometries can lead to interesting behavior in the form of qualitative changes to the band alignments. Hence, we study BOs for both cases, starting with the interface in which In$_x$Al$_{1-x}$As is As terminated (see Fig.~\ref{fig:interface_BOlines} for structure). The results are displayed in Fig.~\ref{fig:VBOs_CBOs_InxAl1-xAs_As-Ge-int}.

\begin{figure}[t]
\includegraphics[width=\columnwidth]{VBOs_CBOs_InxAl1-xAs_As-Ge-int}
\caption{\label{fig:VBOs_CBOs_InxAl1-xAs_As-Ge-int} Valence and conduction band offsets calculated using DFT+$GW$ for the abrupt As-terminated $\varepsilon$-Ge/In$_x$Al$_{1-x}$As(001) interface. The In content is varied in steps of 0.05, up to 0.25 (where 0.00 corresponds to AlAs). Variations of In content lead to corresponding changes in Ge strain, denoted by $\varepsilon$$_{Ge}$. The band gaps are labelled by the satellite valleys of minimum (maximum) energy for the conduction (valence) bands for both materials; for $x$ $\leq$ 0.20, the minimum energy conduction valley is L for Ge and X for In$_x$Al$_{1-x}$As.}
\end{figure}

With the interfacial configuration fixed to that shown in Fig.~\ref{fig:interface_BOlines} (group-V-terminated), a relatively small change in the valence band alignment is observed as a function of In content; 0.11 eV change in the VBO is observed between $x$ = 0.00 and $x$ = 0.25. The CBO exhibits a larger change of 0.47 eV as a function of In content. Thus a type-I BO is observed for Ge interfaced with As-terminated In$_x$Al$_{1-x}$As, and modifications of the group-III composition of the substrate for 0.00 $\leq$ $x$ $\leq$ 0.25 (neglecting changes due to the randomized cation alloy) does not qualitatively change the band alignment.

\begin{figure}[t]
\includegraphics[width=\columnwidth]{VBOs_CBOs_InxAl1-xAs_III-Ge-int}
\caption{\label{fig:VBOs_CBOs_InxAl1-xAs_III-Ge-int} Valence and conduction band offsets calculated using DFT+$GW$ for the abrupt III-terminated $\varepsilon$-Ge/In$_x$Al$_{1-x}$As interface. The In content is varied in steps of 0.05, up to 0.25 (where 0.00 corresponds to AlAs). Variations of In content lead to corresponding changes in Ge strain, denoted by $\varepsilon$$_{Ge}$. The band gaps are labelled by the satellite valleys of minimum (maximum) energy for the conduction (valence) bands for both materials; for $x$ $\leq$ 0.20, the minimum energy conduction valley is L for Ge and X for In$_x$Al$_{1-x}$As.}
\end{figure}

Changing to the group-III-terminated In$_x$Al$_{1-x}$As, in which the MIML consists of Ge and In/Al cation atoms, a stark contrast is observed in the band alignments compared to the As-terminated case. Fig.~\ref{fig:VBOs_CBOs_InxAl1-xAs_III-Ge-int} shows much larger VBOs and correspondingly smaller CBOs, with the CBO becoming negative (corresponding to the Ge CBE being higher in energy than that of In$_x$Al$_{1-x}$As, see equation (\ref{eq.2})) for small values of $x$; a type-II band offset is calculated for $x$ $<$ 0.05, and so a type-II to type-I transition in the band alignment occurs as a function of III content for the abrupt III-terminated $\varepsilon$-Ge/In$_x$Al$_{1-x}$(001) interface, with the BOs being type-I for $x$ $>$ 0.05.

In addition to showing the BO dependence on substrate stoichiometry, this is also a strong indication of the high sensitivity of band alignments to interfacial stoichiometry for $\varepsilon$-Ge/In$_{x}$Al$_{1-x}$As(001) (compare Figs.~\ref{fig:VBOs_CBOs_InxAl1-xAs_As-Ge-int} and ~\ref{fig:VBOs_CBOs_InxAl1-xAs_III-Ge-int} for a given value of $x$), and shows that the band alignment can also change from type-I to type-II when comparing As-terminated to III-terminated Ge/AlAs interfaces. This is in qualitative agreement with the results of Pavarelli {\it et al}.\cite{Pavarelli13} who reported an analogous change in the calculated band offset type for anion and cation dominated interface stoichiometries in the $\varepsilon$-Ge/In$_{0.3}$Ga$_{0.7}$As(001) interface. The results also indicate a comparable change in the VBO and CBO as a function of In content for both the III-terminated case and the As-terminated case, although a slightly larger change is seen for the III-terminated case. This is explained by the presence of group-III atoms at the interface. As the latter corresponds to a III rich In$_x$Al$_{1-x}$As surface, the larger variation of the VBO (0.15 eV) and CBO (0.5 eV) with respect to the In$_x$Al$_{1-x}$ stoichiometry is observed due to the slightly larger effect that $x$ has on the interface potential term $dV$, where the latter is derived from the atomic potentials present in the interface supercell.

\subsection{Interdiffusion} \label{sec-intdiff}

In order to investigate the effects of interdiffusion of atomic species across the interface on band offsets, the position of the MIML was shifted up to 2 monolayers away from the abrupt interfacial layer separating the materials, either towards Ge or towards In$_x$Al$_{1-x}$As (Fig.~\ref{fig:GeOnAlAs_for_paper_ML012-2_AlGe}).  This corresponds to a maximum thickness of $\sim$6 {{\AA}} over which atomic diffusion is considered (i.e. $\pm$$\sim$3 {{\AA}} from the ML0 position, see Fig.~\ref{fig:GeOnAlAs_for_paper_ML012-2_AlGe}), which is consistent with previous experimental reports of interface abruptness in comparable heterostructures.\cite{Clavel2015,Nguyen2015} However, these interfacial configurations are unrealistic, and for heterostructures present in experimental samples, interfacial configurations involving mixed depths of diffusing species throughout the interfacial region are much more likely to occur. As a first approximation, this can be investigated by linearly varying the stoichiometric balance of atoms between adjacent MIMLs (while always maintaining charge neutral configurations) near the interface.

For example, consider the Ge/AlAs heterojunction with an abrupt interface in which the MIML consists of Ge and Al atoms (corresponding to the band offsets on the far left for $x$ = 0 and $\varepsilon$$_{Ge}$ = 0 in Fig.~\ref{fig:VBOs_CBOs_InxAl1-xAs_III-Ge-int}). This position of the MIML is referred to as ML0 (see right panel of Fig.~\ref{fig:GeOnAlAs_for_paper_ML012-2_AlGe}). By using the VCA to linearly mix the atoms of ML0 and ML1 (see middle panel of Fig.~\ref{fig:GeOnAlAs_for_paper_ML012-2_AlGe}), an approximation to an interfacial configuration involving mixed diffusion depths of Al atoms into the Ge slab can be achieved. For the case of Al atoms diffusing from ML0 to ML1, the stoichiometric balance between the monolayers required to maintain neutrality results in the relation

\vspace{5mm}

\centerline{[Al$_{0.5-−a}$Ge$_{0.5+a}$]$^\textrm{ML0}$ = [Al$_{a}$Ge$_{1−-a}$]$^\textrm{ML1}$}

\vspace{5mm}

\noindent where [Al$_{a}$Ge$_{1-a}$]$^\textrm{ML0/1}$ is the composition of ML0/1, and $a$ is varied from 0 to 0.5. This is repeated for the case of Al atoms diffusing between ML1 and ML2, with $b$ used as the stoichiometry parameter instead of $a$ to avoid confusion. For the case of As atoms diffusing into Ge (see Sec.~\ref{sec-Asdiff}), the stoichiometric relation is analogous, with Al sites being replaced by As. This procedure is also repeated for the case of Ge atoms diffusing into In$_x$Al$_{1-x}$As (see Sec.~\ref{sec-Gediff}) which would more likely correspond to the scenario of a III-V slab grown on a Ge substrate.\cite{Chia2008} The stoichiometries of the endpoints (e.g. Al$_{0.5}$Ge$_{0.5}$ in ML0, ML1, or ML2, see Fig.~\ref{fig:GeOnAlAs_for_paper_ML012-2_AlGe}) are calculated using explicit atomistic models (see Fig.~\ref{fig:VBOs_CBOs_InxAl1-xAs_III-Ge-int}) and compared to the corresponding VCA results for comparison.

As an additional assessment of the error associated with modeling the mixed layer stoichiometries with the VCA, the cluster expansion formalism is used to generate a special quasirandom structure (SQS)\cite{Wei90} representation of the mixed monolayer with $a$ = 0.5. The ATAT code\cite{ATAT02,ATAT-mcsqs13} is used to generate the periodic monolayer cell which exhibits multisite correlation functions for $m$th nearest neighbor $k$-atom clusters $\bar{\Pi}_{k,m}^\text{2D}$ that match those of an infinite random 2 dimensional binary alloy with 50/50 composition, for up to $m$ = 2 and $k$ = 3. This monolayer SQS is used to compare to the ordered monolayer structures, and to the end-point VCA stoichiometries. This is done for Al diffusing into Ge, and for Ge diffusing into AlAs.

The results of these simulations are also compared to an analytical model based on a linear response theory for polar, heterovalent interfaces\cite{Peressi98,Harrison78}. This model is described in Sec.\ref{sec-analysis}, and the results obtained from this model are shown as dashed lines in Figs.~\ref{fig:cat-diffusion_Ge-InxAl1-xAs}, ~\ref{fig:Ge-diffusion_GecatML_Ge-InxAl1-xAs}, and ~\ref{fig:Ge-diffusion_GeAsML_Ge-InxAl1-xAs}.

\begin{figure} [t]
\includegraphics[width=10cm,height=3.5cm]{GeOnAlAs_for_paper_ML012-2_AlGe}
\caption{\label{fig:GeOnAlAs_for_paper_ML012-2_AlGe} (Left) Model of MIML residing exactly between the materials forming the heterojunction; this position is labelled ML0. (Middle) MIML positioned one monolayer further from ML0, towards the Ge slab, with position labeled ML1. (Right) MIML positioned 2 monolayers towards the Ge slab, with position labeled ML2. For Ge diffusing into In$_{x}$Al$_{1-x}$As, we consider Ge atoms residing up to two monolayers away from the ML0 position, towards In$_{x}$Al$_{1-x}$As, with position labeled ML-2. Ge atoms are purple, group-V As atoms are green, and group-III In and Al atoms are blue. In this figure, the case of group-III atoms residing in the top In$_{x}$Al$_{1-x}$As layer is used as an example. For the cases of As atoms residing in the top layer, all green and blue atoms are exchanged.}
\end{figure}

\begin{figure*}

{
\includegraphics[width=\columnwidth]{VBOs_CBOs_AlAs_Al-diffusion_ML012}
\includegraphics[width=\columnwidth]{VBOs_CBOs_InAlAs_InAl-diffusion_ML012}}

{
\includegraphics[width=\columnwidth]{VBOs_Al-interdiffusion_VCA_Ge-AlAs}
\includegraphics[width=\columnwidth]{VBOs_InAl-interdiffusion_VCA_Ge-InAlAs}}

\caption[width=\columnwidth]{\label{fig:cat-diffusion_Ge-InxAl1-xAs}In (a) and (b), band offsets are presented for explicit (ordered) models of group-III In and Al atoms in the Ge slab, with increasing distance from the ML0 position. In (c) and (d), VBOs are plotted for group-III atoms diffusing into Ge, using the VCA to approximate the stoichiometry of monolayers near the interfacial plane. Left panels ((a) and (c)) correspond to Ge/AlAs(001), right panels ((b) and (d)) correspond to $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001). The \textbf{{\texttimes}} symbols label VBOs calculated using the VCA. The \textbf{$\triangle$} symbols correspond to explicit models of the atomic configurations for endpoint interface stoichiometries, ordered along the (110) direction parallel to the interface. The \textbf{$\bigtriangledown$} symbols represent the SQS model for the mixed monolayer. The dashed lines correspond to the linear response model (described in Sec.~\ref{sec-analysis}) for polar interfaces, applied to diffusion. As group-III In$_{x}$Al$_{1-x}$ cations diffuse away from the substrate into Ge, the band offsets become increasingly type-II in character for Ge/AlAs(001), and change from type-I to type-II for $\varepsilon$-Ge/In$_{x}$Al$_{1-x}$As(001). Note that negative values of the CBO correspond to the Ge CBE residing at a higher energy than the AlAs CBE.}
\end{figure*}

\begin{figure*}

{
\includegraphics[width=\columnwidth]{VBOs_CBOs_AlAs_Ge-diffusion_GeAlML0-2}
\includegraphics[width=\columnwidth]{VBOs_CBOs_InAlAs_Ge-diffusion_GeInAlML0-2}}

{
\includegraphics[width=\columnwidth]{VBOs_Ge-interdiffusion_VCA_GeAlML0-2}
\includegraphics[width=\columnwidth]{VBOs_Ge-interdiffusion_VCA_GeInAlML0-2}}

\caption[width=\columnwidth]{\label{fig:Ge-diffusion_GecatML_Ge-InxAl1-xAs}In (a) and (b), band offsets are presented for explicit models of Ge in a group-III layer of In$_{x}$Al$_{1-x}$As. In (c) and (d), VBOs are plotted for Ge diffusing from ML0 to ML-2 (the second group-III layer away from ML0), using the VCA to approximate the stoichiometry of monolayers near the interfacial plane. In$_{x}$Al$_{1-x}$As is III-terminated. Left panels ((a) and (c)) correspond to Ge/AlAs(001), and right panels ((b) and (d)) correspond to $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001). The \textbf{{\texttimes}} symbols label VBOs calculated using the VCA. The \textbf{$\triangle$} symbols correspond to explicit models of the atomic configurations for endpoint interface stoichiometries, ordered along the (110) direction parallel to the interface. The \textbf{$\bigtriangledown$} symbols represent the SQS model for the mixed monolayer. The dashed lines correspond to the linear response model (described in Sec.~\ref{sec-analysis}) for polar interfaces, applied to diffusion. For this range of diffusion, the band alignment remains type-II as a function of Ge diffusion distance into AlAs, and changes from type-I to type-II for Ge diffusion into In$_{0.25}$Al$_{0.75}$As.}
\end{figure*}

\begin{figure*}

{
\includegraphics[width=\columnwidth]{VBOs_CBOs_AlAs_Ge-diffusion_GeAsML0-2}
\includegraphics[width=\columnwidth]{VBOs_CBOs_InAlAs_Ge-diffusion_GeAsML0-2}}

{
\includegraphics[width=\columnwidth]{VBOs_Ge-interdiffusion_VCA_GeAsML0-2}
\includegraphics[width=\columnwidth]{VBOs_Ge-interdiffusion_InAlAs_VCA_GeAsML0-2}}

\caption[width=\columnwidth]{\label{fig:Ge-diffusion_GeAsML_Ge-InxAl1-xAs}In (a) and (b), band offsets are presented for explicit models of Ge in an As layer of In$_{x}$Al$_{1-x}$As. In (c) and (d), VBOs are plotted for Ge diffusing from ML0 to ML-2 (the second group As layer away from ML0), using the VCA to approximate the stoichiometry of monolayers near the interfacial plane. In$_{x}$Al$_{1-x}$As is As-terminated. Left panels ((a) and (c)) correspond to Ge/AlAs(001), and right panels ((b) and (d)) correspond to $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001). The \textbf{{\texttimes}} symbols label VBOs calculated using the VCA. The \textbf{$\triangle$} symbols correspond to explicit models of the atomic configurations for endpoint interface stoichiometries, ordered along the (110) direction parallel to the interface. The \textbf{$\bigtriangledown$} symbols represent the SQS model for the mixed monolayer. The dashed lines correspond to the linear response model (described in Sec.~\ref{sec-analysis}) for polar interfaces, applied to diffusion. For this range of diffusion, the band alignment remains type-I as a function of Ge diffusion distance into AlAs or In$_{0.25}$Al$_{0.75}$As, with the VBO significantly reduced in both cases.}
\end{figure*}

\begin{table}
\caption{\label{tab:AsGe_BO}
Calculated band offsets of Ge/AlAs(001) and $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001) for As-terminated In$_{x}$Al$_{1-x}$As, in which As atoms have diffused up to two monolayers into Ge. The MIML column refers to the position of the mixed interfacial monolayer, as defined by Fig.~\ref{fig:GeOnAlAs_for_paper_ML012-2_AlGe}. The values in brackets refer to estimates from the linear response model for polar interfaces\cite{Peressi98,Harrison78} applied to diffusion, as described in Sec.~\ref{sec-analysis}. All band offsets are in eV.}
\begin{ruledtabular}
  \begin{tabular}{c|cccc}
MIML & VBO & CBO & \\
\hline\\[-0.2cm]
 &Ge/AlAs(001) && \\[0.1cm]
ML0 & 0.97 & 0.41 & \\
ML1 & 0.74 (0.70) & 0.65 (0.61) & \\
ML2 & 0.46 (0.43) & 0.92 (0.89) & \\
\\[0.1cm]
& $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001) && \\[0.1cm]
ML0 & 0.86 &  0.75 &  \\
ML1 & 0.72 (0.62) &  0.90 (0.80) &  \\
ML2 & 0.48 (0.37) &  1.15 (1.04) &  \\
  \end{tabular}
\end{ruledtabular}
\end{table}

\subsubsection{In$_{x}$Al$_{1-x}$ diffusion into Ge} \label{sec-catdiff}

For the case of Al atoms diffusing away from the Ge/AlAs(001) interface and into Ge, a linear change in the band offset is observed (panels (a) and (c) of Fig.~\ref{fig:cat-diffusion_Ge-InxAl1-xAs}). The band alignment is type-II for the case of the MIML residing at ML0 ([Al$_{0.5}$Ge$_{0.5}$]$^\textrm{ML0}$). Thus, for Ge films grown on Al-terminated AlAs(001), the valence (conduction) band edge of AlAs resides above (below) that of Ge, and for increasing diffusion depth of Al atoms into Ge the CBO becomes increasingly negative and the VBO increasingly positive. As a result, the band alignment is increasingly type-II over this range as a function of diffusion distance of Al. While a diffusion distance of up to 2 monolayers (corresponding to $\sim$3 {{\AA}}) into Ge is particularly short, an increase in the band alignments of 0.50 eV (0.51 eV) is calculated for the explicit (VCA) models of the interface, which shows again the large sensitivity of band alignments to diffusion distance.

Turning to the lattice-mismatched interface $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001), a qualitatively similar movement of VBO and CBO with respect to diffusion distance of group-III (In and Al) atoms compared to Ge/AlAs(001) is calculated. The major difference compared to Ge/AlAs(001) is that the VBO for [(InAl)$_{0.5}$Ge$_{0.5}$]$^\textrm{ML0}$ is small enough to yield a type-I band alignment. A type-I to type-II transition in the band alignment is observed as a function of diffusion distance for this case, with the CBO for [(InAl)$_{0.5}$Ge$_{0.5}$]$^\textrm{ML1}$ being close to flat (0.01 eV) and [(InAl)$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$ exhibiting a type-II band offset (Fig.~\ref{fig:cat-diffusion_Ge-InxAl1-xAs} (b)).

Thus for group-III cations diffusing across the interface and into $\varepsilon$-Ge, calculations show that this can have a large enough effect as to change the character of the band alignment relative to the abrupt interface, even for a very short diffusion distance of two monolayers. From the perspective of device physics, this finding has significant consequences. For example, for devices involving sandwiches of $\varepsilon$-Ge between In$_{0.25}$Al$_{0.75}$As(001) layers, the trapping of both electrons and holes (required for optically active recombination in optoelectronic applications) will be highly dependent on the diffusion depth of In and Al atoms into the $\varepsilon$-Ge layer. As the abrupt $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001) exhibits a type-I band alignment, these calculations show that atomic-scale abruptness of this interface is required to achieve significant optical recombination in the $\varepsilon$-Ge layer, which hinders the use of this particular interface in optical devices.

\subsubsection{As diffusion into Ge} \label{sec-Asdiff}

Calculations of band offsets were also performed for the case of As-terminated In$_{x}$Al$_{1-x}$As, see Table~\ref{tab:AsGe_BO}.\footnote{For this case the As atoms of the MIML are moved into Ge in the manner described in sec.~\ref{sec-intdiff}, where the mixed layer stoichiometries are related by [As$_{0.5-−a}$Ge$_{0.5+a}$]$^\textrm{ML0}$ = [As$_{a}$Ge$_{1−-a}$]$^\textrm{ML1}$ for As atoms diffusing from ML0 to ML1, and [As$_{0.5-−b}$Ge$_{0.5+b}$]$^\textrm{ML1}$ = [As$_{b}$Ge$_{1−-b}$]$^\textrm{ML2}$ for As atoms diffusing from ML1 to ML2.} The results show that band alignments are quite sensitive to diffusion distance into Ge. For the case of As atoms residing in ML1 ([As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML1}$), the VBO is reduced by 0.23 eV compared to the abrupt (ML0) case, while the CBO correspondingly increases by 0.24 eV. For $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001), the VBO (CBO) decreases (increases) by 0.14 eV (0.15 eV). When As atoms have diffused to ML2 ([As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$), the BOs continue to move in the same direction, showing again a linear change with respect to interface stoichiometry as in the case of group-III diffusion into Ge (Sec.~\ref{sec-catdiff}), but with a slope of the opposite sign.

The VBO and CBO of Ge/AlAs for the [As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$ case (0.46 eV and 0.92 eV, respectively) compare very well with recent BO measurements of the Ge/AlAs interface.\cite{Hudait2014} The calculated VBO (CBO) of $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001) for [As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$ is 0.48 eV (1.15 eV). The latter BOs also compare well with unpublished experimental XPS measurements~\cite{Hudait-private} of the band alignment of $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001).\footnote{The manuscript reporting this joint experimental and theoretical effort is currently under preparation. We therefore omit the band offset figures for this case (refer to Fig.~\ref{fig:VBOs_CBOs_InxAl1-xAs_As-Ge-int} for the explicit models of [As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML0}$ in Ge/AlAs(001) and $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001)).}

\subsubsection{Ge diffusion into In$_x$Al$_{1-x}$As} \label{sec-Gediff}

Due to the solid solubility of Ge in GaAs,\cite{Bosi2010} Ge diffusing through the interface towards the overlayer is a common observation in III-V/Ge(001) heterostructures (i.e. a III-Vs grown on Ge) such as GaAs/Ge(001). To a certain extent this diffusion and the overall interface quality can be controlled by growth conditions,\cite{Tanoto2006,Brammertz2008,Bosi2011,Sophia2015,Jia2016} as well as by thin interlayers of AlAs (or alloys thereof) between GaAs and Ge.\cite{Chia2008,Li2013,Qi2014,Chen2016} The latter technique can decrease interdiffusion due to the large Al-As bond energy and yield heterostructures with very sharp interfaces between the III-V region and Ge. However diffusion cannot be completely suppressed and Ge diffusion distances of a few nm to tens of nm into the AlAs region can be observed.\cite{Chia2008} Many factors influence the investigation of heterostructures involving III-Vs grown on Ge, such as the potential of CMOS compatible monolithic integration of optical devices\cite{Fitzgerald1992,Chilukuri2007} where graded GeSi alloys act as a buffer between the III-V overlayer and the Si substrate. Also, high-quality III-V/Ge interfaces with a type-I BO could offer advantages for photovoltaic technologies.\cite{Bosi2007,Guter2009,Qi2014} An understanding of the effects of Ge diffusion through the interface is imperative to the assessment of these potential applications.

In this section, the effects of Ge diffusion into AlAs and In$_{0.25}$Al$_{0.75}$As on the BOs are studied for short diffusion distances. For the interface with In$_{0.25}$Al$_{0.75}$As, Ge is tensile strained to the III-V lattice constant, which models the top In$_{0.25}$Al$_{0.75}$As/$\varepsilon$-Ge interface of a confined $\varepsilon$-Ge region between a III-V overlayer and a III-V substrate, as is considered for optoelectronic applications.\cite{Pavarelli13} Only the positions of Ge atoms which satisfy electron counting rules\cite{Peressi98,Martin80,Pashley89} for interfacial bonding are considered for this investigation, as this prevents the accumulation of an electric field across each slab which would result in unstable interface structures. For this reason, only the position of Ge atoms corresponding to the second monolayer away from the ML0 position and towards In$_{x}$Al$_{1-x}$As (ML-2) is considered. In terms of the stoichiometric expression for the mixed layer as defined at the beginning of Sec.~\ref{sec-intdiff}, this corresponds to only [Ge$_{b}$(III)$_{1−-b}$]$^\textrm{ML-2}$ ([Ge$_{b}$(As)$_{1−-b}$]$^\textrm{ML-2}$) being considered and compared to the abrupt [(III)$_{0.5}$Ge$_{0.5}$]$^\textrm{ML0}$ ([As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML0}$) interfaces for group-III (group-V) terminated In$_{x}$Al$_{1-x}$As.

\begin{figure}
{
\includegraphics[width=1.0\columnwidth]{Eforms}}
\caption{\label{fig:Eforms} Formation energies of substitutional impurities in Ge (purple lines) and impurities in AlAs (green lines), plotted as a function of chemical potential. Solid lines correspond to impurities which result in As bonding to Ge, while dashed lines correspond to impurities which result in Al bonding to Ge. In all cases, impurities which lead to As-Ge bonds have higher stability for the majority of the range of variation of the chemical potential, and particularly for As-rich conditions.}
\end{figure}

\begin{figure*}
{
\includegraphics[width=6.1225cm,height=4.75cm]{AlGeML0_V_and_rho}
\includegraphics[width=5.8025cm,height=4.75cm]{AlGeML1_V_and_rho}
\includegraphics[width=5.8025cm,height=4.75cm]{AlGeML2_V_and_rho}}

\caption{\label{fig:Velectro_rho_Aldiff} Al diffusing into Ge. Top graphs show the planar and macroscopic average of the electrostatic potential plotted as a function of $z$ (normal to interfacial plane). Bottom graphs show the macroscopic average of the electronic charge density plotted as a function of $z$. Left panels (a) correspond to the abrupt interface ([Al$_{0.5}$Ge$_{0.5}$]$^\textrm{ML0}$), middle panels (b) are for [Al$_{0.5}$Ge$_{0.5}$]$^\textrm{ML1}$, and right panels (c) correspond to Al residing two monolayers into Ge ([Al$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$). All values of $dV$ are in eV. Charge density variation $\Delta$$\rho$$^{m}$ is in $e$/{{\AA}}$^3$. Note that the potentials and charge densities are plotted along the same horizontal scale.}
\end{figure*}

\begin{figure*}
{
\includegraphics[width=6.1225cm,height=4.75cm]{AsGeML0_V_and_rho}
\includegraphics[width=5.8025cm,height=4.75cm]{AsGeML1_V_and_rho}
\includegraphics[width=5.8025cm,height=4.75cm]{AsGeML2_V_and_rho}}

\caption{\label{fig:Velectro_rho_Asdiff} As diffusing into Ge. Top graphs show the planar and macroscopic average of the electrostatic potential plotted as a function of $z$ (normal to interfacial plane). Bottom graphs show the macroscopic average of the electronic charge density plotted as a function of $z$. Left panels (a) correspond to the abrupt interface ([As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML0}$), middle panels (b) are for [As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML1}$, and right panels (c) correspond to As residing two monolayers into Ge ([As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$). All values of $dV$ are in eV. Charge density variation $\Delta$$\rho$$^{m}$ is in $e$/{{\AA}}$^3$. Note that the potentials and charge densities are plotted along the same horizontal scale.}
\end{figure*}

\begin{figure*}
{
\includegraphics[width=8.9cm,height=6.6cm]{GeAlML-2_V_and_rho}
\includegraphics[width=8.4cm,height=6.6cm]{GeAsML-2_V_and_rho}}

\caption{\label{fig:Velectro_rho_Gediff} Ge diffusing into AlAs. Top graphs show the planar and macroscopic average of the electrostatic potential plotted as a function of $z$ (normal to interfacial plane). Bottom graphs show the macroscopic average of the electronic charge density plotted as a function of $z$. Left panels (a) correspond to the Ge atoms residing two monolayers into Al-terminated AlAs ([Ge$_{0.5}$Al$_{0.5}$]$^\textrm{ML-2}$), and right panels (b) correspond to Ge residing two monolayers into As-terminated AlAs ([Ge$_{0.5}$As$_{0.5}$]$^\textrm{ML-2}$). All values of $dV$ are in eV. Charge density variation $\Delta$$\rho$$^{m}$ is in $e$/{{\AA}}$^3$. Compare $\Delta$$\rho$$^{m}$ of the left panel to that of [Al$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$ in Fig.~\ref{fig:Velectro_rho_Aldiff}. Compare $\Delta$$\rho$$^{m}$ of the right panel to that of [As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$ in Fig.~\ref{fig:Velectro_rho_Asdiff}. Note that the potentials and charge densities are plotted along the same horizontal scale.}
\end{figure*}

In contrast to the results of Secs.~\ref{sec-catdiff} and ~\ref{sec-Asdiff} involving In$_{x}$Al$_{1-x}$As atoms diffusing into Ge, the band alignments in this section vary by a larger amount for a given diffusion distance. For group-III terminated In$_{x}$Al$_{1-x}$As (see Fig.~\ref{fig:Ge-diffusion_GecatML_Ge-InxAl1-xAs}), an increase of 0.55 eV (0.56 eV) in the VBO is calculated for Ge diffusing to the ML-2 position in AlAs (In$_{0.25}$Al$_{0.75}$As). For AlAs, this almost results in a broken gap band alignment, as the CBE of AlAs is only 0.09 eV above the VBE of Ge. The CBE of In$_{0.25}$Al$_{0.75}$As(001) is also close to the VBE of $\varepsilon$-Ge, but with a larger separation (0.12 eV) compared to Ge-AlAs. Assuming continued linearity of the BOs as a function of diffusion distance, broken gap alignments are expected for these interfaces with a further diffusion of Ge into In$_{x}$Al$_{1-x}$As.

This has important consequences for devices involving AlAs (with possibly small proportions of In) grown on Ge. At variance, movement of the VBO in the opposite direction is calculated for Ge atoms diffusing into AlAs (In$_{x}$Al$_{1-x}$As) through an As terminated interface (see Fig.~\ref{fig:Ge-diffusion_GeAsML_Ge-InxAl1-xAs}). In this case the VBO \textit{decreases} by 0.75 eV (0.64 eV), which is qualitatively similar but significantly higher than the maximum VBO variation of 0.51 eV (0.38 eV) for As atoms diffusing through the Ge/AlAs(001) ($\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001)) interface.

An apparent bowing of the VBO as a function of the mixed layer stoichiometry $b$ can be observed in panels (c) and (d) of Figs.~\ref{fig:Ge-diffusion_GecatML_Ge-InxAl1-xAs} and~\ref{fig:Ge-diffusion_GeAsML_Ge-InxAl1-xAs}, whereas this bowing effect is largely suppressed for the case of group-III atoms diffusing into Ge (Fig.~\ref{fig:cat-diffusion_Ge-InxAl1-xAs} (c) and (d)). The bowing effect in Figs.~\ref{fig:Ge-diffusion_GecatML_Ge-InxAl1-xAs} and~\ref{fig:Ge-diffusion_GeAsML_Ge-InxAl1-xAs} is likely an artifact of the VCA model of the interfacial region; the VCA cannot correctly capture local structural properties\cite{Jaros85} which translates to errors in bond lengths and interlayer distances. These errors are exacerbated when the mixed monolayer, represented by the VCA, bonds to the neighboring ionic layers within the III-V crystal. The difference in bond lengths between III-V bonds and Ge-III/V bonds makes an important contribution to the local potential within the III-V slab and this contribution is missed in the VCA representation of the mixed layers for Ge diffusing into AlAs or In$_{0.25}$Al$_{0.75}$As. This causes larger errors for the intermediate values of $b$ which involve two types of VCA `atoms' in the supercell, thus producing the bowing effect. For group-III atoms diffusing into Ge (see Sec.~\ref{sec-catdiff}), the VCA sites are now bonding to covalent rather than to ionic layers and the structural errors of the VCA are not so apparent.

The origin of the apparent bowing effect is further investigated by comparing the VCA results to explicit models of the mixed monolayer which are statistically representative of a 2 dimensional 50/50 random alloy (see panel (c) of Figs.~\ref{fig:cat-diffusion_Ge-InxAl1-xAs}, ~\ref{fig:Ge-diffusion_GecatML_Ge-InxAl1-xAs}, and ~\ref{fig:Ge-diffusion_GeAsML_Ge-InxAl1-xAs}). For the cases of Ge diffusing into AlAs, the VBOs obtained by the SQS monolayer are much closer to those obtained by the ordered model, compared to those obtained by the VCA. This lends further credence to the possibility that the apparent bowing effect seen in the VCA VBOs is due to structural errors associated with the VCA, as opposed to a realistic effect.
This is also the case for Al diffusing one monolayer into Ge (see Fig.~\ref{fig:Ge-diffusion_GecatML_Ge-InxAl1-xAs}), although for two monolayers of Al diffusion the VBO from the ordered model resides midway between the VCA and SQS result. In addition, the reduced bowing in this case (Fig.~\ref{fig:Ge-diffusion_GecatML_Ge-InxAl1-xAs}) indicates that the VCA is a better approximation for modeling mixed layers in materials with purely covalent bonding, compared to materials with some degree of ionic bonding.

\subsubsection{Stability of diffused impurities} \label{sec-Eform}

The formation energies\cite{VandewalNeugebauer04,Freysholdt14,ZhangNorthrup91} of substitutional impurities were calculated in bulk cells in order to establish the relative stability (under conditions of thermodynamic equilibrium) of diffused impurities present in either Ge or AlAs after growth on top of either an AlAs substrate or a Ge substrate, respectively. Thus, the formation energetics establish, as a function of growth conditions, which diffused impurities are more likely to be present in either material after growth. The formation energies E$_{form}$($\mu$$_\alpha$) are plotted as a function of $\mu$$_\alpha$ for the each diffused impurity in Fig~\ref{fig:Eforms}. For the majority of the range of $\mu$$_\alpha$, the substitutional impurities which result in bonds between As and Ge have consistently lower formation energies than impurities corresponding to Al bonding to Ge.

In particular, these As-Ge bonding impurities have very low formation energies (note that negative formation energies correspond to impurities which form spontaneously under thermodynamic equilibrium, hence a kinetic process would be required to prevent their formation) under As-rich conditions. The latter has been used to realize high quality, abrupt interfaces,\cite{Clavel2015,Nguyen2015} hence we expect As-rich growth conditions to be favored for applications of these heterostructures. We also mention that our calculated heat of formation of AlAs is $-$2.27 eV, which overestimates the magnitude compared to the experimental value of $-$1.53 eV\cite{Berger96semicon}. While this affects the formation energetics, our purpose is simply to establish an approximate, qualitative picture of the relative stabilities, and the error (0.74 eV) does not reverse the relative stability of As-Ge bonding impurities and Al-Ge bonding impurities under As-rich growth conditions.

\subsection{Analysis --- Relation between band offsets and interface configurations} \label{sec-analysis}
\subsubsection{Electrostatic potential, charge density, and interface diffusion} \label{sec-V_rho_diff}

The changes in band offsets presented in Sec.~\ref{sec-intdiff} arise purely from changes in the $dV$ term in Eqs.~(\ref{eq.1}) and (\ref{eq.2}). This is equivalent to stating that the changes in band offsets arise purely from interfacial effects, specifically from changes in the interface dipole derived from the macroscopic average of the atomic potentials near the interface, $V^{m}$$(z)$ (where the growth orientation is aligned to the $z$ direction). There is no contribution from bulk properties in the band alignment variations observed when comparing different interface structures (for a given group-III stoichiometry of In$_{x}$Al$_{1-x}$As and strain state of Ge).

In general, atomic mixing affects the electrostatic potential line up by changing the charge density profile across the interface $\rho(z)$.\cite{Harrison78,Brillson16} In fact, it can be shown that the electrostatic potential (Hartree potential $V_{H}$ + bare ionic $V_{ion}$) step across the interface is given by
\begin{equation}
  4\pi\,e^2\int\,z\rho^{m}(z)\text{d}z,
\end{equation}
and it is equivalent to the interface dipole ($e$ is the electronic charge, $\rho^{m}(z)$ is the macroscopic average of $\rho(z)$).\cite{Peressi98} Then, modifications to the local charge density arising from changes to the bonding configuration near the interface can provide either an enhancement or reduction of the interface dipole,\cite{Peressi98,McKinley92} depending on the polarity of bonds to the diffusing species, and their diffusion depth. For this reason, the VBO and CBO variations can be explained by electrostatic considerations involving the effect of positions of IV-III and IV-V bonds on the local potential.

As a result of the valence charge carried by the diffusing atoms, we expect Ge-III bonds to contribute positively to $dV$ as a function of diffusion distance of III atoms into Ge, and Ge-V bonds to contribute negatively to $dV$ as a function of diffusion distance. This is indeed consistent with what we observe in Figs.~\ref{fig:Velectro_rho_Aldiff} and~\ref{fig:Velectro_rho_Asdiff}. The former shows the planar and macroscopic averages of $V_{H}$+$V_{ion}$, and $\rho^{m}(z)$ for the explicit models of [Al$_{0.5}$Ge$_{0.5}$]$^\textrm{ML0}$, [Al$_{0.5}$Ge$_{0.5}$]$^\textrm{ML1}$, and [Al$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$ for the Ge-AlAs interface; the latter shows the same quantities for the [As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML0}$, [As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML1}$, and [As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$ interface configurations of Ge/AlAs(001). It can be seen that as Ge-III (Ge-V) bonds move away from the abrupt interfacial layer and into Ge the step in the electrostatic potential increases (decreases), while the region over which charge transfer occurs widens. A similar conclusion is reached by plotting $V$$^{m}$$(z)$ and $\rho^{m}$$(z)$ for the $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As(001) interfaces, which are not shown for brevity.

For Ge diffusing into In$_{x}$Al$_{1-x}$As, (see Fig.~\ref{fig:Velectro_rho_Gediff}) a larger change in $dV$ relative to the abrupt interfaces is observed compared to the change in $dV$ for Al and As atoms diffusing the same distance into Ge. This is not unexpected, given the relation between $dV$ and $\rho^{m}$$(z)$\cite{Peressi98}; the variations in density across the interface $\Delta$$\rho$$^{m}$ have a slightly larger amplitude for Ge diffusion into Al- or As-terminated AlAs compared to [Al$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$ or [As$_{0.5}$Ge$_{0.5}$]$^\textrm{ML2}$  (compare to corresponding $\Delta$$\rho$$^{m}$ values in Figs.~\ref{fig:Velectro_rho_Asdiff} and~\ref{fig:Velectro_rho_Aldiff}), and this translates to a larger effect on the interface dipole for Ge diffusion.

\subsubsection{Linear response theory applied to interface diffusion} \label{LRT}
Here we derive a simple model to describe the relationship between interface dipole and mixed layer stoichiometry across a heterovalent interface. We follow the linear response theory approach\cite{Peressi98} put forward by Peressi {\it et al.} which is based on the model for polar interfaces proposed by Harrison $et$ $al$\cite{Harrison78}. Within this approach, the interface is treated as a perturbation of a periodic reference crystal and the potential lineup consists of an isovalent (i.e. interface independent) and heterovalent terms $dV$ = $dV_\text{iso}$ + $dV_\text{het}$. The $dV_\text{het}$ is then obtained via the Poisson equation from the additional nuclear charges (carried by the perturbation) at each site.

For Al diffusing into Ge, we consider bulk Ge as the reference crystal. Hence, the additional nuclear charge per site along each monolayer across the interface is (schematically)
\begin{equation}
\resizebox{\columnwidth}{!}{$\dots -\underbrace{\text{Ge}}_{0}-\underbrace{\text{Ge}}_{0}- \left\langle -\underbrace{\text{Ge}_{1-a'}\text{Al}_{a'}}_{(a')} \right\rangle - \left\langle \underbrace{\text{Ge}_{1-(a-a')}\text{Al}_{(a-a')}}_{(a-a')} \right\rangle - \left\langle \underbrace{\text{Ge}_{0.5+a}\text{Al}_{0.5-a}}_{0.5-a} \right\rangle - \underbrace{\text{As}}_{-1} - \underbrace{\text{Al}}_{+1}- \cdots$}
\end{equation}
where 0 $\leq a' \leq a \leq 0.5$ is the mixed layer stoichiometry. The accumulated charge, found by summing adjacent sites from left to right, is then used to find the net contribution of interfacial charge to $dV_\text{het}$, which for Al diffusing into Ge becomes
\begin{equation}
dV_\text{het}(\text{AlGe}) = \frac{\pi e^2}{2a_0\epsilon}(0.5 + a + a'),
\end{equation}
where $e$ is the electron charge, $a_0$ the lattice constant of a GeAlAs alloy\footnote{Since Ge and AlAs are lattice matched this will be the bulk lattice constant of either Ge or AlAs} and $\epsilon$ the dielectric constant of the same alloy obtained as an average of the Ge and the AlAs dielectric constant. This is similar for the case of As diffusing into Ge, but with the opposite sign,
\begin{equation}
dV_\text{het}(\text{AsGe}) = -\frac{\pi e^2}{2a_0\epsilon}(0.5 + a + a').
\end{equation}

For Ge diffusing into Al terminated AlAs, a similar line of reasoning results in the following interface contribution to the potential line up (again, $0 \leq b \leq 0.5$ is used here for the mixed stoichiometry instead of $a$)
\begin{equation}\label{eq:GeinAlAs}
dV_\text{het}(\text{GeAl}) = \frac{\pi e^2}{2a_0\epsilon}(0.5 + 2b),
\end{equation}

and for Ge diffusing into As terminated AlAs,

\begin{equation}\label{eq:GeinAsAl}
dV_\text{het}(\text{GeAs}) = -\frac{\pi e^2}{2a_0\epsilon}(0.5 + 2b).
\end{equation}

By considering $dV_\text{iso}$ as the average of the abrupt (ML0, $a$ = $a'$ = $b$ = 0) cases for Al and As terminated AlAs, the isovalent contribution to the VBO follows from Eq.~\ref{eq.1}. $dV_\text{het}$ for either Al(+) or As($-$) terminated ML0 cases is then obtained from the difference $dV$ - $dV_\text{iso}$ = $dV_\text{het}$, giving a value for the proportionality constant $\pi\,e^{2}/(2a_0\epsilon)=$~0.27~eV in Ge/AlAs and 0.245 eV in $\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As. The contribution due to diffusing away from the ML0 plane is then simply an additional 0.27 (0.245) eV per monolayer of diffusion through the Ge/AlAs ($\varepsilon$-Ge/In$_{0.25}$Al$_{0.75}$As) interface, which results in a linear relation between the VBO and stoichiometry of mixed layers containing diffused impurities.\footnote{We have also derived $\pi\,e^{2}/(2a_0\epsilon)$ from first-principle by substituting in the expression the $a_0$ and $\epsilon$ values estimated from the LDA. In this case we obtained 0.29~eV and 0.27~eV respectively which would give comparable, though somewhat worse agreement with the values from the simulations.}

Results show that this model agrees qualitatively with VBOs obtained from supercell calculations. We observe generally a better agreement between this model and calculations involving explicit interface configurations (non-VCA) than with VBOs obtained from the VCA representation of the interfaces (with the exception of Al diffusing 2 monolayers into Ge). The latter is particularly true for Ge atoms diffusing into (In)AlAs, which again shows the weakness of using VCA to represent mixed layers in a ionically bonded material.

\section{Conclusions} \label{conclusions}

First-principles calculations of valence and conduction band offsets have been performed using the DFT+$GW$ approach. The $GW$ correction was applied to obtain accurate bulk bandgaps, while DFT within the LDA formulation provided the interfacial profile of the self-consistent potential from which the interface dipole $dV$ can be derived. By varying the stoichiometry of monolayers near the interface using the VCA, the atomic diffusion away from the abrupt interfacial layer can be modeled. Within this approach, the $dV$ term can be changed depending on the interlayer stoichiometry with a sensitivity large enough to, in some cases, change the character of the band alignment.

The results of this work are qualitatively consistent with the linear response theory developed for semiconductor interfaces,\cite{Resta89} where for heterovalent interfaces the change in interface dipole (and hence the change in band offset) should be linear in the stoichiometries of mixed layers.\cite{Peressi98,Bratina94} We attribute the deviations from linearity showing an apparent bowing effect, especially for the cases of Ge diffusing into the III-V slab to the structural errors associated with the VCA.

The VCA has also been used to model the group-III alloy of the III-V slab, thus introducing a further error in the calculations of the band offsets. This error has been investigated in Ref.~\onlinecite{Greene-Diniz16} for In$_{0.5}$Ga$_{0.5}$As.
By comparing with the most accurate SQS, it was found that most of the error in the VCA resides in the indirect L-point satellite valley band gap, while the minimum error of the VCA corresponds to the direct $\Gamma$-point band gap.
As indicated by the early studies on SQS models, errors in band gaps obtained by averaging between the constituent binary materials generally follow the same trend for different III-V materials,\cite{Wei90} hence the trends in VCA-errors should be transferable to In$_{x}$Al$_{1-x}$As. For $x=25\%$---the highest In content alloy studied in the present work---the band gap is direct at the $\Gamma$-point, and we expect the least amount of error.
While this error is not negligible (likely $\lessapprox$ 0.1 eV), it is not large enough to change qualitative conclusions and trends of the present study.

Future studies will involve a wider range of explicit models of disordered configurations for the interface, in which various SQS\cite{Zunger90,Wei90} representations of the interfacial layers will be compared against each other. This will shed more light on the band offset bowing effect and, by comparison, more accurately quantify the error in the band offsets when representing the mixed layer stoichiometries by the VCA. SQSs will also be used to model the group-III alloy of the III-V slab.

While the importance of the interface structure for heterovalent interfaces along with the associated departure from band offset transitivity seen for many isovalent interfaces is by now well-established, this work shows that variations in the interface stoichiometry can be enough to dramatically change the band alignment characteristics for the lattice (mis)matched ($\varepsilon$-)Ge/In$_{x}$Al$_{1-x}$As(001) interface. Combining this with the experimentally validated band offsets achievable from DFT+$GW$ for conduction and valence band offsets, this work shows that due to variations in the interface dipole, both type-I and type-II band offsets should be observable for this interface depending on the details of the interface structure. Calculations of the formation energetics of diffused substitutional impurities indicate consistently greater stability of impurities which involve As bonding to Ge, for both materials comprising the interface. For the commonly used experimental approach of growing Ge on As-rich (nominally As-terminated) III-As substrates, from which atomically sharp interfaces can be achieved, these results are consistent with the observation of type-I band offsets for ($\varepsilon$-)Ge/In$_{x}$Al$_{1-x}$As(001) for 0 $\leq$ $x$ $\leq$ 0.25.

\vfill

\begin{acknowledgments}
  The authors thank J. C. Abreu for providing the SQS models. The authors are grateful for helpful discussions with J. C. Abreu, F. Murphy-Armando, T. J. Ochalski, D. Saladukha, M. B. Clavel, M. K. Hudait, and J. Kohanoff.
  The authors acknowledge the use of computational facilities at the Atomistic Simulation Centre---Queen's University Belfast. This work is financially supported by the Department for the Employment of Northern Ireland and InvestNI through the US-Ireland R\&D partnership programme (USI-073).
\end{acknowledgments}

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text:
ACR+ joins a coalition calling the European Commission to deliver an ambitious EU Strategy for a Sustainable Built Environment
31 signatories, representing a diverse range of stakeholders, call for delivery of EU Strategy for a Sustainable Built Environment in a letter [1] addressed to European Commission's executive vice president Frans Timmermans, and commissioners Thierry Breton and Virginijus Sinkevičius.
Brussels, Belgium - One year after the launch of the Circular Economy Action Plan (CEAP), there is no clear timeline for a EU Strategy for a Sustainable Built Environment. At the moment, the European Commission is even openly questioning its intentions to go ahead with this strategy. This has triggered 31 organisations to call for an ambitious EU Strategy for a Sustainable Built Environment (SSBE) to be published by the end of 2021, in line with commitments set in the CEAP.
Such strategy is essential to tackle the substantial impacts of EU buildings and the construction industry, which account for an estimated 50% of energy consumption, 36% of CO2 emissions, 50% of raw materials, and 33% of waste and water use [2].
Signatories include environmental NGOs, industry stakeholders, and representatives from cities and regions.
The Association of Cities and Regions for sustainable Resource management (ACR+) strongly invites the Commission to stick to its commitments announced one year ago in the Circular Economy Action Plan.
A strategy is essential to address the sector's high impacts and make clear links between existing legislative proposals highlighted within the CEAP [3], and all other relevant legislation currently being revised [4].
Françoise Bonnet, Secretary General at ACR+, stated that: "As a network of cities and regions authorities, who are directly responsible for urban development policies, we strongly invite the Commission to accelerate the uptake of sustainable and circular building solutions."
"In order to generate adequate investments, our members need visibility and a clear commitment by the EU to develop a coherent legislative framework to drive sustainability and circularity of buildings and tackle the construction sector's major environmental impacts."
Key messages from the letter:
A Strategy for a Sustainable Built Environment was announced to be published by the end of 2021.
The substantial impacts of the sector need to be addressed as soon as possible for the EU to meet its climate goals in 2030 and 2050 respectively.
In order to accelerate the uptake of sustainable and circular building solutions and harmonised methodologies, and generate adequate investment, the construction value chain as a whole needs visibility and a clear commitment by the EU to develop a coherent legislative framework.
This strategy is needed to drive sustainability, in part through circular economy practices, to tackle the impacts of buildings and the construction sector.
Citizens and stakeholder groups now all need clarity and strong coordination from the European Commission – a strategy to deliver a comprehensive approach to sustainability of the built environment.
Full list of signatories:
ACR+ Association of Cities and Regions for sustainable Resource management
Carbon Neutral Cities Alliance (CNCA)
Climate Action Network (CAN) Europe
Corporate Leaders Group (CLG) Europe
Energy Cities
Environmental Coalition on Standards (ECOS)
European Environmental Bureau (EEB)
ICLEI - Local Governments for Sustainability - Europe
International Federation of Landscape Architects - IFLA Europe
Fire Safe Europe
RICS – Royal Institute of Chartered Surveyors
RREUSE
Sandbag - smarter climate policy
World Green Building Council (WGBC) Europe
Ecocity (Greece)
Ecoteca (Romania)
Environment Engineering Group (Serbia)
Deutsche Umwelthlife (Germany)
The Circular Economy Institute - IGOZ (Poland)
Friends of the Earth Bulgaria
Global2000 (Austria)
Levego Munkacsoport (Hungary)
Natuur & Milieu (Netherlands)
Mediterranean Information Office for Environment Culture and Sustainable Development MIO-ECSDE (Greece)
Repairably (Slovakia)
VšĮ "Žiedinė ekonomika" (Lithuania)
Zala Briviba (Latvia)
ZERO – Associação Sistema Terrestre Sustentável (Portugal)
Zero Waste France (France)
Zero Waste Association (Poland)
[1] https://acrplus.org/en/online-resources/position-papers/2838-stakeholders-call-for-delivery-of-eu-strategy-for-a-sustainable-built-environment
[2] European Commission figures: https://ec.europa.eu/environment/topics/circular-economy/levels_en#ecl-inpage-261 and https://ec.europa.eu/easme/en/news/sustainable-buildings-europe-s-climate-neutral-future
[3] Policies proposes to form part of EU Strategy for a Sustainable Built Environment: Construction Products Regulation, use of LEVEL(s) in public procurement and the EU sustainable finance framework, addressing Construction & Demolition Waste, LEVEL(s) and soil-related policies, as well as the Renovation Wave
[4] Relevant policies not mentioned in the CEAP: Energy Efficiency Directive and Energy Performance of Buildings Directive
-- ENDS --
ACR+ Secretariat – Núria Cases I Sampere
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Online ticket sales for The 3rd Annual Guy Cooking with Best Buddies Celebrity Chef Food and Wine Festival have ended.
Tickets are still available for purchase at the door with a credit card.
Enjoy an evening of incredible food, wine, and spirits prepared by over 30 of New England's Top Chefs at the Guy Cooking with Best Buddies Celebrity Chef Food and Wine Festival presented by Pepsi-Cola and Shaw's and Star Market Foundation.
Meet Celebrity Chef Guy Fieri at the Guy Cooking with Best Buddies Celebrity Chef Food and Wine Festival presented by Pepsi-Cola and Shaw's and Star Market Foundation. Get your photo taken with Guy Fieri and a limited edition Guy Cooking with Best Buddies t-shirt.


ALTON — Coach Tom Bourdeau preaches defense and in two games last week, his Prospect Mountain boys' hoop team showed what good defense can do.
The Timber Wolves held both Winnisquam and Farmington to under 10 points in the first half of games last week and walked off the court with two more wins to move to 3-0 on the season.
"That's what we're going to have to live by," Bourdeau said of his team's defense against Farmington on Friday, Dec. 16. "We're going to be in every game if we play defense like we did tonight."
Prospect came charging out of the gate with the first 10 points of the game. Zack Drouin hit the first five, converting two free throws then finishing a three-point play. Jay Mousseau followed with a hoop off his own steal and Pat Cassidy finished off the 10-0 start with a three-pointer for a 10-0 lead before Farmington got on the board with a long range shot with two minutes to play in the quarter.
However, Prospect's Austin Perrin answered the three-pointer with one of his own and the Timber Wolves carried a 13-3 lead to the second quarter.
Mousseau scored the first points of the second and Ethan Henderson followed with a three-pointer to stretch the lead to 18-3. Farmington got on the board with a foul shot, but Logan Roberts hit from the line and Drouin hit a hoop and drained a free throw for a 22-4 lead.
Farmington came back with a three-pointer, which Drouin promptly answered with his own shot from downtown. Farmington managed a final free throw but still trailed 25-8 at the halftime break.
Mousseau scored the first bucket of the second half and after Farmington answered, Drouin finished off his own steal for a 29-10 lead. Cassidy then drained a bucket off another Drouin steal for a 31-10 lead. After a Farmington hoop, Cassidy sank a three-pointer to up the lead to 34-12.
Farmington scored the next four points, but Zach Robertson closed out the quarter with a bucket and the teams headed to the final quarter with Prospect in control, 36-16.
Drouin drained a hoop and Mousseau hit two from the line in the opening minutes of the fourth quarter. After a Farmington hoop, Mousseau hit another, but again, the Tigers answered. Cassidy then converted a three-point play. After another Farmington bucket, Matt Joy closed out Prospect's scoring with a hoop. The Tigers added the game's final basket.
While his team walked away with its third win, Bourdeau remains worried about his team's offense.
"I am still concerned about the offense," he said. "But we are going in the right direction, so I can't be disappointed."
He noted that he was sure Farmington was pumped up for the game, as he served as the Tigers' head coach last season and he was sure they wanted to beat him, but the intensity was matched on his side.
"I am sure they came up all pumped up wanting to beat me," he said. "Just about as much as I didn't want to lose."
Bourdeau said he came in wanting to hold Farmington big man Derek Jeffery to 20 to 25 points and the Timber Wolves kept him at 12 for the night.
For the day, Drouin finished with 15 points, while Cassidy added 11 and Mousseau chipped in with 10.
Prospect opened its home season in style with a 59-17 win over Winnisquam on Dec. 13. Prospect led 25-2 after one and 36-8 at the halftime break.
Drouin scored 12 points, including eight in the first quarter, while Cassidy also added 12 and Mousseau chipped in with 11.
Next up for the Timber Wolves is the Lakes Region Holiday Tournament in Gilford beginning Tuesday, Dec. 27. Prospect drew Moultonborough in the first round, with game time set for 5:30 p.m.
"That should be interesting," Bourdeau said of the matchup. "We get to play the Conants and Berlins, so we might as well play the top teams in Division IV too."
However, he was quick to point out nobody was looking that far ahead, as the boys were focused on Gilford, which happened after deadline Tuesday.
The tournament opens with the 5:30 p.m. game Dec. 27. If the Timber Wolves lose, they play Wednesday, Dec. 28, at 2 p.m. However, if they win the opener, they play Wednesday, Dec. 28, at 8:30 p.m. and the finals are set for Thursday, Dec. 29, at 7:30 p.m.
The next regular season game for the Timber Wolves is Tuesday, Jan. 3, at home against Somersworth.
The JV Timber Wolves bested Farmington 43-32. Justin Mitza led the way with 11 points and Brian Borelli added nine.


Taking a meal to someone with a food allergy can be extremely intimidating. We have two children with peanut and tree nut allergies, so I'm used to being careful about ingredients. With that said, I still find it challenging to prepare a meal for a family with a different allergy from ours. The first time I was invited to take a meal to our friend with Celiac disease, I opted for a gift card to her favorite restaurant because I wasn't confident enough to prepare a meal.
In many ways, friends with food allergies are even more appreciative of meals because they know cooking for them can be a little challenging. Don't let the list below intimidate you. The intent is to equip you to take your meal with confidence.
1. Go with a basic menu.
This one tip will make taking an allergy-friendly meal so much simpler. Think of whole foods that go well together and then evaluate each one against the known allergies. A great starter meal would be baked chicken, a vegetable, rice and a fruit dessert. You can get more complicated over time, but this first step will make the rest of the preparation much easier.
2. Make sure your kitchen tools and ingredients aren't cross contaminated.
When you aren't dealing with food allergies in your own home, you might tap off your measuring cup after scooping out some flour and return it to the drawer. You also might use that same measuring cup to scoop out some sugar. These shortcuts are not bad for your family, but you'll want to keep this in mind if you are making a meal for a family that cannot have gluten. Washing your kitchen tools or buying a small bag of new ingredients will keep the family safe.
Another consideration is thinking about where you might be double dipping ingredients. My children cannot eat jelly sandwiches (instead of peanut butter and jelly sandwiches) when they are visiting friends because families without allergies will sometimes use the same knife for peanut butter and jelly. Again, no one is doing anything wrong, but think about the ingredients you are using in your recipes to make sure this isn't an issue.
If in doubt, use newly purchased ingredients.
3. Read the ingredient list on all items used in your recipes.
When planning your meal, be sure to read the ingredients on EVERYTHING that will be used for the meal. Also, let the receiving family know what brands/ingredients you used in case you miss an allergen. Maureen, who is very familiar with food allergies and maintains our site's recipe section, recommends sending along your recipe as well, so the recipient can double check everything. Items like salad dressings and barbecue sauce may surprise you with what they contain. If your recipe calls for an ingredient that contains multiple ingredients, read the label just in case. I was surprised to learn that most soy sauce contains gluten and almost accidentally used it in a friend's meal.
4. Send a meal that everyone can eat unless the family specifies.
If someone in the family has a food allergy, I typically send a meal where that person can enjoy all of the dishes. This limits any chance of cross contamination as well. In some cases, the recipient will insist on not accommodating the allergy and in that case I respect her wishes. Otherwise, I take a meal that everyone can enjoy together.
I often will transport my meals in disposable dishes that I can leave with the family. Sometimes, a friend will return a disposable dish and I'll reuse it. In the case of taking an allergy-friendly meal, I always use new dishes and containers for transporting the meal. This way, I know that there wasn't anything served in the dish that may contain the allergen.
6. Check out our RECIPE SECTION.
On our site, we have a FABULOUS recipe section that is broken down by specific allergens. Maureen, who is our well-deserved, yet informal, food allergy expert, has collected and tested all of these recipes for us. If you are looking for recipes that will suit some common food allergies, you can find them on our site.
7. Give a restaurant gift card.
If you are intimidated for any reason about preparing an allergy-friendly meal, don't hesitate to show your kindness in another way. Ask the recipient where their family loves to eat and offer to pick up carry out for them or mail a gift card with an encouraging note.
This tip might seems a little odd, but sometimes when cooking for someone with allergies, it can seem like the person is being picky. This is not the case at all! I dread when I have to ask a fellow school mom about the ingredients in her cupcakes to know if my child can eat one. For the most part, people are understanding, but it can feel like I'm being difficult or judging the cupcakes (or the mom). For some with food allergies, it really is a matter of life of death. For others, it is days of feeling sick. The consequences are severe and the person would never chose to have the allergy.
Also, don't get offended if the person declines your offer for a meal. Some people have allergies that are so severe that it's just not worth the risk. Again, this isn't rudeness, but protection.
Like I wrote at the beginning, it's possible to take an allergy-friendly meal with ease as long as you keep the above tips in mind. These individuals and families in particular are especially appreciative of your effort because they know it takes some thought. So, if you decide to take on the challenge of taking an allergy-friendly meal, you will be spreading a little extra kindness.


Standbyer looking for bridge tonight.
Discussion in 'Halo 3 Boosting and Matches' started by Dang Not ViSioN, Jun 17, 2009 with 5 replies and 273 views.
Looking to standby something to night, around 8-9PM EST all through out the night. If anyone is interested, please leave your gamertag.
[H3 Bridge] LOOKING FOR A STANDBYER!!
Looking for standbyer! Free Bridging!
This Game Suxz, addy me.
I cant bridge or standby, but i need somebody to get me up 5 levels in Team slayer. If you let me tag along ill give u a 1 month or booster account. GT in sig.


text:
Welcome to St. Matthew's BBQ, where exceptional quality timely service and authentic Portuguese cuisine are not only our jobs but our way of life. In 1994, Antonio Pinto and Maria Pinto opened up St. Matthew's BBQ on these very principles.
Utilizing recipes that were passed down from generation to generation, Maria e Antonio started serving the community dishes that are made with unparalleled quality & attention to detail.
Specializing in authentic "Transmontano" cuisine as Bacalhau, Dobrada, Feijoada, Caldo and Churrasco, St. Matthews has maintained its place as a vivid member of the Rogers Road Community.
Over the years, these recipes, traditions and values have been passed down to their son and daughter-in-law Ricardo and Catarina, who are managing St. Matthews following same principles.
Exceptional quality timely service and authentic Portuguese cuisine are not only our jobs but our way of life.
Specializing in authentic "Transmontano" cuisine, St. Matthews has maintained its place as a vivid member of the Rogers Road Community.
Utilizing recipes that were passed down from generation to generation, St. Matthews serves the community dishes that are made with unparalleled quality & attention to detail.
The Best BBQ Chicken in Toronto 2018
That our food meets the highest standards of quality, freshness and traditional Portuguese style of cooking. To consistently provide our customers with impeccable service by demonstrating graciousness, efficiency, knowledge, warmth, professionalism and integrity in our work.
To have every customer who comes through our doors leave impressed by St. Matthew's and excited to come back again.
CATARINA ROBALO
I have always had a passion for cooking!
My mother is a chef and the sounds and smells from a bustling kitchen are engraved in my memory, whether it was the warmth and comfort from my mother's intoxicating smell of fresh baked bread in the morning, or the sizzling sounds of sharp onion and garlic hitting a hot pan of olive oil.
I think that one of the reasons why I first fell in love with cooking was that food is the universal language of love. Everyone loves a delicious plate of food! The kitchen is my happy place; it's where I get to create dishes that take me back to my childhood.
I feel incredibly blessed to be in a position where I am able to share my passion with customers and watch as they enjoy our variety of food.
RICARDO PINTO
St. Matthews BBQ is as much a part of me as my black hair, green eyes and beating heart!
From a very young age my parents always instilled in me these simple yet fundamental concepts: respect the customers, always treat your team well, conflict management and nothing comes easy without hard work.
Using these concepts, I was able to witness my parents build St. Matthews BBQ into an avid member of the Rogers Road community. I want to honor my parent's legacy and honor their hard work by working hard and continually moving the business forward.
I look forward to what the future has in store for St Matthew's BBQ Chicken.
527 Rogers Road (at old Weston RD.), Toronto, on - M6M 1B4
Info@stmatthewsbbq.ca
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text:
https://sputniknews.com/20151123/us-soldiers-ukraine-training-1030627282.html
About 300 US Soldiers Training Six Ukrainian Battalions - Pentagon
Some 300 US soldiers are taking part in a new phase of Ukrainian forces training, which involves several battalions of regular and special forces, US Defense... 23.11.2015, Sputnik International
https://cdnn1.img.sputniknews.com/img/103057/51/1030575126_0:362:5026:3189_1920x0_80_0_0_754abbdc474f9cfb57ae6e6369a60937.jpg
https://cdnn1.img.sputniknews.com/img/103057/51/1030575126_147:0:4880:3550_1920x0_80_0_0_28d5c36325dbcc7309c9aa7c3215677e.jpg
newsfeed, europe, after minsk: will peace come to ukraine?, ukraine, pentagon
© AP Photo / Aleksandr ShulmanUS special forces instructor, left, trains Ukrainian soldiers at the military training ground in Ukraine's Khmelnitsk region Saturday, Nov. 21, 2015
© AP Photo / Aleksandr Shulman
Some 300 US soldiers are taking part in a new phase of Ukrainian forces training, which involves several battalions of regular and special forces, US Defense Department spokesperson Jeff Davis said in a press release.
WASHINGTON (Sputnik) — The Pentagon said it had provided Ukraine with more than $265 million in equipment and training. Washington has been providing non-lethal military assistance to Kiev since the conflict between Ukrainian government troops and pro-independence militias began in the spring of 2014.
"The phase that began today will train up to five battalions of [Ukrainian] Ministry of Defense personnel and one battalion of special operations forces personnel," the release said on Monday.
The spokesperson noted that US soldiers represent the 173rd Airborne Brigade, and NATO allies and other US personnel will also participate in the training.
"This is part of our ongoing efforts to contribute to Ukraine's long-term military reform and professionalism, and to help improve Ukraine's internal defense capabilities and training capacity," Davis said.
The training will take place at the International Peacekeeping and Security Center at Yavoriv, and the special operations forces will be trained in Khmelnitsky, according to the release.
After Minsk: Will Peace Come to Ukraine?


text:
package at.ac.tuwien.dsg.smartsociety.demo.rest.exceptions;

import javax.ws.rs.WebApplicationException;
import javax.ws.rs.core.Response;
import javax.ws.rs.core.Response.Status;

public class AlreadyExistsException extends WebApplicationException {
	private static final long serialVersionUID = 6817489620338221395L;

	public AlreadyExistsException() {
		super(
			Response
				.status( Status.CONFLICT )
				.build()
		);
	}
}

redpajama_set_name: RedPajamaGithub


The ANB team is participating in the American Cancer Society's 2011 Relay For Life of Hope, which will be held at Westminster Academy in Fort Lauderdale on June 3 and 4, 2011. Go to http://bit.ly/fCDkj0 for more information.
This entry was posted on Wednesday, February 23rd, 2011 at 8:14 pm and is filed under Uncategorized.	You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.


text: module.exports = require('./lib/src/sample-class');