= Solution
A suitable sequence is
$$
\boxed{D\ \longrightarrow\ C\ \longrightarrow\ F\ \longrightarrow\ A\ \longrightarrow\ B\ \longrightarrow\ E}.
$$
First pattern the source/drain resist, then deposit and lift off the corresponding metal. Anneal these contacts to produce the low-resistance source/drain interfaces. Remove the exposed cap layer before gate lithography, leaving the cap beneath the contact metal; this uses the contact pads as an etch mask, with suitable protection where required. Finally define and deposit the gate onto exposed AlGaAs and lift off.
The key dependencies are that source/drain metal lands on the n+ cap, the gate lands on AlGaAs after cap removal, and the contact anneal precedes formation of the sensitive Schottky gate. A gate-recess variant can put gate lithography before the local cap etch if that resist is deliberately used as its mask, but it must additionally specify how unwanted conducting cap elsewhere is removed or isolated. The sequence above directly matches the cap remaining only beneath the source/drain contacts in the diagram.
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