  A residual disorder in the gate system is the main problem on the way to
create artificial graphene based on two-dimensional electron gas. The disorder
can be significantly screened/reduced due to the many-body effects. To analyse
the screening/disorder problem we consider AlGaAs/GaAs/AlGaAs heterostructure
with two metallic gates. We demonstrate that the design least susceptible to
the disorder corresponds to the weak coupling regime (opposite to tight
binding) which is realised via system of quantum anti-dots. The most relevant
type of disorder is the area disorder which is a random variation of areas of
quantum anti-dots. The area disorder results in formation of puddles. Other
types of disorder, the position disorder and the shape disorder, are
practically irrelevant. The formation/importance of puddles dramatically
depends on parameters of the nanopatterned heterostructure. A variation of the
parameters by 20--30\% can change the relative amplitude of puddles by orders
of magnitude. Based on this analysis we formulate criteria for the acceptable
design of the heterostructure aimed at creation of the artificial graphene.
