  Using the method developed in a recent paper (Euro. Phys. J. B 92.8 (2019):
1-28) we consider $1/f$ noise in two-dimensional electron gas (2DEG). The
electron coherence length of the system is considered as a basic parameter for
discretizing the space, inside which the dynamics of electrons is described by
quantum mechanics, while for length scales much larger than it the dynamics is
semi-classical. For our model, which is based on the Thomas-Fermi-Dirac
approximation, there are two control parameters: temperature $T$ and the
disorder strength ($\Delta$). Our Monte Carlo studies show that the system
exhibits $1/f$ noise related to the electronic avalanche size, which can serve
as a model for describing the experimentally observed flicker noise in 2DEG.
The power spectrum of our model scales with frequency with an exponent in the
interval $0.3<\alpha_{PS}<0.6$. We numerically show that the electronic
avalanches are scale-invariant with power-law behaviors in and out of the
metal-insulator transition line.
