  Nematicity in quantum Hall systems has been experimentally well established
at excited Landau levels. The mechanism of the symmetry breaking, however, is
still unknown. Pomeranchuk instability of Fermi liquid parameter $F_{\ell} \le
-1$ in the angular momentum $\ell=2$ channel has been argued to be the relevant
mechanism, yet there are no definitive theoretical proofs. Here we calculate,
using the variational Monte Carlo technique, Fermi liquid parameters $F_\ell$
of the composite fermion Fermi liquid with a finite layer width. We consider
$F_{\ell}$ in different Landau levels $n=0,1,2$ as a function of layer width
parameter $\eta$. We find that unlike the lowest Landau level, which shows no
sign of Pomeranchuk instability, higher Landau levels show nematic instability
below critical values of $\eta$. Furthermore, the critical value $\eta_c$ is
higher for the $n=2$ Landau level, which is consistent with observation of
nematic order in ambient conditions only in the $n=2$ Landau levels. The
picture emerging from our work is that approaching the true 2D limit brings
half-filled higher Landau-level systems to the brink of nematic Pomeranchuk
instability.
