We present a theoretical study of the phonon field's quantum proprieties confinement in the steady-state regime in the near ground state domain of the mechanical vibration. The model consists of a quantum dot (QD) embedded in a semiconductor lattice and driven by an intense laser light. The QD's spontaneous e1nission leads to the amplification of the phonon field, while distributed Bragg reflectors may be used to select a single mode of the phonon field (see Figure 1). The discussed model is analytically solvable using the density matrix fonnalism. The system's Hamiltonian is defined, as usual, by the free QD and phonon field tenns and by the QD-phonon and QD­laser interaction tenns [ 1], with the laser light treated classically. hi the steady-state case, the projection of the density operator on QD-phonon system basis gives an infinite system of lineai- equations containing all the required info1mation on the phonon field. The obtained system can be easily trnncated at a suitable precision and then numerically solved, e.g., using a matrix linear algebra algorithm. We focus on lasing effects of the phonon field, i.e., a coherent distribution of mechanical vibrational quanta. This is done via studying the second-order coITelation function: it equals one for a coherent field and goes below one in the presence of quantum effects. We show that for well-chosen laser's parameters as frequency and intensity, our model predicts both the coherent phonon lasing and non­classical features [2] (see Figure 2).