Non-volatile multilevel optical memory is an urgent needed artificial component in neuromorphic computing. In this paper, based on ferroelectric based electrostatic doping (Fe-ED) and optical readout due to plasma dispersion effect, we propose an electrically programmable, multi-level non-volatile photonics memory cell, which can be fabricated by standard complementary-metal-oxide-semiconductor (CMOS) compatible processes. Hf0.5Zr0.5O2 (HZO) film is chosen as the ferroelectric ED layer and combines with polysilicon layers for an enhanced amplitude modulation between the carrier accumulation and the confined optical field. Insertion loss below 0.4 dB in erasing state and the maximum recording depth of 9.8 dB are obtained, meanwhile maintaining an extremely low dynamic energy consumption as 1.0-8.4 pJ/level. Those features make this memory a promising candidate for artificial optical synapse in neuromorphic photonics and parallel computing.