HEMT-based 1K front-end electronics for the heat and ionization Ge CryoCube of the future RICOCHET CE$\nu$NS experiment

The RICOCHET reactor neutrino observatory is planned to be installed at the Laue Langevin Institute (ILL) starting mid-2022. Its scientific goal is to perform a low-energy and high precision measurement of the coherent elastic neutrino-nucleus scattering (CE$\nu$NS) spectrum in order to explore exotic physics scenarios. RICOCHET will host two cryogenic detector arrays: the CryoCube (Ge target) and the Q-ARRAY (Zn target), operated at 10 mK. The 1 kg Ge CryoCube will consist of 27 Ge crystals instrumented with NTD-Ge thermal sensors and charge collection electrodes for a simultaneous heat and ionization readout to reject the electromagnetic backgrounds (gamma, beta, x-rays). We present the status of its front-end electronics. The first stage of amplification is made of High Electron Mobility Transistor (HEMT) developed by CNRS/C2N laboratory, optimized to achieve ultra-low noise performance at 1K with a dissipation as low as 15 $\mu$W per channel. Our noise model predicts that 10 eV heat and 20 eVee RMS baseline resolutions are feasible with a high dynamic range for the deposited energy (up to 10 MeV) thanks to loop amplification schemes. Such resolutions are mandatory to have a high discrimination power between nuclear and electron recoils at the lowest energies.