We studied the thermal stability of Ge channel modulation doped structures fabricated by solid source molecular beam epitaxy utilizing low-temperature buffer technique. Drastic decrease of mobility and increase of carrier density was observed after annealing at temperature above 600 C. SIMS measurements indicated that this was not due to the B diffusion into Ge channel layers but the Si-Ge interdiffusion at the Ge/SiGe interface. In addition, it was found that the strain relaxation of Ge channel layers could occur after annealing at temperatures even below 500 degreesC and cause the decreased mobility when the channel layers thickness were beyond equilibrium critical one.