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The effect of group velocity dispersion and free carrier lifetime on pulse quality and nonlinear phase acquisition is studied in a two-stage pulse compressor on a silicon chip. Appropriately, designing the dispersion in the nonlinear medium enables compressed pulses with more than 90% of the pulse energy confined in the main lobe to be generated. Free carrier lifetime is observed to impact nonlinear phase acquisition in the single pulse regime. The pulse compression factor decreases monotonically as the pulse repetition rate increases. Conditions for efficient compression at high repetition rates in the absence of free carrier quenching techniques are discussed.