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In this paper, we propose a novel method, called "eXtreme chirped pulse amplification (X-CPA)," to overcome the fundamental energy storage limit of a semiconductor optical amplifier. The method is studied numerically and experimentally. Based on the X-CPA concept, 1.4-kW record peak power is generated from an all-semiconductor X-CPA system. Prior to an extreme pulse compression stage, greater than microjoules output energies of 20 ns extremely stretched pulses are extracted from a flared semiconductor optical amplifier.