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The IC chip ejecting and pick-up process in electronic assembly plays a critical role in advanced packaging since the success ratio and productivity are determined by the delamination of thin chips from the underlying substrate. For a chip-on-substrate structure subjected to a transverse concentrated load resulting from the ejecting needle, a competing relationship between chip peeling-off and chip cracking is discovered from the perspective of integral structure. A competing index, Γ, is defined to characterize the competing fracture behavior between cracking and peeling-off, and the competing fracture mechanism is then uncovered fundamentally. Based on the index, the effects of chip geometry on competing behavior are investigated using the virtual crack-closure technique with dummy nodes. Critical thickness and length, which separate chip peeling-off and cracking modes, are found and they represent the extremity of successful pick-up process. The critical values are determined by critical competing index, Γ - Γc. The competing mechanism uncovered applies to general pick-up process with various chip sizes and materials. The critical sizes and the method of evaluating critical values are meaningful for chip profile design, optimization of pick-up process, and propelling new designs of electronic assembly process, especially for thin chips.