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We propose a model for three-terminal thermionic heat engines based on semiconductor heterostructures.According to electron transport theory,we drive the formulas for the charge current and energy current flowing from the electron reservoir and we then obtain the power output and efficiency in the linear and nonlinear regimes.Furthermore,we analyze the performance characteristic of the thermionic heat engine and get the maximum power output by optimizing the performance parameters.Finally,we optimize the thermodynamic performance of the thermionic heat engine by maximizing the product of the power output and efficiency.