In this paper,an irreversible thermionic refrigerator model based on van der Waals heterostructure with various irreversibilities is established by utilizing combination of non-equilibrium thermodynamics and finite time thermodynamics.The basic perfor-mance characteristics of the refrigerator are obtained.The effects of key factors,such as bias voltages,Schottky barrier heights and heat leakages,on the performance are studied.Results show that cooling rates and coefficients of performances (COPs) can attain the double maximum with proper modulation of barrier heights and bias voltages.Increasing cross-plane thermal re-sistance as well as decreasing electrode-reservoir thermal resistance and reservoir-reservoir thermal resistance can enhance the performance of the device.The optimal performance region is the interval between the maximum cooling rate point and the maximum COP point.By modulating the bias voltage,the working state of the device can fall into the optimal performance region.The optimal performance of the refrigerator when using single layer graphene and a few layers graphene as electrode material is also compared.