Here is a good paper

http://scitation.aip.org/content/aip/journal/apl/86/14/10.1063/1.1899255

http://scitation.aip.org/content/aip/journal/apl/82/18/10.1063/1.1571655

http://scitation.aip.org/content/aip/journal/apl/86/14/10.1063/1.1899255

Influence of surface defect charge at AlGaN-GaN-HEMT upon Schottky gate leakage current and breakdown voltage-  ----W Saito, M Kuraguchi, Y Takada… - Electron Devices, …, 2005 - ieeexplore.ieee.org

Copper gate AlGaN/GaN HEMT with low gate leakage current

-------JP Ao, D Kikuta, N Kubota, Y Naoi… - Electron Device Letters, …, 2003 - ieeexplore.ieee.org

Large gate leakage current in AlGaN/GaN high electron mobility transistors

S Mizuno, Y Ohno, S Kishimoto… - Japanese journal of …, 2002 - iopscience.iop.org

Leakage current can be zero if perfect insulation or passivization exist. But it is ideal. Leakage current proportion to high electric field.

Dear Zakaria Rahioui,

Please check the link below

1.https://aip.scitation.org/doi/10.1063/1.4974959#:~:text=The%20gate%20leakage%20current%20mechanism,I).

2. Article Gate current leakage and breakdown mechanism in unpassivated...