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The graded AlGaN∶Si back barrier can form the majority of three-dimensional electron gases (3DEGs) at the GaN/graded AlGaN∶Si heterostructure and create a composite two-dimensional (2D)-three-dimensional (3D) channel in AlGaN/GaN/graded-AlGaN∶Si/GaN∶C heterostructure (DH∶Si/C).Frequency-dependent capacitances and conductance are measured to investigate the characteristics of the multi-temperature trap states of in DH∶Si/C and AlGaN/GaN/GaN∶C heterostructure (SH∶C).There are fast,medium,and slow trap states in DH∶Si/C,while only medium trap states exist in SH∶C.The time constant/trap density for medium trap state in SH∶C heterostructure are (11 μs-17.7 μs)/(1.1 ×1013 cm-2·eV-1-3.9× 1013 cm-2·eV-1) and (8.7 μs-14.1 μs)/(0.7× 1013 cm-2·eV-1-l.9× 1013 cm-2·eV-1) at 300 K and 500 K respectively.The time constant/trap density for fast,medium,and slow trap states in DH∶Si/C heterostructure are (4.2 μs-7.7 μs)/(1.5 × 1013 cm-2·eV-1-3.2× 1013 cm-2·eV-1),(6.8 μs-11.8 μs)/(0.8 × 1013 cm-2·eV-1-2.8×1013 cm-2·eV-1),(30.1 μs-151 μs)/(7.5×1012 cm-2·eV-1-7.8×1012 cm-2·eV-1) at 300 K and (3.5 μs-6.5 μs)/(0.9×1013 cm 2·eV-1-1.8×1013 cm-2·eV 1),(4.9 μs-9.4 μs)/(0.6×1013 cm 2·eV 1-1.7×1013 cm-2·eV-1),(20.6 μs-61.9 μs)/(3.2× 1012 cm-2·eV-1-3.5× 1012 cm-2·eV-1) at 500 K,respectively.The DH∶Si/C structure can effectively reduce the density of medium trap states compared with SH∶C structure.