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-1–1.9× 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.