Gallium Nitride high electron mobility transistors （HEMTs） have promising prospects for high frequency，high voltage and high power applications，due to their unique advantages of the material^［1-2］. As the bridge between technological process and circuit design，models for GaN devices are critical. So far，behavioral models，empirical models and physical models have been reported^［3-5］. Among these，ASM-HEMT （Advanced SPICE Model for HEMT），a physical surface-potential-based model，can accurately characterize the electrical characteristics of GaN devices with technological structure and physical mechanism well combined. Currently，ASM-HEMT has developed into the mainstream and been certified as the industry standardization^［6］.

As an intrinsic reliability problem of GaN devices，kink effect features an abrupt rise in drain-source current I_ds after collapse at a certain drain-source voltage V_ds. The phenomenon deteriorates the stability of the device with a drop in the transconductance g_m1，an increase in the output conductance g_ds1 as well as a shift in the threshold voltage V_off^［7-9］. Because the kink effect on GaN devices cannot be completely eliminated，its influence in circuit design cannot be ignored. However，the current collapse and kink effect are not taken into consideration in the original ASM-HEMT. In order to more accurately characterize the performance of GaN devices，it is necessary to introduce the description of current collapse and kink effect to the model.

In this paper，an improved ASM-HEMT model for kink effect is proposed. This proposed model accurately describes the current collapse and kink effect，so as to precisely characterize the DC characteristics of GaN devices in the full operating range.

By solving Schrodinger's and Poisson’s equations，the potential of Fermi level corresponding to two-dimensional electron gas （2DEG） at GaN/AlGaN hetero-junction can be calculated as^［10］：

where H（V_goeff） is the function of V_go，C_g is the gate capacitance per unit area，q is the electronic charge， D is the density of states，V_th is the thermal voltage，eta0 and vdscale are the Drain Induced Barrier Lowing （DIBL） parameters，V_offis the threshold voltage，and V_dsx = sqrt（V_ds²+0.01）.

So the potential at the source end φ_s and the potential at the drain end φ_d are obtained as follows^［11］：

where V_s is the source voltage，and V_deffis the effective drain voltage.

Combining the drift-diffusion mechanism with real device effects，the drain-source current I_ds is given as^［12］：

where W is the gate width，L is the gate length，n_f is the number of fingers，μ_eff is the effective mobility，θ_sat is the velocity saturation parameter，V_tv is the correction of V_th，φ_m = （φ_s+φ_d）/2，φ_ds = φ_d-φ_s，and λ is the channel length modulation coefficient.

The current collapse and kink effect can be obviously observed in the output characteristic curve of GaN devices，as shown in Fig. 1. At low V_ds （V_ds≈0-8 V），electrons are trapped，leading to a decrease in channel carriers and a drop in the drain-source current，which is current collapse. As V_ds continues to increase，the trapped electrons are released，resulting in a rapid increase in the drain-source current，which features as the kink effect. The drain-source voltage where the kink effect occurs，defined as V_ds-k，is marked by the red triangle in Fig. 1. Meanwhile，when V_gs gradually increases，V_ds-k first drops and then increases. The above phenomenon demonstrates that both V_ds and V_gs play an important role in the current collapse and kink effect.

On account of the shift in the threshold voltage caused by the current collapse and kink effect，V_off in Eq. 2 needs to be corrected. By introducing the function CK（V_ds，V_gs） related to V_ds and V_gs，the correction of the threshold voltage can be expressed as：

The tendency of I_ds rapidly increasing after collapse can be modeled by a hyperbolic tangent function tanh^［13］，which is exactly the form of CK（V_ds，V_gs）：

where d0 and d1 are fitting parameters，which determine the amplitude of current collapse and kink effect.

Considering the nonlinear relationship between V_ds-k and V_gs，V_ds-k is given as a polynomial related to V_gs：

where gk （k = 0，1，2...） is the fitting parameter.

Substituting Eq. 7 for V_off in Eq. 2，the final drain-source current I_ds can be rewritten as：

Two depletion-mode GaN HEMTs used in the paper are developed by Nanjing Electronic Devices Institute with gate widths of 6×200 µm and 2×200 µm，as shown in Fig. 2.

Firstly，as shown in Fig. 3，on-wafer measurement is carried out at room temperature （T = 300 K） for the DC characteristics，and the measured data is obtained through the IVCAD software of Maury Company. Secondly，the improved model is realized by Verilog-A and simulated on the ICCAP software. Finally，based on the measurements，parameters of the improved model are extracted and the DC characteristics are fitted，including the output characteristics I_ds-V_ds，the output conductance （the first derivative of I_ds with respect to V_ds） g_ds1-V_ds，the transfer characteristics I_ds-V_gs and the transconductance （the first derivative of I_ds with respect to V_gs） g_m1-V_gs，measured and simulated with the value of V_ds varying from 0 V to 36 V in the step of 0.2 V and the value of V_gs changing from -4 V to 0 V in the step of 0.1 V.

For the output characteristics and the S-parameter，the fitting results of the original ASM-HEMT and the improved model are shown in Figs. 4-6.

Seen from Fig. 4（a） and Fig. 5（a），both the original ASM-HEMT and the improved model fits to the measured curve well in the saturation region，but there are obvious differences in the regions where the current collapse and kink effect occur. The accuracy of the original ASM-HEMT is insufficient，as shown in Fig. 4（b） and Fig. 5（b）. For the improved model，I_ds behaves an abrupt rise after collapse as V_ds increases，and V_ds-k under different V_gs is also perfect fitted.

The S-parameter simulation results from 400 MHz to 40 GHz of the original model and the improved model are compared with the measurements for two devices，as shown in Fig. 6.

For the small signal characteristic at V_gs = -2.2 V and V_ds = 28 V，the good agreement between the measured results and both of the simulated results is obtained. Because the input is the small signal，the impact of kink effect on the RF characteristics can be ignored.

Finally，the extracted parameters are obtained in Table 1 and Table 2.

The above results indicate that the improved model can accurately describe the current collapse and kink effect，and characterize the output characteristics of GaN devices with different sizes.

The fitting result of the output conductance （V_gs = -1.2 V for the 1.2-mm-wide device in this paper） is shown in Fig. 7. It can be seen that the improved model appears a peak near V_ds = 4 V，which agrees with the description in Ref. ［14］ and is well matched with the measured data，further proving that the improved model accurately describes the current collapse and kink effect of GaN devices.

Figure 8 shows the fitting results of the transfer characteristics at V_ds = 4 V and V_ds = 28 V. The original ASM-HEMT fits well where V_ds is high （V_ds = 28 V for the 1.2-mm-wide device in this paper），but the fitting error is large where V_ds is low （V_ds = 4 V for the 1.2-mm-wide device in this paper），while the improved model can achieve an excellent fit under all V_ds. Accordingly，the transconductance of the improved model agrees well with the measured data，as shown in Fig. 9，indicating that the improved model accurately characterizes the transfer characteristics of GaN devices by introducing parameters related to the current collapse and kink effect.

According to the above results，the improved model perfectly fits the kink effect of GaN devices. Clearly，the improved model accurately describes the current collapse and kink effect，so as to precisely characterize the DC characteristics of GaN devices in the full operating range.

To further verify the accuracy of the improved model，a load-pull simulation is built in ADS，as shown in Fig. 10. The improved model is validated by simulating the large signal behavior at 3 GHz and I_dsq= 12 mA at V_ds = 28 V，with the input power Pin swept from 1 dBm to 24 dBm.

As shown in Fig. 11，both the original ASM-HEMT and the improved model can predict the output power for the maximum power matching of GaN devices well. However，compared with the original ASM-HEMT，the improved model predicts the power-added efficiency （PAE） for the maximum efficiency matching more accurately，with 4% improved，which has a good agreement with the measured result.

An improved model for kink effect based on ASM-HEMT is presented in this paper，considering the impact of V_ds and V_gs. Validated with the experimental data，the improved model can accurately describe the current collapse and kink effect，and more accurately characterize the DC characteristics of GaN devices in the full range of voltage，with the fitting error less than 3%. Compared with the original ASM-HEMT，the improved model predicts the power-added efficiency for the maximum efficiency matching more accurately without changing the accuracy of the output power for the maximum power matching. The improved model is of great guiding significance for the accurate design of high-performance GaN amplifiers，and can also play a crucial role in reducing circuit design costs and shortening the product development cycle. Since GaN devices used in the paper adopt a process of 0.35 μm，they are not suitable for millimeter waves. To further broaden the applicability of the improved model，GaN devices for higher frequency will be studied in the future.