The InAs/AlSb hererojunction field-effect transistor (HFET) is receiving attention as a promising candidate of next-generation devices for high-frequency, high-speed, and low-dissipation applications because of its high electron mobility and peak velocity of the carriers, especially at cryogenic temperature.^{[1, 2]} However, the very narrow band gap of the InAs channel (0.35 eV) results in the impact ionization effect easily happening and causes the performance of the device to degrade. At higher drain bias, the carriers with enough energy impact with lattice atoms to generate a lot of electron–hole pairs, and the generated holes can transmit from channel to gate electrode to form a leakage current access because of the lack of an effective hole barrier in the InAs/AlSb HEMT structure, leading to an enhanced gate-leakage current of InAs/AlSb HFET which could be observed.^{[3, 4]} On the other hand, the ionized holes accumulated in the gate-drain region of the buffer form a positive space charge region, which causes the channel to further open and thus enhances the drain current.^{[5, 6]} When a small signal with radio frequency is input, the influence of the impact ionization effect on the device's RF performance shows strong frequency dependency.^{[7, 8]} This influence occurs at low frequency, whereas it becomes insignificant as the frequency increases continually, and cannot be observed up to several gigahertz.^{[7, 8]} Therefore, the modeling of the frequency dependency of impact ionization is necessary to investigate InAs/AlSb HFET technology, and is important for further circuit design. In Ref. [9], we proposed a model with a fitting function of to characterize the frequency dependency of the impact ionization effect, but without a very high accuracy degree. Therefore, in this paper, we propose an enhanced model with fitting function in the form of the least square method in order to further enhance the accuracy of the small-signal model for characterizing the influence of frequency dependency of impact ionization on the RF performance of InAs/AlSb HFET.

On the basis of our small-signal model (SSM) in Ref. [9], a further enhanced SSM is proposed, focusing on the frequency dependency of the impact ionization effect by introducing a new least square fitting function , its equivalent circuit is shown in Fig. 1.

Fig. 1.

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	Fig. 1. Small-signal equivalent circuit for the InAs/AlSb HFET. The part in the dotted line square frame shows the intrinsic parameters, and the part outside the frame presents the extrinsic parameters.

Two voltage controlling current sources and , regulated by and respectively, are introduced to model the gate-leakage current as a function of gate bias and drain bias. Actually, the gate-leakage current is composed of the Schottky leakage current , and the hole leakage current , according to Eqs. (1)–(3), and given by

The is induced by the electrons transferring across the Schottky barrier, and it is not sensitive to frequency, thus is modeled by two constants and . On the other hand, is induced by the impact ionization effect, and it is modeled by and . Because the impact ionization effect takes effect mainly at a low frequency and it can be neglected as frequency increases, hence the influence of the modeling components on also follows the frequency dependency, which could be characterized by a function . Constant infers the happening rate of impact ionization, which decreases dramatically at the ultra-low drain bias without impact ionization, and it also suggests the transit time of holes from the impact generation to accumulation into positive field.^{[4, 8]} Therefore, the two current sources and for modeling the gate-leakage current are expressed as

Because the device performance influenced by impact ionization at the varied frequency points can be considered as a collection of discrete data, we propose to take to be the form of best square approximation, with its least mean square error, in order to make the modeled results approach the measurements in a high degree. The expression of is given as follows:

In this paper, the AlSb/InAs HFET experimental data extracted from Ref. [4] are referred for evaluating our new fitting function . It was said in Ref. [4] that the bias condition of V and –1 V has been proved with impact ionization. The extrinsic parameter values of SSM at this bias voltage in Ref. [4] are directly used in our model. In order to simplify our extraction procedure of intrinsic parameters, the dimension of the fitting function m is initially taken to be 1, and the values of and are determined as 0 and 1, respectively. In this case, the optimal values of the intrinsic parameters can be extracted directly with the method in Ref. [9], as shown in Table 1.

Table 1.

Table 1.

Table 1. Values of extracted intrinsic parameters. . Parameter V V V V fF 108 117.7 143.1 fF 15.4 15 24.2 fF 26.2 25.5 14.8 mS 47.2 55 65.4 10 7.6 7.9 20.5 30 41.8 159 162.1 183.9 ps 0.2 0.4 0.38 mS 0.395 1.486 3.021 mS 2.528 6.035 11.236 mS 0.804 2.548 4.975 mS 1.395 3.676 4.019 mS 22.1 23.2 15.9 mS 20 30.3 30 ps 82 54 38

Table 1. Values of extracted intrinsic parameters. .

Next, the influence of with different-dimension value m can be achieved by tuning [ ] and [ ] with different values. The error function ({EF}) between the modeled result and measurement for S parameters is obtained as

At the bias of V and V, EF as a function of N and m for S parameters by dB unit is shown in Fig. 2 it is easily found that {EF} decreases with increasing sample number N and fitting function dimension m. When m is higher than 3, its continual increasing makes little enhancement of EF, but can strongly increase the simulation complexity and calculation time. Therefore, m = 3 can be considered as an appropriate value. Table 2 gives the comparison among EF results with different m values (ranging from 1 to 3 when N = 500), and for the case of m = 3 the lowest {EF} value of 0.84 is achieved.

Fig. 2.

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	Fig. 2. Least square error function EF versus sample number N and the fitting function dimension m for S parameter simulation for 0.5–40.5 GHz.

Table 2.

Table 2.

Table 2. EF values with different m values when n is 500. . m = 1 m = 2 m = 3 EF 3.75 1.21 0.84

Table 2. EF values with different m values when n is 500. .

The experimental result of the InAs/AlSb HFETs fabricated in Ref. [4] under the bias condition of V and –1 V is referred in this paper to evaluate the accuracy of our enhanced model. The S parameters for 0.05–40.5 GHz are modeled. Figures 3 and 4 show the comparisons of the key S-parameter between the simulation results from the model with m = 3 and the measurements. The and are the input and output reflection coefficient, respectively, and can be considered as the output gain of the device. It is found that the simulation result from the SSM with the fitting function achieves good agreement with the measurement.

Fig. 3.

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	Fig. 3. Simulation results of (a) input reflection coefficient and (b) output reflection coefficient for in a frequency range of 0.05–40.5 GHz.

Fig. 4.

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	Fig. 4. Output gain simulation result in a frequency range of 0.05–40.5 GHz.

An enhanced small-signal equivalent circuit model of InAs/AlSb HEFT, focusing on the impact ionization effect, is proposed. Two couples of voltage controlling current sources – and – are introduced to model the influences of the impact ionization effect on the gate-leakage current and the ionized-drain current, respectively. An optimized fitting function in the form of least square approximation is proposed in order to further enhance the accuracy in modeling the frequency dependency of the impact ionization effect. It is found that the improved model with can accurately characterize the key S parameters of InAs/AlSb HEFT in a wide frequency range, and a much lower error function {EF} can be achieved with m = 3. It is demonstrated that the new fitting function is helpful in further improving the modeling accuracy degree.