An Improved Large Signal Model for 0.1 μm AlGaN/GaN High Electron Mobility Transistors (HEMTs) Process and Its Applications in Practical Monolithic Microwave Integrated Circuit (MMIC) Design in W band

An improved empirical large signal model for 0.1 µm AlGaN/GaN high electron mobility transistor (HEMT) process is proposed in this paper. The short channel effect including the drain induced barrier lowering (DIBL) effect and channel length modulation has been considered for the accurate description of DC characteristics. In-house AlGaN/GaN HEMTs with a gate-length of 0.1 μm and different dimensions have been employed to validate the accuracy of the large signal model. Good agreement has been achieved between the simulated and measured S parameters, I-V characteristics and large signal performance at 28 GHz. Furthermore, a monolithic microwave integrated circuit (MMIC) power amplifier from 92 GHz to 96 GHz has been designed for validation of the proposed model. Results show that the improved large signal model can be used up to W band.


Introduction
Wide band gap semiconductor Gallium Nitride (GaN) high electron mobility transistors (HEMTs) are excellent candidates in high frequency power electronics due to their unique advantages of higher breakdown voltage and higher output power density [1]. With the rapid development of process, the feature size of GaN HEMTs have been shrinking to less than 0.1 µm. GaN HEMTs with good performance for application in W band have been reported [2][3][4][5]. Also, over the past few years, several GaN HEMT based monolithic microwave integrated circuits (MMICs) up to W-band have been developed, due to their applications in high speed wireless communications or radar systems [6]. A GaN MMIC power amplifier at 91 GHz was reported to have 1.7 W output power that is associated with 11% power added efficiency [7]. A W-Band MMIC power amplifier with 3.46 W/mm output power density and 21% associated power added efficiency was then reported. The associated power gain is 13.7 dB. It offers a peak small signal gain of 16.7 dB over 90-97 GHz [2].
For applications of these devices in circuit design, compact nonlinear device modeling plays an important role in practical design. Recently, a few physical based compact models have sprung up due was then reported. The associated power gain is 13.7 dB. It offers a peak small signal gain of 16.7 dB over 90-97 GHz [2].
For applications of these devices in circuit design, compact nonlinear device modeling plays an important role in practical design. Recently, a few physical based compact models have sprung up due to their advantages in less fitting parameters and good accuracy up to the Ka band [8][9][10][11]. However, things will be different when the frequency is up to W band. Firstly, the parasitic effect will become obvious with the increasing of frequency and make the parameter extraction more difficult [12,13]. This problem can be solved by FW-EM (Full-wave electromagnetic) simulation [14]. Secondly, along with the reduction of feature size, the short channel effect becomes obvious. This phenomenon will in the end give rise to shift of threshold voltage. Thirdly, the gradual channel approximation (GCA) that is used in many kinds of physical based compact model [15,16] is no more effective as the channel length modulation is obvious in short channel devices. These effects will largely decrease the accuracy of physical based compact model. The empirical modeling method has been widely used due to their excellent performance in convergence and accuracy [17][18][19][20][21][22]. An effective validation of large signal model is validated by on-wafer load-pull measurement [23,24]. However, due to the complication of load-pull measurement, only one input/output impedance is validated. Nevertheless, more input/output impedances need to be validated for a large signal model in practical MMIC power amplifier design [25].
In this paper, the short channel effect, including the DIBL effect and channel length modulation, is studied. An improvement for the accuracy of the area near the pinch-off region in IV curve is performed based on an empirical modeling method as the GCA is no more effective in most physical based model. In-house AlGaN/GaN HEMTs with gate length of 0.1 µm is used for validation of the model. Performance, including S parameters, DC characteristics, and large signal characteristics at 28 GHz is validated by on-wafer measurement. Finally, a MMIC power amplifier is designed based on the proposed model for further validation.
This paper is organized as follows. In Section 2, the investigation on short channel effect is presented. The modeling method of it, which is based on an empirical method, is given in detail. In Section 3, the proposed large signal model is validated with two GaN HEMTs with different gate width. In Section 4, a MMIC power amplifier based on the large signal model in this work is designed for further validation of the model in W band. Finally, in Section 5, the conclusion of this work is presented.

Short Channel Effects
Along with the decrease of gate length, the short channel effect, such as the drain induced barrier lowering (DIBL) effect will become obvious. The thickness of the barrier will not only be modulated by gate voltage, but also drain voltage. This will, in the end, lead to the drift of threshold voltage along with the drain voltage. This phenomenon can be easily captured in the static IV curve of 0.1 µm AlGaN/GaN HEMTs with different gate width in this work, which have been shown in Figure 1. It can be seen from Figure 1 that the DIBL effect will weaken the effect that is brought by gate voltage. The device will be turned from off-state to on-state with the rise of drain voltage. This phenomenon must be taken into consideration, especially for high efficiency power amplifier or switching applications.
In order to accurately describe the output performance of AlGaN/GaN HEMTs with short gate length in large signal modeling, the short channel effect, including the DIBL effect and channel length modulation, should be taken into consideration. An empirical method that is based on the Angelov model is employed for the devices in this work. As we know that the coefficients of the ψ polynomial in Angelov model, which is shown in Equation (1), mainly affect the accuracy of the region close to pinch-off state.
To accurately model the DIBL effect, the drain-source voltage V ds has been included in P n (n = 1, 2, 3) to take the modulation effect of V ds into consideration, as shown in Equation (2).
where P n0 , P n1 , P n2 and α are all fitting parameters. The modification was validated by a comparison between simulation results and measured data. The comparison between the original Angelov model and modified one are shown in Figure 2. The gate-source voltage V gs is from −6 V to −3 V and the drain source voltage V ds is from 0 V to 20 V. It can be seen from Figure.1 that the DIBL effect will weaken the effect that is brought by gate voltage. The device will be turned from off-state to on-state with the rise of drain voltage. This phenomenon must be taken into consideration, especially for high efficiency power amplifier or switching applications.
In order to accurately describe the output performance of AlGaN/GaN HEMTs with short gate length in large signal modeling, the short channel effect, including the DIBL effect and channel length modulation, should be taken into consideration. An empirical method that is based on the Angelov model is employed for the devices in this work. As we know that the coefficients of the ψ polynomial in Angelov model, which is shown in Equation (1), mainly affect the accuracy of the region close to pinch-off state.
To accurately model the DIBL effect, the drain-source voltage Vds has been included in Pn (n = 1, 2, 3) to take the modulation effect of Vds into consideration, as shown in Equation (2).
where Pn0, Pn1, Pn2 and α are all fitting parameters. The modification was validated by a comparison between simulation results and measured data. The comparison between the original Angelov model and modified one are shown in Figure 2. The gate-source voltage Vgs is from −6 V to −3 V and the drain source voltage Vds is from 0 V to 20 V. It is clear in Figure 2 that the original Angelov model cannot accurately describe the DC characteristics when Vgs is close to the pinch-off voltage. The DIBL effect can be successfully modeled by using proposed model.
Apart from the DIBL effect, the channel length modulation can also be captured in the static IV curves, as shown in Figure 3. It is clear in Figure 2 that the original Angelov model cannot accurately describe the DC characteristics when V gs is close to the pinch-off voltage. The DIBL effect can be successfully modeled by using proposed model.
Apart from the DIBL effect, the channel length modulation can also be captured in the static IV curves, as shown in Figure 3.
It clearly shows that the partial derivative of I ds to V ds is not equal to zero due to channel length modulation. The channel length effect is mainly induced by expanding of the depletion region towards the source. The effective channel is then shortened. This phenomenon is shown in Figure 4. It clearly shows that the partial derivative of Ids to Vds is not equal to zero due to channel length modulation. The channel length effect is mainly induced by expanding of the depletion region towards the source. The effective channel is then shortened. This phenomenon is shown in Figure 4.

Large Signal Model up to W Band
With the frequency up to W band, the RF dispersion will become more and more obvious due to the parasitic effects inside devices. A wide band small signal model [14], which has been proved to be able to cover the frequency band from 0.2-110 GHz, is employed in this work. The topology of the large signal model is shown in Figure 5. The main part of the nonlinear current model as well as the capacitance model, including Cgs and Cgd mentioned in [21], is employed in this work. The improvement for accurate characterization of short channel effect, which is mentioned in the previous section, has also been included in the It clearly shows that the partial derivative of Ids to Vds is not equal to zero due to channel length modulation. The channel length effect is mainly induced by expanding of the depletion region towards the source. The effective channel is then shortened. This phenomenon is shown in Figure 4.

Large Signal Model up to W Band
With the frequency up to W band, the RF dispersion will become more and more obvious due to the parasitic effects inside devices. A wide band small signal model [14], which has been proved to be able to cover the frequency band from 0.2-110 GHz, is employed in this work. The topology of the large signal model is shown in Figure 5. The main part of the nonlinear current model as well as the capacitance model, including Cgs and Cgd mentioned in [21], is employed in this work. The improvement for accurate characterization of short channel effect, which is mentioned in the previous section, has also been included in the

Large Signal Model up to W Band
With the frequency up to W band, the RF dispersion will become more and more obvious due to the parasitic effects inside devices. A wide band small signal model [14], which has been proved to be able to cover the frequency band from 0.2-110 GHz, is employed in this work. The topology of the large signal model is shown in Figure 5. It clearly shows that the partial derivative of Ids to Vds is not equal to zero due to channel length modulation. The channel length effect is mainly induced by expanding of the depletion region towards the source. The effective channel is then shortened. This phenomenon is shown in Figure 4.

Large Signal Model up to W Band
With the frequency up to W band, the RF dispersion will become more and more obvious due to the parasitic effects inside devices. A wide band small signal model [14], which has been proved to be able to cover the frequency band from 0.2-110 GHz, is employed in this work. The topology of the large signal model is shown in Figure 5. The main part of the nonlinear current model as well as the capacitance model, including Cgs and Cgd mentioned in [21], is employed in this work. The improvement for accurate characterization of short channel effect, which is mentioned in the previous section, has also been included in the The main part of the nonlinear current model as well as the capacitance model, including C gs and C gd mentioned in [21], is employed in this work. The improvement for accurate characterization of short channel effect, which is mentioned in the previous section, has also been included in the nonlinear current model. In order to accurately characterize the self-heating effect in AlGaN/GaN HEMT. The three-pole thermal network in [25] is used. Thermal resistances as well as the thermal capacitances are extracted by a method based on FEM simulation in ANSYS. The trapping effect is modeled by the equivalent voltage method in [26]. The scalability of the model parameters, including the I pk0 , R th , and C th has been realized with the method that is mentioned in [22] for practical monolithic microwave integrated circuit design. With the help of MATLAB coding, model parameters, except the coefficients in Equation (2), are all extracted with the method in [27]. In terms of parameters in Equation (2), they are all extracted by fitting the transfer characteristics curve with the least square method.

Small Signal Characterization
The large signal model was embedded into Keysight ADS (Advanced Design System) by a symbolically defined device (SDD) tool. Small signal characteristics of the devices are measured by cascade probe station (Summit 11000B, FormFactor, Livermore, CA, USA), which is shown in Figure 6. The vector network analyzer is Keysight N5247A (Keysight Technologies, Santa Rosa, CA, USA). The frequency extenders close to probes are used to achieve the S parameters ranging from 75 GHz to 110 GHz as the vector network analyzer can only reach up to 67 GHz.
Micromachines 2018, 9, x FOR PEER REVIEW 5 of 12 nonlinear current model. In order to accurately characterize the self-heating effect in AlGaN/GaN HEMT. The three-pole thermal network in [25] is used. Thermal resistances as well as the thermal capacitances are extracted by a method based on FEM simulation in ANSYS. The trapping effect is modeled by the equivalent voltage method in [26]. The scalability of the model parameters, including the Ipk0, Rth, and Cth has been realized with the method that is mentioned in [22] for practical monolithic microwave integrated circuit design. With the help of MATLAB coding, model parameters, except the coefficients in Equation (2), are all extracted with the method in [27]. In terms of parameters in Equation (2), they are all extracted by fitting the transfer characteristics curve with the least square method.

Small Signal Characterization
The large signal model was embedded into Keysight ADS (Advanced Design System) by a symbolically defined device (SDD) tool. Small signal characteristics of the devices are measured by cascade probe station (Summit 11000B, FormFactor, Livermore, CA, USA), which is shown in Figure 6. The vector network analyzer is Keysight N5247A (Keysight Technologies, Santa Rosa, CA, USA). The frequency extenders close to probes are used to achieve the S parameters ranging from 75 GHz to 110 GHz as the vector network analyzer can only reach up to 67 GHz. The proposed model was validated by 0.1 µm AlGaN/GaN HEMTs with different gate width. AlGaN/GaN HEMTs were all fabricated on a 4-inch SiC substrate. T-shape-gate technology was introduced to reduce the contact resistance. The fT of the 0.1 µm GaN process is 90 GHz, while fmax is 220 GHz. The peak power density for a specific device can reach up to 3.46 W/mm. The photography of devices is shown in Figure 7. The comparison of simulated and measured S parameters is shown in Figure 8. Results show that the proposed model can predict the small signal characteristics ranging from 0.2 GHz to 110 GHz for devices with different gate width and under different bias. The proposed model was validated by 0.1 µm AlGaN/GaN HEMTs with different gate width. AlGaN/GaN HEMTs were all fabricated on a 4-inch SiC substrate. T-shape-gate technology was introduced to reduce the contact resistance. The f T of the 0.1 µm GaN process is 90 GHz, while f max is 220 GHz. The peak power density for a specific device can reach up to 3.46 W/mm. The photography of devices is shown in Figure 7. nonlinear current model. In order to accurately characterize the self-heating effect in AlGaN/GaN HEMT. The three-pole thermal network in [25] is used. Thermal resistances as well as the thermal capacitances are extracted by a method based on FEM simulation in ANSYS. The trapping effect is modeled by the equivalent voltage method in [26]. The scalability of the model parameters, including the Ipk0, Rth, and Cth has been realized with the method that is mentioned in [22] for practical monolithic microwave integrated circuit design. With the help of MATLAB coding, model parameters, except the coefficients in Equation (2), are all extracted with the method in [27]. In terms of parameters in Equation (2), they are all extracted by fitting the transfer characteristics curve with the least square method.

Small Signal Characterization
The large signal model was embedded into Keysight ADS (Advanced Design System) by a symbolically defined device (SDD) tool. Small signal characteristics of the devices are measured by cascade probe station (Summit 11000B, FormFactor, Livermore, CA, USA), which is shown in Figure 6. The vector network analyzer is Keysight N5247A (Keysight Technologies, Santa Rosa, CA, USA). The frequency extenders close to probes are used to achieve the S parameters ranging from 75 GHz to 110 GHz as the vector network analyzer can only reach up to 67 GHz. The proposed model was validated by 0.1 µm AlGaN/GaN HEMTs with different gate width. AlGaN/GaN HEMTs were all fabricated on a 4-inch SiC substrate. T-shape-gate technology was introduced to reduce the contact resistance. The fT of the 0.1 µm GaN process is 90 GHz, while fmax is 220 GHz. The peak power density for a specific device can reach up to 3.46 W/mm. The photography of devices is shown in Figure 7. The comparison of simulated and measured S parameters is shown in Figure 8. Results show that the proposed model can predict the small signal characteristics ranging from 0.2 GHz to 110 GHz for devices with different gate width and under different bias.

The Large Signal Model Validation
The DC characteristics for the proposed scalable large signal model was validated by different gate width, including 4 × 20 µm and 4 × 50 µm, as shown in Figure 9. The gate-source voltage Vgs is investigated from −6 V to 0 V, while the drain-source voltage Vds is from 0 V to 20 V for these two devices.  Figure 9 shows that the DIBL effect is accurately characterized based on the improvement in Equation (2). The channel length modulation effect is also the same.
Due to the absent of W band load-pull system, the load pull performance at 28 GHz was used to validate the large signal model first, as shown in Figure 10. The system is on cascade probe station (Summit 12000, FormFactor, Livermore, CA, USA), the input signal generator is Agilent E8257D (Keysight Technologies, Santa Rosa, CA, USA), and the output power is detected by power meter Agilent N1912A (Keysight Technologies, Santa Rosa, CA, USA) and Vector Network Analyzer (Keysight Technologies, Santa Rosa, CA, USA).

The Large Signal Model Validation
The DC characteristics for the proposed scalable large signal model was validated by different gate width, including 4 × 20 µm and 4 × 50 µm, as shown in Figure 9. The gate-source voltage V gs is investigated from −6 V to 0 V, while the drain-source voltage V ds is from 0 V to 20 V for these two devices.

The Large Signal Model Validation
The DC characteristics for the proposed scalable large signal model was validated by different gate width, including 4 × 20 µm and 4 × 50 µm, as shown in Figure 9. The gate-source voltage Vgs is investigated from −6 V to 0 V, while the drain-source voltage Vds is from 0 V to 20 V for these two devices.  Figure 9 shows that the DIBL effect is accurately characterized based on the improvement in Equation (2). The channel length modulation effect is also the same.
Due to the absent of W band load-pull system, the load pull performance at 28 GHz was used to validate the large signal model first, as shown in Figure 10. The system is on cascade probe station (Summit 12000, FormFactor, Livermore, CA, USA), the input signal generator is Agilent E8257D (Keysight Technologies, Santa Rosa, CA, USA), and the output power is detected by power meter Agilent N1912A (Keysight Technologies, Santa Rosa, CA, USA) and Vector Network Analyzer (Keysight Technologies, Santa Rosa, CA, USA).  Figure 9 shows that the DIBL effect is accurately characterized based on the improvement in Equation (2). The channel length modulation effect is also the same.
Due to the absent of W band load-pull system, the load pull performance at 28 GHz was used to validate the large signal model first, as shown in Figure 10. The system is on cascade probe station (Summit 12000, FormFactor, Livermore, CA, USA), the input signal generator is Agilent E8257D (Keysight Technologies, Santa Rosa, CA, USA), and the output power is detected by power meter Agilent N1912A (Keysight Technologies, Santa Rosa, CA, USA) and Vector Network Analyzer (Keysight Technologies, Santa Rosa, CA, USA).
The maximum output power load-pull measurement is performed. The bias is chosen at V gs = −2.6 V, V ds = 15 V, which is at deep class AB working state. The quiescent drain current is 82 mA at this bias. The optimum source and load resistance for the maximum output power are Z S = (13.44 + 12.41 × j) Ω and Z L = (27.19 + 27.44 × j) Ω. The power sweep was then performed based on the optimum resistance with the input power ranging from −4 dBm to 22 dBm. The comparison between the simulated and measured results, including output power (Pout), gain, and power added efficiency (PAE) are shown in Figure 11. Also, the influence that is brought by the DIBL effect has also been investigated in Figure 11. Results show that the DIBL effect will lead to the reduction of Pout, gain, and PAE. This can be explained by the variation of static bias point due to the DIBL effect.
Due to the absent of W band load-pull system, the load pull performance at 28 GHz was used to validate the large signal model first, as shown in Figure 10. The system is on cascade probe station (Summit 12000, FormFactor, Livermore, CA, USA), the input signal generator is Agilent E8257D (Keysight Technologies, Santa Rosa, CA, USA), and the output power is detected by power meter Agilent N1912A (Keysight Technologies, Santa Rosa, CA, USA) and Vector Network Analyzer (Keysight Technologies, Santa Rosa, CA, USA). The maximum output power load-pull measurement is performed. The bias is chosen at Vgs = −2.6 V, Vds = 15 V, which is at deep class AB working state. The quiescent drain current is 82 mA at this bias. The optimum source and load resistance for the maximum output power are ZS = (13.44 + 12.41 × j) Ω and ZL = (27.19 + 27.44 × j) Ω. The power sweep was then performed based on the optimum resistance with the input power ranging from −4 dBm to 22 dBm. The comparison between the simulated and measured results, including output power (Pout), gain, and power added efficiency (PAE) are shown in Figure 11. Also, the influence that is brought by the DIBL effect has also been investigated in Figure 11. Results show that the DIBL effect will lead to the reduction of Pout, gain, and PAE. This can be explained by the variation of static bias point due to the DIBL effect. Figure 11. Investigation on the influence brought by DIBL effect on large signal performance.
The simulated and measured impedance charts achieved by maximum Pout and PAE load-pull measurement are presented in Figure 12.

W Band MMIC Power Amplifier Design
For further validation of the proposed large signal model for applications in the W band, a MMIC power amplifier whose operation frequency is 92 GHz-96 GHz was designed. Based on the above large signal model, a W-band power amplifier is designed. Figure 13 presents the schematic of the W band amplifier. The simulated and measured impedance charts achieved by maximum Pout and PAE load-pull measurement are presented in Figure 12. The maximum output power load-pull measurement is performed. The bias is chosen at Vgs = −2.6 V, Vds = 15 V, which is at deep class AB working state. The quiescent drain current is 82 mA at this bias. The optimum source and load resistance for the maximum output power are ZS = (13.44 + 12.41 × j) Ω and ZL = (27.19 + 27.44 × j) Ω. The power sweep was then performed based on the optimum resistance with the input power ranging from −4 dBm to 22 dBm. The comparison between the simulated and measured results, including output power (Pout), gain, and power added efficiency (PAE) are shown in Figure 11. Also, the influence that is brought by the DIBL effect has also been investigated in Figure 11. Results show that the DIBL effect will lead to the reduction of Pout, gain, and PAE. This can be explained by the variation of static bias point due to the DIBL effect. Figure 11. Investigation on the influence brought by DIBL effect on large signal performance.
The simulated and measured impedance charts achieved by maximum Pout and PAE load-pull measurement are presented in Figure 12.

W Band MMIC Power Amplifier Design
For further validation of the proposed large signal model for applications in the W band, a MMIC power amplifier whose operation frequency is 92 GHz-96 GHz was designed. Based on the above large signal model, a W-band power amplifier is designed. Figure 13 presents the schematic of the W band amplifier.

W Band MMIC Power Amplifier Design
For further validation of the proposed large signal model for applications in the W band, a MMIC power amplifier whose operation frequency is 92 GHz-96 GHz was designed. Based on the above large signal model, a W-band power amplifier is designed. Figure 13 presents the schematic of the W band amplifier.
The output stage used the planar spatial power combiner to realize the impedance transformation and combine the four-way power element. The millimeter wave GaN device is very easy to oscillation at low frequency due to the high gain. Multi-order RC network was used to improve the stability of the circuit. In order to enable the former stage to have enough power to drive the latter stage, the driving ratio of amplifier circuit is 1:2:4. Passive components include micro-strip line, MIM (Metal-insulator-Metal) capacitance, and resistor. All of the passive components were simulated by EM simulator in ADS. Figure 14 shows photograph of a W-band GaN MMIC amplifier.  TL15   TL16   TL17   TL18   TL19   TL22   VDS   TL21   C3   0.4pF  TL24   TL23   TL25   TL26   TL27   TL28   TL29   TL30   TL31   TL33   TL32   TL34   TL35   TL36   TL43  TL37   TL38   TL39   TL40   TL41   TL42  25Ω  12   The output stage used the planar spatial power combiner to realize the impedance transformation and combine the four-way power element. The millimeter wave GaN device is very easy to oscillation at low frequency due to the high gain. Multi-order RC network was used to improve the stability of the circuit. In order to enable the former stage to have enough power to drive the latter stage, the driving ratio of amplifier circuit is 1:2:4. Passive components include micro-strip line, MIM (Metal-insulator-Metal) capacitance, and resistor. All of the passive components were simulated by EM simulator in ADS. Figure 14 shows photograph of a W-band GaN MMIC amplifier.  TL1   TL2   TL3   TL4   TL5   TL7   TL6   TL8   C2   0.5pF   TL9   TL10   TL11   TL12   TL13   TL14   R1=50Ω   4x30μm   4x30μm   The output stage used the planar spatial power combiner to realize the impedance transformation and combine the four-way power element. The millimeter wave GaN device is very easy to oscillation at low frequency due to the high gain. Multi-order RC network was used to improve the stability of the circuit. In order to enable the former stage to have enough power to drive the latter stage, the driving ratio of amplifier circuit is 1:2:4. Passive components include micro-strip line, MIM (Metal-insulator-Metal) capacitance, and resistor. All of the passive components were simulated by EM simulator in ADS. Figure 14 shows photograph of a W-band GaN MMIC amplifier. The chip was loaded into a jig for measurement. The schematic of the measurement setup for large-signal measurements is shown in Figure 15. The large signal measurement was performed at room temperature. The commercial amplifier, frequency multiplier, and signal analyzer in Figure 15 are used to assistant the measurement. Other instruments including power meter (VDI Erickson, Virginia Diodes, Inc., Charlottesville, VA, USA), DC sources (Agilent E3633A and E3634A, Keysight Technologies, Santa Rosa, CA, USA), and attenuator (Rebes, Suzhou, China) were also employed. The amplifier is measured in CW (Continuous Wave) mode over 90 GHz-97 GHz frequency. The device was bias at V ds = 15 V and V gs = −2 V. The chip was loaded into a jig for measurement. The schematic of the measurement setup for large-signal measurements is shown in Figure 15. The large signal measurement was performed at room temperature. The commercial amplifier, frequency multiplier, and signal analyzer in Figure 15 are used to assistant the measurement. Other instruments including power meter (VDI Erickson, Virginia Diodes, Inc., Charlottesville, VA, USA), DC sources (Agilent E3633A and E3634A, Keysight Technologies, Santa Rosa, CA, USA), and attenuator (Rebes, Suzhou, China) were also employed. The amplifier is measured in CW (Continuous Wave) mode over 90 GHz-97 GHz frequency. The device was bias at Vds = 15 V and Vgs = −2 V.   Figure 16 may come from the cavity and gold wire used for assisting the measurement. Their influence on frequency shift has not been taken into consideration during the MMIC design. However, this accuracy is sufficient for the application of practical circuit design. Figure 17 shows Gain, PAE, and output power. Over 90 GHz-97 GHz frequency range, the output power is greater than 1 W. The peak output power is 1.2 W. Except for 94 GHz and 98 GHz, the measured PAE was greater than 15%.   Figure 16 may come from the cavity and gold wire used for assisting the measurement. Their influence on frequency shift has not been taken into consideration during the MMIC design. However, this accuracy is sufficient for the application of practical circuit design. Figure 17 shows Gain, PAE, and output power. Over 90 GHz-97 GHz frequency range, the output power is greater than 1 W. The peak output power is 1.2 W. Except for 94 GHz and 98 GHz, the measured PAE was greater than 15%.

Conclusions
In this paper, an improved large signal model for AlGaN/GaN HEMT up to the W band is presented. The short channel effects including the DIBL effect and channel length modulation are added in the Angelov model. In-house AlGaN/GaN HEMTs with gate length of 0.1 µm are used for the validation of the model. A MMIC power amplifier is designed based on the proposed model for further validation. Results show that the large signal model can give good accuracy up to W band. The results of this paper can provide guidance to many other kinds FET (Field Effect Transistor) devices modeling in the W band. Also, they are useful for the improvement of the GaN process and also are helpful for the practical MMIC design in the W band.

Conclusions
In this paper, an improved large signal model for AlGaN/GaN HEMT up to the W band is presented. The short channel effects including the DIBL effect and channel length modulation are added in the Angelov model. In-house AlGaN/GaN HEMTs with gate length of 0.1 µm are used for the validation of the model. A MMIC power amplifier is designed based on the proposed model for further validation. Results show that the large signal model can give good accuracy up to W band. The results of this paper can provide guidance to many other kinds FET (Field Effect Transistor) devices modeling in the W band. Also, they are useful for the improvement of the GaN process and also are helpful for the practical MMIC design in the W band.

Conclusions
In this paper, an improved large signal model for AlGaN/GaN HEMT up to the W band is presented. The short channel effects including the DIBL effect and channel length modulation are added in the Angelov model. In-house AlGaN/GaN HEMTs with gate length of 0.1 µm are used for the validation of the model. A MMIC power amplifier is designed based on the proposed model for further validation. Results show that the large signal model can give good accuracy up to W band. The results of this paper can provide guidance to many other kinds FET (Field Effect Transistor) devices modeling in the W band. Also, they are useful for the improvement of the GaN process and also are helpful for the practical MMIC design in the W band.

Conflicts of Interest:
The authors declare that there is no conflict of interests regarding the publication of this article.