A New GaN HEMT Small-Signal Model Considering Source via Effects for 5G Millimeter-Wave Power Amplifier Design

amplifier Abstract: A new gallium nitride (GaN) high electron mobile transistor (HEMT) small-signal model is proposed considering source via effects. In general, GaN HEMTs adopt a source via structure to reduce device degradation due to self-heating. In this paper, the modified drain-source capacitance (C ds ) circuit considering the source via structure is proposed. GaN HEMTs fabricated using a commercial 0.15 μ m GaN HEMT process are measured with a 67 GHz vector network analyzer (VNA). The fabricated device is an individual source via (ISV) type. As a result, it is difficult to predict the measured S12 in the conventional small-signal model equivalent circuit. This causes errors in maximum stable gain/maximum available gain (MSG/MAG) and stability factor (K), which are important for circuit design. This paper proposes a small-signal equivalent circuit that adds the drain-source inductance to the drain-source capacitance considering the source via structure. The proposed equivalent circuit better reproduces the measured S12 without compromising the accuracy of other S-parameters up to 67 GHz and improves the accuracy of MSG/MAG and K. It is expected that the proposed model can be utilized in a large-signal model for 5G millimeter-wave GaN HEMT power amplifier design in the future.


Introduction
Gallium nitride (GaN) semiconductors have a high breakdown voltage due to inherent wide-bandgap and high current density, which is advantageous for use as power semiconductors [1,2].In addition, since the high electron mobility transistor (HEMT) structure has high electron mobility due to the generation of its unique 2-D electron gas (2-DEG), GaN HEMTs have been widely studied and utilized in high-frequency power amplifiers [3][4][5][6][7].Since GaN HEMTs exhibit high power density but have a self-heating effect, a source via structure that can dissipate heat well to substrates is widely used in transistor layouts.As a result, accurate large-signal modeling reflecting the self-heating effect is essential [8][9][10][11].Recently, with the commercialization of 5G communication, research on millimeter-wave power amplifiers using GaN HEMTs is being actively conducted [12][13][14][15].Therefore, GaN HEMT large-signal modeling that reflects self-heating effects up to the millimeter-wave band is required.On the other hand, for accurate large-signal modeling, an accurate smallsignal model should be prioritized.In particular, as the operating frequency increases, a small-signal equivalent circuit that reflects the S-parameter according to the frequency well is required.Until now, many studies on GaN HEMT modeling have been successfully published [16][17][18][19][20][21][22][23][24][25].Recently, some papers dealing with GaN HEMT small-signal modeling up to 110 GHz have reported on millimeter-wave monolithic microwave integrated circuit (MMIC) design [22][23][24][25].However, depending on the process, there was no consideration of the coupling effect that may appear with the source via process.This suggests that it may be necessary to modify the traditional HEMT small-signal equivalent circuit that has been Appl.Sci.2021, 11, 9120 2 of 14 used for millimeter-wave GaN HEMT small-signal modeling.In this paper, we propose a new GaN HEMT small-signal equivalent circuit considering the source via structure, usable at frequencies up to 67 GHz including 5G communication frequencies.The structure of this paper is as follows: In Section 2, we propose a small-signal equivalent circuit reflecting the source via effect from the GaN HEMT structure to which an individual source via (ISV) is applied.Then, an extraction method and procedure of the proposed small-signal model are mentioned.Section 3 introduces the 67 GHz S-parameter measurement setup conducted in this work and verifies the validity of the proposed model by comparing the conventional small-signal model and the proposed one with the measurement results.Finally, the conclusion follows.

0.15 µm GaN HEMT ISV Structure and Source via Effect
Due to high output power of several watts generated from a GaN HEMT device with a size of hundreds of micrometers, heat is inevitably generated from the device itself.The self-heating effect is a phenomenon in which device characteristics deteriorate due to temperature rise caused by power consumption in the device.In order to minimize this degradation, it is important to have a device layout that can dissipate heat well.An ISV structure in which heat is dissipated through multiple grounds by placing a backside ground via per source finger is widely used [26].Figure 1 shows the ISV layout structure of a commercial GaN HEMT having a gate length of 0.15 µm and a gate width of 4 × 50 µm.As shown in Figure 1b, the heat generated by the device is dissipated to the ground through the backside vias connected to each source.via process.This suggests that it may be necessary to modify the traditional HEMT smallsignal equivalent circuit that has been used for millimeter-wave GaN HEMT small-signal modeling.In this paper, we propose a new GaN HEMT small-signal equivalent circuit considering the source via structure, usable at frequencies up to 67 GHz including 5G communication frequencies.The structure of this paper is as follows: In Section 2, we propose a small-signal equivalent circuit reflecting the source via effect from the GaN HEMT structure to which an individual source via (ISV) is applied.Then, an extraction method and procedure of the proposed small-signal model are mentioned.Section 3 introduces the 67 GHz S-parameter measurement setup conducted in this work and verifies the validity of the proposed model by comparing the conventional small-signal model and the proposed one with the measurement results.Finally, the conclusion follows.

0.15 μm GaN HEMT ISV Structure and Source via Effect
Due to high output power of several watts generated from a GaN HEMT device with a size of hundreds of micrometers, heat is inevitably generated from the device itself.The self-heating effect is a phenomenon in which device characteristics deteriorate due to temperature rise caused by power consumption in the device.In order to minimize this degradation, it is important to have a device layout that can dissipate heat well.An ISV structure in which heat is dissipated through multiple grounds by placing a backside ground via per source finger is widely used [26].Figure 1 shows the ISV layout structure of a commercial GaN HEMT having a gate length of 0.15 μm and a gate width of 4 × 50 μm.As shown in Figure 1b, the heat generated by the device is dissipated to the ground through the backside vias connected to each source.The size of the backside via used in this process is about 60 × 90 um, and the height is about 100 um.Due to this source via structure, the conventional small-signal equivalent circuit also needs to be modified.In particular, parasitics related to the source via structure, which have not been considered in the past, may have a non-negligible effect at the frequencies of the millimeter-wave band above 30 GHz.In this work, the parasitic effect due to the coupling between drain and source feeding lines surrounding the source via structure is mainly investigated.Figure 2 shows an enlarged GaN HEMT layout around the source via structure and an equivalent circuit representing it.Parasitic components that are actually generated are more complex but are simplified for convenience.It is true that additional proof is needed to clarify the exact physical phenomenon of the proposed equivalent circuit, but the possible physical structure is inferred from the more accurate equivalent circuit found empirically.At high frequencies, parasitic inductance and via re- The size of the backside via used in this process is about 60 × 90 um, and the height is about 100 um.Due to this source via structure, the conventional small-signal equivalent circuit also needs to be modified.In particular, parasitics related to the source via structure, which have not been considered in the past, may have a non-negligible effect at the frequencies of the millimeter-wave band above 30 GHz.In this work, the parasitic effect due to the coupling between drain and source feeding lines surrounding the source via structure is mainly investigated.Figure 2 shows an enlarged GaN HEMT layout around the source via structure and an equivalent circuit representing it.Parasitic components that are actually generated are more complex but are simplified for convenience.It is true that additional proof is needed to clarify the exact physical phenomenon of the proposed equivalent circuit, but the possible physical structure is inferred from the more accurate equivalent circuit found empirically.At high frequencies, parasitic inductance and via resistance and inductance may be generated for a long path among multiple paths generated, while signals are coupled and passed in various directions of the source via from the drain feeding line.As shown in Figure 2, these are modeled by C ds1 , L ds , R s , and L s .Some paths may be short and there may be coupling signals that drop directly to ground.This is modeled by C ds2 .More detailed verification of this will be carried out in a follow-up study.
Appl.Sci.2021, 11, x FOR PEER REVIEW 3 of 14 sistance and inductance may be generated for a long path among multiple paths generated, while signals are coupled and passed in various directions of the source via from the drain feeding line.As shown in Figure 2, these are modeled by Cds1, Lds, Rs, and Ls.Some paths may be short and there may be coupling signals that drop directly to ground.This is modeled by Cds2.More detailed verification of this will be carried out in a follow-up study.To confirm this, 2.5 dimensional electromagnetic (EM) simulation is performed on the drain-source layout of the GaN HEMT device using ADS momentum software.Figure 3a,b shows the EM layout and simulation results of the simplified one-port drain-source via structure.In particular, EM analysis is performed up to 120 GHz to confirm the inductance effect.The layout shown in Figure 3a is mostly composed of metal layers, so the resistance of the metal itself is very small.Since the GaN HEMT substrate has a semiinsulated structure similar to that of GaAs, the substrate loss is also small.Therefore, the EM simulation result shows almost no loss.The change in phase from −180° to +180° also occurs when a capacitive component changes to an inductive component.When looking at the Smith chart, the point going from the lower semicircle to the upper semicircle is the instantaneous transition point.From the simulation result shown on the Smith chart in Figure 3b, it can be confirmed that parasitic inductance exists in the coupling components between the drain and source feeding lines.To confirm this, 2.5 dimensional electromagnetic (EM) simulation is performed on the drain-source layout of the GaN HEMT device using ADS momentum software.Figure 3a,b shows the EM layout and simulation results of the simplified one-port drain-source via structure.In particular, EM analysis is performed up to 120 GHz to confirm the inductance effect.The layout shown in Figure 3a is mostly composed of metal layers, so the resistance of the metal itself is very small.Since the GaN HEMT substrate has a semi-insulated structure similar to that of GaAs, the substrate loss is also small.Therefore, the EM simulation result shows almost no loss.
Appl.Sci.2021, 11, x FOR PEER REVIEW 3 of 14 sistance and inductance may be generated for a long path among multiple paths generated, while signals are coupled and passed in various directions of the source via from the drain feeding line.As shown in Figure 2, these are modeled by Cds1, Lds, Rs, and Ls.Some paths may be short and there may be coupling signals that drop directly to ground.This is modeled by Cds2.More detailed verification of this will be carried out in a follow-up study.To confirm this, 2.5 dimensional electromagnetic (EM) simulation is performed on the drain-source layout of the GaN HEMT device using ADS momentum software.Figure 3a,b shows the EM layout and simulation results of the simplified one-port drain-source via structure.In particular, EM analysis is performed up to 120 GHz to confirm the inductance effect.The layout shown in Figure 3a is mostly composed of metal layers, so the resistance of the metal itself is very small.Since the GaN HEMT substrate has a semiinsulated structure similar to that of GaAs, the substrate loss is also small.Therefore, the EM simulation result shows almost no loss.The change in phase from −180° to +180° also occurs when a capacitive component changes to an inductive component.When looking at the Smith chart, the point going from the lower semicircle to the upper semicircle is the instantaneous transition point.From the simulation result shown on the Smith chart in Figure 3b, it can be confirmed that parasitic inductance exists in the coupling components between the drain and source feeding lines.The change in phase from −180 • to +180 • also occurs when a capacitive component changes to an inductive component.When looking at the Smith chart, the point going from the lower semicircle to the upper semicircle is the instantaneous transition point.From the simulation result shown on the Smith chart in Figure 3b, it can be confirmed that parasitic inductance exists in the coupling components between the drain and source feeding lines.
Figure 4 shows the comparison of the S11 EM data obtained above with the simulation according to the equivalent circuit.Up to 30 GHz, there is no significant difference even when modeling the coupling phenomenon of the drain and source feeding lines as a shunt parasitic capacitor alone, but at 30 GHz or more, there is a difference, and it can be seen that the equivalent circuit, including a parasitic inductor, reproduces the EM data more accurately.
Figure 4 shows the comparison of the S11 EM data obtained above with the simulation according to the equivalent circuit.Up to 30 GHz, there is no significant difference even when modeling the coupling phenomenon of the drain and source feeding lines as a shunt parasitic capacitor alone, but at 30 GHz or more, there is a difference, and it can be seen that the equivalent circuit, including a parasitic inductor, reproduces the EM data more accurately.

New GaN HEMT Small-Signal Equivalent Circuit Considering Source via Effects
The well-known small-signal equivalent circuit of Ⅲ-Ⅴ-based HEMTs including GaN HEMTs is shown in Figure 5a.For better understanding, the port numbers are also indicated when measuring S-parameters.The source port is usually connected to ground.It consists of a pad model composed of pad parasitic capacitances (Cpg, Cpd) and pad parasitic inductances (Lpg, Lpd), an extrinsic part depending on the layout structure, and an intrinsic part whose value changes according to the channel variation of the transistor by applied biases [27][28][29].Usually, the Cds is classified as an intrinsic model parameter, but empirically, the difference in values extracted according to biases is not large, so in some cases it is set as a constant [27][28][29].In this work, it is assumed that both the extrinsic part and the intrinsic part of Cds exist.

New GaN HEMT Small-Signal Equivalent Circuit Considering Source via Effects
The well-known small-signal equivalent circuit of III-V-based HEMTs including GaN HEMTs is shown in Figure 5a.For better understanding, the port numbers are also indicated when measuring S-parameters.The source port is usually connected to ground.It consists of a pad model composed of pad parasitic capacitances (C pg , C pd ) and pad parasitic inductances (L pg , L pd ), an extrinsic part depending on the layout structure, and an intrinsic part whose value changes according to the channel variation of the transistor by applied biases [27][28][29].Usually, the C ds is classified as an intrinsic model parameter, but empirically, the difference in values extracted according to biases is not large, so in some cases it is set as a constant [27][28][29].In this work, it is assumed that both the extrinsic part and the intrinsic part of C ds exist.
Figure 5b shows the modified small-signal equivalent circuit including the source via effect discussed in the previous section.As shown in Figure 5b, the "C ds " part is modified to reflect the coupling effect between the drain and source via feeding lines.For convenience, we divide the C ds into C ds1 and C ds2 , one including the source via inductance indicating that the coupling signal path is long and the other part directly falling to the ground, and the intrinsic C ds will be included in the latter.
tion according to the equivalent circuit.Up to 30 GHz, there is no significant diff even when modeling the coupling phenomenon of the drain and source feeding lin shunt parasitic capacitor alone, but at 30 GHz or more, there is a difference, and it seen that the equivalent circuit, including a parasitic inductor, reproduces the EM more accurately.

New GaN HEMT Small-Signal Equivalent Circuit Considering Source via Effects
The well-known small-signal equivalent circuit of Ⅲ-Ⅴ-based HEMTs includin HEMTs is shown in Figure 5a.For better understanding, the port numbers are als cated when measuring S-parameters.The source port is usually connected to gro consists of a pad model composed of pad parasitic capacitances (Cpg, Cpd) and pad sitic inductances (Lpg, Lpd), an extrinsic part depending on the layout structure, intrinsic part whose value changes according to the channel variation of the transi applied biases [27][28][29].Usually, the Cds is classified as an intrinsic model paramet empirically, the difference in values extracted according to biases is not large, so in cases it is set as a constant [27][28][29].In this work, it is assumed that both the extrins and the intrinsic part of Cds exist.Figure 5b shows the modified small-signal equivalent circuit including the sou effect discussed in the previous section.As shown in Figure 5b, the "Cds" part is mo to reflect the coupling effect between the drain and source via feeding lines.For co ience, we divide the Cds into Cds1 and Cds2, one including the source via inductanc cating that the coupling signal path is long and the other part directly falling ground, and the intrinsic Cds will be included in the latter.

Small-Signal Extraction Procedure Partially Assisted by EM Simulation
In order to extract the model parameters of the modified small-signal equivale cuit proposed in the previous section, the conventional extraction method is used with the EM-based extraction method.
The first step is to extract the model parameters of the conventional small equivalent circuit [28,29].First, pad model parameters can be extracted through m ing the pad test pattern.After de-embedding the pad model, extrinsic model para can be extracted through S-parameters measured in the cold bias region where the source voltage (Vds) is 0 V. Figure 6 shows the small-signal equivalent circuit in th bias region.

Small-Signal Extraction Procedure Partially Assisted by EM Simulation
In order to extract the model parameters of the modified small-signal equivalent circuit proposed in the previous section, the conventional extraction method is used along with the EM-based extraction method.
The first step is to extract the model parameters of the conventional small-signal equivalent circuit [28,29].First, pad model parameters can be extracted through measuring the pad test pattern.After de-embedding the pad model, extrinsic model parameters can be extracted through S-parameters measured in the cold bias region where the drain-source voltage (V ds ) is 0 V. Figure 6 shows the small-signal equivalent circuit in the cold bias region.Figure 5b shows the modified small-signal equivalent circuit including the source via effect discussed in the previous section.As shown in Figure 5b, the "Cds" part is modified to reflect the coupling effect between the drain and source via feeding lines.For convenience, we divide the Cds into Cds1 and Cds2, one including the source via inductance indicating that the coupling signal path is long and the other part directly falling to the ground, and the intrinsic Cds will be included in the latter.

Small-Signal Extraction Procedure Partially Assisted by EM Simulation
In order to extract the model parameters of the modified small-signal equivalent circuit proposed in the previous section, the conventional extraction method is used along with the EM-based extraction method.
The first step is to extract the model parameters of the conventional small-signal equivalent circuit [28,29].First, pad model parameters can be extracted through measuring the pad test pattern.After de-embedding the pad model, extrinsic model parameters can be extracted through S-parameters measured in the cold bias region where the drainsource voltage (Vds) is 0 V. Figure 6 shows the small-signal equivalent circuit in the cold bias region.From the equivalent circuit of Figure 6, the Z parameters can be expressed as follows: Appl.Sci.2021, 11, 9120 6 of 14 where R s , R g , R ch , and R d are the source, gate, channel, and drain resistance, respectively, L s , L g , and L d are the extrinsic source, gate, and drain inductance, respectively.R sdj and C sdj are the Schottky diode resistance and capacitance, respectively, and ω is the angular frequency.Charges in the depletion region vary according to the gate bias, and as the charge increases, the channel resistance decreases.Using this relation, R s + R d can be extracted through the equation for the amount of charge and the real part of Z 22 according to the gate biases.Then, using the R s + R d value obtained earlier, R ch at a specific bias can be found from the real part of Z 22 of Equation ( 3), and R s can be extracted from the real part of Z 12 of Equation ( 2).When R s is found, R d can also be extracted from the R s + R d value.L s and L d can be extracted using the imaginary parts of Z 12 and Z 22 in a similar manner.However, R g and L g cannot be extracted as simply as above due to R sdj and C sdj .
By applying the method used in [29] as it is, L g and R g can be extracted by approximating Z 11 using the fact that 1 jωC sdj becomes very small compared to R sdj at high frequencies above 35 GHz.
In Figure 5a, the Y-parameters of intrinsic parts that change according to the bias can be expressed by the following Equations ( 4)- (7). (5) where R i , R gd , and R ds are the input, gate-drain, and output resistance, respectively, and C gs , C gd , and G m are the gate-source, gate-drain capacitance, and transconductance, respectively.Intrinsic model parameters can be extracted for each bias using the above equations from the Y-parameters obtained by de-embedding the pad model and extrinsic part from the measured S-parameters.The second step is to replace the existing C ds obtained in the first step with the "modified C ds " shown in Figure 5b.It can be obtained by deriving an analytic equation, but in this work, EM simulation is used in an intuitive way without using complex equations.Since the "modified C ds " reflecting the source via effect is due to the layout structure, parameter extraction is possible with EM simulation and does not depend on the bias.Figure 7 shows the top view of full EM simulation of a GaN HEMT using ADS Momentum software.To obtain more realistic results, the measured GaN HEMT layout is brought directly into the EM simulation setup.In the layout shown in Figure 7, the gate layer is visible, but in ADS momentum, there is a function that does not activate this layer in the EM simulation setup.Therefore, the effect of the gate layer can be easily excluded, and the simulation is performed so that only the drain-source layout effect is shown.Finally, the modified C ds can be extracted from the EM simulation result between the drain and source terminals.

67 GHz S-Parameter Measurement Set-Up
A 67 GHz S-parameter measurement setup was implemented to verify the new GaN HEMT small-signal model considering the source via effect proposed in Section 2. Figure 9 shows the block diagram of a 67 GHz S-parameter measurement setup.Two-port RF signals come from a 67 GHz vector network analyzer, and through on-wafer probing, the RF signals are input and output to a GaN HEMT device under test with dc biases through a dc source generator and two bias tees.This setup is connected to a PC through general purpose interface bus (GPIB) cables and automatically measures S-parameters according to biases and frequencies through IC-CAP software.In particular, since GaN HEMT devices have high operating voltage and high output power, it is necessary to carefully check the maximum input voltage and RF power allowed by the equipment and accessories.Cds1, Cds2, and Lds composing the "modified Cds" are extracted through fitting or optimization by comparing S22 obtained through EM simulation with the modeled S-parameter of the drain-source part extracted previously.The fitted Cds2 does not yet contain an intrinsic part.Therefore, the intrinsic part can be added through the final comparison with the measured S-parameter, and the final small-signal model is completed through finetuning of each model parameter.Figure 8 is a block diagram showing the small-signal modeling procedure proposed in this work.

67 GHz S-Parameter Measurement Set-Up
A 67 GHz S-parameter measurement setup was implemented to verify the new GaN HEMT small-signal model considering the source via effect proposed in Section 2. Figure 9 shows the block diagram of a 67 GHz S-parameter measurement setup.Two-port RF signals come from a 67 GHz vector network analyzer, and through on-wafer probing, the RF signals are input and output to a GaN HEMT device under test with dc biases through a dc source generator and two bias tees.This setup is connected to a PC through general purpose interface bus (GPIB) cables and automatically measures S-parameters according to biases and frequencies through IC-CAP software.In particular, since GaN HEMT devices have high operating voltage and high output power, it is necessary to carefully check the maximum input voltage and RF power allowed by the equipment and accessories.

67 GHz S-Parameter Measurement Set-Up
A 67 GHz S-parameter measurement setup was implemented to verify the new GaN HEMT small-signal model considering the source via effect proposed in Section 2. Figure 9 shows the block diagram of a 67 GHz S-parameter measurement setup.Two-port RF signals come from a 67 GHz vector network analyzer, and through on-wafer probing, the RF signals are input and output to a GaN HEMT device under test with dc biases through a dc source generator and two bias tees.This setup is connected to a PC through general purpose interface bus (GPIB) cables and automatically measures S-parameters according to biases and frequencies through IC-CAP software.In particular, since GaN HEMT devices have high operating voltage and high output power, it is necessary to carefully check the maximum input voltage and RF power allowed by the equipment and accessories.

Measurement results
The proposed small-signal modeling was performed on an ISV-type 4 × 50 μm GaN HEMT fabricated using a commercial 0.15 μm GaN HEMT process.First, the pad equivalent model parameters are extracted through the S-parameter measurement of the pad test pattern.The extracted values of Cpg and Cpd are both 18 fF, and those of Lpg and Lpd are both 30 pH.Next, S-parameters are measured from 0.2 to 67 GHz in the cold and hot bias regions.The pinch-off voltage of the device is about −2.8 V, and the measurement bias region is a drain-source voltage of 0 to 28 V and a gate-source voltage (Vgs) of −2.8 to −0.8 V. Table 1 shows the initial extrinsic and intrinsic parameters extracted using the conventional small-signal model parameter extraction method.Next, to replace the Cds obtained above with the "modified Cds" shown in Figure 5b, EM simulation is used as shown in Figure 7. Based on the EM simulation result, the values of Cds1, Lds, and Cds2 extracted by iterative fitting are 40 fF, 40 pH, and 50 fF, respectively.Figure 10 shows the comparison of the S-parameter of the extracted "modified Cds" circuit with the EM simulated one.The "modified Cds" circuit agrees better with the EM result than the conventional Cds.

Measurement Results
The proposed small-signal modeling was performed on an ISV-type 4 × 50 µm GaN HEMT fabricated using a commercial 0.15 µm GaN HEMT process.First, the pad equivalent model parameters are extracted through the S-parameter measurement of the pad test pattern.The extracted values of C pg and C pd are both 18 fF, and those of L pg and L pd are both 30 pH.Next, S-parameters are measured from 0.2 to 67 GHz in the cold and hot bias regions.The pinch-off voltage of the device is about −2.8 V, and the measurement bias region is a drain-source voltage of 0 to 28 V and a gate-source voltage (V gs ) of −2.8 to −0.8 V. Table 1 shows the initial extrinsic and intrinsic parameters extracted using the conventional small-signal model parameter extraction method.Next, to replace the C ds obtained above with the "modified C ds " shown in Figure 5b, EM simulation is used as shown in Figure 7. Based on the EM simulation result, the values of C ds1 , L ds , and C ds2 extracted by iterative fitting are 40 fF, 40 pH, and 50 fF, respectively.Figure 10 shows the comparison of the S-parameter of the extracted "modified C ds " circuit with the EM simulated one.The "modified C ds " circuit agrees better with the EM result than the conventional C ds .Finally, the intrinsic part of Cds, which is about 25 fF, can be added through the final comparison with the measured S-parameter, and the complete small-signal model is optimized through fine-tuning of each model parameter.
To verify the validity of the small-signal model completed through the above procedure, the S-parameters of small-signal models and the measured S-parameters are compared from 0.2 to 67 GHz with respect to several biases around the load line, which is important for power amplifier design.In addition, the stability factor (K) and MSG/MAG that can be calculated from the S-parameter results are also compared.The formulas can be expressed as follows [30]: Finally, the intrinsic part of C ds, which is about 25 fF, can be added through the final comparison with the measured S-parameter, and the complete small-signal model is optimized through fine-tuning of each model parameter.
To verify the validity of the small-signal model completed through the above procedure, the S-parameters of small-signal models and the measured S-parameters are compared from 0.2 to 67 GHz with respect to several biases around the load line, which is important for power amplifier design.In addition, the stability factor (K) and MSG/MAG that can be calculated from the S-parameter results are also compared.The formulas can be expressed as follows [30]:  Finally, the intrinsic part of Cds, which is about 25 fF, can be added through the final comparison with the measured S-parameter, and the complete small-signal model is optimized through fine-tuning of each model parameter.
To verify the validity of the small-signal model completed through the above procedure, the S-parameters of small-signal models and the measured S-parameters are compared from 0.2 to 67 GHz with respect to several biases around the load line, which is important for power amplifier design.In addition, the stability factor (K) and MSG/MAG that can be calculated from the S-parameter results are also compared.The formulas can be expressed as follows [30]:

Figure 2 .
Figure 2. Enlarged source via structure of a GaN HEMT with its equivalent circuit.

Figure 3 .
Figure 3. (a) EM layout and (b) simulation result of the simplified one-port drain-source via structure.

Figure 2 .
Figure 2. Enlarged source via structure of a GaN HEMT with its equivalent circuit.

Figure 2 .
Figure 2. Enlarged source via structure of a GaN HEMT with its equivalent circuit.

Figure 3 .
Figure 3. (a) EM layout and (b) simulation result of the simplified one-port drain-source via structure.

Figure 3 .
Figure 3. (a) EM layout and (b) simulation result of the simplified one-port drain-source via structure.

Figure 4 .
Figure 4. Comparison of S11 (a) on the Smith chart and (b) on the phase between EM data and equivalent circuits.

Figure 4 .
Figure 4. Comparison of S11 (a) on the Smith chart and (b) on the phase between EM data and equivalent circuits.

Figure 4 .
Figure 4. Comparison of S11 (a) on the Smith chart and (b) on the phase between EM d equivalent circuits.

Figure 5 .
Figure 5. (a) Conventional and (b) proposed small-signal equivalent circuit of a GaN HEMT.

Figure 5 .
Figure 5. (a) Conventional and (b) proposed small-signal equivalent circuit of a GaN HEMT.

Figure 6 .
Figure 6.Schematic of GaN HEMT small-signal equivalent circuit in the cold bias region.Figure 6.Schematic of GaN HEMT small-signal equivalent circuit in the cold bias region.

Figure 6 .
Figure 6.Schematic of GaN HEMT small-signal equivalent circuit in the cold bias region.Figure 6.Schematic of GaN HEMT small-signal equivalent circuit in the cold bias region.

Figure 7 .
Figure 7. Top view of full EM simulation of a GaN HEMT using ADS momentum.Cds1, Cds2, and Lds composing the "modified Cds" are extracted through fitting or optimization by comparing S22 obtained through EM simulation with the modeled S-parameter of the drain-source part extracted previously.The fitted Cds2 does not yet contain an intrinsic part.Therefore, the intrinsic part can be added through the final comparison with the measured S-parameter, and the final small-signal model is completed through finetuning of each model parameter.Figure8is a block diagram showing the small-signal modeling procedure proposed in this work.

Figure 8 .
Figure 8. Block diagram of the proposed GaN small-signal modeling procedure.

Figure 7 . 14 Figure 7 .
Figure 7. Top view of full EM simulation of a GaN HEMT using ADS momentum.C ds1 , C ds2 , and L ds composing the "modified C ds " are extracted through fitting or optimization by comparing S22 obtained through EM simulation with the modeled S-parameter of the drain-source part extracted previously.The fitted C ds2 does not yet contain an intrinsic part.Therefore, the intrinsic part can be added through the final comparison with the measured S-parameter, and the final small-signal model is completed through fine-tuning of each model parameter.Figure 8 is a block diagram showing the small-signal modeling procedure proposed in this work.

Figure 8 .
Figure 8. Block diagram of the proposed GaN small-signal modeling procedure.

Figure 8 .
Figure 8. Block diagram of the proposed GaN small-signal modeling procedure.

Figure 9 .
Figure 9. Block diagram of a 67 GHz S-parameter measurement setup.

Figure 9 .
Figure 9. Block diagram of a 67 GHz S-parameter measurement setup.

Figure 10 .
Figure 10.Comparison of the S-parameter of the extracted "modified Cds" circuit with the EM simulated one through (a) Smith chart and (b) phase.

Figures 11 -Figure 10 .
show the comparison of S-parameters, MSG/MAG, and K under some biases according to the load line.

Figures 11 -
show the comparison of S-parameters, MSG/MAG, and K under some biases according to the load line.

Figure 10 .
Figure 10.Comparison of the S-parameter of the extracted "modified Cds" circuit with the EM simulated one through (a) Smith chart and (b) phase.

Figures 11 -
show the comparison of S-parameters, MSG/MAG, and K under some biases according to the load line.