Modelling of Dynamic Properties of Silicon Carbide Junction Field-E ﬀ ect Transistors (JFETs)

: The paper deals with the problem of modelling and analyzing the dynamic properties of a Junction Field E ﬀ ect Transistor (JFET) made of silicon carbide. An examination of the usefulness of the built-in JFET Simulation Program with Integrated Circuit Emphasis (SPICE) model was performed. A modiﬁed model of silicon carbide JFET was proposed to increase modelling accuracy. An evaluation of the accuracy of the modiﬁed model was performed by comparison of the measured and calculated capacitance–voltage characteristics as well as the switching characteristics of JFETs.


Introduction
Nowadays, the dynamic development of high-power electronic systems requires modern electronic components and devices that are characterized by improved electrical and thermal properties [1][2][3][4]. A new generation of junction field-effect transistors made of silicon carbide (SiC-JFETs) has appeared on the market as a result of technological progress in the construction of semiconductor devices [1,3,5]. SiC-JFETs are characterized by better static properties, i.e., higher values of absolute maximum ratings of operating currents, terminal voltages and dissipated power as well as dynamic properties related to short switching times [5][6][7].
The dynamic properties of a JFET depend on, among others, the values of diffusion and junction capacitances of the internal gate-source and gate-drain p-n junctions of the transistor [8][9][10]. Both capacitances are functions of the terminal voltage applied and play an important role in the forward and the reverse polarization of the device. On the other hand, the dynamic properties of JFETs are characterized by parasitic capacitances resulting from the non-zero size of the transistor structure [8][9][10][11].
In the design and analysis of power electronic devices and circuits, an appropriate computer tool containing reliable models of semiconductor devices is needed. One of the most popular computer programs used for the modeling and analysis of electronic devices and circuits is the Simulation Program with Integrated Circuit Emphasis (SPICE) [12]. SPICE contains a large number of passive and active device models. The accuracy of SPICE models for various semiconductor devices, such as MOSFET, BJT, SJT and IGBT transistors, has already been studied [13][14][15][16][17][18].
In the case of JFET characteristics modelling, a Shichman-Hodges (S-H) model is used [12]. Recently, a successful attempt at modeling the static characteristics and parameters of SiC-JFETs using the S-H model have been reported [19,20]. On the other hand, selected aspects of modelling dynamic characteristics of JFETs were presented in [8][9][10][21][22][23][24].
The paper deals with the problem of modelling capacitance-voltage (C-V) as well as switching characteristics of SiC-JFETs. Appropriate modifications of the Shichman-Hodges model were proposed in order to improving its accuracy. The modified model was experimentally verified by comparison of The main element of the presented model is the controlled source Idrain modeling static drain current of the transistor for three operational regions, according to the equations [12,19]: • in the cut-off region (for VGS−VTO(T) < 0): • in the linear region (for VDS ≤ VGS−VTO(T)): • in the saturation region (for 0 < VGS−VTO(T) < VDS): where: VGS-gate-source voltage, VDS-drain-source voltage, LAMBDA-channel-length modulation coefficient, BETA(T)-temperature dependence of transconductance coefficient, VTO(T)temperature dependence of the threshold voltage.
Resistors RG, RD and RS ( Figure 1) represent series resistances of the gate, the drain and the source of the transistor. Diodes D1 and D2 describe currents of the gate-source and the gate-drain p-n junctions, respectively. An extended description of the static S-H model is given for instance in [20] or is available in the SPICE user manual [12].
Capacitors Cgs and Cgd ( Figure 1) represent nonlinear junction capacitances of p-n junctions, according to equations [3,8]: • for Vgd ≤ FC·PB The main element of the presented model is the controlled source I drain modeling static drain current of the transistor for three operational regions, according to the equations [12,19]: • in the cut-off region (for V GS −V TO (T) < 0): • in the linear region (for V DS ≤ V GS −V TO (T)): • in the saturation region (for 0 < V GS −V TO (T) < V DS ): where: V GS -gate-source voltage, V DS -drain-source voltage, LAMBDA-channel-length modulation coefficient, BETA(T)-temperature dependence of transconductance coefficient, V TO (T)-temperature dependence of the threshold voltage.
Resistors R G , R D and R S (Figure 1) represent series resistances of the gate, the drain and the source of the transistor. Diodes D 1 and D 2 describe currents of the gate-source and the gate-drain p-n junctions, respectively. An extended description of the static S-H model is given for instance in [20] or is available in the SPICE user manual [12].

Results of Simulations of the Shichman-Hodges Model
A normally-OFF trench silicon carbide power Junction Field-Effect Transistor of absolute maximum drain-source voltage equal to 1700 V (SJEP170R550) fabricated by SemiSouth [25] was chosen for investigations. Measurements of capacitance characteristics were performed using the measuring source Keithley 2602. The JFET model parameters were calculated using an estimation method described in [26].

Results of Simulations of the Shichman-Hodges Model
A normally-OFF trench silicon carbide power Junction Field-Effect Transistor of absolute maximum drain-source voltage equal to 1700 V (SJEP170R550) fabricated by SemiSouth [25] was chosen for investigations. Measurements of capacitance characteristics were performed using the measuring source Keithley 2602. The JFET model parameters were calculated using an estimation method described in [26]. Values of static model parameters for the considered transistor are: BETA As seen, for small VGS and VGD bias voltages of around 1 V a good agreement between the simulation and measurement results can be observed. However, quantitative and qualitative discrepancies reaching even one order of magnitude are observed in the case of CGS(V) and CGD(V) characteristics (Figure 2a As seen, for small V GS and V GD bias voltages of around 1 V a good agreement between the simulation and measurement results can be observed. However, quantitative and qualitative discrepancies reaching even one order of magnitude are observed in the case of C GS (V) and C GD (V) characteristics (Figure 2a The manufacturers of the JFET transistors present in datasheets [25] the characteristics of capacitances C iss , C oss and C rss as a function of specified terminal voltages. These capacitances constitute an appropriate combination of transistor junction capacitances. Capacitances C iss , C oss and C rss are expressed with the following formulas [10]: C rss = C gd (10) where C gs -gate-source capacitance, C gd -gate-drain capacitance, and C ds -drain-source capacitance.
Calculations of C-V characteristics of the transistor can be realized using specialized SPICE simulation circuits [10]. The network forms of C iss and C rss measurement fixtures are presented in Figures 3 and 4, respectively.
Calculations of C-V characteristics of the transistor can be realized using specialized SPICE simulation circuits [10]. The network forms of Ciss and Crss measurement fixtures are presented in Figures 3 and 4, respectively.
Calculated and measured characteristics Ciss and Crss versus drain-source voltage are presented in Figure 5. Points and solid lines in Figure 5 denote the results of measurements and calculations, respectively. Figure 3. C iss measurement fixture.
Calculations of C-V characteristics of the transistor can be realized using specialized SPICE simulation circuits [10]. The network forms of Ciss and Crss measurement fixtures are presented in Figures 3 and 4, respectively.
Calculated and measured characteristics Ciss and Crss versus drain-source voltage are presented in Figure 5. Points and solid lines in Figure 5 denote the results of measurements and calculations, respectively.
where: i g , i d , V gs , V gd , V ds -amplitude of alternating currents and voltages marked in Figures 3 and 4. Calculated and measured characteristics C iss and C rss versus drain-source voltage are presented in Figure 5. Points and solid lines in Figure 5 denote the results of measurements and calculations, respectively. As seen from Figure 5, there are discrepancies between the measurements and the calculations. For example, the calculated values of capacitance Ciss for the drain-source voltage up to 500 V are smaller than the values obtained from measurement by about 40%. In the range of relatively small values of drain-source voltage VDS, capacitance values decrease rapidly with the increase of the voltage VDS. However, in the range of drain-source voltage above 100 V capacitance changes are barely noticeable.
Qualitative discrepancies between the measurements and S-H model simulations observed in Figures 2 and 5 are a sufficient reason to introduce appropriate model modifications.

Modifications of the Shichman-Hodges Model
The original Shichman-Hodges model assumes [12] that the gate-source and the gate-drain junctions appearing in the transistor structure are identical in terms of physical properties and electrical parameters. Therefore, the model parameters such as M, PB and FC are used to describe properties of the junctions in common (see Equations (4)- (7)). This means that an attempt to determine the values of these parameters in order to achieve a good agreement between simulation and measurement results of the gate-drain junction automatically changes the shape of calculated gate-source junction characteristics.
On the other hand, the structure of a real JFET contains p-n junctions of different electrical properties [21], so a separate set of M, PB and FC parameters has to be used. In the proposed model, independent descriptions of each junction were introduced to increase the modelling accuracy, according to equations: • for VGS ≤ FC1·PBCGS • for Vgd > FC2·PBCGD As seen from Figure 5, there are discrepancies between the measurements and the calculations. For example, the calculated values of capacitance C iss for the drain-source voltage up to 500 V are smaller than the values obtained from measurement by about 40%. In the range of relatively small values of drain-source voltage V DS , capacitance values decrease rapidly with the increase of the voltage V DS . However, in the range of drain-source voltage above 100 V capacitance changes are barely noticeable.
Qualitative discrepancies between the measurements and S-H model simulations observed in Figures 2 and 5 are a sufficient reason to introduce appropriate model modifications.

Modifications of the Shichman-Hodges Model
The original Shichman-Hodges model assumes [12] that the gate-source and the gate-drain junctions appearing in the transistor structure are identical in terms of physical properties and electrical parameters. Therefore, the model parameters such as M, PB and FC are used to describe properties of the junctions in common (see Equations (4)- (7)). This means that an attempt to determine the values of these parameters in order to achieve a good agreement between simulation and measurement results of the gate-drain junction automatically changes the shape of calculated gate-source junction characteristics.
On the other hand, the structure of a real JFET contains p-n junctions of different electrical properties [21], so a separate set of M, PB and FC parameters has to be used. In the proposed model, independent descriptions of each junction were introduced to increase the modelling accuracy, according to equations: for Vgd > FC2·PBCGD (17) where: FC1, PBCGS, MGS, FC2, PBCGD, MGD represent a new set of model parameters.
Energies 2020, 13, 187 6 of 9 The modified model was implemented to SPICE as a subcircuit with the use of the ABM (Analog Behavioral Modeling) option (using controlled sources). The network form of the proposed model is presented in Figure 6. Controlled-current sources G CGD and G CGS represent currents flowing through C GD and C GS capacitances. An additional parameter estimation procedure was carried out. New values of the model parameters describing the gate-source and the gate-drain junction are as follows: where: FC1, PBCGS, MGS, FC2, PBCGD, MGD represent a new set of model parameters.
The modified model was implemented to SPICE as a subcircuit with the use of the ABM (Analog Behavioral Modeling) option (using controlled sources). The network form of the proposed model is presented in Figure 6. Controlled-current sources GCGD and GCGS represent currents flowing through CGD and CGS capacitances. An additional parameter estimation procedure was carried out. New values of the model parameters describing the gate-source and the gate-drain junction are as follows:  As seen, the results of modeling using the modified model provide much greater modelling accuracy than the original S-H model.

Simulation Results of Dynamic Characteristics of JFET
Measurements and calculations of the dynamic characteristics of the transistor were carried out in order to check the suitability of the modified JFET model. For this purpose, the simplest measurement system was chosen-a switching circuit presented in Figure 9. As seen, the results of modeling using the modified model provide much greater modelling accuracy than the original S-H model.

Simulation Results of Dynamic Characteristics of JFET
Measurements and calculations of the dynamic characteristics of the transistor were carried out in order to check the suitability of the modified JFET model. For this purpose, the simplest measurement system was chosen-a switching circuit presented in Figure 9. In the switching circuit, the source VDS is responsible for determining the operating point of the transistor, whereas the source eG(t) with an amplitude equal to 2.5 V and frequency of 10 kHz forces stimulation on the transistor gate.
Measurement and calculation results of VGS(t) and VDS(t) waveforms of the JFET are presented in Figure 10. Points and solid lines in Figure 10 denote the results of measurements and calculations, respectively. A good agreement between the results of measurements and calculations of waveforms VGS(t) and VDS(t) is observed, which confirms the correctness of the modified model. The turn-on (tON) and turn-off (tOFF) delay times of the transistor are equal to about 0.3 and 0.8 µs, respectively.

Conclusions
In this paper, the usefulness of the Shichman-Hodges model of the JFET built-in in SPICE is examined. The SJEP170R550 transistor offered by SemiSouth Inc. is considered in detail. Owing to the observed discrepancies between the device's simulated and measured characteristics some In the switching circuit, the source V DS is responsible for determining the operating point of the transistor, whereas the source e G (t) with an amplitude equal to 2.5 V and frequency of 10 kHz forces stimulation on the transistor gate.
Measurement and calculation results of V GS (t) and V DS (t) waveforms of the JFET are presented in Figure 10. Points and solid lines in Figure 10 denote the results of measurements and calculations, respectively. As seen, the results of modeling using the modified model provide much greater modelling accuracy than the original S-H model.

Simulation Results of Dynamic Characteristics of JFET
Measurements and calculations of the dynamic characteristics of the transistor were carried out in order to check the suitability of the modified JFET model. For this purpose, the simplest measurement system was chosen-a switching circuit presented in Figure 9. In the switching circuit, the source VDS is responsible for determining the operating point of the transistor, whereas the source eG(t) with an amplitude equal to 2.5 V and frequency of 10 kHz forces stimulation on the transistor gate.
Measurement and calculation results of VGS(t) and VDS(t) waveforms of the JFET are presented in Figure 10. Points and solid lines in Figure 10 denote the results of measurements and calculations, respectively. A good agreement between the results of measurements and calculations of waveforms VGS(t) and VDS(t) is observed, which confirms the correctness of the modified model. The turn-on (tON) and turn-off (tOFF) delay times of the transistor are equal to about 0.3 and 0.8 µs, respectively.

Conclusions
In this paper, the usefulness of the Shichman-Hodges model of the JFET built-in in SPICE is examined. The SJEP170R550 transistor offered by SemiSouth Inc. is considered in detail. Owing to the observed discrepancies between the device's simulated and measured characteristics some A good agreement between the results of measurements and calculations of waveforms V GS (t) and V DS (t) is observed, which confirms the correctness of the modified model. The turn-on (t ON ) and turn-off (t OFF ) delay times of the transistor are equal to about 0.3 and 0.8 µs, respectively.

Conclusions
In this paper, the usefulness of the Shichman-Hodges model of the JFET built-in in SPICE is examined. The SJEP170R550 transistor offered by SemiSouth Inc. is considered in detail. Owing to the observed discrepancies between the device's simulated and measured characteristics some modifications of the model to improve its accuracy are proposed. The modifications concern a change