Circuit simulation device and output characteristic model formula generation method for MOS system transistor

Abstract

To provide a circuit simulation device comprising an output characteristic model formula of a MOS system transistor defining a main terminal voltage, a control terminal voltage and a temperature as independent parameters.SOLUTION: A circuit simulation device simulates operation of a circuit 34 including a MOS system transistor 15. A first main terminal, a second main terminal and a control terminal of the MOS system transistor 15 are defined as x, y and z. An output characteristic model formula 10 which outputs a main terminal current Iy when inputted with a main terminal voltage Vyx, a control terminal voltage Vzx and a temperature T, is expressed as a form of a predetermined formula f including a first main coefficient C0, a second main coefficient C1 and a third main coefficient C2. The first main coefficient C0 and the second main coefficient C1 define the control terminal voltage Vzx and the temperature T as parameters and the third main coefficient C2 defines the control terminal voltage Vzx as a parameter. The predetermined formula f defining α as a parameter and defining ε as an adjustment constant has a form of C0 / (1+(C1 / (ε+α)^C2)).SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present disclosure relates to a circuit simulation device and a method for generating an output characteristic model formula of a MOS (Metal-Oxide-Semiconductor) transistor.

Background Art

[0002] In power electronics, a circuit simulation device (circuit simulator) is frequently used in the design of power conversion circuits. As a model of a MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor), which is one of the MOS transistors used in circuit simulation devices, the SPICE (Simulation Program with Integrated Circuit Emphasis) model is widely used, and the output characteristics of the current output by the MOSFET are expressed by mathematical formulas. The output characteristics of the current output by the MOSFET, also called output current characteristics, are specifically the drain terminal current Id - drain terminal voltage Vds characteristics (Id - Vds characteristics or Id - Vds output characteristics) including gate terminal voltage Vgs dependency.

[0003] As parameters used in the mathematical formula of the SPICE model, structural parameters such as the thickness of the gate oxide film of the MOSFET device targeted by the model and the impurity concentration of the substrate, and physical parameters such as the electron mobility in the channel are used. Such a model is called a physical model, but it tends to become complicated because it includes many parameters (see, for example, FIG. 17 of Patent Document 1).

[0004] As another one of the SPICE models, a mathematical formula that does not include structural parameters and physical parameters has been proposed (see, for example, Table 1 of Non-Patent Document 1). Such a mathematical formula model that does not include structural parameters and physical parameters is called a behavioral model. The model formula of the Id-Vds characteristics shown in Table 1 of Non-Patent Document 1 is described using several fitting parameters with the drain terminal voltage Vds and the gate terminal voltage Vgs as independent variables. Usually, in a behavioral model, these fitting parameters do not have a physical meaning, but there is an advantage that it can be described with a relatively small number of parameters. However, regarding the Id-Vds characteristics in the behavioral model of Non-Patent Document 1, the drain terminal current Id is described as a function having only the drain terminal voltage Vds and the gate terminal voltage Vgs as independent variables, and temperature is not included as an independent variable.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

Non-Patent Documents

[0006]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0007] The parameters used in the model formula of the Id-Vds characteristics, which are the output current characteristics shown in Patent Document 1, are generally extracted from the characteristics obtained by evaluating actual devices and the data sheets provided by device manufacturers. For example, in Patent Document 1, intermediate data is generated from the evaluation characteristics of MOSFETs of different sizes, and the parameters are extracted by combining the intermediate data and the device structure data. However, information about device structure data is difficult for users of general circuit simulation devices to know.

[0008] Many users who use circuit simulation devices cannot know the device structure such as MOSFETs, and it is difficult to appropriately set the parameters used in the physical model formula. On the other hand, when using a behavioral model formula, information about the device structure is not required, and because there are few parameters, fitting from actual measurements is relatively easy. However, in the mathematical model regarding the Id-Vds characteristics of Non-Patent Document 1, since temperature is not included as an independent variable, simulation other than the extracted temperature becomes difficult. In power conversion circuits in power electronics, simulations in various temperature situations are required, and simulations cannot be sufficiently carried out with only limited temperature settings.

[0009] MOS transistors include IGBT (Insulated Gate Bipolar Transistor) in addition to MOSFETs. Here, let the first main terminal, the second main terminal, and the control terminal of the MOS transistor be x, y, and z respectively, let the main terminal voltage, which is the voltage of the second main terminal with respect to the first main terminal, be Vyx, let the control terminal voltage, which is the voltage of the control terminal with respect to the first main terminal, be Vzx, and let the main terminal current, which is the current flowing from the second main terminal to the first main terminal, be Iy.

[0010] An object of the present disclosure is to obtain a circuit simulation device including an output characteristic model formula, which is a model formula of the output characteristics of the current output by a MOS transistor having temperature T as an independent variable together with the main terminal voltage Vyx and the control terminal voltage Vzx.

Means for Solving the Problem

[0011] The circuit simulation device according to the present disclosure simulates the operation of a circuit including MOS transistors by the calculation of a processing unit. The circuit simulation device has an output characteristic model formula of a MOS transistor that outputs a main terminal current with a main terminal voltage, a control terminal voltage, and a temperature as inputs. Let the first main terminal, the second main terminal, and the control terminal of the MOS transistor be x, y, and z, respectively, let the main terminal voltage, which is the voltage of the second main terminal with respect to the first main terminal, be Vyx, let the control terminal voltage, which is the voltage of the control terminal with respect to the first main terminal, be Vzx, let the main terminal current, which is the current flowing from the second main terminal to the first main terminal, be Iy, and let the temperature of the MOS transistor be T. The output characteristic model formula of the MOS transistor is represented by Formula AA1.

Equation

Advantages of the Invention

[0012] Since the circuit simulation device of the present disclosure has an output characteristic model formula of a MOS transistor in which the main terminal current Iy is represented by Formula AA1, it can have an output characteristic model formula that is a model formula of the output characteristic of the main terminal current Iy output by a MOS transistor having the temperature T as an independent variable together with the main terminal voltage Vyx and the control terminal voltage Vzx.

Brief Description of the Drawings

[0013]

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Mode for Carrying Out the Invention

[0014] Embodiment 1. FIG. 1 is a diagram showing an output characteristic model formula of a MOS transistor according to Embodiment 1 and a method for generating an output characteristic model formula of a MOS transistor, and FIG. 2 is a diagram showing a configuration of a circuit simulation apparatus according to Embodiment 1. FIG. 3 is a diagram showing a first example of a MOS transistor according to Embodiment 1, and FIG. 4 is a diagram showing a second example of a MOS transistor according to Embodiment 1. FIG. 5 is a diagram showing a circuit example including a MOS transistor according to Embodiment 1. FIG. 6 is a diagram showing a hardware configuration example for realizing the functions of the circuit simulation apparatus of FIG. 2 by digital operations. FIG. 7 is a diagram schematically showing a transition state when the switching element of FIG. 5 is turned on, and FIG. 8 is a diagram schematically showing a transition state when the switching element of FIG. 5 is turned off. FIG. 9 is a diagram showing a transition process in an output characteristic diagram when the switching element of FIG. 5 is turned on, and FIG. 10 is a diagram showing a transition process in an output characteristic diagram when the switching element of FIG. 5 is turned off. FIGS. 11 to 15 are diagrams showing output characteristic data of a MOSFET at different temperatures, respectively. FIGS. 16 to 18 are diagrams showing first to third examples of output characteristics of a MOSFET according to the first model formula of FIG. 1, respectively. FIG. 19 is a diagram for explaining the control terminal voltage dependency in the output characteristics of a MOSFET. FIGS. 20 to 22 are diagrams showing data of a first main coefficient C0, a second main coefficient C1, and a third main coefficient C2 with respect to a control terminal voltage extracted from the first temperature output characteristic data of FIG. 11, respectively. FIGS. 23 to 25 are diagrams showing data of a first main coefficient C0, a second main coefficient C1, and a third main coefficient C2 with respect to a control terminal voltage extracted from the second temperature output characteristic data of FIG. 12, respectively. FIGS. 26 to 28 are diagrams showing data of a first main coefficient C0, a second main coefficient C1, and a third main coefficient C2 with respect to a control terminal voltage extracted from the third temperature output characteristic data of FIG. 13, respectively. FIGS. 29 to 31 are diagrams showing data of a first main coefficient C0, a second main coefficient C1, and a third main coefficient C2 with respect to a control terminal voltage extracted from the fourth temperature output characteristic data of FIG. 14, respectively. FIGS. 32 to 34 are diagrams showing data of a first main coefficient C0, a second main coefficient C1, and a third main coefficient C2 with respect to a control terminal voltage extracted from the fifth temperature output characteristic data of FIG. 15, respectively.Figs. 35 to 38 are diagrams showing data of a first sub - coefficient C00, data of a second sub - coefficient C01, data of a third sub - coefficient C02, and data of a fourth sub - coefficient C03 of a second model formula with respect to temperature T extracted from the data of the first main coefficient C0 of Figs. 20, 23, 26, 29, and 32, respectively. Figs. 39 to 42 are diagrams showing data of a first sub - coefficient C10, data of a second sub - coefficient C11, data of a third sub - coefficient C12, and data of a fourth sub - coefficient C13 of a second model formula with respect to temperature T extracted from the data of the second main coefficient C1 of Figs. 21, 24, 27, 30, and 33, respectively. Fig. 43 is a diagram showing output characteristics according to the output characteristic model formula of Fig. 1 in which the main coefficient and the sub - coefficients are determined.

[0015] Before explaining the output characteristic model formula of the MOS - type transistor of Embodiment 1, the characteristics of the main terminal current Iy with respect to the main terminal voltage Vyx, which are the output characteristics of the MOS - type transistor 15, will be described. The first example of the MOS - type transistor 15 is a MOSFET, and the second example of the MOS - type transistor 15 is an IGBT. Here, mainly taking the example of the MOSFET, the output characteristic model formula 12 of the MOS - type transistor 15, the generation method for generating the output characteristic model formula 12 of the MOS - type transistor 15, and the circuit simulation device 30 will be described, but the same explanation also holds for the IGBT.

[0016] The MOSFET, which is the first example of the MOS transistor 15 shown in FIG. 3, includes a gate terminal g, a drain terminal d, and a source terminal s, and is a transistor Tr having three terminals. Normally, the switching operation is performed by controlling the voltage between the gate terminal g and the source terminal s, that is, the gate terminal voltage Vgs of the gate terminal g with respect to the source terminal s. When the MOSFET is used in the power conversion circuit 20, the drain terminal d has a high voltage with respect to the source terminal s. The voltage between the drain terminal d and the source terminal s, that is, the voltage of the drain terminal d with respect to the source terminal s, that is, the drain terminal voltage, is indicated by the symbol Vds. When the drain terminal voltage Vds is positive and the MOSFET is turned on by controlling the gate terminal voltage Vgs, the current flows from the drain terminal d to the source terminal s. The drain terminal current, which is the current flowing from the drain terminal d to the source terminal s, is indicated by the symbol Id.

[0017] The switching elements 21a and 21b when the MOSFET is used in the power conversion circuit 20 include a transistor Tr and a diode Di. The diode Di may be a parasitic diode of the MOSFET or a diode of another element. The switching elements 21a and 21b when used in the power conversion circuit 20 may be composed of an IGBT, which is a transistor Tr, and a diode Di connected in anti-parallel to the IGBT. FIG. 4 shows the switching element when the IGBT is used in the power conversion circuit 20. The IGBT (transistor Tr) shown in FIG. 4 is the second example of the MOS transistor 15.

[0018] The IGBT, which is a second example of the MOS transistor 15 shown in FIG. 4, includes a gate terminal g, a collector terminal c, and an emitter terminal e, and is a transistor Tr having three terminals. Normally, a switching operation is performed by controlling the voltage between the gate terminal g and the emitter terminal e, that is, the voltage of the gate terminal g with respect to the emitter terminal e, namely the gate terminal voltage Vge. When the IGBT is used in the power conversion circuit 20, the collector terminal c becomes a high voltage with respect to the emitter terminal e. The voltage between the collector terminal c and the emitter terminal e, that is, the voltage of the collector terminal c with respect to the emitter terminal e, namely the collector terminal voltage, is denoted by the symbol Vce. When the collector terminal voltage Vce is positive and the gate terminal voltage Vge is controlled to turn on the IGBT, the current flows from the collector terminal c to the emitter terminal e. The collector terminal current, which is the current flowing from the collector terminal c to the emitter terminal e, is denoted by the symbol Ic.

[0019] FIG. 5 is an example of a circuit in which MOSFETs are used as switching elements 21a and 21b of the power conversion circuit 20. The power conversion circuit 20 shown in FIG. 5 is a half-bridge circuit composed of switching elements 21a and 21b of the upper and lower arms, and drive circuits 22a and 22b for driving the MOSFETs connected to the gate terminals g and source terminals s of the switching elements 21a and 21b. The power conversion circuit 20 shown in FIG. 5 includes an input terminal 28p and 28n to which DC power from a DC power supply 26 is input, and an output terminal 29 that outputs power from the half-bridge circuit. The drain terminal d of the switching element 21a, which is the upper arm, is connected to the positive input terminal 28p to which the positive electrode of the DC power supply 26 is connected via the positive wiring 23. The source terminal s of the switching element 21b, which is the lower arm, is connected to the negative input terminal 28n to which the negative electrode of the DC power supply 26 is connected via the negative wiring 24. The source terminal s of the switching element 21a and the drain terminal d of the switching element 21b are connected to the output terminal 29, and a smoothing capacitor 27 is connected between the positive wiring 23 and the negative wiring 24. For example, an inductive load 25 is connected to the output terminal 29. In the power conversion circuit 20, the power supply voltage Vpn is input from the DC power supply 26 via the input terminals 28p and 28n, and the load current IL is output from the output terminal 29 to the inductive load 25. In FIG. 5, the direction in which the load current IL flows is indicated by the signs + and -. +IL is the load current flowing from the output terminal 29 to the inductive load 25 side, and -IL is the load current flowing from the inductive load 25 to the output terminal 29 side. For convenience, +IL is referred to as the positive load current and -IL as the negative load current.

[0020] In order to control the current flowing through the inductive load 25 connected to the power conversion circuit 20 in FIG. 5, MOS transistors 15 such as MOSFETs and IGBTs are used as the switching elements 21a and 21b. For example, when flowing a load current IL from the power conversion circuit 20 toward the inductive load 25, that is, when flowing a positive load current IL, by turning on the switching element 21a of the upper arm by the drive circuit 22a, the current supplied from the smoothing capacitor 27 can flow through the switching element 21a of the upper arm to the inductive load 25. When the switching element 21a of the upper arm is in the on state, the switching element 21b of the lower arm is in the off state under the control of the drive circuit 22b, and the power supply voltage Vpn of the DC power supply 26 is held without short-circuiting the positive-side wiring 23 and the negative-side wiring 24.

[0021] On the other hand, when flowing a load current IL from the inductive load 25 toward the power conversion circuit 20, that is, when flowing a negative load current IL, by turning on the switching element 21b of the lower arm by the drive circuit 22b, the current supplied from the inductive load 25 can flow through the switching element 21b of the lower arm to the smoothing capacitor 27. When the switching element 21b of the lower arm is in the on state, the switching element 21a of the upper arm is in the off state under the control of the drive circuit 22a, and the power supply voltage Vpn of the DC power supply 26 is held without short-circuiting the positive-side wiring 23 and the negative-side wiring 24.

[0022] In this way, MOS transistors 15 such as MOSFETs and IGBTs are used as the switching elements 21a and 21b to control the load current IL, and their switching operation is an important performance-determining factor of the power conversion circuit 20. In order to explain the importance of the switching operation of the switching elements 21a and 21b in the design of the power conversion circuit 20, the switching waveform of the switching element 21a in the power conversion circuit 20 of FIG. 5 will be explained using its schematic diagram. The operation of the switching element 21b is the same as that of the switching element 21a, so the explanation is omitted.

[0023] FIG. 7 is a switching waveform schematically showing a transient transition state when the switching element 21a is turned on. The upper waveform is the voltage characteristic 41a of the gate terminal voltage waveform, that is, the gate terminal voltage Vgs applied to the gate terminal g. The middle waveform is the voltage characteristic 42a of the drain terminal voltage waveform, that is, the drain terminal voltage Vds applied to the drain terminal d. The lower waveform is the current characteristic 43a of the drain terminal current waveform, that is, the drain terminal current Id flowing from the drain terminal d to the source terminal s. The vertical axis of the voltage characteristic 41a is the gate terminal voltage Vgs, the vertical axis of the voltage characteristic 42a is the drain terminal voltage Vds, and the vertical axis of the current characteristic 43a is the drain terminal current Id. The horizontal axis of the voltage characteristic 41a, the voltage characteristic 42a, and the current characteristic 43a is time.

[0024] In the voltage characteristic 41a, Vth is the threshold voltage, Vm is the mirror voltage, Vg0 is the off-applied voltage applied from the drive circuit 22a, and Vga is the on-applied voltage applied from the drive circuit 22a. In the voltage characteristic 42a, Vq is the on-voltage when Vgs becomes Vm in the linear region of the switching element 21a, and Von is the on-voltage when Vgs is Vga in the linear region of the switching element 21a. Vpn is the DC output voltage of the DC power supply 26, that is, the power supply voltage. In the current characteristic 43a, IL is a constant current flowing through the inductive load 25.

[0025] The start of the transitional transition begins with the operation of supplying charge to the gate terminal g of the switching element 21a by the drive circuit 22a. The time t0 in FIG. 7 indicates the start time of the drive operation of the switching element 21a. From time t0, the gate terminal voltage Vgs rises, and when it reaches the threshold voltage Vth of the MOSFET at time t1, the channel of the MOSFET becomes conductive and the drain terminal current Id starts to flow. During the transition period from time t1 to time t2, the drain terminal current Id and the drain terminal voltage Vds are simultaneously applied to the switching element 21a. When the drain terminal current Id reaches the load current IL at time t2, the drain terminal voltage Vds begins to decrease. The drain terminal voltage Vds decreases until time t3. The transition period from time t2 to time t3 is usually called the mirror period, and the variation of the gate terminal voltage Vgs during this period is relatively small, and its representative value is called the mirror voltage. In FIG. 7, the mirror voltage is denoted as Vm. Also during the period from time t2 to time t3, which is the mirror period, the drain terminal current Id and the drain terminal voltage Vds are simultaneously applied to the switching element 21a. During the transition period from time t3 to time t4, the gate terminal voltage Vgs rises toward the on-applied voltage Vga output from the drive circuit 22a. When the gate terminal voltage Vgs becomes the on-applied voltage Vga, the drain terminal voltage Vds drops from the on voltage Vq to the on voltage Von. Usually, there is no large voltage difference between the on voltage Vq and the on voltage Von.

[0026] During the transition period from time t1 to time t4 shown in FIG. 7, since the drain terminal current Id and the drain terminal voltage Vds are simultaneously applied to the switching element 21a, electrical energy loss occurs in the switching element 21a. The MOSFET generates not only transient heat loss when it turns on but also heat loss during the transient transition period when it turns off. Next, the transient transition state when the switching element 21a turns off will be described.

[0027] FIG. 8 is a switching waveform schematically showing a transient transition state when the switching element 21a turns off. The upper waveform is the gate terminal voltage waveform, that is, the voltage characteristic 41b of the gate terminal voltage Vgs applied to the gate terminal g. The middle waveform is the drain terminal voltage waveform, that is, the voltage characteristic 42b of the drain terminal voltage Vds applied to the drain terminal d. The lower waveform is the drain terminal current waveform, that is, the current characteristic 43b of the drain terminal current Id flowing from the drain terminal d to the source terminal s. The vertical axis of the voltage characteristic 41b is the gate terminal voltage Vgs, the vertical axis of the voltage characteristic 42b is the drain terminal voltage Vds, and the vertical axis of the current characteristic 43b is the drain terminal current Id. The horizontal axes of the voltage characteristic 41b, the voltage characteristic 42b, and the current characteristic 43b are time.

[0028] The start of the transitional off-transition begins with the extraction operation of the charge, i.e., the gate charge, accumulated at the gate terminal g of the switching element 21a by the drive circuit 22a. The time t5 in FIG. 8 indicates the start time of the extraction operation of the gate charge in the switching element 21a. From time t5, the gate terminal voltage Vgs drops, and at time t6, the mirror period starts and continues until time t7. During the mirror period from time t6 to time t7, since the drain terminal current Id and the drain terminal voltage Vds are simultaneously applied to the switching element 21a, electrical energy loss occurs in the switching element 21a. When the drain terminal voltage Vds reaches the power supply voltage Vpn at time t7, the drain terminal current Id begins to decrease. When the gate terminal voltage Vgs reaches the threshold voltage Vth at time t8, the drain terminal current Id becomes zero. During the transition period from time t6 to time t8, since the drain terminal current Id and the drain terminal voltage Vds are simultaneously applied to the switching element 21a, electrical energy loss occurs in the switching element 21a. During the period from time t8 to time t9, the drain terminal current Id and the drain terminal voltage Vds do not change, and the gate terminal voltage Vgs decreases toward the off-applied voltage Vg0 output from the drive circuit 22a. Therefore, during the transition period from time t5 to time t8 shown in FIG. 8, since the drain terminal current Id and the drain terminal voltage Vds are simultaneously applied to the switching element 21a, electrical energy loss occurs in the switching element 21a.

[0029] The electrical energy loss becomes thermal energy and heats the switching elements 21a, 21b themselves and the surrounding members. Therefore, it is important to accurately estimate this switching loss in the design of the power conversion circuit 20. For this purpose, it is necessary to accurately estimate the switching waveform indicating the transitional state when the switching elements 21a, 21b turn on or off. One of the important purposes of circuit simulation is to accurately estimate the switching waveforms of the switching elements 21a, 21b in the target circuit 34 such as the power conversion circuit 20.

[0030] Next, the relationship between the switching waveform and the output characteristics of a MOSFET, which is an example of a switching element, will be described with reference to FIGS. 9 and 10. FIGS. 9 and 10 depict the transition processes corresponding to the times of FIGS. 7 and 8, respectively. In FIGS. 9 and 10, the horizontal axis represents the drain terminal voltage Vds, and the vertical axis represents the drain terminal current Id. In the linear region shown in FIG. 9, the drain terminal current Id increases as the drain terminal voltage Vds increases. Particularly in the region where the drain terminal voltage Vds is small, the drain terminal current Id increases almost proportionally as the drain terminal voltage Vds increases. In the saturation region, the drain terminal current Id does not change significantly even when the drain terminal voltage Vds increases, showing a saturated characteristic.

[0031] First, the transient transition process when the MOSFET turns on, that is, the on-transition process, will be described with reference to FIG. 9. Five current characteristics are shown in FIG. 9. The current characteristics change from the bottom to the top as the gate terminal voltage Vgs increases. The topmost current characteristic 44a is the current characteristic when the gate terminal voltage Vgs is the on-applied voltage Vga. The third current characteristic 44b from the top is the current characteristic when the gate terminal voltage Vgs is the mirror voltage Vm. The points P1, P2, P3, and P4 shown in FIG. 9 are the transition points corresponding to the times t0, t1, t2, t3, and t4 shown in FIG. 7, respectively. At times t0 and t1 in FIG. 7, the gate terminal voltage Vgs is lower than the threshold voltage Vth and no drain terminal current Id flows, so at any time, it is at the point P1 shown in FIG. 9. That is, the point indicating the state at time t0 when the transient transition starts and the point indicating the state at time t1 overlap. During the period from time t0 to time t1, the gate terminal voltage Vgs transitions from the off-applied voltage Vg0 to the threshold voltage Vth, but the drain terminal voltage Vds remains constant at the power supply voltage Vpn, and the drain terminal current Id remains constant at zero.

[0032] When the gate terminal voltage Vgs reaches the threshold voltage Vth at time t1, the drain terminal current Id starts to flow, and the transition point changes in the direction of arrow 45a and reaches point P2 at time t2. That is, the drain terminal current Id increases from point P1 to point P2. During the transition period from time t1 to time t2, the drain terminal voltage Vds is constant, but the gate terminal voltage Vgs increases from the threshold voltage Vth to the mirror voltage Vm. The transition period from time t2 to time t3 is the mirror period, where the mirror voltage Vm and the drain terminal current Id are constant, but the drain terminal voltage Vds decreases significantly from the power supply voltage Vpn to the on-voltage Vq. That is, the point P2 corresponding to time t2 changes in the direction of arrow 45b and reaches point P3 corresponding to time t3. For example, in a power converter operating with a power supply voltage Vpn of 600V, since the on-voltage Vq is about 1V, the fluctuation range of the drain terminal voltage Vds is on the order of the power supply voltage, about 600V. The transition period from time t3 to time t4 is a transition from the saturation region to the linear region, and the fluctuation of the drain terminal voltage Vds during this transition period is not large, usually on the order of several volts to several tens of volts. During this transition period, the drain terminal current Id is constant, but the gate terminal voltage Vgs fluctuates from the mirror voltage Vm to the on-applied voltage Vga. That is, the point P3 corresponding to time t3 changes in the direction of arrow 45c and reaches point P4 corresponding to time t4. From the point P2 corresponding to time t2 to the point P4 corresponding to time t4, the drain terminal current Id is the load current IL.

[0033] When the MOSFET shown in Fig. 7 turns on, the transient transition follows the path from point P1 to point P4 shown in the output characteristics of the MOSFET in Fig. 9. Therefore, the switching characteristics of the MOSFET when it turns on strongly depend on the output characteristics of the MOSFET. Accordingly, the switching characteristics of MOS transistor 15 when MOS transistor 15 turns on strongly depend on the output characteristics of MOS transistor 15. In particular, the transition period during which the drain terminal current Id and the drain terminal voltage Vds are simultaneously applied to the switching element 21a of the MOSFET, that is, the transition period from time t1 to time t3, greatly affects the switching loss of the switching element 21a. The transition period from time t1 to time t3 is included in the saturation region, and it can be seen that high-precision modeling of the saturation region is important in loss estimation of the output characteristics of the MOSFET.

[0034] Next, the transient transition process when the MOSFET turns off, that is, the turn-off transition process, will be described with reference to Fig. 10. The transient transition process when the MOSFET turns off retraces the transient transition process when it turns on shown in Fig. 9 in reverse. The five current characteristics shown in Fig. 10 are the same as the five current characteristics shown in Fig. 9. Points P5, P6, P7, and P8 shown in Fig. 10 are the transition points corresponding to time t5, time t6, time t7, time t8, and time t9 shown in Fig. 8, respectively. The turn-off transition process starts from point P5. At time t5, which is the start time of the turn-off transition process, the drain terminal current Id is in a current conduction state equal to the load current IL, and the gate terminal voltage Vgs is equal to the on-applied voltage Vga of the drive circuit 22a. The transition period from time t5 to time t6 is a transition from the linear region to the saturation region. The variation of the drain terminal voltage Vds during this transition period is not large, and the drain terminal current Id is constant during this transition period. During this transition period, the gate terminal voltage Vgs varies from the on-applied voltage Vga to the mirror voltage Vm. That is, point P5 corresponding to time t5 changes in the direction of arrow 46a and reaches point P6 corresponding to time t6.

[0035] The transition period from time t6 to time t7 is the mirror period, during which the gate terminal voltage Vgs and the drain terminal current Id are constant at the mirror voltage Vm and the load current IL, respectively, but the drain terminal voltage Vds increases significantly from the on-voltage Vq to the power supply voltage Vpn. That is, the point P6 corresponding to time t6 changes in the direction of arrow 46b and reaches the point P7 corresponding to time t7. During the transition period from time t7 to time t8, the drain terminal voltage Vds becomes the power supply voltage Vpn and is constant, but the gate terminal voltage Vgs decreases from the mirror voltage Vm to the threshold voltage Vth, and the drain terminal current Id becomes zero at time t8. That is, the point P7 corresponding to time t7 changes in the direction of arrow 46c and reaches the point P8 corresponding to time t8. During the transition period from time t8 to time t9, neither the drain terminal current Id nor the drain terminal voltage Vds changes, and only the gate terminal voltage Vgs changes from the threshold voltage Vth to the off-applied voltage Vg0. Therefore, the transition point coincides with the point P8 corresponding to time t8 and the point P8 corresponding to time t9.

[0036] When the MOSFET shown in FIG. 8 turns off, the transient transition occurs along the points P5 to P8 shown in the output characteristics of the MOSFET in FIG. 10. Therefore, the switching characteristics of the MOSFET during turn-off depend on the output characteristics of the MOSFET. Therefore, the switching characteristics of the MOS transistor 15 when the MOS transistor 15 turns off greatly depend on the output characteristics of the MOS transistor 15. In particular, the transition period during which the drain terminal current Id and the drain terminal voltage Vds are simultaneously applied to the switching element 21a of the MOSFET, that is, the transition period from time t6 to time t8, greatly affects the switching loss of the switching element 21a. The transition period from time t6 to time t8 is included in the saturation region, and it can be seen that high-precision modeling of the saturation region is important in loss estimation.

[0037] So far, the importance of the output current characteristics of MOSFETs, that is, the Id-Vds characteristics of MOSFETs, has been explained. The Ic-Vce characteristics, which are the output current characteristics of the collector terminal current Ic and the collector terminal voltage Vce of IGBTs, are also important in the switching characteristics and switching loss estimation of IGBTs, just like the Id-Vds characteristics of MOSFETs. That is, it can be seen that the output current characteristics of MOS transistors are as important as those of MOSFETs. Next, the output characteristic model formula of MOS transistors, which is the output current characteristic of the MOS transistor according to Embodiment 1, a circuit simulation device equipped with this output characteristic model formula, and a method for generating the output characteristic model formula of MOS transistors will be described.

[0038] FIG. 1 shows a method of generating, as a behavior model formula, a model formula (output characteristic model formula) of the Iy-Vyx output characteristic, which is the output current characteristic of the main terminal current Iy and the main terminal voltage Vyx of the MOS transistor with the main terminal voltage Vyx, the control terminal voltage Vzx, and the temperature T of the MOS transistor according to Embodiment 1 as independent variables. By the method shown in FIG. 1, the output characteristic model formula of the MOS transistor, which is the output current characteristic of the MOS transistor, can be generated, that is, modeled.

[0039] Based on the measurement data 1 of the Iy-Vyx output characteristic, which is the output current characteristic of the main terminal current Iy and the main terminal voltage Vyx of the MOS transistor 15 with the control terminal voltage Vzx and the temperature T as parameters, and the first model formula 2 of the main terminal current Iy having the first main coefficient C0, the second main coefficient C1, the third main coefficient C2, and the adjustment constant ε with the main terminal voltage Vyx as the positive independent variable, the first process 3, the second process 6, the third process 9, and the fourth process 11 are executed to generate the output characteristic model formula 12 of the MOS transistor 15. The output characteristic model formula 12 is a behavior model formula expressed as a function with the temperature T as an independent variable together with the main terminal voltage Vyx and the control terminal voltage Vzx.

[0040] The first process 3 generates main coefficient extraction data 4 in which the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2 of the first model formula 2 are extracted with temperature T as a parameter and control terminal voltage Vzx as a variable, based on the first model formula 2 and the measurement data 1. The second process 6 generates sub - coefficient extraction data 7 of four sub - coefficients Ci0, Ci1, Ci2, Ci3 extracted with temperature T as a variable, for each of the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2, based on the main coefficient extraction data 4 and the second model formula 5. The second model formula 5 is a model formula of the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2, which has four sub - coefficients Ci0, Ci1, Ci2, Ci3. The third process 9 extracts the coefficients of the sub - coefficient function 8, which is a function of temperature T of the sub - coefficients represented by a polynomial of the four sub - coefficients Ci0, Ci1, Ci2, Ci3 and temperature T for each of the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2, and generates function coefficient extraction data 10. The fourth process 11, after the third process 9, generates the output characteristic model formula 12 of the MOS - type transistor 15 as Formula 1, based on the determined model formula of the first main coefficient C0 with control terminal voltage Vzx and temperature T as variables, the determined model formula of the second main coefficient C1 with control terminal voltage Vzx and temperature T as variables, and the determined model formula of the third main coefficient C2 with control terminal voltage Vzx as a variable.

[0041]

Number

[0042]

Number

Number

Number

[0043] The first model formula 2 used in the first process 3 is represented by formula 5. The first model formula 2 is a model formula of the main terminal current Iy having the main terminal voltage Vyx as a positive independent variable, the first main coefficient C0, the second main coefficient C1, the third main coefficient C2, and the tuning constant ε.

Number

[0044] Replacing the trailing 0, 1, 2 in the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2 with the integer i, the second model formula 5 of the main coefficient Ci having the control terminal voltage Vzx as a positive independent variable is represented by formula 6. The second model formula 5 is used in the second process 6. i is any integer of 0, 1, or 2.

Number

[0045] The sub - coefficient function 8 used in the third process 9 is represented by formula 7. Replacing the trailing 0, 1, 2 in the four sub - coefficients Ci0, Ci1, Ci2, and Ci3 with the integer j, the sub - coefficient function 8 of the sub - coefficient Cij having the temperature T as a variable is represented by formula 7. i of the sub - coefficient Cij is any integer of 0, 1, or 2 and corresponds to the "number i" of the main coefficient Ci. j of the sub - coefficient Cij is any integer of 0, 1, 2, or 3 and corresponds to the trailing number in the four sub - coefficients Ci0, Ci1, Ci2, and Ci3.

Number

[0046] FIG. 2 shows a circuit simulation device 30 having the output characteristic model equation 12 of the MOS transistor 15. The circuit simulation device 30 according to Embodiment 1 simulates the operation of a target circuit 34 including the MOS transistor 15 by the calculation of a processing unit 32. The circuit simulation device 30 includes a target circuit 34 that is a target for simulating the operation, a circuit operation pattern 36 for operating the target circuit 34, a SPICE source code A including the output characteristic model equation 12 of the MOS transistor 15, a SPICE source code X including a model equation X other than the MOS transistor 15, a processing unit 32 for calculating the operation of the target circuit 34, and an output unit 33 such as a display for displaying the calculation result of the processing unit 32. In FIG. 2, reference numerals 35, 38, and 39 are given as the reference numerals of the model equation X, the SPICE source code A, and the SPICE source code X, respectively. The function of the processing unit 32 may be realized by a processor 98 and a memory 99 shown in FIG. 6. FIG. 6 is a diagram showing a hardware configuration example for realizing the function of the circuit simulation device of FIG. 2 by digital calculation. In this case, the processing unit 32 is realized by the processor 98 executing a program stored in the memory 99. Also, a plurality of processors 98 and a plurality of memories 99 may cooperate to execute the function of the processing unit 32.

[0047] In the circuit simulation device 30 according to Embodiment 1, since the output characteristic model formula 12 of the MOS transistor 15 is expressed as a function having the temperature T as an independent variable together with the main terminal voltage Vyx and the control terminal voltage Vzx as in Formula 1, simulation calculations of the target circuit 34 such as the power conversion circuit 20 in various temperature situations can be performed with high accuracy and efficiency, and the design of the target circuit 34 such as the power conversion circuit 20 can be efficiently performed. When calculating the conversion efficiency of the power conversion circuit 20 in FIG. 5 using the circuit simulation device 30, if the behavior model formula of Formula 1 is used as the model formula expressing the Id-Vds characteristics of the switching element 21a and the switching element 21b, simulation calculations of the power conversion operation in various temperature situations can be efficiently performed.

[0048] When the MOS transistor 15 is a MOSFET, the output characteristic model formula 12 is represented by Formula 8.

Equation

[0049]

Equation

Equation

Equation

[0050] C00(T), C01(T), C02(T), C03(T) are the sub - coefficients of the first principal coefficient C0 with temperature T as a variable. C10(T), C11(T), C12(T), C13(T) are the sub - coefficients of the second principal coefficient C1 with temperature T as a variable. C20, C21, C22, C23 are the sub - coefficients of the third principal coefficient C2 without temperature T as a variable. In Equation 9, Equation 10, and Equation 11, the tuning constant δ shown in Equation 6 is 0.

[0051] Next, the method for generating the output characteristic model equation of the MOS - type transistor 15 will be described in detail. Examples of the measurement data 1 of the MOSFET which is the MOS - type transistor 15 are shown in FIGS. 11 to 15. FIGS. 11 to 15 are the measurement data 1 of the Id - Vds output characteristics of the MOSFET with the gate - terminal voltage Vgs and the temperature T as parameters. In FIGS. 11 to 15, the horizontal axis is the drain - terminal voltage Vds [V], and the vertical axis is the drain - terminal current Id [A]. In each data, the gate - terminal voltage Vgs is increased at regular intervals from 11V to 19V. Here, the interval is 2V. Each data in FIGS. 11 to 15 has a different temperature and is increased at regular intervals from 20°C to 140°C. Here, the interval is 30°C. The range of the temperature T is preferably within the range from the lowest junction temperature to the highest junction temperature assumed in the power converter in which the MOSFET is used.

[0052] FIG. 11 shows the measurement data 1 of the MOSFET at the temperature T of 20°C. The measurement data 1 at the temperature T of 20°C is the first - temperature output characteristic data 48. The first - temperature output characteristic data 48 has current characteristics T1g1 to T1g5. The current characteristic T1g1 is the characteristic of the drain - terminal current Id when the gate - terminal voltage Vgs is 11V, the current characteristic T1g2 is the characteristic of the drain - terminal current Id when the gate - terminal voltage Vgs is 13V. The current characteristic T1g3 is the characteristic of the drain - terminal current Id when the gate - terminal voltage Vgs is 15V, the current characteristic T1g4 is the characteristic of the drain - terminal current Id when the gate - terminal voltage Vgs is 17V, and the current characteristic T1g5 is the characteristic of the drain - terminal current Id when the gate - terminal voltage Vgs is 19V.

[0053] Figure 12 shows measurement data 1 of the MOSFET at a temperature T of 50°C. The measurement data 1 at a temperature T of 50°C is the second temperature output characteristic data 49. The second temperature output characteristic data 49 has current characteristics T2g1 to T2g5. The current characteristic T2g1 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 11V, the current characteristic T2g2 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 13V. The current characteristic T2g3 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 15V, the current characteristic T2g4 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 17V, and the current characteristic T2g5 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 19V.

[0054] Figure 13 shows measurement data 1 of the MOSFET at a temperature T of 80°C. The measurement data 1 at a temperature T of 80°C is the third temperature output characteristic data 50. The third temperature output characteristic data 50 has current characteristics T3g1 to T3g5. The current characteristic T3g1 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 11V, the current characteristic T3g2 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 13V. The current characteristic T3g3 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 15V, the current characteristic T3g4 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 17V, and the current characteristic T3g5 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 19V.

[0055] Figure 14 shows measurement data 1 of the MOSFET at a temperature T of 110°C. The measurement data 1 at a temperature T of 110°C is the fourth temperature output characteristic data 51. The fourth temperature output characteristic data 51 has current characteristics T4g1 to T4g5. The current characteristic T4g1 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 11V, and the current characteristic T4g2 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 13V. The current characteristic T4g3 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 15V, the current characteristic T4g4 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 17V, and the current characteristic T4g5 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 19V.

[0056] Figure 15 shows measurement data 1 of the MOSFET at a temperature T of 140°C. The measurement data 1 at a temperature T of 140°C is the fifth temperature output characteristic data 52. The fifth temperature output characteristic data 52 has current characteristics T5g1 to T5g5. The current characteristic T5g1 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 11V, and the current characteristic T5g2 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 13V. The current characteristic T5g3 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 15V, the current characteristic T5g4 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 17V, and the current characteristic T5g5 is the characteristic of the drain terminal current Id when the gate terminal voltage Vgs is 19V.

[0057] Equation 12 is used as the first model equation 2 with the drain terminal voltage Vds as the positive independent variable and the drain terminal current Id as the dependent variable. The first model equation 2 used in the first process 3 is a model equation of the drain terminal current Id having a first main coefficient C0, a second main coefficient C1, a third main coefficient C2, and an adjustment constant ε. The adjustment constant ε is, as described above, a value greater than 0 and extremely smaller than 1.

Number

[0058] Equation 12 provides a tuning constant ε that is greater than 0 and extremely small compared to 1 to prevent calculation errors. In the case of the MOSFET for which the measurement data 1 shown in FIGS. 11 to 15 was measured, ε = 1 × 10^-5 [V]. Drain terminal voltage Vds is directly described in Equation 12, and the drain terminal voltage Vds is included as the positive independent variable.

[0059] Next, the characteristics of the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2, which are the coefficients of Equation 12, will be described. Note that, as appropriate, the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2 are simply denoted as the main coefficient C0, the main coefficient C1, and the main coefficient C2. FIGS. 16, 17, and 18 show the Id-Vds characteristics according to Equation 12 with the main coefficients C0, C1, and C2 as parameters, respectively. In FIGS. 16, 17, and 18, the horizontal axis is the drain terminal voltage Vds [V], and the vertical axis is the drain terminal current Id [A].

[0060] FIG. 16 shows the Id-Vds characteristics when the second main coefficient C1 and the third main coefficient C2 are fixed and the first main coefficient C0 is changed to 0.6, 0.8, and 1.0 in order to observe the characteristics of the first main coefficient C0. Here, C1 = 0.1 and C2 = 1.5. The first main coefficient characteristic 53a is the Id-Vds characteristic when the first main coefficient C0 is 1.0. The first main coefficient characteristic 53b is the Id-Vds characteristic when the first main coefficient C0 is 0.8, and the first main coefficient characteristic 53c is the Id-Vds characteristic when the first main coefficient C0 is 0.6. Arrow 71b indicates the change direction of the Id-Vds characteristic when the first main coefficient C0 is increased in the linear region. Arrow 71a indicates the change direction of the Id-Vds characteristic when the first main coefficient C0 is increased in the saturation region. It can be seen that when the first main coefficient C0 is increased, the slope of the linear region increases slightly, while the saturation current value in the saturation region increases significantly.

[0061] FIG. 17 shows the Id-Vds characteristics when the first principal coefficient C0 and the third principal coefficient C2 are kept constant and the second principal coefficient C1 is changed to 0.1, 0.2, and 0.3 to observe the characteristics of the second principal coefficient C1. Here, C0 = 1.0 and C2 = 1.5. The second principal coefficient characteristic 54a is the Id-Vds characteristic when the second principal coefficient C1 is 0.1. The second principal coefficient characteristic 54b is the Id-Vds characteristic when the second principal coefficient C1 is 0.2, and the second principal coefficient characteristic 54c is the Id-Vds characteristic when the second principal coefficient C1 is 0.3. Arrow 72b indicates the direction of change in the Id-Vds characteristic when the second principal coefficient C1 is increased in the linear region. Arrow 72a indicates the direction of change in the Id-Vds characteristic when the second principal coefficient C1 is increased in the transition region from the linear region to the saturation region. It can be seen that when the second principal coefficient C1 is increased, the slope in the linear region decreases significantly, and in the transition region from the linear region to the saturation region, the transition shape from the linear region to the saturation region becomes slower.

[0062] FIG. 18 shows the Id-Vds characteristics when the first principal coefficient C0 and the second principal coefficient C1 are kept constant and the third principal coefficient C2 is changed to 1.0, 1.5, and 2.0 to observe the characteristics of the third principal coefficient C2. Here, C0 = 1.0 and C1 = 0.2. The third principal coefficient characteristic 55a is the Id-Vds characteristic when the third principal coefficient C2 is 1.0. The third principal coefficient characteristic 55b is the Id-Vds characteristic when the third principal coefficient C2 is 1.5, and the third principal coefficient characteristic 55c is the Id-Vds characteristic when the third principal coefficient C2 is 2.0. Arrow 73b indicates the direction of change in the Id-Vds characteristic when the third principal coefficient C2 is increased in the linear region. Arrow 73a indicates the direction of change in the Id-Vds characteristic when the third principal coefficient C2 is increased in the transition region from the linear region to the saturation region. It can be seen that when the third principal coefficient C2 is increased, the slope decreases in the linear region, and in the transition region from the linear region to the saturation region, the transition shape from the linear region to the saturation region becomes steeper.

[0063] Figure 19 shows the gate terminal voltage Vgs dependence of the Id-Vds characteristics based on the measured waveforms of the MOSFET. In Figure 19, the horizontal axis is the drain terminal voltage Vds [V], and the vertical axis is the drain terminal current Id [A]. Arrow 74c indicates the change direction of the Id-Vds characteristics when the gate terminal voltage Vgs is increased in the linear region. Arrow 74b indicates the change direction of the Id-Vds characteristics when the gate terminal voltage Vgs is increased in the transition region from the linear region to the saturation region. Arrow 74a indicates the change direction of the Id-Vds characteristics when the gate terminal voltage Vgs is increased in the saturation region. Current characteristics 56a, current characteristics 56b, and current characteristics 56c are the Id-Vds characteristics when the gate terminal voltage Vgs is sequentially increased. When the gate terminal voltage Vgs is increased, it can be seen that in the linear region, the slope of the linear region slightly increases, in the transition region from the linear region to the saturation region, the transition shape from the linear region to the saturation region becomes slow, and in the saturation region, the saturation current value increases significantly.

[0064] When comparing the Id-Vds characteristics in Figure 19 with those in Figure 16, in the saturation region of Figure 19, the effect of increasing the gate terminal voltage Vgs as shown by arrow 74a corresponds to the effect of increasing the first principal coefficient C0 in Equation 12 as shown by arrow 71a in the saturation region of Figure 16. This indicates that the first principal coefficient C0 in Equation 12 increases monotonically with the increase in the gate terminal voltage Vgs.

[0065] When comparing the Id-Vds characteristics in Figure 19 with those in Figure 17, in the transition characteristics from the linear region to the saturation region, the effect of the transition shape becoming slow by increasing the gate terminal voltage Vgs as shown by arrow 74b in Figure 19 corresponds to the effect of increasing the second principal coefficient C1 as shown by arrow 72a in Figure 17. This indicates that the second principal coefficient C1 in Equation 12 increases monotonically with the increase in the gate terminal voltage Vgs.

[0066] Compare the Id-Vds characteristics of FIG. 19 with those of FIG. 18. In the linear region of FIG. 19, as the gate terminal voltage Vgs increases as indicated by arrow 74c, the slope of the Id-Vds characteristics slightly increases, and in the transition region from the linear region to the saturation region, the transition shape from the linear region to the saturation region becomes slow as indicated by arrow 74b. In the linear region of FIG. 18, when the third principal coefficient C2 is decreased as indicated by arrow 73b, the slope of the Id-Vds characteristics increases, and when the third principal coefficient C2 is decreased as indicated by arrow 73a in the transition region from the linear region to the saturation region, the transition shape from the linear region to the saturation region becomes slow. This indicates that the third principal coefficient C2 in Equation 12 monotonically decreases as the gate terminal voltage Vgs increases.

[0067] As described above, by fitting the Id-Vds characteristics of the MOSFET using Equation 12, it is expected that its principal coefficients C0, C1, and C2 will vary monotonically with respect to the gate terminal voltage Vgs.

[0068] The principal coefficient extraction data 4, secondary coefficient extraction data 7, and function coefficient extraction data 10 for the MOSFET for which the measurement data 1 shown in FIGS. 11 to 15 were measured are shown in FIGS. 20 to 42. In the first process 3 of FIG. 1, the principal coefficients C0, C1, and C2 of Equation 12 are extracted from the first temperature output characteristic data 48, second temperature output characteristic data 49, third temperature output characteristic data 50, fourth temperature output characteristic data 51, and fifth temperature output characteristic data 52 of the MOSFET shown in FIGS. 11 to 15. The first temperature output characteristic data 48, second temperature output characteristic data 49, third temperature output characteristic data 50, fourth temperature output characteristic data 51, and fifth temperature output characteristic data 52 are imported into graph creation software, and the principal coefficients C0, C1, and C2 of Equation 12 are extracted using the fitting function by the least squares method.

[0069] The first temperature first principal coefficient data 57a, the first temperature second principal coefficient data 58a, and the first temperature third principal coefficient data 59a, which are the results of the gate terminal voltage Vgs dependence of the first principal coefficient C0, the second principal coefficient C1, and the third principal coefficient C2 extracted from the data at a temperature of 20°C by this first process 3, are shown in FIGS. 20, 21, and 22, respectively. The second temperature first principal coefficient data 57b, the second temperature second principal coefficient data 58b, and the second temperature third principal coefficient data 59b, which are the results of the gate terminal voltage Vgs dependence of the first principal coefficient C0, the second principal coefficient C1, and the third principal coefficient C2 extracted from the data at a temperature of 50°C, are shown in FIGS. 23, 24, and 25, respectively. The third temperature first principal coefficient data 57c, the third temperature second principal coefficient data 58c, and the third temperature third principal coefficient data 59c, which are the results of the gate terminal voltage Vgs dependence of the first principal coefficient C0, the second principal coefficient C1, and the third principal coefficient C2 extracted from the data at a temperature of 80°C, are shown in FIGS. 26, 27, and 28, respectively.

[0070] The fourth temperature first principal coefficient data 57d, the fourth temperature second principal coefficient data 58d, and the fourth temperature third principal coefficient data 59d, which are the results of the gate terminal voltage Vgs dependence of the first principal coefficient C0, the second principal coefficient C1, and the third principal coefficient C2 extracted from the data at a temperature of 110°C, are shown in FIGS. 29, 30, and 31, respectively. The fifth temperature first principal coefficient data 57e, the fifth temperature second principal coefficient data 58e, and the fifth temperature third principal coefficient data 59e, which are the results of the gate terminal voltage Vgs dependence of the first principal coefficient C0, the second principal coefficient C1, and the third principal coefficient C2 extracted from the data at a temperature of 140°C, are shown in FIGS. 32, 33, and 34, respectively. However, regarding the results of the gate terminal voltage Vgs dependence of the third principal coefficient C2, in the Id-Vds characteristics of the MOSFET used in the measurement data 1 shown in FIGS. 11 to 15, the results are substantially the same regardless of the temperature T. In FIGS. 20, 23, 26, 29, and 32, the horizontal axis is the gate terminal voltage Vgs [V], and the vertical axis is the first principal coefficient C0 [A]. In FIGS. 21, 24, 27, 30, and 33, the horizontal axis is the gate terminal voltage Vgs [V], and the vertical axis is the second principal coefficient C1 [V]. In FIGS. 22, 25, 28, 31, and 34, the horizontal axis is the gate terminal voltage Vgs [V], and the vertical axis is the third principal coefficient C2.

[0071] The gate terminal voltage Vgs dependencies of the first principal coefficient C0 and the second principal coefficient C1 of Equation 12 at each temperature T vary depending on the temperature T, but the increasing and decreasing tendencies, i.e., the shapes of the graphs, are similar. It can be seen that the gate terminal voltage Vgs dependencies of the first principal coefficient C0, which are the fitting coefficients shown in FIGS. 20, 23, 26, 29, and 32, all increase monotonically with respect to the gate terminal voltage Vgs. Also, the gate terminal voltage Vgs dependencies of the second principal coefficient C1, which are the fitting coefficients shown in FIGS. 21, 24, 27, 30, and 33, have a monotonically increasing waveform in which the change becomes larger as the gate terminal voltage Vgs increases. Note that the gate terminal voltage Vgs dependency of the first principal coefficient C0 can also be said to be a monotonous increase that is linear or close to the tendency of a linear function. Similarly, the gate terminal voltage Vgs dependency of the second principal coefficient C1 can also be said to be a monotonous increase that is quadratic or close to the tendency of a quadratic function.

[0072] On the other hand, it can be seen that the gate terminal voltage Vgs dependency of the third principal coefficient C2, which is the fitting coefficient shown in FIGS. 22, 25, 28, 31, and 34, decreases monotonically with respect to the gate terminal voltage Vgs. The gate terminal voltage Vgs dependency of the third principal coefficient C2 can also be said to be a monotonous decrease that is inversely proportional or close to the tendency of an inverse proportion.

[0073] So far, the behavioral model equations for the Id-Vds characteristics based on the measurement data 1 shown in FIGS. 11 to 15 have been described. By using Equation 12 for the behavioral model equation of the Id-Vds characteristics of the MOSFET, it has been found that the first principal coefficient C0, the second principal coefficient C1, and the third principal coefficient C2 monotonically change with different trends with respect to the gate terminal voltage Vgs at all temperatures. However, the inventors considered that the dependent variables that monotonically change with respect to one independent variable, namely the first principal coefficient C0, the second principal coefficient C1, and the third principal coefficient C2, might be expressible by the same function, and searched for an appropriate function for the first principal coefficient C0, the second principal coefficient C1, and the third principal coefficient C2. As a result, it has been found that these first principal coefficient C0, second principal coefficient C1, and third principal coefficient C2 can be fitted by the same function by using Equation 13 with the gate terminal voltage Vgs as the independent variable.

[0074]

Number

[0075] Regarding the second process 6 in FIG. 1 for the MOSFET in which the measurement data 1 shown in FIGS. 11 to 15 was measured, an explanation will be given. As described above, the third process 9 is a sub - coefficient function 8 which is a function of the temperature T of the sub - coefficients, represented by a polynomial of the sub - coefficient extraction data 7 of the four sub - coefficients Ci0, Ci1, Ci2, Ci3 and the temperature T for each of the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2. Based on this, the coefficients of the sub - coefficient function 8 are extracted to generate the function coefficient extraction data 10. First, the first main coefficient C0 will be explained. The five first - temperature first - main - coefficient data 57a, second - temperature first - main - coefficient data 57b, third - temperature first - main - coefficient data 57c, fourth - temperature first - main - coefficient data 57d, and fifth - temperature first - main - coefficient data 57e extracted in the first process 3 are applied to Equation 13, and the sub - coefficients Ci0, Ci1, Ci2, Ci3 (i = 0) of Equation 13 are extracted using the fitting function that uses the least - squares method of the graph - creating software. C00, C01, C02, C03 are the first sub - coefficient, second sub - coefficient, third sub - coefficient, and fourth sub - coefficient of the first main coefficient C0, respectively. Incidentally, the first sub - coefficient Ci0, the second sub - coefficient Ci1, the third sub - coefficient Ci2, and the fourth sub - coefficient Ci3 are simply denoted as the sub - coefficient Ci0, the sub - coefficient Ci1, the sub - coefficient Ci2, and the sub - coefficient Ci3 as appropriate. i is any integer from 0, 1, 2, and 3.

[0076] The first - temperature first - main - coefficient data 57a is the data of the gate - terminal voltage Vgs dependence of the first main coefficient C0 of Equation 12 extracted from the data at a temperature of 20°C in the first process 3, and the second - temperature first - main - coefficient data 57b is the data of the gate - terminal voltage Vgs dependence of the first main coefficient C0 of Equation 12 extracted in the same way from the data at a temperature of 50°C. The third - temperature first - main - coefficient data 57c is the data of the gate - terminal voltage Vgs dependence of the first main coefficient C0 of Equation 12 extracted in the same way from the data at a temperature of 80°C, the fourth - temperature first - main - coefficient data 57d is the data of the gate - terminal voltage Vgs dependence of the first main coefficient C0 of Equation 12 extracted in the same way from the data at a temperature of 110°C, and the fifth - temperature first - main - coefficient data 57e is the data of the gate - terminal voltage Vgs dependence of the first main coefficient C0 of Equation 12 extracted in the same way from the data at a temperature of 140°C.

[0077] The second main coefficient C1 will be described. Five pieces of first-temperature second-main-coefficient data 58a, second-temperature second-main-coefficient data 58b, third-temperature second-main-coefficient data 58c, fourth-temperature second-main-coefficient data 58d, and fifth-temperature second-main-coefficient data 58e extracted in the first process 3 are applied to Equation 13, and the sub-coefficients Ci0, Ci1, Ci2, Ci3 (i = 1) of Equation 13 are extracted using the fitting function of the graph creation software that uses the least squares method. C10, C11, C12, and C13 are the first sub-coefficient, second sub-coefficient, third sub-coefficient, and fourth sub-coefficient in the second main coefficient C1, respectively.

[0078] The first-temperature second-main-coefficient data 58a is the data of the gate terminal voltage Vgs dependence of the second main coefficient C1 of Equation 12 extracted from the data at a temperature of 20°C in the first process 3, and the second-temperature second-main-coefficient data 58b is the data of the gate terminal voltage Vgs dependence of the second main coefficient C1 of Equation 12 extracted similarly from the data at a temperature of 50°C. The third-temperature second-main-coefficient data 58c is the data of the gate terminal voltage Vgs dependence of the second main coefficient C1 of Equation 12 extracted similarly from the data at a temperature of 80°C, the fourth-temperature second-main-coefficient data 58d is the data of the gate terminal voltage Vgs dependence of the second main coefficient C1 of Equation 12 extracted similarly from the data at a temperature of 110°C, and the fifth-temperature second-main-coefficient data 58e is the data of the gate terminal voltage Vgs dependence of the second main coefficient C1 of Equation 12 extracted similarly from the data at a temperature of 140°C.

[0079] The third main coefficient C2 will be described. Five pieces of first-temperature third-main-coefficient data 59a, second-temperature third-main-coefficient data 59b, third-temperature third-main-coefficient data 59c, fourth-temperature third-main-coefficient data 59d, and fifth-temperature third-main-coefficient data 59e extracted in the first process 3 are applied to Equation 13, and the sub-coefficients Ci0, Ci1, Ci2, Ci3 (i = 2) of Equation 13 are extracted using the fitting function of the graph creation software that uses the least squares method. C20, C21, C22, and C23 are the first sub-coefficient, second sub-coefficient, third sub-coefficient, and fourth sub-coefficient in the third main coefficient C2, respectively.

[0080] The first temperature third principal coefficient data 59a is the data of the gate terminal voltage Vgs dependence of the third principal coefficient C2 of Equation 12 extracted from the data at a temperature of 20°C, and the second temperature third principal coefficient data 59b is the data of the gate terminal voltage Vgs dependence of the third principal coefficient C2 of Equation 12 extracted similarly from the data at a temperature of 50°C. The third temperature third principal coefficient data 59c is the data of the gate terminal voltage Vgs dependence of the third principal coefficient C2 of Equation 12 extracted similarly from the data at a temperature of 80°C, the fourth temperature third principal coefficient data 59d is the data of the gate terminal voltage Vgs dependence of the third principal coefficient C2 of Equation 12 extracted similarly from the data at a temperature of 110°C, and the fifth temperature third principal coefficient data 59e is the data of the gate terminal voltage Vgs dependence of the third principal coefficient C2 of Equation 12 extracted similarly from the data at a temperature of 140°C.

[0081] In FIG. 35, the C0-Vgs data shown in FIGS. 20, 23, 26, 29, and 32, that is, the first temperature first principal coefficient data 57a, the second temperature first principal coefficient data 57b, the third temperature first principal coefficient data 57c, the fourth temperature first principal coefficient data 57d, and the fifth temperature first principal coefficient data 57e, are fitted with Equation 13, and the first sub-coefficient data 60a obtained by plotting the first sub-coefficient C00 against the temperature T shown in absolute temperature is shown. The five round dots are the data extracted at the five temperatures T. In FIG. 35, the horizontal axis is the temperature T [K], and the vertical axis is the first sub-coefficient C00.

[0082] In FIG. 36, the C0-Vgs data shown in FIGS. 20, 23, 26, 29, and 32, that is, the first temperature first principal coefficient data 57a, the second temperature first principal coefficient data 57b, the third temperature first principal coefficient data 57c, the fourth temperature first principal coefficient data 57d, and the fifth temperature first principal coefficient data 57e, are fitted with Equation 13, and the second sub-coefficient data 60b obtained by plotting the second sub-coefficient C01 against the temperature T shown in absolute temperature is shown. The five round dots are the data extracted at the five temperatures T. In FIG. 36, the horizontal axis is the temperature T [K], and the vertical axis is the second sub-coefficient C01.

[0083] Figure 37 shows the third coefficient data 60c obtained by fitting Equation 13 to the C0-Vgs data shown in FIGS. 20, 23, 26, 29, and 32, namely the first temperature first main coefficient data 57a, the second temperature first main coefficient data 57b, the third temperature first main coefficient data 57c, the fourth temperature first main coefficient data 57d, and the fifth temperature first main coefficient data 57e, and plotting the third sub-coefficient C02 against the temperature T shown in absolute temperature. The five round dots are the data extracted at the five temperatures T. In FIG. 37, the horizontal axis is the temperature T [K], and the vertical axis is the third sub-coefficient C02.

[0084] Figure 38 shows the fourth coefficient data 60d obtained by fitting Equation 13 to the C0-Vgs data shown in FIGS. 20, 23, 26, 29, and 32, namely the first temperature first main coefficient data 57a, the second temperature first main coefficient data 57b, the third temperature first main coefficient data 57c, the fourth temperature first main coefficient data 57d, and the fifth temperature first main coefficient data 57e, and plotting the fourth sub-coefficient C03 against the temperature T shown in absolute temperature. The five round dots are the data extracted at the five temperatures T. In FIG. 38, the horizontal axis is the temperature T [K], and the vertical axis is the fourth sub-coefficient C03.

[0085] It can be seen that none of the first sub-coefficient C00, the second sub-coefficient C01, the third sub-coefficient C02, and the fourth sub-coefficient C03 show complex changes with respect to the temperature T shown in absolute temperature.

[0086] Figure 39 shows the first coefficient data 61a obtained by fitting Equation 13 to the C1-Vgs data shown in FIGS. 21, 24, 27, 30, and 33, namely the first temperature second main coefficient data 58a, the second temperature second main coefficient data 58b, the third temperature second main coefficient data 58c, the fourth temperature second main coefficient data 58d, and the fifth temperature second main coefficient data 58e, and plotting the first sub-coefficient C10 against the temperature T shown in absolute temperature. The five round dots are the data extracted at the five temperatures T. In FIG. 39, the horizontal axis is the temperature T [K], and the vertical axis is the first sub-coefficient C10.

[0087] Figure 40 shows the second sub - coefficient data 61b obtained by fitting Equation 13 to the C1 - Vgs data shown in FIGS. 21, 24, 27, 30, and 33, namely the second main - coefficient data 58a at the first temperature, the second main - coefficient data 58b at the second temperature, the second main - coefficient data 58c at the third temperature, the second main - coefficient data 58d at the fourth temperature, and the second main - coefficient data 58e at the fifth temperature, and plotting the second sub - coefficient C11 against the temperature T shown in absolute temperature. The five round dots are the data extracted at the five temperatures T. In Figure 40, the horizontal axis is the temperature T [K], and the vertical axis is the second sub - coefficient C11.

[0088] Figure 41 shows the third sub - coefficient data 61c obtained by fitting Equation 13 to the C1 - Vgs data shown in FIGS. 21, 24, 27, 30, and 33, namely the second main - coefficient data 58a at the first temperature, the second main - coefficient data 58b at the second temperature, the second main - coefficient data 58c at the third temperature, the second main - coefficient data 58d at the fourth temperature, and the second main - coefficient data 58e at the fifth temperature, and plotting the third sub - coefficient C12 against the temperature T shown in absolute temperature. The five round dots are the data extracted at the five temperatures T. In Figure 41, the horizontal axis is the temperature T [K], and the vertical axis is the third sub - coefficient C12.

[0089] Figure 42 shows the fourth sub - coefficient data 61d obtained by fitting Equation 13 to the C1 - Vgs data shown in FIGS. 21, 24, 27, 30, and 33, namely the second main - coefficient data 58a at the first temperature, the second main - coefficient data 58b at the second temperature, the second main - coefficient data 58c at the third temperature, the second main - coefficient data 58d at the fourth temperature, and the second main - coefficient data 58e at the fifth temperature, and plotting the fourth sub - coefficient C13 against the temperature T shown in absolute temperature. The five round dots are the data extracted at the five temperatures T. In Figure 42, the horizontal axis is the temperature T [K], and the vertical axis is the fourth sub - coefficient C13.

[0090] It can be seen that the first sub - coefficient C10, the second sub - coefficient C11, the third sub - coefficient C12, and the fourth sub - coefficient C13 all change slowly with respect to the temperature T shown in absolute temperature.

[0091] The gate terminal voltage Vgs dependence data (C2-Vgs data) of the third main coefficient C2 of Equation 12 shown in FIGS. 22, 25, 28, 31, and 34, that is, the first temperature third main coefficient data 59a, the second temperature third main coefficient data 59b, the third temperature third main coefficient data 59c, the fourth temperature third main coefficient data 59d, and the fifth temperature third main coefficient data 59e, are almost independent of the temperature T. Therefore, the first sub-coefficient C20, the second sub-coefficient C21, the third sub-coefficient C22, and the fourth sub-coefficient C23 extracted in the second process 6 for fitting Equation 13 are all constant values independent of the temperature T. Therefore, figures such as FIGS. 35 to 38 are not shown here.

[0092] Thus, the first sub-coefficient C00, the second sub-coefficient C01, the third sub-coefficient C02, and the fourth sub-coefficient C03 of Equation 13 obtained by fitting the gate terminal voltage Vgs dependence of the first main coefficient C0 of Equation 12 change slowly with respect to the temperature T shown in absolute temperature. Therefore, it can be seen that the sub-coefficient function 8 of the temperature T used in the third process 9 of FIG. 1 is sufficient as a polynomial of the temperature T shown in absolute temperature. Similarly, the first sub-coefficient C10, the second sub-coefficient C11, the third sub-coefficient C12, and the fourth sub-coefficient C13 of Equation 13 obtained by fitting the gate terminal voltage Vgs dependence of the second main coefficient C1 of Equation 12 change slowly with respect to the temperature T shown in absolute temperature. Therefore, it can be seen that the sub-coefficient function 8 of the temperature T used in the third process 9 of FIG. 1 is sufficient as a polynomial of the temperature T shown in absolute temperature. The first sub-coefficient C20, the second sub-coefficient C21, the third sub-coefficient C22, and the fourth sub-coefficient C23 of Equation 13 obtained by fitting the gate terminal voltage Vgs dependence of the third main coefficient C2 of Equation 12 are all constant values independent of the temperature T. Therefore, it can be seen that the sub-coefficient function 8 of the temperature T used in the third process 9 of FIG. 1 is sufficient as a polynomial of the temperature T shown in absolute temperature.

[0093] In the case of the MOSFET for which the measurement data 1 shown in FIGS. 11 to 15 was measured, as the sub - coefficient function 8 of the temperature T used in the third process 9 of FIG. 1, a polynomial of degree 4 or less shown in Equation 7 is used. Each coefficient of the polynomial shown in Equation 7, that is, the coefficients A0ij, A1ij, A2ij, A3ij, A4ij, is a constant that does not depend on the drain - terminal voltage Vds, the gate - terminal voltage Vgs, and the temperature T. i is any integer of 0, 1, 2 and corresponds to the "number i" of the main coefficient Ci. j is any integer of 0, 1, 2, 3 and corresponds to the "number j" of the sub - coefficient Cij.

[0094] In the case of the MOSFET for which the measurement data 1 shown in FIGS. 11 to 15 was measured, by the third process 9 of FIG. 1, the first sub - coefficient C00, the second sub - coefficient C01, the third sub - coefficient C02, and the fourth sub - coefficient C03 of Equation 13 in the first main coefficient C0 are fitted with Equation 7 having only the temperature T shown in absolute temperature as a variable. Similarly, the first sub - coefficient C10, the second sub - coefficient C11, the third sub - coefficient C12, and the fourth sub - coefficient C13 of Equation 13 in the second main coefficient C1 are fitted with Equation 7 having only the temperature T shown in absolute temperature as a variable. The first sub - coefficient C20, the second sub - coefficient C21, the third sub - coefficient C22, and the fourth sub - coefficient C23 of Equation 13 in the third main coefficient C2 are fitted with Equation 7 having only the temperature T shown in absolute temperature as a variable. Note that since the first sub - coefficient C20, the second sub - coefficient C21, the third sub - coefficient C22, and the fourth sub - coefficient C23 in the third main coefficient C2 are constant values that do not depend on the temperature T, it is only the coefficient A0ij of Equation 7. Specifically, the first sub - coefficient C20 is the coefficient A020, the second sub - coefficient C21 is the coefficient A021, the third sub - coefficient C22 is the coefficient A022, and the fourth sub - coefficient C23 is the coefficient A023.

[0095] In FIGS. 35 to 38, the fitting results of the first sub - coefficient C00, second sub - coefficient C01, third sub - coefficient C02, and fourth sub - coefficient C03 in the first main coefficient C0 according to Equation 7 are shown by broken lines. Also, in FIGS. 39 to 42, the fitting results of the first sub - coefficient C10, second sub - coefficient C11, third sub - coefficient C12, and fourth sub - coefficient C13 in the second main coefficient C1 according to Equation 7 are shown by broken lines. For fitting, the fitting function using the least - squares method of graph - creating software is used. The first sub - coefficient characteristic 65a shown by the broken line in FIG. 35 is the determined sub - coefficient function 8 of the first sub - coefficient C00. The second sub - coefficient characteristic 65b shown by the broken line in FIG. 36 is the determined sub - coefficient function 8 of the second sub - coefficient C01. The third sub - coefficient characteristic 65c shown by the broken line in FIG. 37 is the determined sub - coefficient function 8 of the third sub - coefficient C02. The fourth sub - coefficient characteristic 65d shown by the broken line in FIG. 38 is the determined sub - coefficient function 8 of the fourth sub - coefficient C03. The first sub - coefficient characteristic 66a shown by the broken line in FIG. 39 is the determined sub - coefficient function 8 of the first sub - coefficient C10. The second sub - coefficient characteristic 66b shown by the broken line in FIG. 40 is the determined sub - coefficient function 8 of the second sub - coefficient C11. The third sub - coefficient characteristic 66c shown by the broken line in FIG. 41 is the determined sub - coefficient function 8 of the third sub - coefficient C12. The fourth sub - coefficient characteristic 66d shown by the broken line in FIG. 42 is the determined sub - coefficient function 8 of the fourth sub - coefficient C13.

[0096] In the first embodiment, although a polynomial of degree 4 or less is used as the sub - coefficient function 8 of the temperature T used in the third process 9, it is not limited to this. If the sub - coefficient function 8 is an elementary function implemented in ordinary graph - creating software, similar results can be obtained.

[0097] By the fourth process 11, Equation 8 is obtained as the output characteristic model formula 12, which is a behavior model formula of the Id - Vds output characteristic with the drain terminal voltage Vds, gate terminal voltage Vgs, and temperature T of the MOSFET, which is finally the MOS - type transistor 15, as independent variables.

[0098] In the case of the MOSFET for which the measurement data 1 shown in FIGS. 11 to 15 was measured, since ε = 1×10^-5 [V] as described above, the output characteristic model formula 12 to which this tuning constant ε is applied becomes formula 14.

Number

[0099] The first main coefficient C0(Vgs,T), the second main coefficient C1(Vgs,T), and the third main coefficient C2(Vgs) in formula 8 and formula 14 are represented by formula 9, formula 10, and formula 11, respectively. The first sub - coefficient C00, the second sub - coefficient C01, the third sub - coefficient C02, and the fourth sub - coefficient C03 of formula 9 are polynomials having only the temperature T shown in absolute temperature as a variable. The first sub - coefficient C10, the second sub - coefficient C11, the third sub - coefficient C12, and the fourth sub - coefficient C13 of formula 10 are polynomials having only the temperature T shown in absolute temperature as a variable.

[0100] FIG. 43 shows the current characteristics 63a, 63b, and 63c indicated by three solid lines which are the actually measured Id - Vds output characteristics, and the current characteristics 62a, 62b, and 62c of the output characteristic model formula 12 obtained by formula 14 to which the temperature T and the gate terminal voltage Vgs of the measurement conditions corresponding to the three current characteristics 63a, 63b, and 63c are applied. The current characteristics 62a, 62b, and 62c are indicated by broken lines. In FIG. 43, the horizontal axis is the drain terminal voltage Vds [V], and the vertical axis is the drain terminal current Id [A]. The temperature T and the gate terminal voltage Vgs of the measurement conditions corresponding to the three current characteristics 63a, 63b, and 63c are different from the temperature T and the gate terminal voltage Vgs of the Id - Vds output characteristic data shown in FIGS. 11 to 15. It can be seen that the predicted Id - Vds output characteristics, that is, the current characteristics 62a, 62b, and 62c by formula 14, are in good agreement with the actually measured characteristics, that is, the current characteristics 63a, 63b, and 63c.

[0101] As described above, by the output characteristic model formula generation method shown in FIG. 1, a behavior model formula of the Id-Vds output characteristic with the drain terminal voltage Vds, gate terminal voltage Vgs, and temperature T of the MOSFET which is the MOS transistor 15 as independent variables, that is, the output characteristic model formula 12 can be obtained.

[0102] Also, in the first embodiment, the output characteristic model formula generation method mainly using the MOSFET as the MOS transistor 15 has been described. Similarly, for the IGBT which is the MOS transistor 15, a behavior model formula of the Ic-Vce output characteristic with the collector terminal voltage Vce, gate terminal voltage Vge, and temperature T as independent variables, that is, the output characteristic model formula 12 can be obtained. Therefore, a behavior model formula of the Iy-Vyx output characteristic with the main terminal voltage Vyx, control terminal voltage Vzx, and temperature T of the MOS transistor 15 as independent variables, that is, the output characteristic model formula 12 can be obtained.

[0103] Note that the first model formula 2 shown by Formula 5 in the first embodiment is called the Hill formula and has the form of Formula 15.

Equation

[0104] Also, the second model formula 5 shown by Formula 6 in the first embodiment has the form of Formula 16.

Equation

[0105] The effect of the coefficient θ in Formula 16 only moves the value of the dependent variable f as a whole and does not affect the graph shape with the independent variable α. Also, if the constant σ in Formula 16 has a value of 0 or more and extremely small compared to 1, it does not significantly affect the value of the dependent variable f. Therefore, it can be said that it is appropriate to call Formula 16 the Hill formula with the same name as Formula 15.

[0106] Equation 5 is the first model equation 2 for fitting the measurement data 1 in the first process 3 of FIG. 1 in the first embodiment, and it is possible to fit the measurement data 1 with high precision. The drain terminal voltage Vds dependence in the predicted Id-Vds output characteristics of the broken line shown in FIG. 43 is the characteristic of Equation 5. Therefore, it can be seen that by using Equation 5 which is the Hill equation, it is possible to obtain high-precision Id-Vds output characteristics with the drain terminal voltage Vds as the independent variable.

[0107] Also, Equation 6 is the second model equation 5 used for fitting the gate terminal voltage Vgs dependence in the coefficients within Equation 5 which is the Hill equation in the second process 6 of FIG. 1 in the first embodiment, and it is the Hill equation. The gate terminal voltage Vgs dependence in the predicted Id-Vds output characteristics of the broken line shown in FIG. 43 reflects the characteristic of Equation 6. Therefore, it can be seen that by using Equation 6 which is the Hill equation within Equation 5 which is the Hill equation, it is possible to obtain high-precision Id-Vds output characteristics of the MOSFET which is the MOS transistor 15 with the drain terminal voltage Vds and the gate terminal voltage Vgs as the independent variables.

[0108] Also, Equation 1 representing the output characteristic model equation 12 of the MOS transistor 15, Equation 8 representing the output characteristic model equation 12 of the MOSFET, and Equation 14 representing the output characteristic model equation 12 of a specific MOSFET with a determined tuning constant ε are composed of the Hill equation in the same manner as Equation 5. The first main coefficient C0 and the second main coefficient C1 in Equation 1, and the first sub - coefficient C00, the second sub - coefficient C01, the third sub - coefficient C02, the fourth sub - coefficient C03, the first sub - coefficient C10, the second sub - coefficient C11, the third sub - coefficient C12, and the fourth sub - coefficient C13 in Equations 2 and 3 depend on the temperature T. Similarly, the first main coefficient C0 and the second main coefficient C1 in Equation 8 and Equation 14, and the first sub - coefficient C00, the second sub - coefficient C01, the third sub - coefficient C02, the fourth sub - coefficient C03, the first sub - coefficient C10, the second sub - coefficient C11, the third sub - coefficient C12, and the fourth sub - coefficient C13 in Equations 9 and 10 depend on the temperature T. Therefore, Equation 1 representing the output characteristic model equation 12 of the MOS transistor 15 can obtain the high - precision Iy - Vyx output characteristics of the MOS transistor 15 with the main terminal voltage Vyx, the control terminal voltage Vzx, and the temperature T as independent variables. Also, Equation 8 representing the output characteristic model equation 12 of the MOSFET and Equation 14 representing the output characteristic model equation 12 of a specific MOSFET with a determined tuning constant ε can obtain the high - precision Id - Vds output characteristics of the MOSFET, which is the MOS transistor 15, with the drain terminal voltage Vds, the gate terminal voltage Vgs, and the temperature T as independent variables.

[0109] As described above, the output characteristic model equation 12 of the MOS transistor 15 according to Embodiment 1 outputs the main terminal current with the main terminal voltage, the control terminal voltage, and the temperature as inputs. Let the first main terminal, the second main terminal, and the control terminal of the MOS transistor 15 be x, y, and z respectively. Let the main terminal voltage, which is the voltage of the second main terminal y with respect to the first main terminal x, be Vyx, let the control terminal voltage, which is the voltage of the control terminal z with respect to the first main terminal x, be Vzx, let the main terminal current, which is the current flowing from the second main terminal y to the first main terminal x, be Iy, let the temperature of the MOS transistor 15 be T, and the output characteristic model equation 12 that outputs the main terminal current Iy with the main terminal voltage Vyx, the control terminal voltage Vzx, and the temperature T as inputs is represented by Equation 1. C0(Vzx,T) and C1(Vzx,T) in Equation 1 are the first main coefficient and the second main coefficient with the control terminal voltage Vzx and the temperature T as variables respectively, C2(Vzx) in Equation 1 is the third main coefficient with the control terminal voltage Vzx as a variable, and ε in Equation 1 is an adjustment constant. Since the output characteristic model equation 12 of the MOS transistor 15 according to Embodiment 1 represents the main terminal current Iy by Equation 1, the output characteristics of the current (main terminal current Iy) of the MOS transistor 15 can be expressed as a function with the main terminal voltage Vyx, the control terminal voltage Vzx, and the temperature T as independent variables.

[0110] The circuit simulation device 30 according to Embodiment 1 simulates the operation of a circuit (target circuit 34) including the MOS transistor 15 by the calculation of the processing unit 32. The circuit simulation device 30 includes an output characteristic model formula 12 of the MOS transistor 15 that takes the main terminal voltage Vyx, the control terminal voltage Vzx, and the temperature T as inputs and outputs the main terminal current Iy. Let the first main terminal, the second main terminal, and the control terminal of the MOS transistor 15 be x, y, and z, respectively. Let the main terminal voltage, which is the voltage of the second main terminal y with respect to the first main terminal x, be Vyx, let the control terminal voltage, which is the voltage of the control terminal z with respect to the first main terminal x, be Vzx, let the main terminal current, which is the current flowing from the second main terminal y to the first main terminal x, be Iy, and let the temperature of the MOS transistor 15 be T. The output characteristic model formula 12 of the MOS transistor 15 is expressed by Formula 1. C0(Vzx,T) and C1(Vzx,T) in Formula 1 are the first main coefficient and the second main coefficient with the control terminal voltage Vzx and the temperature T as variables, respectively. C2(Vzx) in Formula 1 is the third main coefficient with the control terminal voltage Vzx as a variable, and ε in Formula 1 is an adjustment constant. With this configuration, the circuit simulation device 30 according to Embodiment 1 includes the output characteristic model formula 12 of the MOS transistor 15 in which the main terminal current Iy is expressed by Formula 1. Therefore, it can include the output characteristic model formula 12, which is a model formula of the output characteristic of the main terminal current Iy output by the MOS transistor 15 with the temperature T as an independent variable together with the main terminal voltage Vyx and the control terminal voltage Vzx. Furthermore, in the circuit simulation device 30 according to Embodiment 1, since the output characteristic model formula 12 of the MOS transistor 15 is expressed as a function with the temperature T as an independent variable together with the main terminal voltage Vyx and the control terminal voltage Vzx as in Formula 1, the simulation calculation of a circuit (target circuit 34) such as the power conversion circuit 20 in various temperature situations can be carried out with high accuracy and efficiency, and the design of a circuit (target circuit 34) such as the power conversion circuit 20 can be carried out efficiently.

[0111] The output characteristic model formula generation method according to Embodiment 1 generates the output characteristic model formula 12 of the MOS transistor 15. Let the first main terminal, the second main terminal, and the control terminal of the MOS transistor 15 be x, y, and z respectively, the main terminal voltage Vyx which is the voltage of the second main terminal y with respect to the first main terminal x, the control terminal voltage Vzx which is the voltage of the control terminal z with respect to the first main terminal x, the main terminal current Iy which is the current flowing from the second main terminal y to the first main terminal x, and the temperature of the MOS transistor 15 be T. The first model formula 2 of the main terminal current Iy having the first main coefficient C0, the second main coefficient C1, the third main coefficient C2, and the adjustment constant ε, with the main terminal voltage Vyx as the positive independent variable, is expressed as Equation 5. By replacing the trailing 0, 1, 2 in the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2 with the integer i, the second model formula 5 of the main coefficient Ci with the control terminal voltage Vzx as the positive independent variable is expressed as Equation 6. Ci0, Ci1, Ci2, and Ci3 in Equation 6 are sub - coefficients each having the temperature T as a variable, and δ is another adjustment constant. The output characteristic model formula generation method according to Embodiment 1 includes a first process 3 that generates main coefficient extraction data 4 by extracting the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2 of the first model formula 2 based on the measurement data 1 that measures the output characteristic which is the characteristic of the main terminal current Iy with respect to the main terminal voltage Vyx, with the control terminal voltage Vzx and the temperature T as parameters, a second process 6 described later, a third process 9, and a fourth process 11. The second process 6 generates sub - coefficient extraction data 7 of four sub - coefficients Ci0, Ci1, Ci2, and Ci3 extracted with the temperature T as a variable for each of the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2, based on the main coefficient extraction data 4 and the second model formula 5. The third process 9 extracts the coefficients of the function (sub - coefficient function 8) based on the sub - coefficient extraction data 7 of the four sub - coefficients Ci0, Ci1, Ci2, and Ci3 and the function (sub - coefficient function 8) represented by a polynomial of temperature for each of the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2, and generates function coefficient extraction data 10.The fourth process 11 generates, as Equation 1, an output characteristic model equation 12 of the MOS transistor 15 based on the determined model equations of the first main coefficient C0 with the control terminal voltage Vzx and the temperature T as variables, the determined model equations of the second main coefficient C1 with the control terminal voltage Vzx and the temperature T as variables, and the determined model equations of the third main coefficient C2 with the control terminal voltage Vzx as a variable. The output characteristic model equation generation method according to Embodiment 1 can generate, with this configuration, an output characteristic model equation 12 of the MOS transistor 15 in which the output characteristics of the current (main terminal current Iy) of the MOS transistor 15 are expressed as a function with the main terminal voltage Vyx, the control terminal voltage Vzx, and the temperature T as independent variables.

[0112] Although various exemplary embodiments and examples are described in the present disclosure, the various features, aspects, and functions described in the embodiments are not limited to the application of a specific example, but are applicable to the embodiments alone or in various combinations. Therefore, countless variations not illustrated are envisioned within the scope of the technology disclosed in this specification. For example, it includes the case of modifying, adding, or omitting at least one component, and further, the case of extracting at least one component and combining it with the components of other embodiments.

Description of Reference Numerals

[0113] 1... Measurement data, 2... First model formula, 3... First process, 4... Main coefficient extraction data, 5... Second model formula, 6... Second process, 7... Sub-coefficient extraction data, 8... Sub-coefficient function, 9... Third process, 10... Function coefficient extraction data, 11... Fourth process, 12... Output characteristic model formula, 15... MOS transistor, 20... Power conversion circuit, 21a, 21b... Switching element (MOS transistor), 30... Circuit simulation device, 32... Processing unit, 34... Target circuit, Ci... Main coefficient, C0, C0(Vzx,T)... First main coefficient, C1, C1(Vzx,T)... Second main coefficient, C2, C2(Vzx)... Third main coefficient, Cij... Sub-coefficient, Ci0, C00, C10, C20, C00(T), C10(T)... First sub-coefficient, Ci1, C01, C11, C21, C01(T), C11(T)... Second sub-coefficient, Ci2, C02, C12, C22, C02(T), C12(T)... Third sub-coefficient, Ci3, C03, C13, C23, C03(T), C13(T)... Fourth sub-coefficient, Iy... Main terminal current, T... Temperature, Vyx... Main terminal voltage, Vzx... Control terminal voltage, x... First main terminal, y... Second main terminal, z... Control terminal, ε... Tuning constant, δ... Tuning constant (other tuning constant)

Claims

1. A circuit simulation device that simulates the operation of a circuit including a MOS transistor by the calculation of a processing unit, wherein the first main terminal, the second main terminal, and the control terminal of the MOS transistor are respectively denoted as x, y, and z, the main terminal voltage that is the voltage of the second main terminal with respect to the first main terminal is denoted as Vyx, the control terminal voltage that is the voltage of the control terminal with respect to the first main terminal is denoted as Vzx, the main terminal current that is the current flowing from the second main terminal to the first main terminal is denoted as Iy, and the temperature of the MOS transistor is denoted as T, which has an output characteristic model formula of the MOS transistor that outputs the main terminal current with the main terminal voltage, the control terminal voltage, and the temperature as inputs, wherein the output characteristic model formula of the MOS transistor is represented by Formula A1, 【Number 1】 wherein C0(Vzx, T) and C1(Vzx, T) in Formula A1 are a first main coefficient and a second main coefficient that take the control terminal voltage and the temperature as variables, respectively, wherein C2(Vzx) in Formula A1 is a third main coefficient that takes the control terminal voltage as a variable, wherein ε in Formula A1 is an adjustment constant, A circuit simulation device.

2. wherein the first main coefficient is represented by Formula A2, 【Number 2】 wherein the second main coefficient is represented by Formula A3, 【Number 3】 wherein the third main coefficient is represented by Formula A4, [Number 4] wherein C00(T), C01(T), C02(T), and C03(T) in Formula A2 are sub - coefficients of the first main coefficient that take the temperature as a variable, respectively, wherein C10(T), C11(T), C12(T), and C13(T) in Formula A3 are sub - coefficients of the second main coefficient that take the temperature as a variable, respectively, wherein C20, C21, C22, and C23 in Formula A4 are sub - coefficients of the third main coefficient, respectively, The circuit simulation device according to Claim 1.

3. The four sub - coefficients of the first main coefficient and the four sub - coefficients of the second main coefficient are functions that take only the temperature as a variable, The circuit simulation device according to Claim 2.

4. A method for generating an output characteristic model formula of a MOS transistor, which generates an output characteristic model formula of a MOS transistor, Let the first main terminal, the second main terminal, and the control terminal of the MOS transistor be x, y, and z, respectively. Let the main terminal voltage, which is the voltage of the second main terminal with respect to the first main terminal, be Vyx, and let the control terminal voltage, which is the voltage of the control terminal with respect to the first main terminal, be Vzx. Let the main terminal current, which is the current flowing from the second main terminal to the first main terminal, be Iy, and let the temperature of the MOS transistor be T. The first model equation of the main terminal current, which has the main terminal voltage as a positive independent variable and the first main coefficient C0, the second main coefficient C1, the third main coefficient C2, and the adjustment constant ε, is expressed as Equation A5. 【Number 5】 Replacing the trailing 0, 1, 2 in the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2 with the integer i, the second model equation of the main coefficient Ci with the control terminal voltage as a positive independent variable is expressed as Equation A6. 【Number 6】 Ci0, Ci1, Ci2, and Ci3 in Equation A6 are sub - coefficients with the temperature as a variable, respectively, and δ is another adjustment constant. Based on the first model equation, the measurement data obtained by measuring the output characteristics, which are the characteristics of the main terminal current with respect to the main terminal voltage with the control terminal voltage and the temperature as parameters, a first process of generating main coefficient extraction data by extracting the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2 of the first model equation with the temperature as a parameter and the control terminal voltage as a variable. For each of the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2. Based on the main coefficient extraction data and the second model equation, a second process of generating sub - coefficient extraction data of the four sub - coefficients extracted with the temperature as a variable. For each of the first main coefficient C0, the second main coefficient C1, and the third main coefficient C2. Based on the sub - coefficient extraction data of the four sub - coefficients and the function of the sub - coefficients expressed by a polynomial of the temperature, a third process of extracting the coefficients of the function to generate function coefficient extraction data. After the third process, Based on the determined model equation of the first main coefficient C0 with the control terminal voltage and the temperature as variables, the determined model equation of the second main coefficient C1 with the control terminal voltage and the temperature as variables, and the determined model equation of the third main coefficient C2 with the control terminal voltage as a variable. A fourth process of generating the output characteristic model equation of the MOS transistor as Equation A7. 【Number 7】 Including A method for generating the output characteristic model equation of a MOS transistor.

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