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Modelling the temperature influence on dc characteristics of the IGBT
Microelectronics Reliability 79 (2017) 96–103
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Modelling the temperature influence on dc characteristics of the IGBT
MARK
⁎
Paweł Górecki, Krzysztof Górecki , Janusz Zarębski Department of Marine Electronics, Gdynia Maritime University, Gdynia, Poland
A R T I C L E I N F O
A B S T R A C T
Keywords: IGBT Thermal phenomena Dc characteristics Modelling
This paper concerns modelling the influence of temperature on dc characteristics of IGBTs. In the paper, the form of two popular literature models of this device are analysed and their disadvantages are pointed out. The authors' model of the IGBT for the SPICE software is proposed. A description of this model, a manner of its parameters estimation and the results of experimental verification of its correctness are presented in various operating ranges and in a wide range of ambient temperature values. On the basis of the obtained results of calculations and measurements the range of applications of the authors' model and the investigated literature models is discussed.
1. Introduction
magnetic devices [19]. So far, a lot of articles on modelling IGBTs have been published in the literature, e.g. [20,21,22]. Different approaches, such as physical or behavioral, were used to model this type of a transistor. The known models are dedicated for different simulation software. The simplest model of the transistor, often used in the analysis of power converters, is the ideal switch, with on-state resistance equal to zero and infinitely high off-state resistance [1]. This type of model allows for preliminary verification of the system design, but it does not allow taking into account impact of transistor properties on the system characteristics. A model of the transistor in the form of a resistor of resistance described by a piece-wise linear function [1] or a nonlinear large-signal model [23] is also often used. In the literature a lot of models of IGBTs of different accuracy can be found. Such models may have the form of detailed models [24,25] or compact models [26,27,28,29]. The highest accuracy could be achieved by detailed models, which make it possible to obtain space-time distribution of current density or potentials in the structure of the considered device. Such a kind of models is useful, first of all, for designers of semiconductor devices. On the other hand a high degree of their complexity causes problems with their practical use in the analysis of electronic systems containing more semiconductor components, because such analyses are time consuming or, as it is observed a problem with convergence of analyses then occurs [30]. Additionally, in this case a problem with the synchronous use of software dedicated for the electronics network analysis and software dedicated for the analysis of detailed models is observed. Therefore, in the analysis of electronic circuits, compact models of semiconductor components are commonly used, describing dependences between voltages and currents at the
Power semiconductor devices are commonly used in switch-mode power supplies circuits and analogue electronic circuits operating in a continuous mode [1,2,3]. Within a range of high values of voltages and currents, IGBTs (Insulated Gate Bipolar Transistors) are often used in practice [2]. Over the period of the last thirty years different structures of IGBTs have been elaborated. There are: non-punch-through (NPT), punch-through (PT), field-stop (FS) [4,5] IGBTs and new generations of this device—the third generation (IGBT3) [6,7] and the fourth generation (IGBT4) [8]. As it is commonly known, characteristics and technical parameters of semiconductor devices strongly depend on temperature [4,8,9]. Additionally, it is commonly known that an increase of device temperature causes shortening of their lifetime [10]. While designing electronic circuits, computer simulations are typically performed to verify correctness of the project. Reliability of the obtained results of calculations depends on accuracy of the applied models [11,12,13]. Higher accuracy is characteristic for detailed models, but on the other hand a high degree of their complexity practically makes it impossible to use them in the analysis of networks containing a high number of semiconductor devices [11,14]. Therefore, in the analysis of electronic networks, compact models of semiconductor devices describing dependences between voltages and currents on the terminals of these devices are typically used. Due to widespread popularity of the SPICE software [14], models of semiconductor devices and integrated circuits dedicated for this software are important for designers of electronic circuits. Such models were proposed in many papers by many authors, among others, for semiconductor devices [15,16,17], integrated circuits [18] and
⁎
Corresponding author. E-mail addresses: [email protected] (P. Górecki), [email protected] (K. Górecki), [email protected] (J. Zarębski).
http://dx.doi.org/10.1016/j.microrel.2017.10.019 Received 29 May 2017; Received in revised form 1 September 2017; Accepted 18 October 2017 0026-2714/ © 2017 Elsevier Ltd. All rights reserved.
Microelectronics Reliability 79 (2017) 96–103
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C
terminals of these components. Such models are described e.g. in the papers [6,31,32,33,34,35,36,37]. In the paper [31] a PSpice based evaluation platform for high power IGBT devices is presented. This platform makes it possible to simulate influence of the selected parameters of the extended Hefner model on static and dynamic properties of the considered device operating in switch-mode power converters. In the cited paper the influence of temperature on IGBT properties are taken into account, but operation of this device at a weak control signal is not considered. An electrothermal model of the IGBT is proposed in the paper [32]. This model is based on the Hefner model and it is implemented in the PSpice source C-code. This model is dedicated to study properties of the considered device operating at high current values with thermal phenomena taken into account. In the paper [6] properties of three generations of IGBTs at very low temperature are considered. A model of this transistor is proposed and the results of its verification over the range 50–300 K are presented. Using this model the analysis of one leg of the PWM inverter at cryogenic temperature was performed. In turn, the compact thermal model of IGBT module is proposed in the paper [33]. This model has a form of the nonlinear Cauer network, in which the values of parameters depend on temperature. The model was practically verified for the 1700 V/1000 A IGBT module. In the paper [34] the compact models of NPT-IGBT and PT-IGBT dedicated for the SABER software are proposed. Using these models some dc and transient characteristics are calculated. Particularly, a power dissipation during the turn-off is considered. Unfortunately, these models use technological parameters, the values of which are typically not well-known for the user of the models. A behavioral model of the IGBT is proposed in the paper [35]. This model is based on the empirical formula and it is dedicated for the SABER software. In the paper [37] the method of modelling NPT IGBTs is described. On the basis of the solution ambipolar diffusion equation the compact model of this device is formulated in the form of three differentiation equations. Experimental verification of this model is performed only when the considered device is switched. The model of high-voltage IGBTs is proposed in the paper [36]. This model is dedicated to the PSpice software and is formulated dividing the modelled transistor into two parts: unipolar and bipolar. The unipolar part is described with the use of the built-in in SPICE simplest model of MOSFETs, whereas the bipolar part of the model consists of many controlled voltage and current sources. The procedure of parameters estimation is complicated and it requires e.g. 2D simulation of the considered IGBT structure. The authors proposed an IGBT model, published in the paper [26]. The model presented in the mentioned paper does not distinguish series resistance of the collector and the diode, which significantly influences the shape of the obtained characteristics. The dependence of the generation current and the saturation current of the diode on temperature was also improved. This model was verified for one ambient temperature only. The purpose of this paper is to formulate the IGBT model for the SPICE software that correctly describes the temperature influence on its characteristics and to verify experimentally this model, as well as to compare accuracy of the calculation results obtained using the authors' model and popular literature models of IGBTs. In Section 2, popular literature models are presented and described. In Section 3, the form of the formulated by the authors model is presented, in Section 4 the manner of model parameters estimation is proposed and in Section 5—the results of verification of its correctness are shown.
G E Fig. 1. Network representation of the IGBT structure.
this transistor, shown in Fig. 1, is typically used. In this circuit a connection of the MOS transistor, the bipolar transistor and the p-n diode is visible [38]. For the considered structure, many models have been already formulated. Some of them were described in the paper [20]. Currently, two IGBT models are commonly used in the SPICE-aided analysis of electronic networks. These are: the Hefner's model (HM), which was built-in in the PSPICE software [21] and the model proposed on the manufacturer's website [29] and called in this paper MM. These models will be described in the further part of this section. The network representation of the model HM is shown in Fig. 2 [39]. The model shown in Fig. 2 is based on the connection of an input MOS transistor and an output bipolar transistor. The MOS transistor is described by Shichman-Hodges equations [40], whereas the bipolar transistor—by the charge model. In the network presented in Fig. 2, the capital letters indicate physical terminals of the IGBT transistor, and small letters—the MOS transistor (d, s) and the bipolar transistor (b, e) terminals that are not exposed outside the package. This model consists of five controlled current sources describing the DC current components of these devices and six controlled current sources describing nonlinear capacitances in the IGBT structure. The source IMOS represents the channel current of the MOS transistor, the source Imult describes the avalanche phenomenon, sources ICSS and IBSS respectively model the steady-state (bipolar) collector current and the steady-state base current of the bipolar transistor, and the source IT models the IGBT collector current. The other current sources describe currents flowing through nonlinear capacitances, respectively: gatesource (source dQgs/dt), drain-gate (source dQmult/dt), source-drain
G E(s) dQdg/dt dQgs/dt
Imos
dQds/dt Imult b(d)
dQmult/dt
Icss
Ibss
dQcer/dt
dQeb/dt
e IT
2. The selected literature models
C Fig. 2. Network representation of the Hefner's isothermal model built-in in PSPICE [23].
In order to analyse properties of the IGBT, the equivalent circuit of 97
Microelectronics Reliability 79 (2017) 96–103
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current source GCH. Currents of these sources are described by [23]
C FI1
⎞ ⎛ LIMIT(vGE1 − vPH , 0, vVT − vPH ) ⎞ ⎛ Ugo ⎞ ⎛ Tj − 1⎟ IGST = IP0⋅⎛ ⎞⋅exp ⎜− k ⎟⋅⎜exp ⎜ ⎟ k ⎟ ⎜ ⎜ ⋅Tj ⎟ ⎜ ⎟ ⋅n ⋅T ⎝ T0 ⎠ q P j ⎠ ⎝ ⎝ q ⎠⎝ ⎠ (1)
FI2
⎜
RD Q1 RG
RDS
M1
G
D1 RER
IGCH =
LE
RS
VF1
RCAP
D2
RL
CAP
EV D3
⎟
vBE1 ⋅B⋅vmi |vBE1|
(2)
In the Eqs. (1), (2) IPO, np and B are parameters of the AM model, whose values are estimated in the reference temperature T0, Ugo is equal to 1.206 V for silicon, k is the Boltzmann constant and q—the electron charge. Tj denotes temperature of the investigated transistor. The value of the standard SPICE function LIMIT(x, min, max) is equal to min if x < min, then it is equal to max if x > max and finally it is equal to x in the other cases. The voltages vBE1 and vGE1 are marked in Fig. 4. In turn, vPH and vmi denote voltages between the connectors of the controlled voltage sources E4 and E1, respectively. The controlled voltage sources E1, E2 are used to calculate values of the voltage vmi according to the equations included in the paper [20], whereas voltages on the controlled voltage sources E3 and E4 describe linear dependences of the threshold voltage and the Fermi's level on temperature. In these dependences the linear temperature coefficients αPH, αT and the values of these quantities VT0 and PH0 corresponding to the reference temperature T0 are taken in account. The controlled current source GBE describes the current flowing between the base and the emitter of the bipolar transistor included in the modelled structure. The current of this source is described by the dependence of the form [30]
E
VF2
D4 Fig. 3. Network representation of the IGBT model available on the International Rectifier website [26].
(source dQds/dt), base-emitter (source dQeb/dt) and collector-emitter connector (source dQcer/dt). A detailed description of this model can be found in the papers [39,41]. A disadvantage of the considered model is that the user must enter model parameters of a technological character. These parameters are not published by producers, for example: base doping and ambipolar recombination lifetime. Models available on the websites of semiconductor devices manufacturers are characterised by widespread popularity. The network representation of one of such models (MM) proposed by International Rectifier [42] for modelling the IGBT is shown in Fig. 3. In the considered model the built-in in the SPICE software models of the MOS transistor M1 (the Schihman-Hodges model), of the bipolar transistor Q1 and of the diodes D1–D4 are used. Terminals of the model represent the gate (G), the collector (C) and the emitter (E) of the considered transistor, respectively. Additionally, in the considered model series resistances of the gate, the source and the drain of the input MOS transistor by means of resistors RG, RS and RD, leakage resistance of the MOS structure RDS, series resistance of the emitter RER and the reverse diode D1, are taken into account. The remaining elements visible in Fig. 3 are used to describe electric inertia of the considered IGBT. A detailed description of this model is presented in [42]. The models presented in Figs. 2 and 3 have numerous disadvantages. They are characterised by technological parameters that are not available for the model users, for example base doping, ambipolar recombination lifetime and metallurgical base width. Additionally, in both the considered models the influence of temperature on all characteristics of the considered device are not taken into account.
IGBE = −
2 ⎞ ⎛ −v ⎞ ⎛ Ugo ⎞ ⎛ I0 ⎛ Tj ⎞ ⋅⎜exp ⎜ k BC1 ⎟ − 1⎟ ⋅ ⋅exp ⎜− k ⎟ ⎟ ⎜ ⎟ ⎜ βF ⎝ T0 ⎠ ⎟ ⋅n1⋅Tj ⎜ ⋅n1⋅Tj ⎠⎝ ⎝q ⎠ ⎝ q ⎠ ⎜
⎟
(3)
where I0 and n1 are parameters of the model, voltage vBC1 is marked in Fig. 4, while βF is the current gain factor for the forward-active mode of the bipolar transistor given by [30]
βF = β0F⋅
1 + aF⋅(Tj − T0 ) 1 + bF⋅(1 + cF⋅(Tj − T0)⋅|iC |)
(4)
where aF, β0F, cF, bF denote the model parameters in the forward active mode and iC is the collector current of the IGBT. In turn, the controlled current source GBC represents the current flowing between the base and the collector of the bipolar transistor included in the modelled structure. The current of its source is described by
IGBC = −
2 ⎞ ⎛ ⎛ −v ⎞ Ugo ⎞ ⎛ I0 ⎛ Tj ⎞ ⋅ ⋅exp ⎜− k ⋅⎜exp ⎜ k BE1 ⎟ − 1⎟ ⎟ ⎜ ⋅n1⋅Tj ⎟ ⎜ ⎜ ⋅n10⋅Tj ⎟ βR ⎝ T0 ⎠ ⎟ ⎝ q ⎠⎝ ⎝q ⎠ ⎠ ⎜
⎟
(5)
where βR is the current gain factor for the reverse-active mode of the bipolar transistor and is given by [30]
βR = β0R ⋅(1 + αF⋅(Tj − T0))
3. The authors' model
(6)
where β0R is equal to the value of the current gain factor for the reverseactive mode at the reference temperature T0. The main current of the IGBT is modelled by the controlled current source GCE described by [30]
In Fig. 4, the circuit representation of the authors' IGBT model (AM) is presented. In this figure signals on the terminals G, C and E correspond to signals occurring on the terminals of the gate, the collector and the emitter of the modelled IGBT. The series resistances of the emitter and the collector are modelled by linear resistors RE and RC. The linear dependence of series resistance on temperature models the controlled voltage source ERC. Resistors RCE, RBE and RGE model leakages between the connectors of the transistor. The drain current of the MOS transistor, existing in the structure of the considered IGBT, is equal to the sum of two components: the threshold current modelled by the controlled current source GST and the channel current of the MOS structure represented by the controlled
⎛ Tj 2 Ugo ⎞ ⎛ vCE ⎞ IGCE = I0⋅⎛ ⎞ ⋅exp ⎜− k ⎟⎟⋅ 1 + V ⎜ T AN ⎠ ⋅ ⋅ n T ⎝ ⎝ 0⎠ 1 j ⎠ ⎝ q ⎜
⎟
⎜
⎛ ⎛ −v ⎞ ⎛ −v ⎞ ⎞ ⋅⎜exp ⎜ k BC1 ⎟ − exp ⎜ k BE1 ⎟ ⎟ ⎜ ⋅n10⋅Tj ⎟ ⎜ ⋅n1⋅Tj ⎟ ⎟ ⎜ ⎝q ⎠ ⎝q ⎠⎠ ⎝ where VAN denotes the Early's voltage. 98
⎟
(7)
Microelectronics Reliability 79 (2017) 96–103
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Fig. 4. Network representation of the AM model of the IGBT.
C VC li
mi
pt
q
RC
E1
E2
E4
E3
vBC1
MOS transistor model
bipolar transistor iC model
diode model RDD
ERC
GBE GDB
vBE1 vCE1 RBE GST
RGE G
GCH
GBC
RE
RCE
GCE
E
vGE1
considered dependence is linear;
The dc characteristic of the reverse diode describes the controlled current source GDB. The current of this source is given by the following formula
• The value of the PH parameter at temperature T
⎞ ⎛ −v ⎞ ⎛ Tj 3 Ugo ⎞ ⎛ Tj 1.5 IGDB = I0D⋅⎛ ⎞ ⋅exp ⎜− k ⋅⎜exp ⎜ k CE1 ⎟ − 1⎟ + IGD⋅⎛ ⎞ ⎟ ⎜ ⋅nD⋅Tj ⎟ ⎜ ⋅nD⋅Tj ⎟ ⎜ ⎟ ⎝ T0 ⎠ ⎝ T0 ⎠ ⎠⎝ ⎝q ⎠ ⎝ q ⎠ ⎜
⎟
⎞ ⎛ −v ⎞ ⎛ Ugo ⎞ ⎛ ⋅⎜exp ⎜ k CE1 ⎟ − 1⎟ ⋅exp ⎜− k ⎟ ⎜ ⋅nD1⋅Tj ⎟ ⎜ ⋅nD1⋅Tj ⎟ ⎜ ⎟ ⎠⎝ ⎝q ⎠ ⎝ q ⎠
⎜
• •
⎟
(8)
where I0D, I0G, nD and nD1 are parameters of the presented model. The form of Eq. (8) was obtained on the basis of the equation presented in [43] describing ideal and non-ideal components of the current of p-n junction, where the knee current phenomena is disregarded. In Eqs. (1)–(8) one internal temperature of all components of the considered IGBT is assumed. The proposed model is not complicated and only 25 parameters are used in this model. In contrast to the considered literature models, in equations describing the AM model the subthreshold region is also taken into account.
• • • • • •
4. Estimation of model parameters Practical use of the proposed model requires estimation of its parameters values. These values were estimated using the conception of the local estimation procedure described in the papers [23,44]. This procedure involves measurements of characteristics of the considered device and next calculations of model parameters values using the coordinates of the selected points lying on the measured characteristics and transformed equations describing the model. In order to estimate parameters values of the AM model it is indispensable to realise the following steps:
• •
• Measurements of transfer characteristics I (V
•
• •
•
• •
C GE) at VCE = const of the considered transistor at two values (T0 and T01) of the ambient temperature in a wide range of the collector current IC values; Presentation courses of the measured characteristics in the lin-log axis scale; Selection of two points lying in the linear range of the characteristic corresponding to T0 temperature and calculation of the value of np parameters; Using the coordinates of one of the considered point the product of values of parameters β0F and IP0 can be calculated. For the selected value of IP0 the value of β0F is calculated; From the same characteristics the value of parameter PH0 could be obtained as the minimum value of the voltage VGE, at which the
• • 99
1 could be estimated in the same way as it is described above. Using the estimated values of the PH parameter at the considered values of temperature the parameter αPH is calculated; Presentation courses of the measured characteristics IC(VGE) in the lin-sqrt axis scale; The characteristics in the linear range should be approximated with the straight line. The voltage value in the point, where this straight line cross the horizontal axis is equal to the value of the parameter VT0. In the same manner the value of the threshold voltage at temperature T1 should be estimated. Using the estimated values of the threshold voltage in both the temperature values the value of parameter αT is calculated; Using the coordinates of one point lying in the linear range of the considered characteristic the value of the parameter B is calculated; Measurements of the output characteristic IC(VCE) at VGE voltage smaller than VT0 should be performed; Using the coordinates of two points lying in the active range of this characteristic the value of parameter VAN is calculated; Measurements of the output characteristic IC(VCE) at VGE voltage higher than VT0 should be performed; Using the coordinates of two points lying in the active range of this characteristic the value of parameter λ is calculated; Measurements of the output characteristic IC(VCE) at VGE voltage much higher than VT0 should be performed for two values of temperature; Presentation courses of the measured characteristics in the lin-log axis scale; Selection of two points lying in the linear range of the characteristic corresponding to T0 temperature and next calculating the value of n1 and I0 parameters; Using the coordinates of one point lying on the measured characteristic at the highest measured values of IC current and temperature T0 the value of RC parameter is calculated; Using the coordinates of one point lying on the measured characteristic at the highest measured values of IC current and temperature T1 the value of RC(T1) is calculated. Next, using this value and the value of RC parameter the parameter αRC is calculated; Using the measured characteristic IC(VGE) at VCE = const and the previously estimated values of parameters IP0, B, I0 and np the characteristic βF(IC) is calculated. Approximating the obtained characteristic by Eq. (4) the value of the parameter bF is estimated. Repeating operations described in the previous point, values of the parameters aF and cF are calculated.
Microelectronics Reliability 79 (2017) 96–103
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9
1
VCE = 5 V
8
AM
AM
0,1
MM
7
0,01
HM 4
0,0001
3
0,00001
HM
2
0,000001
MM
1
0,0000001
0
0,00000001 0
1
2
3
4
5
6
7
8
9
0
VGE[V]
10
15
20
Fig. 7. Measured and calculated output characteristics of the investigated transistor at the input voltage equal to VGE = 5.6 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
• The output characteristics I (V ) in the reverse mode at V = 0 should be measured; • By approximating these characteristics with Eq. (8) values of paraC
5
VCE[V]
Fig. 5. Measured and calculated transfer characteristics of the investigated transistor at the output voltage equal to VCE = 5 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
CE
10
GE
VGE = 6 V
meters nD, I0D, IGD, nD1 and RDD are calculated.
AM
1
IC[A]
5. The results To verify correctness of the AM model described in Section 3, dc characteristics of the arbitrary selected IGBT of the type IRG4PC40UD by International Rectifier were measured and calculated. This transistor belongs to the fourth generation of IGBTs [8] and it is characterised with the admissible value of the reverse voltage VCEmax = 600 V, with the admissible value of the collector current ICmax = 20 A and with the admissible value of the dissipated power Ptot = 65 W [8,45]. In Figs. 5–10 the results of calculations using the three considered models and measurements of dc characteristics of the considered transistor obtained at different values of the ambient temperature are collected. The parameters values of the investigated literature models (HM and MM) were presented in the papers [30,42]. The values of parameters of the AM model of the IGBT used in the calculations and estimated using the method described in the previous section are collected in Table 1. In order to verify practical usefulness of the models described above, the characteristics of the considered transistor using these models were calculated and the obtained results were compared with the results of the measurements in Figs. 5–10. The measurements were carried out for several temperature values ranging from 22 to 110 °C,
0,1
HM
0,01
MM 0,001 0
2
4
6
8
10
VCE[V] Fig. 8. Measured and calculated output characteristics of the investigated transistor at the input voltage equal to VGE = 6 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
10 9
VGE = 10 V
8 7
AM
IC[A]
6
1
HM
MM
5 4 3
0,1
2
VGE = 5.1 V
AM
IC[A]
VGE = 5.6 V
0,001
5
IC[A]
IC[A]
6
0,01
1
0,001
0 0
0,0001
1
2
3
VCE[V]
4
5
6
HM
0,00001
Fig. 9. Measured and calculated output characteristics of the investigated transistor at the input voltage equal to VGE = 10 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
MM
0,000001 0,0000001
whereas this section presents the results for only two extreme temperature values. The results corresponding to 22 °C are marked by blue color and the results corresponding to 110 °C—by red color. In all figures, points represent the results of measurements, bar-dotted lines—the results of calculations using the model provided by the manufacturer (MM) along with the values of parameters given for the investigated transistor in [8], bar lines—the results of calculations using
0,00000001 0
50
100
150
200
VCE[V] Fig. 6. Measured and calculated output characteristics of the investigated transistor at the input voltage equal to VGE = 5.1 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
100
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0 -1
and calculations is obtained for the AM model. Visible differences between the results of measurements and calculations using this model are observed in a high currents range at room temperature. In this case, these differences are not higher than 3.6%. It is worth noting that both the literature models describe incorrectly the threshold voltage of the transistor. In both the models the threshold voltage is equal to 6 V and does not change with temperature changes. In fact, this voltage strongly depends on temperature and at room temperature the threshold voltage of the investigated transistor is equal to about 5.6 V, whereas at 110 °C—only to about 5 V. In Figs. 6–10 the output characteristics of the considered transistor obtained at different values of the input voltage are presented. In order to illustrate properties of the considered models in different ranges of operation of the IGBT, the output characteristics are calculated for the VGE voltage equal to 5.1 V much smaller than the threshold voltage (Fig. 6), for VGE = 5.6 V equal to the threshold voltage (Fig. 7), for VGE = 6 V higher than the threshold voltage (Fig. 8) and for VGE = 10 V typically used for controlling the IGBT operating as an electronic switch (Fig. 9). Additionally, in Fig. 10 the output characteristic of the reverse biased IGBT is shown. Figs. 6 and 7 show the output characteristics of the transistor operating in the sub-threshold region with the VGE voltage equal to 5.1 V and 5.6 V, respectively. In this range only the AM model allows obtaining satisfactory agreement between the results of measurements and calculations. Good accuracy of this model is due to the fact that the sub-threshold phenomenon is taken into account in its description. In contrast, this phenomenon is taken into account by neither of the considered literature models. Therefore, the calculated values of the collector current by both the literature models are significantly underestimated (do not exceed 10 μA) and they are equal for both VGE voltage values. On the other hand, the measured values of the IC currents are up to 990 mA. This implies a discrepancy between the results of calculations and measurements reaching 5 orders of magnitude. It is also worth noting that the measured values of the collector current strongly depend on temperature. The change of the value of this current with temperature in the range from 22 to 110 °C is up to 11,000%. Particularly, the Early's effect is visible in this range. Fig. 8 shows the output characteristics of the investigated transistor at VGE = 6 V. Good agreement between the results of calculations and measurements was obtained only for the authors' model, except the range of the collector currents below 100 mA, where at temperature equal to 110 °C this agreement significantly deteriorates. In the case of calculations using the literature models, there is a large difference between the results of calculations and measurements across the whole investigated range. This difference is both quantitative and qualitative. Comparing the results of calculations performed using the Hefner model and the measurements results, it can be seen that these values differ even three hundred times. In addition, it is evident that this model does not take into account the influence of temperature on the considered characteristics. The manufacturer's model [25] is characterised by better accuracy and in the investigated range the collector current is an increasing function of the VCE voltage. However, the calculated values of the collector current are over twenty times lower than the measured values. Fig. 9 shows the output characteristics of the investigated transistor operating at the high input voltage VGE = 10 V. In this case, significant improvement of the compliance of the results of calculations using the two literature models is visible, but the model built-in in the SPICE software significantly overstates the output voltages that are up to three times higher than the measured values within the investigated range. In the case of the model presented in the paper [26], differences between the calculated and measured values of the VCE voltages do not exceed 15%. It is noteworthy that an increase of temperature causes a decrease of the VCE voltage, but in the calculated
HM
-2
I C [A]
-3
MM
VGE = 0 V
-4
AM
-5 -6 -7 -8 -9 -10 -1,6
-1,4
-1,2
-1
-0,8
-0,6
-0,4
-0,2
0
VCE[V] Fig. 10. Measured and calculated reverse output characteristics of the investigated transistor at the input voltage equal to VGE = 0 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Table 1 Parameters values of the AM model of the transistor IRG4PC40UD. Parameter Value Parameter Value Parameter Value Parameter Value Parameter Value
VT0 [V] 5.62 PH0 [V] 0.85 βOR 3 IP0 [kA] 4 nD1 5.7
αT [K− 1] 1.4 × 10− 3 αPH [K− 1] 3 × 10− 3 aF [K− 1] 6 × 10− 3 nP 5.8 RC [mΩ] 40
B [A/V2] 0.1 I0 [kA] 1 cF [K− 1] 2 × 10− 3 I0D [kA] 60 RE [mΩ] 5
T0 [K] 300 n1 1.4 bF [A− 1] 3 nD 1.02 αRC [K− 1] 1.8 × 10− 3
λ [V− 1] 2 × 10− 3 βOF 65 VAN [V] 150 IGD [A] 12.5 RDD [mΩ] 50
the model built-in in SPICE (HM) with the values of parameters estimated by the authors in Model Editor [39,46], and solid lines represent the calculations results obtained using the AM model. The characteristics of the considered device were measured using the sourcemeter Keithley 2612a. In order to stabilise the value of the ambient temperature, the investigated transistor was placed in the thermal test chamber. The characteristics were measured using the impulse method. Measurement pulses had a 50 ms period and the duty factor equal to 1%. Such measurement conditions made it possible to neglect a self-heating phenomenon and determine the characteristics of the investigated transistor at its internal temperature practically equal to the ambient temperature. Fig. 5 shows transfer characteristics of the investigated transistor at low output voltage equal to VCE = 5 V. Qualitative compliance of the measured and calculated characteristics using the three considered models at room temperature was obtained. However, the best agreement was obtained for the AM model. It can be seen that the MM model does not take into account the influence of temperature on the considered characteristics and, additionally, the maximum collector current is limited. Yet, such a limit is not visible in the measured characteristics. This phenomenon is characteristic for MOSFET power transistors and it is described in [26]. Its appearance in the literature transistor models is due to the use of equations describing the discrete MOSFET, which is an incorrect approach, because the MOS structure in the IGBT transistor and the discrete MOSFET significantly differ from each other [21]. On the other hand, using the HM model the positive temperature coefficient of VGE voltage is obtained, whereas the value of this coefficient obtained from measurements is approximately equal to −1 mV/ K. This difference demonstrates incorrect modelling of temperature influence on the considered characteristics. The VGE voltage calculated using this model, at the constant value of the collector current IC, is higher than the measured value by up to 25%. Definitely the best agreement between the results of measurements 101
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Acknowledgements
(using the literature models) characteristics the opposite trend is visible. In the case of the MM model [25], this trend is visible in the whole investigated range of currents, and in the case of HM model—only for the collector currents below 3 A. Fig. 10 shows the reverse output characteristics of the investigated transistor. The shape of these characteristics is determined by properties of the antiparallel diode existing in the transistor structure between the collector and the emitter. This diode was included in the MM model, but in the HM model this diode is not included. Therefore, in the calculations results made with the use of the HM model the collector current is practically equal to zero in the whole investigated range (the curve coincides with the horizontal axis). On the other hand, the HM model, despite taking into account the antiparallel diode, does not allow obtaining good agreement between the results of calculations and measurements. In particular, the calculated characteristic shows overestimation of the forward voltage and a too low value of series resistance resulting in a very steep course of the considered characteristics. The difference between the calculated and measured VCE voltages for high values of the IC currents and high temperatures exceeds even 30%. Better agreement was obtained for the authors' model, which in terms of currents above 1 A is characterised by the difference between the calculated and measured VCE values not exceeding 10% at both the ambient temperatures.
The scientific work financed with the Polish science budget resources in the years 2017–2021, as the investigation project No. DI 2015 0075 45 within the framework of the program “Diamentowy Grant”. References [1] R. Ericson, D. Maksimovic, Fundamentals of Power Electronics, Kluwer Academic Publisher, Norwell, 2001. [2] M.H. Rashid, Power Electronic Handbook, Academic Press, Elsevier, 2007. [3] M.K. Kazimierczuk, Pulse-width Modulated DC-DC Power Converters, John Wiley & Sons, Ltd., 2008. [4] J. Yeon, Introduction of New Generation Field-stop Shorted-anode IGBT, Digi-Key Electronics, 2014. [5] Sattar A., Insulated Gate Bipolar Transistor (IGBT) Basics. IXYS Corporation, (Application Note IXAN0063) www.ixys.com/Documents/AppNotes/IXYS_IGBT_ Basic_I.pdf. [6] A.J. Forsyth, S.Y. Yang, P.A. Mawby, P. Igic, Measurement and modelling of power electronic devices at cryogenic temperatures, IEE Proc. Circuits Devices Syst. 153 (5) (2006) 407–415. [7] G. Busatto, C. Abbate, B. Abbate, F. Iannuzzo, IGBT modules robustness during turnoff commutation, Microelectron. Reliab. 48 (8–9) (2008) 1435–1439. [8] IRG4PC40UD Insulated Gate Bipolar Transistor with Ultrafast Soft Recovery Diode, Data sheet, International Rectifier, 1997. [9] J. Singh, Semiconductor Devices. Basic Principles, John Wiley & Sons, 2001. [10] A. Castellazzi, Y.C. Gerstenmaier, R. Kraus, G.K.M. Wachutka, Reliability analysis and modeling of power MOSFETs in the 42-V-PowerNet, IEEE Trans. Power Electron. 21 (3) (2006) 603–612. [11] K. Górecki, J. Zarębski, Influence of MOSFET model form on characteristics of the boost converter, Informacije MIDEM 41 (1) (2011) 1–7. [12] D. Maksimovic, A.M. Stankovic, V.J. Thottuvelil, G.C. Verghese, Modelling and simulation of power electronic converters, Proc. IEEE 89 (6) (2001) 898–912. [13] N. Mohan, W.P. Robbins, T.M. Undeland, R. Nilssen, O. Mo, Simulation of power electronic and motion control systems—an overview, Proc. IEEE 82 (1994) 1287–1302. [14] M. Rashid, H. Rashid, SPICE for Power Electronics and Electronic Power, Taylor and Francis Group, LCC, EngNetBase, 2005. [15] P.A. Mawby, P.M. Igic, M.S. Towers, Physically based compact device models for circuit modelling applications, Microelectron. J. 32 (5–6) (2001) 433–447. [16] Ł. Starzak, M. Zubert, M. Janicki, T. Torzewicz, M. Napieralska, G. Jabloński, A. Napieralski, Behavioral approach to SiC MPS diode electrothermal model generation, IEEE Trans. Electron Devices 60 (2) (2013) 630–638. [17] A. Poppe, Multi-domain compact modelling of LEDs, an overview of models and experimental data, Microelectron. J. 46 (12) (2015) 1138–1151. [18] J. Zarębski, K. Górecki, SPICE-aided modelling of the UC3842 current mode PWM controller with selfheating taken in account, Microelectron. Reliab. 47 (7) (2007) 1145–1152. [19] K. Górecki, K. Detka, Electrothermal model of choking-coils for the analysis of dc-dc converters, Mater. Sci. Eng., B 177 (15) (2015) 1248–1253. [20] K. Sheng, B.W. Williams, S.J. Finney, A review of IGBT models, IEEE Trans. Power Electron. 15 (6) (2000) 1250–1266. [21] A.R. Hefner, D.M. Diebolt, An experimentaly verified IGBT model implemented in the saber circuit simulator, IEEE Trans. Power Electron. 9 (5) (1994) 532–542. [22] B.J. Baliga, Analytical modelling of IGBTs: challenges and solutions, IEEE Trans. Electron Devices 60 (2) (2013) 535–543. [23] J. Zarębski, K. Górecki, The electrothermal large-signal model of power MOS transistors for SPICE, IEEE Trans. Power Electron. 25 (5–6) (2010) 1265–1274. [24] Z. Wang, W. Qiao, B. Tian, L. Qu, An effective heat propagation path-based online adaptive thermal model for IGBT modules, 29th Annual IEEE Applied Power Electronics Conference and Exposition, APEC 2014, Fort Worth, 2014, pp. 513–518. [25] E. Marcault, J.L. Massol, P. Tounsi, J.M. Dorkel, Distributed electrothermal modelling methodology for MOS gated power devices simulations, Proceedings of the 20th International Conference on Mixed Design of Integrated Circuits and Systems, MIXDES 2013, Gdynia, 2013, pp. 301–305. [26] K. Górecki, P. Górecki, Modelling the influence of self-heating on characteristics of IGBTs, Proceedings of the 21st International Conference on Mixed Design of Integrated Circuits & Systems, MIXDES, (2014), pp. 298–302 Lublin. [27] S. Gamage, V. Pathirana, F. Udrea, Fully coupled dynamic selfheating model for power SOI lateral insulated gate bipolar transistors, Proceedings of the IEEE Bipolar/BiCMOS Circuits and Technology Meeting, (2006), p. 4100245 Maastricht. [28] S.S.H.U. Gamage, V. Pathirana, F. Udrea, Electrothermal model for an SOI-based LIGBT, IEEE Trans. Electron Devices 53 (7) (2006) 1698–1704. [29] R. Azar, F. Udrea, W.T. Ng, F. Dawson, W. Findlay, P. Waind, G. Amaratunga, Advanced electrothermal spice modelling of large power IGBTs, IEE Proc. Circuits Devices Syst. 151 (3) (2004) 249–253. [30] J. Zarębski, K. Górecki, SPICE-aided modelling of dc characteristics of power bipolar transistors with selfheating taken in account, Int. J. Numer. Modell. Electron. Networks Devices Fields 22 (6) (2009) 422–433. [31] G.E. Sfakianakis, M. Nawaz, Development of a modeling platform for 4.5 kV IGBT power modules, IECON 2014—40th Annual Conference of the IEEE Industrial Electronics Society, Dallas, 2014, pp. 1416–1422.
6. Conclusions The paper analyses properties of the two literature models of the IGBT—the model HM built-in in SPICE and the model MM available on the manufacturer's website, and the authors' model (AM) of the IGBT. The study was performed for the International Rectifier IRG4PC40UD transistor over a wide range of temperature. The considered literature models do not take into account important phenomena observed in the modelled IGBT. The HM model does not take into account the existence of an antiparallel diode in the structure of the investigated transistor, which results in incorrect calculations of the reverse output characteristics of this device. On the other hand, the subthreshold effect is included in neither of the considered literature models. It results in lower (often far) collector current values at the VGE voltage lower than the threshold voltage values (equal to 5.6 V). In the SPICE model, the temperature influence on the characteristics of the investigated transistor is not practically taken into account, and the estimated values of parameters result in significantly higher values of voltage VCE even in the high input voltages conditions. In turn, with the MM model the correct calculations of the dc characteristics of the investigated transistor are observed when the device operates at room temperature in high input voltages conditions only. In conclusion, neither of the considered literature models provides good accuracy of calculations of IGBT characteristics over a wide range of temperatures and a wide range of values of the input voltage VGE. The AM model of the IGBT proposed by the authors is based on an electrical equivalent of the structure of this transistor. Satisfactory agreement between the results of measurements and calculations of the transfer and output device characteristics over the entire temperature range was achieved only for the AM model. This is particularly evident in the subthreshold range, where the literature models are characterised by discrepancy of not less than 5 orders of magnitude. The model proposed by the authors can be useful for designers of electronic and power electronic networks operating in a wide range of changing temperature values and at different values of the control voltage. It is also visible in the presented results of calculations and measurements that a change of the temperature value visibly influences the characteristics of the considered transistor. In the next step dynamic properties of the considered transistors will be investigated.
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Electron Devices 31 (6) (1984) 821–828. [39] PSpice A/D Reference Guide. Product Version 15.7, (2006). [40] H. Shichman, D.A. Hodges, Modelling and simulation of insulated-gate field-effect transistor switching circuits, IEEE J. Solid State Circuits SC-3 (1968) 285–289. [41] A.R. Hefner Jr., An investigation of the drive circuit requirements for the Power Insulated Gate Bipolar Transistor (IGBT), IEEE Trans. Power Electron. 6 (2) (April 1991) 208–219. [42] Spice Models and Saber Models, Web-site of International Rectifier, http://www.irf. com/product-info/models/saber/. [43] B.M. Wilamowski, R.C. Jaeger, Computerized Circuit Analysis Using SPICE Programs, McGraw-Hill, New York, 1997. [44] J. Zarębski, K. Górecki, Parameters estimation of the d.c. electrothermal model of the bipolar transistor, Int. J. Numer. Modell. Electron. Networks Devices Fields 15 (2) (2002) 181–194. [45] K. Górecki, P. Górecki, The analysis of accuracy of selected methods of measuring the thermal resistance of IGBTs, Metrol. Meas. Syst. 22 (3) (2015) 455–464. [46] P. Górecki, K. Górecki, J. Zarębski, Investigations of properties of selected IGBTs models, Przegląd Elektrotechniczny 93 (7) (2017) 81–85.
[32] O. Apeldoorn, S. Schmitt, R.W. De Doncker, An electrical model of a NPT-IGBT including transient temperature effects realized with PSpice device equations modeling, Proceedings of the IEEE International Symposium on Industrial Electronics, ISIE '97, Guimaraes, Portugal, 1997, pp. 223–228. [33] R. Wu, H. Wang, K.B. Pedersen, K. Ma, P. Ghimire, F. Iannuzzo, F. Blaabjerg, A. Temperature-Dependent Thermal, Model of IGBT modules suitable for circuitlevel simulations, IEEE Trans. Ind. Appl. 52 (4) (2016) 3306–3314. [34] P.M. Igic, P.A. Mawby, M.S. Towers, W. Jamal, S. Batcup, Investigation of the power dissipation during IGBT turn-off using a new physics-based IGBT compact model, Microelectron. Reliab. 42 (7) (2002) 1045–1052. [35] O. Hyeong-Seok, M. El Nokali, A new IGBT behavioral model, Solid State Electron. 45 (12) (2001) 2069–2075. [36] F. Iannuzzo, G. Busatto, Physical CAD model for high-voltage IGBTs based on lumped-charge approach, IEEE Trans. Power Electron. 19 (4) (2004) 885–893. [37] J. Meng, P. Ning, X. Wen, A physical modeling method for NPT IGBTs verified by experiments, 2014 IEEE Conference and Expo Transportation Electrification AsiaPacific ITEC Asia-Pacific, Beijing, 2014, pp. 1–6. [38] B.J. Baliga, M.S. Adler, R.P. Love, P.V. Gray, N.D. Zommer, The insulated gate transistor—a new 3-terminal MOS-controlled bipolar power device, IEEE Trans.
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Modelling the temperature influence on dc characteristics of the IGBT
MARK
⁎
Paweł Górecki, Krzysztof Górecki , Janusz Zarębski Department of Marine Electronics, Gdynia Maritime University, Gdynia, Poland
A R T I C L E I N F O
A B S T R A C T
Keywords: IGBT Thermal phenomena Dc characteristics Modelling
This paper concerns modelling the influence of temperature on dc characteristics of IGBTs. In the paper, the form of two popular literature models of this device are analysed and their disadvantages are pointed out. The authors' model of the IGBT for the SPICE software is proposed. A description of this model, a manner of its parameters estimation and the results of experimental verification of its correctness are presented in various operating ranges and in a wide range of ambient temperature values. On the basis of the obtained results of calculations and measurements the range of applications of the authors' model and the investigated literature models is discussed.
1. Introduction
magnetic devices [19]. So far, a lot of articles on modelling IGBTs have been published in the literature, e.g. [20,21,22]. Different approaches, such as physical or behavioral, were used to model this type of a transistor. The known models are dedicated for different simulation software. The simplest model of the transistor, often used in the analysis of power converters, is the ideal switch, with on-state resistance equal to zero and infinitely high off-state resistance [1]. This type of model allows for preliminary verification of the system design, but it does not allow taking into account impact of transistor properties on the system characteristics. A model of the transistor in the form of a resistor of resistance described by a piece-wise linear function [1] or a nonlinear large-signal model [23] is also often used. In the literature a lot of models of IGBTs of different accuracy can be found. Such models may have the form of detailed models [24,25] or compact models [26,27,28,29]. The highest accuracy could be achieved by detailed models, which make it possible to obtain space-time distribution of current density or potentials in the structure of the considered device. Such a kind of models is useful, first of all, for designers of semiconductor devices. On the other hand a high degree of their complexity causes problems with their practical use in the analysis of electronic systems containing more semiconductor components, because such analyses are time consuming or, as it is observed a problem with convergence of analyses then occurs [30]. Additionally, in this case a problem with the synchronous use of software dedicated for the electronics network analysis and software dedicated for the analysis of detailed models is observed. Therefore, in the analysis of electronic circuits, compact models of semiconductor components are commonly used, describing dependences between voltages and currents at the
Power semiconductor devices are commonly used in switch-mode power supplies circuits and analogue electronic circuits operating in a continuous mode [1,2,3]. Within a range of high values of voltages and currents, IGBTs (Insulated Gate Bipolar Transistors) are often used in practice [2]. Over the period of the last thirty years different structures of IGBTs have been elaborated. There are: non-punch-through (NPT), punch-through (PT), field-stop (FS) [4,5] IGBTs and new generations of this device—the third generation (IGBT3) [6,7] and the fourth generation (IGBT4) [8]. As it is commonly known, characteristics and technical parameters of semiconductor devices strongly depend on temperature [4,8,9]. Additionally, it is commonly known that an increase of device temperature causes shortening of their lifetime [10]. While designing electronic circuits, computer simulations are typically performed to verify correctness of the project. Reliability of the obtained results of calculations depends on accuracy of the applied models [11,12,13]. Higher accuracy is characteristic for detailed models, but on the other hand a high degree of their complexity practically makes it impossible to use them in the analysis of networks containing a high number of semiconductor devices [11,14]. Therefore, in the analysis of electronic networks, compact models of semiconductor devices describing dependences between voltages and currents on the terminals of these devices are typically used. Due to widespread popularity of the SPICE software [14], models of semiconductor devices and integrated circuits dedicated for this software are important for designers of electronic circuits. Such models were proposed in many papers by many authors, among others, for semiconductor devices [15,16,17], integrated circuits [18] and
⁎
Corresponding author. E-mail addresses: [email protected] (P. Górecki), [email protected] (K. Górecki), [email protected] (J. Zarębski).
http://dx.doi.org/10.1016/j.microrel.2017.10.019 Received 29 May 2017; Received in revised form 1 September 2017; Accepted 18 October 2017 0026-2714/ © 2017 Elsevier Ltd. All rights reserved.
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C
terminals of these components. Such models are described e.g. in the papers [6,31,32,33,34,35,36,37]. In the paper [31] a PSpice based evaluation platform for high power IGBT devices is presented. This platform makes it possible to simulate influence of the selected parameters of the extended Hefner model on static and dynamic properties of the considered device operating in switch-mode power converters. In the cited paper the influence of temperature on IGBT properties are taken into account, but operation of this device at a weak control signal is not considered. An electrothermal model of the IGBT is proposed in the paper [32]. This model is based on the Hefner model and it is implemented in the PSpice source C-code. This model is dedicated to study properties of the considered device operating at high current values with thermal phenomena taken into account. In the paper [6] properties of three generations of IGBTs at very low temperature are considered. A model of this transistor is proposed and the results of its verification over the range 50–300 K are presented. Using this model the analysis of one leg of the PWM inverter at cryogenic temperature was performed. In turn, the compact thermal model of IGBT module is proposed in the paper [33]. This model has a form of the nonlinear Cauer network, in which the values of parameters depend on temperature. The model was practically verified for the 1700 V/1000 A IGBT module. In the paper [34] the compact models of NPT-IGBT and PT-IGBT dedicated for the SABER software are proposed. Using these models some dc and transient characteristics are calculated. Particularly, a power dissipation during the turn-off is considered. Unfortunately, these models use technological parameters, the values of which are typically not well-known for the user of the models. A behavioral model of the IGBT is proposed in the paper [35]. This model is based on the empirical formula and it is dedicated for the SABER software. In the paper [37] the method of modelling NPT IGBTs is described. On the basis of the solution ambipolar diffusion equation the compact model of this device is formulated in the form of three differentiation equations. Experimental verification of this model is performed only when the considered device is switched. The model of high-voltage IGBTs is proposed in the paper [36]. This model is dedicated to the PSpice software and is formulated dividing the modelled transistor into two parts: unipolar and bipolar. The unipolar part is described with the use of the built-in in SPICE simplest model of MOSFETs, whereas the bipolar part of the model consists of many controlled voltage and current sources. The procedure of parameters estimation is complicated and it requires e.g. 2D simulation of the considered IGBT structure. The authors proposed an IGBT model, published in the paper [26]. The model presented in the mentioned paper does not distinguish series resistance of the collector and the diode, which significantly influences the shape of the obtained characteristics. The dependence of the generation current and the saturation current of the diode on temperature was also improved. This model was verified for one ambient temperature only. The purpose of this paper is to formulate the IGBT model for the SPICE software that correctly describes the temperature influence on its characteristics and to verify experimentally this model, as well as to compare accuracy of the calculation results obtained using the authors' model and popular literature models of IGBTs. In Section 2, popular literature models are presented and described. In Section 3, the form of the formulated by the authors model is presented, in Section 4 the manner of model parameters estimation is proposed and in Section 5—the results of verification of its correctness are shown.
G E Fig. 1. Network representation of the IGBT structure.
this transistor, shown in Fig. 1, is typically used. In this circuit a connection of the MOS transistor, the bipolar transistor and the p-n diode is visible [38]. For the considered structure, many models have been already formulated. Some of them were described in the paper [20]. Currently, two IGBT models are commonly used in the SPICE-aided analysis of electronic networks. These are: the Hefner's model (HM), which was built-in in the PSPICE software [21] and the model proposed on the manufacturer's website [29] and called in this paper MM. These models will be described in the further part of this section. The network representation of the model HM is shown in Fig. 2 [39]. The model shown in Fig. 2 is based on the connection of an input MOS transistor and an output bipolar transistor. The MOS transistor is described by Shichman-Hodges equations [40], whereas the bipolar transistor—by the charge model. In the network presented in Fig. 2, the capital letters indicate physical terminals of the IGBT transistor, and small letters—the MOS transistor (d, s) and the bipolar transistor (b, e) terminals that are not exposed outside the package. This model consists of five controlled current sources describing the DC current components of these devices and six controlled current sources describing nonlinear capacitances in the IGBT structure. The source IMOS represents the channel current of the MOS transistor, the source Imult describes the avalanche phenomenon, sources ICSS and IBSS respectively model the steady-state (bipolar) collector current and the steady-state base current of the bipolar transistor, and the source IT models the IGBT collector current. The other current sources describe currents flowing through nonlinear capacitances, respectively: gatesource (source dQgs/dt), drain-gate (source dQmult/dt), source-drain
G E(s) dQdg/dt dQgs/dt
Imos
dQds/dt Imult b(d)
dQmult/dt
Icss
Ibss
dQcer/dt
dQeb/dt
e IT
2. The selected literature models
C Fig. 2. Network representation of the Hefner's isothermal model built-in in PSPICE [23].
In order to analyse properties of the IGBT, the equivalent circuit of 97
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current source GCH. Currents of these sources are described by [23]
C FI1
⎞ ⎛ LIMIT(vGE1 − vPH , 0, vVT − vPH ) ⎞ ⎛ Ugo ⎞ ⎛ Tj − 1⎟ IGST = IP0⋅⎛ ⎞⋅exp ⎜− k ⎟⋅⎜exp ⎜ ⎟ k ⎟ ⎜ ⎜ ⋅Tj ⎟ ⎜ ⎟ ⋅n ⋅T ⎝ T0 ⎠ q P j ⎠ ⎝ ⎝ q ⎠⎝ ⎠ (1)
FI2
⎜
RD Q1 RG
RDS
M1
G
D1 RER
IGCH =
LE
RS
VF1
RCAP
D2
RL
CAP
EV D3
⎟
vBE1 ⋅B⋅vmi |vBE1|
(2)
In the Eqs. (1), (2) IPO, np and B are parameters of the AM model, whose values are estimated in the reference temperature T0, Ugo is equal to 1.206 V for silicon, k is the Boltzmann constant and q—the electron charge. Tj denotes temperature of the investigated transistor. The value of the standard SPICE function LIMIT(x, min, max) is equal to min if x < min, then it is equal to max if x > max and finally it is equal to x in the other cases. The voltages vBE1 and vGE1 are marked in Fig. 4. In turn, vPH and vmi denote voltages between the connectors of the controlled voltage sources E4 and E1, respectively. The controlled voltage sources E1, E2 are used to calculate values of the voltage vmi according to the equations included in the paper [20], whereas voltages on the controlled voltage sources E3 and E4 describe linear dependences of the threshold voltage and the Fermi's level on temperature. In these dependences the linear temperature coefficients αPH, αT and the values of these quantities VT0 and PH0 corresponding to the reference temperature T0 are taken in account. The controlled current source GBE describes the current flowing between the base and the emitter of the bipolar transistor included in the modelled structure. The current of this source is described by the dependence of the form [30]
E
VF2
D4 Fig. 3. Network representation of the IGBT model available on the International Rectifier website [26].
(source dQds/dt), base-emitter (source dQeb/dt) and collector-emitter connector (source dQcer/dt). A detailed description of this model can be found in the papers [39,41]. A disadvantage of the considered model is that the user must enter model parameters of a technological character. These parameters are not published by producers, for example: base doping and ambipolar recombination lifetime. Models available on the websites of semiconductor devices manufacturers are characterised by widespread popularity. The network representation of one of such models (MM) proposed by International Rectifier [42] for modelling the IGBT is shown in Fig. 3. In the considered model the built-in in the SPICE software models of the MOS transistor M1 (the Schihman-Hodges model), of the bipolar transistor Q1 and of the diodes D1–D4 are used. Terminals of the model represent the gate (G), the collector (C) and the emitter (E) of the considered transistor, respectively. Additionally, in the considered model series resistances of the gate, the source and the drain of the input MOS transistor by means of resistors RG, RS and RD, leakage resistance of the MOS structure RDS, series resistance of the emitter RER and the reverse diode D1, are taken into account. The remaining elements visible in Fig. 3 are used to describe electric inertia of the considered IGBT. A detailed description of this model is presented in [42]. The models presented in Figs. 2 and 3 have numerous disadvantages. They are characterised by technological parameters that are not available for the model users, for example base doping, ambipolar recombination lifetime and metallurgical base width. Additionally, in both the considered models the influence of temperature on all characteristics of the considered device are not taken into account.
IGBE = −
2 ⎞ ⎛ −v ⎞ ⎛ Ugo ⎞ ⎛ I0 ⎛ Tj ⎞ ⋅⎜exp ⎜ k BC1 ⎟ − 1⎟ ⋅ ⋅exp ⎜− k ⎟ ⎟ ⎜ ⎟ ⎜ βF ⎝ T0 ⎠ ⎟ ⋅n1⋅Tj ⎜ ⋅n1⋅Tj ⎠⎝ ⎝q ⎠ ⎝ q ⎠ ⎜
⎟
(3)
where I0 and n1 are parameters of the model, voltage vBC1 is marked in Fig. 4, while βF is the current gain factor for the forward-active mode of the bipolar transistor given by [30]
βF = β0F⋅
1 + aF⋅(Tj − T0 ) 1 + bF⋅(1 + cF⋅(Tj − T0)⋅|iC |)
(4)
where aF, β0F, cF, bF denote the model parameters in the forward active mode and iC is the collector current of the IGBT. In turn, the controlled current source GBC represents the current flowing between the base and the collector of the bipolar transistor included in the modelled structure. The current of its source is described by
IGBC = −
2 ⎞ ⎛ ⎛ −v ⎞ Ugo ⎞ ⎛ I0 ⎛ Tj ⎞ ⋅ ⋅exp ⎜− k ⋅⎜exp ⎜ k BE1 ⎟ − 1⎟ ⎟ ⎜ ⋅n1⋅Tj ⎟ ⎜ ⎜ ⋅n10⋅Tj ⎟ βR ⎝ T0 ⎠ ⎟ ⎝ q ⎠⎝ ⎝q ⎠ ⎠ ⎜
⎟
(5)
where βR is the current gain factor for the reverse-active mode of the bipolar transistor and is given by [30]
βR = β0R ⋅(1 + αF⋅(Tj − T0))
3. The authors' model
(6)
where β0R is equal to the value of the current gain factor for the reverseactive mode at the reference temperature T0. The main current of the IGBT is modelled by the controlled current source GCE described by [30]
In Fig. 4, the circuit representation of the authors' IGBT model (AM) is presented. In this figure signals on the terminals G, C and E correspond to signals occurring on the terminals of the gate, the collector and the emitter of the modelled IGBT. The series resistances of the emitter and the collector are modelled by linear resistors RE and RC. The linear dependence of series resistance on temperature models the controlled voltage source ERC. Resistors RCE, RBE and RGE model leakages between the connectors of the transistor. The drain current of the MOS transistor, existing in the structure of the considered IGBT, is equal to the sum of two components: the threshold current modelled by the controlled current source GST and the channel current of the MOS structure represented by the controlled
⎛ Tj 2 Ugo ⎞ ⎛ vCE ⎞ IGCE = I0⋅⎛ ⎞ ⋅exp ⎜− k ⎟⎟⋅ 1 + V ⎜ T AN ⎠ ⋅ ⋅ n T ⎝ ⎝ 0⎠ 1 j ⎠ ⎝ q ⎜
⎟
⎜
⎛ ⎛ −v ⎞ ⎛ −v ⎞ ⎞ ⋅⎜exp ⎜ k BC1 ⎟ − exp ⎜ k BE1 ⎟ ⎟ ⎜ ⋅n10⋅Tj ⎟ ⎜ ⋅n1⋅Tj ⎟ ⎟ ⎜ ⎝q ⎠ ⎝q ⎠⎠ ⎝ where VAN denotes the Early's voltage. 98
⎟
(7)
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Fig. 4. Network representation of the AM model of the IGBT.
C VC li
mi
pt
q
RC
E1
E2
E4
E3
vBC1
MOS transistor model
bipolar transistor iC model
diode model RDD
ERC
GBE GDB
vBE1 vCE1 RBE GST
RGE G
GCH
GBC
RE
RCE
GCE
E
vGE1
considered dependence is linear;
The dc characteristic of the reverse diode describes the controlled current source GDB. The current of this source is given by the following formula
• The value of the PH parameter at temperature T
⎞ ⎛ −v ⎞ ⎛ Tj 3 Ugo ⎞ ⎛ Tj 1.5 IGDB = I0D⋅⎛ ⎞ ⋅exp ⎜− k ⋅⎜exp ⎜ k CE1 ⎟ − 1⎟ + IGD⋅⎛ ⎞ ⎟ ⎜ ⋅nD⋅Tj ⎟ ⎜ ⋅nD⋅Tj ⎟ ⎜ ⎟ ⎝ T0 ⎠ ⎝ T0 ⎠ ⎠⎝ ⎝q ⎠ ⎝ q ⎠ ⎜
⎟
⎞ ⎛ −v ⎞ ⎛ Ugo ⎞ ⎛ ⋅⎜exp ⎜ k CE1 ⎟ − 1⎟ ⋅exp ⎜− k ⎟ ⎜ ⋅nD1⋅Tj ⎟ ⎜ ⋅nD1⋅Tj ⎟ ⎜ ⎟ ⎠⎝ ⎝q ⎠ ⎝ q ⎠
⎜
• •
⎟
(8)
where I0D, I0G, nD and nD1 are parameters of the presented model. The form of Eq. (8) was obtained on the basis of the equation presented in [43] describing ideal and non-ideal components of the current of p-n junction, where the knee current phenomena is disregarded. In Eqs. (1)–(8) one internal temperature of all components of the considered IGBT is assumed. The proposed model is not complicated and only 25 parameters are used in this model. In contrast to the considered literature models, in equations describing the AM model the subthreshold region is also taken into account.
• • • • • •
4. Estimation of model parameters Practical use of the proposed model requires estimation of its parameters values. These values were estimated using the conception of the local estimation procedure described in the papers [23,44]. This procedure involves measurements of characteristics of the considered device and next calculations of model parameters values using the coordinates of the selected points lying on the measured characteristics and transformed equations describing the model. In order to estimate parameters values of the AM model it is indispensable to realise the following steps:
• •
• Measurements of transfer characteristics I (V
•
• •
•
• •
C GE) at VCE = const of the considered transistor at two values (T0 and T01) of the ambient temperature in a wide range of the collector current IC values; Presentation courses of the measured characteristics in the lin-log axis scale; Selection of two points lying in the linear range of the characteristic corresponding to T0 temperature and calculation of the value of np parameters; Using the coordinates of one of the considered point the product of values of parameters β0F and IP0 can be calculated. For the selected value of IP0 the value of β0F is calculated; From the same characteristics the value of parameter PH0 could be obtained as the minimum value of the voltage VGE, at which the
• • 99
1 could be estimated in the same way as it is described above. Using the estimated values of the PH parameter at the considered values of temperature the parameter αPH is calculated; Presentation courses of the measured characteristics IC(VGE) in the lin-sqrt axis scale; The characteristics in the linear range should be approximated with the straight line. The voltage value in the point, where this straight line cross the horizontal axis is equal to the value of the parameter VT0. In the same manner the value of the threshold voltage at temperature T1 should be estimated. Using the estimated values of the threshold voltage in both the temperature values the value of parameter αT is calculated; Using the coordinates of one point lying in the linear range of the considered characteristic the value of the parameter B is calculated; Measurements of the output characteristic IC(VCE) at VGE voltage smaller than VT0 should be performed; Using the coordinates of two points lying in the active range of this characteristic the value of parameter VAN is calculated; Measurements of the output characteristic IC(VCE) at VGE voltage higher than VT0 should be performed; Using the coordinates of two points lying in the active range of this characteristic the value of parameter λ is calculated; Measurements of the output characteristic IC(VCE) at VGE voltage much higher than VT0 should be performed for two values of temperature; Presentation courses of the measured characteristics in the lin-log axis scale; Selection of two points lying in the linear range of the characteristic corresponding to T0 temperature and next calculating the value of n1 and I0 parameters; Using the coordinates of one point lying on the measured characteristic at the highest measured values of IC current and temperature T0 the value of RC parameter is calculated; Using the coordinates of one point lying on the measured characteristic at the highest measured values of IC current and temperature T1 the value of RC(T1) is calculated. Next, using this value and the value of RC parameter the parameter αRC is calculated; Using the measured characteristic IC(VGE) at VCE = const and the previously estimated values of parameters IP0, B, I0 and np the characteristic βF(IC) is calculated. Approximating the obtained characteristic by Eq. (4) the value of the parameter bF is estimated. Repeating operations described in the previous point, values of the parameters aF and cF are calculated.
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9
1
VCE = 5 V
8
AM
AM
0,1
MM
7
0,01
HM 4
0,0001
3
0,00001
HM
2
0,000001
MM
1
0,0000001
0
0,00000001 0
1
2
3
4
5
6
7
8
9
0
VGE[V]
10
15
20
Fig. 7. Measured and calculated output characteristics of the investigated transistor at the input voltage equal to VGE = 5.6 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
• The output characteristics I (V ) in the reverse mode at V = 0 should be measured; • By approximating these characteristics with Eq. (8) values of paraC
5
VCE[V]
Fig. 5. Measured and calculated transfer characteristics of the investigated transistor at the output voltage equal to VCE = 5 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
CE
10
GE
VGE = 6 V
meters nD, I0D, IGD, nD1 and RDD are calculated.
AM
1
IC[A]
5. The results To verify correctness of the AM model described in Section 3, dc characteristics of the arbitrary selected IGBT of the type IRG4PC40UD by International Rectifier were measured and calculated. This transistor belongs to the fourth generation of IGBTs [8] and it is characterised with the admissible value of the reverse voltage VCEmax = 600 V, with the admissible value of the collector current ICmax = 20 A and with the admissible value of the dissipated power Ptot = 65 W [8,45]. In Figs. 5–10 the results of calculations using the three considered models and measurements of dc characteristics of the considered transistor obtained at different values of the ambient temperature are collected. The parameters values of the investigated literature models (HM and MM) were presented in the papers [30,42]. The values of parameters of the AM model of the IGBT used in the calculations and estimated using the method described in the previous section are collected in Table 1. In order to verify practical usefulness of the models described above, the characteristics of the considered transistor using these models were calculated and the obtained results were compared with the results of the measurements in Figs. 5–10. The measurements were carried out for several temperature values ranging from 22 to 110 °C,
0,1
HM
0,01
MM 0,001 0
2
4
6
8
10
VCE[V] Fig. 8. Measured and calculated output characteristics of the investigated transistor at the input voltage equal to VGE = 6 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
10 9
VGE = 10 V
8 7
AM
IC[A]
6
1
HM
MM
5 4 3
0,1
2
VGE = 5.1 V
AM
IC[A]
VGE = 5.6 V
0,001
5
IC[A]
IC[A]
6
0,01
1
0,001
0 0
0,0001
1
2
3
VCE[V]
4
5
6
HM
0,00001
Fig. 9. Measured and calculated output characteristics of the investigated transistor at the input voltage equal to VGE = 10 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
MM
0,000001 0,0000001
whereas this section presents the results for only two extreme temperature values. The results corresponding to 22 °C are marked by blue color and the results corresponding to 110 °C—by red color. In all figures, points represent the results of measurements, bar-dotted lines—the results of calculations using the model provided by the manufacturer (MM) along with the values of parameters given for the investigated transistor in [8], bar lines—the results of calculations using
0,00000001 0
50
100
150
200
VCE[V] Fig. 6. Measured and calculated output characteristics of the investigated transistor at the input voltage equal to VGE = 5.1 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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0 -1
and calculations is obtained for the AM model. Visible differences between the results of measurements and calculations using this model are observed in a high currents range at room temperature. In this case, these differences are not higher than 3.6%. It is worth noting that both the literature models describe incorrectly the threshold voltage of the transistor. In both the models the threshold voltage is equal to 6 V and does not change with temperature changes. In fact, this voltage strongly depends on temperature and at room temperature the threshold voltage of the investigated transistor is equal to about 5.6 V, whereas at 110 °C—only to about 5 V. In Figs. 6–10 the output characteristics of the considered transistor obtained at different values of the input voltage are presented. In order to illustrate properties of the considered models in different ranges of operation of the IGBT, the output characteristics are calculated for the VGE voltage equal to 5.1 V much smaller than the threshold voltage (Fig. 6), for VGE = 5.6 V equal to the threshold voltage (Fig. 7), for VGE = 6 V higher than the threshold voltage (Fig. 8) and for VGE = 10 V typically used for controlling the IGBT operating as an electronic switch (Fig. 9). Additionally, in Fig. 10 the output characteristic of the reverse biased IGBT is shown. Figs. 6 and 7 show the output characteristics of the transistor operating in the sub-threshold region with the VGE voltage equal to 5.1 V and 5.6 V, respectively. In this range only the AM model allows obtaining satisfactory agreement between the results of measurements and calculations. Good accuracy of this model is due to the fact that the sub-threshold phenomenon is taken into account in its description. In contrast, this phenomenon is taken into account by neither of the considered literature models. Therefore, the calculated values of the collector current by both the literature models are significantly underestimated (do not exceed 10 μA) and they are equal for both VGE voltage values. On the other hand, the measured values of the IC currents are up to 990 mA. This implies a discrepancy between the results of calculations and measurements reaching 5 orders of magnitude. It is also worth noting that the measured values of the collector current strongly depend on temperature. The change of the value of this current with temperature in the range from 22 to 110 °C is up to 11,000%. Particularly, the Early's effect is visible in this range. Fig. 8 shows the output characteristics of the investigated transistor at VGE = 6 V. Good agreement between the results of calculations and measurements was obtained only for the authors' model, except the range of the collector currents below 100 mA, where at temperature equal to 110 °C this agreement significantly deteriorates. In the case of calculations using the literature models, there is a large difference between the results of calculations and measurements across the whole investigated range. This difference is both quantitative and qualitative. Comparing the results of calculations performed using the Hefner model and the measurements results, it can be seen that these values differ even three hundred times. In addition, it is evident that this model does not take into account the influence of temperature on the considered characteristics. The manufacturer's model [25] is characterised by better accuracy and in the investigated range the collector current is an increasing function of the VCE voltage. However, the calculated values of the collector current are over twenty times lower than the measured values. Fig. 9 shows the output characteristics of the investigated transistor operating at the high input voltage VGE = 10 V. In this case, significant improvement of the compliance of the results of calculations using the two literature models is visible, but the model built-in in the SPICE software significantly overstates the output voltages that are up to three times higher than the measured values within the investigated range. In the case of the model presented in the paper [26], differences between the calculated and measured values of the VCE voltages do not exceed 15%. It is noteworthy that an increase of temperature causes a decrease of the VCE voltage, but in the calculated
HM
-2
I C [A]
-3
MM
VGE = 0 V
-4
AM
-5 -6 -7 -8 -9 -10 -1,6
-1,4
-1,2
-1
-0,8
-0,6
-0,4
-0,2
0
VCE[V] Fig. 10. Measured and calculated reverse output characteristics of the investigated transistor at the input voltage equal to VGE = 0 V. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Table 1 Parameters values of the AM model of the transistor IRG4PC40UD. Parameter Value Parameter Value Parameter Value Parameter Value Parameter Value
VT0 [V] 5.62 PH0 [V] 0.85 βOR 3 IP0 [kA] 4 nD1 5.7
αT [K− 1] 1.4 × 10− 3 αPH [K− 1] 3 × 10− 3 aF [K− 1] 6 × 10− 3 nP 5.8 RC [mΩ] 40
B [A/V2] 0.1 I0 [kA] 1 cF [K− 1] 2 × 10− 3 I0D [kA] 60 RE [mΩ] 5
T0 [K] 300 n1 1.4 bF [A− 1] 3 nD 1.02 αRC [K− 1] 1.8 × 10− 3
λ [V− 1] 2 × 10− 3 βOF 65 VAN [V] 150 IGD [A] 12.5 RDD [mΩ] 50
the model built-in in SPICE (HM) with the values of parameters estimated by the authors in Model Editor [39,46], and solid lines represent the calculations results obtained using the AM model. The characteristics of the considered device were measured using the sourcemeter Keithley 2612a. In order to stabilise the value of the ambient temperature, the investigated transistor was placed in the thermal test chamber. The characteristics were measured using the impulse method. Measurement pulses had a 50 ms period and the duty factor equal to 1%. Such measurement conditions made it possible to neglect a self-heating phenomenon and determine the characteristics of the investigated transistor at its internal temperature practically equal to the ambient temperature. Fig. 5 shows transfer characteristics of the investigated transistor at low output voltage equal to VCE = 5 V. Qualitative compliance of the measured and calculated characteristics using the three considered models at room temperature was obtained. However, the best agreement was obtained for the AM model. It can be seen that the MM model does not take into account the influence of temperature on the considered characteristics and, additionally, the maximum collector current is limited. Yet, such a limit is not visible in the measured characteristics. This phenomenon is characteristic for MOSFET power transistors and it is described in [26]. Its appearance in the literature transistor models is due to the use of equations describing the discrete MOSFET, which is an incorrect approach, because the MOS structure in the IGBT transistor and the discrete MOSFET significantly differ from each other [21]. On the other hand, using the HM model the positive temperature coefficient of VGE voltage is obtained, whereas the value of this coefficient obtained from measurements is approximately equal to −1 mV/ K. This difference demonstrates incorrect modelling of temperature influence on the considered characteristics. The VGE voltage calculated using this model, at the constant value of the collector current IC, is higher than the measured value by up to 25%. Definitely the best agreement between the results of measurements 101
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Acknowledgements
(using the literature models) characteristics the opposite trend is visible. In the case of the MM model [25], this trend is visible in the whole investigated range of currents, and in the case of HM model—only for the collector currents below 3 A. Fig. 10 shows the reverse output characteristics of the investigated transistor. The shape of these characteristics is determined by properties of the antiparallel diode existing in the transistor structure between the collector and the emitter. This diode was included in the MM model, but in the HM model this diode is not included. Therefore, in the calculations results made with the use of the HM model the collector current is practically equal to zero in the whole investigated range (the curve coincides with the horizontal axis). On the other hand, the HM model, despite taking into account the antiparallel diode, does not allow obtaining good agreement between the results of calculations and measurements. In particular, the calculated characteristic shows overestimation of the forward voltage and a too low value of series resistance resulting in a very steep course of the considered characteristics. The difference between the calculated and measured VCE voltages for high values of the IC currents and high temperatures exceeds even 30%. Better agreement was obtained for the authors' model, which in terms of currents above 1 A is characterised by the difference between the calculated and measured VCE values not exceeding 10% at both the ambient temperatures.
The scientific work financed with the Polish science budget resources in the years 2017–2021, as the investigation project No. DI 2015 0075 45 within the framework of the program “Diamentowy Grant”. References [1] R. Ericson, D. Maksimovic, Fundamentals of Power Electronics, Kluwer Academic Publisher, Norwell, 2001. [2] M.H. Rashid, Power Electronic Handbook, Academic Press, Elsevier, 2007. [3] M.K. Kazimierczuk, Pulse-width Modulated DC-DC Power Converters, John Wiley & Sons, Ltd., 2008. [4] J. Yeon, Introduction of New Generation Field-stop Shorted-anode IGBT, Digi-Key Electronics, 2014. [5] Sattar A., Insulated Gate Bipolar Transistor (IGBT) Basics. IXYS Corporation, (Application Note IXAN0063) www.ixys.com/Documents/AppNotes/IXYS_IGBT_ Basic_I.pdf. [6] A.J. Forsyth, S.Y. Yang, P.A. Mawby, P. Igic, Measurement and modelling of power electronic devices at cryogenic temperatures, IEE Proc. Circuits Devices Syst. 153 (5) (2006) 407–415. [7] G. Busatto, C. Abbate, B. Abbate, F. 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6. Conclusions The paper analyses properties of the two literature models of the IGBT—the model HM built-in in SPICE and the model MM available on the manufacturer's website, and the authors' model (AM) of the IGBT. The study was performed for the International Rectifier IRG4PC40UD transistor over a wide range of temperature. The considered literature models do not take into account important phenomena observed in the modelled IGBT. The HM model does not take into account the existence of an antiparallel diode in the structure of the investigated transistor, which results in incorrect calculations of the reverse output characteristics of this device. On the other hand, the subthreshold effect is included in neither of the considered literature models. It results in lower (often far) collector current values at the VGE voltage lower than the threshold voltage values (equal to 5.6 V). In the SPICE model, the temperature influence on the characteristics of the investigated transistor is not practically taken into account, and the estimated values of parameters result in significantly higher values of voltage VCE even in the high input voltages conditions. In turn, with the MM model the correct calculations of the dc characteristics of the investigated transistor are observed when the device operates at room temperature in high input voltages conditions only. In conclusion, neither of the considered literature models provides good accuracy of calculations of IGBT characteristics over a wide range of temperatures and a wide range of values of the input voltage VGE. The AM model of the IGBT proposed by the authors is based on an electrical equivalent of the structure of this transistor. Satisfactory agreement between the results of measurements and calculations of the transfer and output device characteristics over the entire temperature range was achieved only for the AM model. This is particularly evident in the subthreshold range, where the literature models are characterised by discrepancy of not less than 5 orders of magnitude. The model proposed by the authors can be useful for designers of electronic and power electronic networks operating in a wide range of changing temperature values and at different values of the control voltage. It is also visible in the presented results of calculations and measurements that a change of the temperature value visibly influences the characteristics of the considered transistor. In the next step dynamic properties of the considered transistors will be investigated.
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