Base Stored Charge Modeling of Insulated Gate Bipolar
Transistor
Avijit Das
email: [email protected]
Masud-ul Haq
email: [email protected]Md. Nazmul Islam
email: [email protected]Md. Ziaur Rahman Khan
email: [email protected]Abstract: This work presents an analytical model of the base stored charge of a Non Punch Through Insulated Gate Bipolar Transistor for all minority carrier lifetime conditions. Parabolic approximation has been used for derivation of minority carrier concentration within the base. Better agreements with the actual hyperbolic model have been found compared to the linear model generally used. This model can be useful in modeling IGBT parameters for Reverse Blocking applications where nonlinear characteristics play a prominent role.
Keywords: Parabolic Approximation, Minority Excess Charge Concentration, Effective Base Width, Ambipolar Diffusion Length, Carrier Lifetime Control.
I.
I
NTRODUCTIONThe Insulated Gate Bipolar Transistor is a preferred
switching device in a variety of power converters and motor drive applications. The device combines the advantages of high current density bipolar operation that results in low conduction losses with the advantages of fast switches and low drive power of MOSFET gate devices [1]. It is a functional integration of power MOSFET and BJT devices in monolithic form, combining the best attributes of both to achieve optimal characteristics.
One of the major disadvantages of the IGBT is its switching speed which is superior to that of BJT but worse than that of MOSFET. This results in an undesirable amount of switching power loss which needs to be calculated [2]. This has caused heavy interest in the modeling of the transient characteristics of the IGBT, both in power converters [3] as well as high voltage applications [4]. The basis for this transient turn-off modelling depends on the minority carrier charge concentration in the base region that builds up during the steady-state operation of the IGBT.
Several physics-based models have been proposed for the transient characteristic of the IGBT. However, none of them lead to any exact solution. So certain assumptions are made when considering the imposed boundary conditions. One of the assumptions generally considered is to approximate the minority carrier charge distribution with a linear expression (high carrier lifetime) instead of its hyperbolic form. In most of the cases [5]-[10] this assumption was followed to model the steady state and transient characteristics of IGBT. But all these models were more or less confined with some limitations. Later on, free carrier injection in switching conditions was
introduced in modeling IGBT [11]-[13], which showed the significance of all minority carrier lifetime conditions in the transient operation.
The assumption of a linear profile for the minority carrier charge concentration is generally made for high carrier lifetime conditions, where effective base width is much smaller than the ambipolar diffusion length. But situations due to moderately low carrier lifetime can not be taken into account, which is essential for carrier lifetime control in IGBT. Recently, minority carrier lifetime control has become a commonly accepted strategy for optimizing device characteristics of NPT IGBT. Specially irradiation of electrons for carrier lifetime control results in reduction of reverse leakage current of Reverse Blocking IGBTs [15]. Currently, Reverse Blocking IGBTs (RB IGBTs) with carrier control system are used in high efficiency matrix converters which have great possibility to replace DC-linked type circuits [16]. Moreover, practical matrix converter with RB IGBTs can be used to drive motor system [17]. The use of carrier lifetime control in these applications makes it necessary to use IGBT models with nonlinear profile of carrier distribution, which are valid over a wide range of carrier lifetimes.
In this work, a parabolic approximation is considered for the steady state minority carrier concentration. Using this approximation in the ambipolar diffusion equation, an expression is developed for the transient minority carrier distribution. Simulation is used to validate the accuracy of the proposed nonlinear expression. This expression is then used to derive the analytical model for time dependent stored base charge during steady state operation.
II.
B
ASICS
TRUCTURE&
O
PERATION OFIGBT
The cross section of a typical IGBT structure has been shown in Fig. 1. The structure of the device is similar to that of a Vertical Double diffused MOSFET (VDMOSFET) with the exception that a highly doped p-type substrate is used in lieu of a highly doped n-p-type drain contact in the VDMOSFET. A lightly doped thick n-type epitaxial layer N = cm− is grown on top of the p-type substrate to support the high blocking voltage in the reverse bias mode state. A highly doped p-type region N = 9cm− is added to the structure to prevent the
Fig 1. A Cross Section Schematic of IGBT half cell [1]
Fig 2. 1-D coordinate system used in the modeling of NPT IGBT [17]
When a positive gate voltage greater than the threshold voltage � is applied, a path is formed for charges to flow between the n+ source and the n drift region. Applying a positive voltage to the anode terminal of the IGBT causes the emitter of the IGBT section to be at a higher voltage than the collector. Minority carrier (holes) are injected from the emitter (P+ region) into the base (n− drift region). As the positive bias on the emitter of the BJT part of the IGBT increases, the concentration of the injected holes eventually exceeds the background doping level of the n− drift region; hence the conductivity modulation phenomenon. The injected carriers reduce the resistance of the n− drift region and, as a result, the injected holes are recombined with the electrons flowing from the source of the MOSFET to produce the anode current (on state).
The MOSFET gate voltage controls the IGBT switching action. The turn-OFF takes place when the gate voltage is less than the threshold voltage ( �). The inversion layer at
the surface of the P+ body under the gate cannot be kept and therefore no electron current is available in the MOSFET channel. The remaining minority carrier holes, which were stored during the on state of the IGBT, require some time in order to be removed or extracted. The switching losses of the IGBT are dominated by the losses which occur during the much slower second phase of the turn-off period transient because of the time required in removing or extracting the injected carriers in this phase. This is a major disadvantage of the IGBT device as it suffers from high-switching losses.
III.
E
XPRESSION FORM
INORITYC
ARRIERC
ONCENTRATIONThe main foundation of the previously established models was based on the assumption that effective base width must be much smaller than the carrier diffusion length that means high carrier lifetime. But these models are inefficient in case of moderate or low carrier lifetime and thus fail to optimize power in NPT and PT IGBTs. The proposed model takes this into account and provides consistent results in all carrier lifetime conditions.
The minority carrier concentration is given by
� = ��ℎ
− � � ��ℎ �
is the minority carrier charge concentration in the collector-base junction. Expanding the hyperbolic functions into Taylor series and taking parabolic approximation, we can get
��ℎ �− �= �− �+ 6 �− �
��ℎ � = � + 6 �
The initial approximation for carrier concentration is
� =
− �
� + 6 �− �
� + 6 �
which turns out to be
� = + 6
− � � + 6 �
The ambipolar diffusion equation in the base region is
� �,
�� =
�,
� + �
� �, ��
minority carrier concentration in the n drift base is found
Integrating the excess carrier concentration with respect to time and multiplying by q & A, an expression for stored base charge is found
= � [ − 4� ]
For W
L<< 1, �
� and the equation is reduced to the exact
form reported in [6].
IV.
R
ESULT ANDD
ISCUSSIONSFig 3, Fig. 4 and Fig. 5 show the simulation results of the parabolic approximation taken in this proposal. Here effective base width (W) is considered to be 4.2* − cm. The results are compared to those of the hyperbolic and the linear forms used in [6]. Simulations are shown for three cases:
A.
Case : High Carrier Lifetime
For τ��=3.92µs, it is seen in Fig. 3 that both the proposed model and linear model are in good agreement with the hyperbolic model. This is due to the fact that a large number of charges fail to recombine before they reach the collector-base junction. This results in huge charge building up in the base region. Both the parabolic and linear expression depicts this build up correctly.
Fig 3. Minority carrier distribution in the base with respect to distance from base for high carrier lifetime (���=
3.92µs)
Fig 4. Minority carrier distribution in the base with respect to distance from base for moderate carrier lifetime
(���=1µs)
B.
Case 2: Moderate Carrier Lifetime
In case of τ��=1µs, it is seen in Fig. 4 that the linear model shows some deviation with the actual one, while the proposed model shows better consistency. This follows from the fact that when carrier lifetime is neither high nor low, only some of the charge carriers are able to reach the collector base junction before recombination. As a result, significant recombination occurs and a smaller amount of charge builds up in the base. The proposed model is able to account for this effect correctly but the linear model fails to do so.
5
2 3
0
2 2 2
( )
( , ) [4 ( ) ]
4 (6 ) 5
P W x
P x t L W x
L W L W
2 2
0
2 2 2 2
1 1 12 3
. . . .
4 (6 ) 12
P W L W
D W t W L W L W
5
2 3 ( )
[4 ( ) ]
5
W x
L Wx
3
2 2
0
2 2 2
1
. . .[(6 )
(6 ) 6
P W x
L W
D W L W t
4 5 ] 6 20 x x W 3 2 2 0
2 2 2
2 1
. . .[ ( 6 )
(6 ) 6
P W x
W W L
D W L W t
4 5
2 2
(2 6 ) ]
12 20
x x
W L W
2 2 2 2
0
2 2 2 2
1 20 6
. . . [ ]
5 (6 ) 12
P x W L W L W
D t L W L W
2 2 2
0
2 2 2
1 10
. [ ]
(6 ) 10
P xW W W L
D L W t
2 2 0 0 0
2 2 2
20
. .
20 (6 )
P x P x L W W
P
W L W L
2 2 2 2 2
0
2 2 2 2 2
20 1 12 3
. [ . . ]
20 (6 ) 12
P L W W W L W
W
L W L D t L W
Fig 5. Minority carrier distribution in the base with respect to distance from base for low carrier lifetime (���=0.32µs)
C.
Case 3: Low Carrier Lifetime
Fig. 5 shows the case of low carrier lifetime, where τ�� is considered to be 0.32µs. The parabolic model continues to maintain good consistency with the hyperbolic model. However, the linear model shows a larger deviation in this case as the approximation it is based upon, no longer holds true when the base width is larger than the ambipolar diffusion length. The carrier lifetime being low, causes only small amount of excess minority carriers to reach the collector-base junction, resulting in even smaller build-up of charge in the base. Once again, the proposed model is able to predict this phenomenon, while the linear model falls short.
Table1: Data analysis of Minority carrier concentration in different carrier lifetimes
Carrier lifetimes
(µs)
High (3.92)
Distance from base ( −)cm
Minority carrier concentration ( 6) cm−
Actual Proposed Linear
0.0 3.93263 3.90713 3.98488 0.2 3.13931 3.13445 3.21706 0.4 2.38121 2.30832 2.41523 0.6 1.69600 1.59881 1.75918 0.8 0.75324 0.850432 1.05454
Moderat e
(1.00)
0.0 3.56587 3.53619 3.58073 0.2 3.34362 3.32878 3.38815 0.4 3.17325 3.15842 3.23264 0.6 2.94730 2.92876 3.06233 0.8 2.75842 2.74359 2.88832
Low (0.32)
0.0 2.52156 2.49803 2.53331 0.2 2.32904 2.30943 2.39962 0.4 2.13648 2.11688 2.27767 0.6 1.96745 1.93608 2.15963 0.8 1.79843 1.76707 2.04159 Table 1 shows the comparison of minority carrier concentration in different carrier lifetimes and thus verifies the accuracy of the proposed model.
Fig. 6. Variation of stored base charge with effective base width
Fig 7. Variation of stored base charge with base doping concentration
Fig. 6 shows the variation of Stored base charge (Q) with Effective base width (W). Here variation of base width can be accounted for different carrier lifetime profiles. As effective base width is increased, carrier lifetime is decreased. As a result, the amount of recombination occurring in the base region increases, reducing the amount of charge stored in the base. It is seen that the proposed expression is better able to predict the variation of charge with base width compared to the linear expression.
V.
C
ONCLUSIONAfter review and comparison with actual and linear models, a parabolic model is introduced in this work to derive the excess minority carrier distribution and base stored charge of NPT IGBT. This model is valid for all minority carrier lifetime conditions. It can be used in the ambipolar diffusion equation to find out the transient profile of NPT IGBT with carrier lifetime control. It is expected that the transient profile would be essential for improvement of NPT IGBTs, specially those with reverse blocking capability
R
EFERENCES[1] V. K. Khanna, Insulated Gate Bipolar Transistor (IGBT) Theory
and Design, 445 Hoes Lane, Piscataway, NJ: IEEE Press, 2003, pp.
38-45 and 229-240.
[2] A. M. Bazzi, P.T. Kerin, J.W. Kimball and K. Kepley, “IGBT and Diode loss estimation under hysteresis switching”, IEEE
Transactions on Power Electronics, vol. 27, issue 3, Aug. 2011, pp.
1044-1048.
[3] M. Jin and M. Weiming, “Power converter EMI analysis including IGBT nonlinear switching transient model”, IEEE Transactions on Industrial Electronics, vol. 53, issue 5, Oct. 2006, pp. 1557-1583. [4] G. Feng, Z. Zhao, L. Yuan, S. Ji and J. Zhao, “Research on
HVIGBT transient mixture model and parameter extraction method”, Conference on Transportation Electrification Asia Pacific, Beijing, Aug. 31- Sep. 3, 2014, pp. 1-6.
[5] D.S. Kuo, C. Hu and S.P. Sapp, “An analytical model for the power bipolar MOS transistor”, Solid State Electronics, vol. 29, 1986, pp. 1229-1237.
[6] A. R. Hefner and D.L. Blackburn, “An analytical model for the steady-state and transient characteristics of the power insulated-gate bipolar transistor” , Solid State Electronics, vol. 31, no. 10, 1988, pp. 1513-1532.
[7] A. R. Hefner, “Analytical modeling of device-circuit interactions for the power Insulated Gate Bipolar Transistor (IGBT) ”, IEEE Transactions on Industry Applications, vol. 26, no. 06, Nov.-Dec. 1990.
[8] M. Trivedi and K. Shenai, “Modeling the turn-off of IGBTs in hard and soft-switching applications”, IEEE Transaction on Electron
Devices, vol. 44, May 1997, pp. 887-893.
[9] A. Ramamurthy, S. Sawant and B.J. Baliga, “Modeling the dV/dt of the IGBT during inductive turn-off”, IEEE Transactions on Power Electronics, vol. 14, no. 04, July 1999.
[10] B. Fatemizadeh and D. Silber, “A versatile model for IGBT including thermal effects”, 24th IEEE Power Electronics Specialists
Conference (PESC ’93),Seattle,USA, June 1993, pp. 85-92. [11] Y. Yue, J.J. Liou and I. Bataresh, “A steady-state and transient
model valid for all free-carrier injection conditions”, 12th IEEE
Applied Power Electronics, 1997.
[12] P. Leturcq, “A study of distributed switching processes in IGBTs and other power bipolar devices”, IEEE 28th Annual Power
Electronics Specialists Conference (PESC ’97), vol. 01, 1997, pp. 139-147.
[13] J. Sgg, P. Tuerkes and R. Kraus, “Parameter extraction methodology and validation for an electro-thermal physics-based NPT IGBT mode”, IEEE Industry Applications Society Annual
Meeting, New Orleans, Louisiana, Oct. 1997, pp. 1166-1173.
[14] R. Siemieniec, R. Herzer, M. Netzel and J. Lutz, “Applications of carrier lifetime control by irradiation to 1.2KV NPT IGBTs”, 24th
International Conference on Microelectronics (MIEL), Serbia and
Montenegro, May 16-19, 2004.
[15] M. Takai, T. Naito and K. Ueno, “Reverse Blocking IGBT for matrix converter with ultra-thin wafer technology”, IEEE
Proceedings-Circuits, Devices and Systems, vol. 151, issue 3, June
2004, pp. 243-247.
[16] J. Itoh, I. Sato, A. Odaka, H. Ohguchi, H. Kadachi and N. Eguchi, “A Novel Approach to Practical Matrix Converter Motor Drive System with Reverse Blocking IGBT”, IEEE Transactions on
Pow-er Electronics, vol. 20, no. 6, November 2005.
[17] S. Ryu, M. Lee, M.A. Hajji, H. Ahn, D. Han and M.E. Nokali, “A Transient Model for Insulated Gate Bipolar Transistors (IGBTs) ”, International Journal of Electronics, vol. 95, issue 4, 2008, pp. 399-409.
