Upload
xuening-li
View
215
Download
2
Embed Size (px)
Citation preview
Analytical GTO turn-off model under snubberless turn-off condition
Xuening Li1, A.Q. Huang*, Yuxin Li
Center for Power Electronics Systems, Virginia Polytechnic Institute and State University, 657 Whittemore Hall (0111), Blacksburg, VA 24061, USA
Received 17 September 2002; revised 25 October 2002; accepted 1 November 2002
Abstract
Based on the analysis of numerical simulation results, an analytical turn-off model for the gate turn-off thyristor under snubberless
condition is developed. The turn-off process predicted by the analytical model is in good agreement with numerical simulation.
q 2003 Elsevier Science Ltd. All rights reserved.
Keywords: Power devices; Modeling; Gate turn-off thyristor; Thyristor
1. Introduction
It is well known that insulated gate bipolar transistor
(IGBT) and gate turn-off thyristor (GTO) are very important
switching components for high power application. Under-
standing their internal physics during the turn-off process is
useful for manufacturers and application engineers. The
IGBT turn-off process under snubberless condition has been
discussed extensively [1–5] and analytical models of IGBT
turn-off have been reported. Recently, snubberless turn-off
GTOs, such as GCT, IGCT and ETO [6,7,10] have become
available. During on-state conduction, these devices
behaves like a GTO with double side carrier injection
hence the carrier distribution is significantly different from
that of the IGBT. Although an analytical turn-off model has
been developed for the IGBT [4] turn-off based on IGBT’s
carrier distribution, a new turn-off model is needed to
describe the snubberless turn-off process of the GTO.
The cross-section of a typical high voltage GTO structure
is shown in Fig. 1. Typical n base length is above 500 mm
for 4.5 kV blocking capability. Compared with the drift
length, the cell pitch is small so that we can treat the GTO as
a one-dimensional (1D) device. When it conducts, the anode
and cathode inject holes and electrons into the n and p base
regions and the device enters into high modulation state and
the n base and p base charge are quasi-neutral. Fig. 2 shows
a schematic 1D carrier distribution in the n and p bases.
The exact carrier profile can be obtained by solving the
ambipolar diffusion equation:
›2n
›x2¼
n
L2a
þ1
Da
›n
›tð1Þ
The electron and hole currents are
Jn ¼b
1 þ bJT 2 qDa
›n
›xð2Þ
Jp ¼1
1 þ bJT þ qDa
›n
›xð3Þ
where b ; mn=mp:
In the forward conduction state, the carrier injection
efficiency for the anode and cathode can be assumed to be gn
and gp; respectively. The carrier profile in the drift region
can then be further solved from Eq. (1) by using the
following boundary conditions
›n
›x
����x¼0
¼JT
qDa
b
1 þ b2 gn
� �¼
JTLa
qDa
La
b
1 þ b2 gn
� �
;n0
La
a ð4Þ
and
›p
›x
����x¼W
¼JT
qDa
gp 21
1 þ b
� �;
n0
La
b ð5Þ
n0, a and b are defined as
n0 ;JTLa
qDa
; a ;b
1 þ b2 gn; b ; gp 2
1
1 þ b
0026-2692/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved.
PII: S0 02 6 -2 69 2 (0 2) 00 1 70 -2
Microelectronics Journal 34 (2003) 297–304
www.elsevier.com/locate/mejo
1 Current address: Intersil Corporation, P.O. Box 13996, Research
Triangle Park, NC 27709-3996, USA.
* Corresponding author. Tel.: þ1-540-231-8057; fax: þ1-540-231-6390.
E-mail address: [email protected] (A.Q. Huang).
Solving the steady-state ambipolar equation, the carrier
concentration is
nðxÞ ¼n0
sinhW
La
� � b coshx
La
� �2 a cosh
x 2 W
La
� �� �ð6Þ
The calculated carrier concentration is shown in Fig. 3 for
gn ¼ 0:43 and gp ¼ 0:76: The carrier concentration
obtained by the analytic model agrees well with numerical
simulation result obtained by MEDICI simulation [8].
Snubberless GTO turn-off is typically accomplished
under the unity turn-off gain condition which is defined as
IT=IGmax # 1: The unity gain is required to be reached within
the storage phase [9,10]. At the end of the storage phase, the
GTO turn-off process is like an open base PNP transistor
and can be divided into three phases. Fig. 4 shows the anode
voltage and current, carrier distributions, and electron
current distributions during the three phases obtained from
MEDICI simulation. The first phase is the voltage rise phase
with a constant anode current between point a and b. The
second one is the fast current decay phase between point b
and point c when the anode voltage remains constant. The
last one is the tail current phase after point c. Fig. 4(b) shows
the carrier distribution calculated by MEDICI during the
device turn-off process. There are three regions in the n base
region based on observations of the carrier distribution: a
depletion region near the p base which sustains the anode
voltage, a quasi-neutral region where carrier distribution
remains unchanged during the first two phases, and a
boundary region between the depletion region and quasi-
neutral region.
2. The voltage rise phase
Once unity turn-off gain is established, the electron
injection at the cathode emitter stops. Anode current flows
through the n base to the p base and then flows out of the
gate. The absence of electron injection results in net
extraction of minority carriers from the n base (hole)
since a constant load current has to be maintained due to
Nomenclature
Jn, Jp, JT electron, hole and total current density
IT anode current
Jn0 at the end of the fast current decay phase, the
electron current density at xp1IGmax maximum gate current at the device turn-off
process
VA the anode voltage
VA0 the anode bus voltage
Dp, Da hole, ambipolar diffusivity
La ambipolar diffusion length
tHL high level excess carrier life time
xd location of the interface between the depletion
region and boundary region
x1 location of the boundary layer and quasi-neutron
region
xpd; xp1 xd; x1 at end of the fast current decay phase
xd0 xd when blocking bus voltage at steady-state
gn electron inject efficiency at cathode junction
gp hole inject efficiency at anode junction
1Si dielectric constant of silicon
vsat carrier saturation drift velocity
Nd doping concentration in n base
Npd effective positive charge in depletion region
W width of n 2 drift region
d width of the boundary region during voltage rise
phase
Q total excess carrier charge in boundary layer
Fig. 1. Device structure of a high voltage GTO thyristor. Fig. 2. 1D carrier distribution of the GTO in forward conduction state.
X. Li et al. / Microelectronics Journal 34 (2003) 297–304298
the inductive load characteristic. The open base PNP
transistor voltage will have to rise at a fast rate to support
an expansion of the depletion region at the p-base/n-base
junction. The expansion of the depletion region is a direct
result of the net carrier extraction in order to have an
additional space charge current component to maintain the
constant load current. The other current component that can
be sustained without expansion of the depleting region is the
normal PNP collector diffusion current.
In Fig. 4(b), curves between (a) and (b) are the carrier
profiles of the n base during voltage rise phase. The
boundary layer existing between the depletion region and
the quasi-neutral region is highly modulated. A linear
carrier distribution approximation can be used in the
boundary region as shown in Fig. 5. During the voltage
rise phase, the carrier profile in the quasi-neutral region is
the same as the GTO in the forward conducting state as
clearly shown in Fig. 4(b). Let us now consider the carrier
distribution and current in the boundary layer. At the left
hand side of the boundary layer, holes are extracted away
from the modulated boundary region, passing through the
depleting region to the p base at their saturation velocity.
Fig. 4(c) shows that the electron current at the left hand side
of the boundary layer is zero. The current component is
therefore only the hole diffusion current without electron
current:
qpvsat ¼ Jp
���x¼xd
¼ JT ð7Þ
At the right hand side of the boundary layer, electron current
is not zero and electrons therefore flow out of the boundary
layer. This electron current component results in the net
carrier extraction from the boundary layer and the expansion
of the depletion region. At the same time, the anode voltage
increases with the expansion of the depletion region hence
the boundary layer moves toward the anode. Because
the linear carrier distribution is assumed in the boundary
layer, so the carrier distribution shape keeps unchanged
inside the boundary layer. This is verified in Fig. 4(b).
Furthermore, the boundary layer thickness d can be ignored
when considering with charge control process. The carrier
continuity equation within the boundary layer is therefore
dQ
dt¼ 2Jnjx¼xdþd<xd
ð8Þ
According to Fig. 5, the net n base charge change due to the
moving boundary layer can also be expressed as
dQ
dt< qnðxÞ
dxd
dtð9Þ
The electron current at the boundary region and quasi-
neutral region interface is
Jnjx¼xd¼
b
1 þ bJT 2 qDa
›n
›x
����x¼xd
ð10Þ
It is obvious from Fig. 4(c) that the electron current in the
quasi-neutral region is the same as that in the forward
conducting state. So, electron current at the right hand side
of the boundary layer can be calculated by Eq. (10) using the
forward conducting carrier distribution (a0 in Fig. 4(b)).
Combining Eqs. (8)–(10) yield
qnðxÞdxd
dt¼
b
1 þ bJT 2 qDa
n0
La sinhW
La
� � b sinhxd
La
� ��8>><>>:
2 a sinhxd 2 W
La
� ��9>>>=>>>;
ð11Þ
Fig. 3. Calculated carrier distribution in the GTO and its comparison with MEDICI simulation.
X. Li et al. / Microelectronics Journal 34 (2003) 297–304 299
The voltage in the depletion region is therefore
VAðtÞ ¼qNp
D
21Si
x2dðtÞ ð12Þ
The positive charge in depletion region is
NpD ¼ ND þ
JT
qvsat
ð13Þ
where the carrier saturation drift velocity is [4]
vsat ¼2:4 £ 107 cm=s
1 þ 0:8 expðT=600 KÞð14Þ
Assuming that the total carrier distribution outside the
depletion region does not change in the voltage rise phase,
the voltage rise curve can then be obtained from the analytic
model Eqs. (8)–(14). Fig. 6 shows a comparison of the
calculated anode voltage rise with that obtained by MEDICI
simulation. Very good match with MEDICI simulation is
obtained.
3. Fast current decay model
In the fast current decay phase, the anode voltage
remains unchanged (constant voltage). The carrier distri-
bution varies as that shown in Fig. 4(b) between curve b and
c. The boundary layer is becoming wider and the slope of
the carrier distribution inside the boundary layer decreases.
The both edges of the boundary layer are also moving
toward the anode side at a different speed. Fig. 7 shows the
two boundaries moving with time when a linear carrier
distribution in the boundary layer is again assumed. The
depletion layer edge xd will move slowly because the
effective charge density in the depleting layer, NpD decreases
with the decrease of the anode current. The right side of the
boundary layer moves because of continued carrier extrac-
tions at the left hand side of the boundary layer, although the
rate of carrier extraction is much slower compared with
the voltage rise phase. The net extraction of carriers causes
the interface of the boundary region and the quasi-neutral
region, x1; moving toward the anode. At the edge of the
depletion region, xd, the total current is still hole current
which can be expressed as
Jhjx¼xd¼ JTðtÞ ¼ 2qDp
dn
dx
����xd
¼ 2qDp
nðx1Þ
x1 2 xd
ð15Þ
A linear carrier distribution in the boundary layer is used in
the above equation. From Eq. (15), it is clear that due to the
widening of the boundary layer, the total current will
decrease. This total current decreasing also leads to the
depletion region edge, xdðtÞ; moving slowly towards the
anode. With the current decreasing, x1 must move faster
than the xd. The carrier distribution in the quasi-neutral
region can still be assumed unchanged. To derive an
analytical model for this phase, the charge-controlled-
model is again considered within the moving boundary
region. Between x1 and the xd, the net excess charge
changing rate is
dQ
dt¼ 2Jnjx¼x1
2Q
tHL
ð16Þ
The recombination effect in the boundary region is now
considered in Eq. (16). The electron current at the interface
between the boundary region and quasi-neutral region can
be obtained from Eq. (10) by substituting xd with x1
JnðtÞjx¼x1¼
b
1 þ bJTðtÞ2 qDa
›n
›x
����x¼x1
ð17Þ
Fig. 4. (a) Simulated current and voltage waveforms during turn-off. (b)
Carrier distributions from MEDICI simulation during the turn-off process.
(c) Electron current density during the turn-off process: (a ) forward
conduction ðta ¼ 0:93 msÞ; (b ) at the end of the voltage rise phase ðtb ¼
2:73 msÞ; and (c ) at the beginning of the tail phase ðtc ¼ 5:8 msÞ:
X. Li et al. / Microelectronics Journal 34 (2003) 297–304300
Fig. 5. Schematic diagram showing the moving boundary in the voltage rise phase.
Fig. 7. Schematic diagram of the two moving boundaries in the fast current decay phase.
Fig. 6. Comparison of calculated and MEDICI simulated voltage rise.
X. Li et al. / Microelectronics Journal 34 (2003) 297–304 301
From Fig. 7, the excess charge changing rate in the
boundary region can be expressed as
dQ
dt¼ 2
1
2
dx1dt
þdxd
dt
� �qnðx1Þ ð18Þ
The total excess charge in the boundary region is
Q ¼ 12
qnðx1Þðx1 2 xdÞ ð19Þ
Combining Eqs. (15)–(19) yields
dx1dt
þdxd
dt
� �; Qðx1; xdÞ ð20Þ
where
Qðx1; xdÞ ;2Da
x1 2 xd
22Da
nðx1Þ
�›n
›xx1
��� þ
ðx1 2 xdÞ
tHL
ð21Þ
In the fast current decay phase, VA ¼ VA0; combining Eqs.
(12) and (13)
JT ¼ qNDvsat
x2d 2 x2
d0
x2d0
ð22Þ
where
xd0 ;
ffiffiffiffiffiffiffiffiffiffiffi21SiVA0
qND
s
Substitute JT in Eq. (15) by Eq. (22) yields
x1 ¼2Dpnðx1Þx
2d
NDvsatðx2d0 2 x2
dÞþ xd ð23Þ
therefore
dx1dxd
; Cðx1; xdÞ ð24Þ
where
Cðx1; xdÞ ;4Dpnðx1Þxdx2
d0
NDvsatþðx2
d02x2dÞ
2
ðx2d02x2
dÞ22
2Dp›n›x
���x1
x2dðx
2d02x2
dÞ
NDvsat
ð25Þ
and solving Eqs. (20) and (24), the two moving boundaries,
x1ðtÞ and xdðtÞ; as a function of time can be obtained. Then,
the anode current change with the time can be derived from
Eq. (15).
Fig. 8 shows a comparison of the above analytical model
with MEDICI simulation. The simulated current takes
3.1 ms to decrease from 50 to 9 A/cm2 compared with
3.3 ms calculated by the analytical model during the fast
current decay phase.
4. The tail current phase
After the fast current decay phase, the device enters the
current tail phase. The carrier profile in the current tail phase
is approximated by a linear profile [5], as is shown in Fig. 9.
The electron current at x ¼ xpd is zero. Therefore, from Eq.
(2), the anode current can be expressed as
JTðtÞ ¼ 2qDp
›n
›x
����x¼xp
d
¼ 2qDp
nðWÞ
W 2 xpdð26Þ
In Fig. 9, total excess charge in n quasi-neutral region is
Q ¼ 12
qðW 2 xpdÞnðWÞ ð27Þ
Therefore anode current is
JTðtÞ ¼4Dp
ðW 2 xpdÞ2
QðtÞ ð28Þ
The current tail model can be obtained from a simple charge
control equation
dQ
dt¼ 2
Q
tHL
2 Jnjx¼W ð29Þ
where electron current Jn is proportional to the carrier
concentration at the anode junction [5]
Jnjx¼W¼ Kn2ðWÞ ð30Þ
where K is a constant related to anode structures and can be
extracted from the initial condition at the beginning of the
tail phase
K ¼JnðW ; t ¼ tcÞ
n2ðW ; t ¼ tcÞ<
Jn0
n2ðW ; t ¼ tcÞð31Þ
nðW ; t ¼ tcÞ can be calculated from the linear assumption:
nðW ; tcÞ ¼W 2 xpdxp1 2 xpd
nðxp1Þ ð32Þ
Combining Eqs. (27)–(30) yield
dJTðtÞ
dt¼ 2
JTðtÞ
tHL
2KJ2
TðtÞ
Dpq2ð33Þ
Fig. 8. Calculated and simulated current waveforms ðVA ¼ 2000 VÞ:
X. Li et al. / Microelectronics Journal 34 (2003) 297–304302
The solution of Eq. (33) is
JTðtÞ ¼JTðtcÞ
JTðtcÞ
J1
þ 1
� �exp
t 2 tc
tHL
� �2
JTðtcÞ
J1
� � ð34Þ
where
J1 ;q2Dp
KtHL
The anode current in the current tail process is therefore
expressed in Eq. (34). The calculated tail current is shown in
Fig. 8 after point c.
It is important to point out that the carrier profile at the
anode junction also changes during the fast current decay
phase to accommodate the decreasing current. Therefore
another moving boundary, x01; actually exists at the anode
side as shown in Fig. 4(b) and (c). The change of the anode
side carrier profile (between curve b and curve c) is similar
to a forward bias PN junction when its current is reduced.
The fast current decay phase ends when the two boundary
layers meet and the electron current at their interface equals
to each other. From Eqs. (31) and (32) the electron current at
the end of the fast current decay phase is
Jn0 ¼ Kn2ðxp1ÞðW 2 xpdÞ
2
ðxp1 2 xpdÞ2
ð35Þ
At the same time, the carrier distribution is approximated by
a linear profile from xpd to the anode [5], as is shown in Fig.
4(b) (curve c).
At the end of the fast current decay phase, the electron
current at xp1 is Jn0 ¼ 5 A=cm2 (shown in Fig. 4(c)) and is
used as the initial condition for calculating the current tail
phase. Eq. (35) also shows that the anode current
decreases faster than the exponential term because of
the electron back injection.
Fig. 9. Schematic diagram of carrier distribution in the current tail phase.
Fig. 10. (a) MEDICI simulated current waveforms at different voltages. (b)
Calculated current waveforms at different voltages.
X. Li et al. / Microelectronics Journal 34 (2003) 297–304 303
5. Model validations at different voltages
For turn-off at different voltages, the GTO have
different turn-off current waveforms. For higher voltage,
the current decay rate is slower. This is because that for
higher voltage, the depletion edge is closer to the anode
where a higher carrier concentration exists as shown in
Fig. 4(b). The electron current component Jn in Eq. (16)
lower at regions closer to the anode. So, the moving
boundaries move slower at higher voltages. The analytical
and MEDICI simulation results show good agreements for
GTO turn-off at different voltages as shown in Fig. 10(a)
and (b), respectively.
6. Conclusion
A physics based analytical model for GTO turn-off under
snubberless condition is derived. A linear carrier distri-
bution is used in the boundary region. The voltage rise phase
and fast current decay phase can be calculated by solving
the movement of the boundary region. The MEDICI
simulations show that the analytic model describes the
turn-off process with reasonably good accuracy. Based on
this model, the turn-off process is dominantly determined by
the initial carrier distribution. This approach can be applied
to other snubberless turn-off devices with arbitrary initial
carrier distribution. Further validations of this model with
experimental result would be next step work.
References
[1] D.-S. Kuo, C. Hu, S.P. Sapp, An analytical model for the power
bipolar-MOS transistor, Solid State Electron. 29 (12) (1986)
1229–1237.
[2] J.G. Fossum, R.J. Mcdonald, Charge-control analysis of the COMFET
turn-off transient, IEEE Trans. ED 33 (9) (1986) 1377–1381.
[3] A.R. Hefner Jr., D.L. Blackburn, A performance and trade-off for
teinsulated gate bipolar: buffer layer versus base lifetime reduction,
IEEE Trans. PE 2 (3) (1987) 194–206.
[4] W. Feiler, W. Gerlach, U. Wiese, On the turn-off behaviour of the
NPT-IGBT under clamped inductive loads, Solid State Electron. 39
(1) (1996) 59–67.
[5] A.R. Hefner Jr., D.L. Blackburn, An analytical model for the steady-
state and transient characteristics of the power insulated-gate bipolar
transistor, Solid State Electron. 31 (10) (1988) 1513–1532.
[6] P.K. Steimer, H.E. Gruning, J. Werninger, E. Carroll, S. Klaka, S.
Linder, IGCT—a new emerging technology for high power, low cost
inverters, IEEE IAS 32 (1997) 1592–1599.
[7] I. Takata, M. Bessho, K. Koyanagi, M. Akamatsu, K. Satoh, K.
Kurachi, T. Nakagawa, Snubberless turn-off capability of four-inch
4.5 kV GCT thyristor, ISPSD (1998) 177–180.
[8] MEDICITM User’s Manual.
[9] H.E. Gruening, A. Zuckerberger, Hard drive of high power GTOs:
better switching capability obtained through improved gate-units,
IEEE IAS 31 (1996) 1474–1480.
[10] Y. Li, A.Q. Huang, F.C. Lee, Introducing the emitter turn-off thyristor
(ETO), IEEE IAS 33 (1998) 860–864.
X. Li et al. / Microelectronics Journal 34 (2003) 297–304304