Analytical GTO turn-off model under snubberless turn-off condition

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: huang@vt.edu (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.

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