Solid-State Electronics 47 (2003) 727–739
www.elsevier.com/locate/sse
Analysis of the turn-off failure mechanism of silicon
power diode
Alex Q. Huang *, Victor Temple 1, Yin Liu 2, Yuanzhu Li
3
Center for Power Electronics Systems, The Bradley Department of Electrical and Computer Engineering,
Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
Received 22 July 2002; accepted 19 August 2002
Abstract
A series of simulations were carried out to investigate the failure mechanism of large area silicon power diodes. Static
breakdown behavior of high voltage diodes is first investigated at elevated temperatures. Sustain-mode dynamic avalanche is then discussed. It was found that under isothermal and homogeneity condition, the reverse bias safe operation
area (RBSOA) of power diodes is the same as the sustain-mode dynamic avalanche. After introducing current inhomogeneity, the failure will occur at reverse power density that is much less than the RBSOA predicted by the sustainmode dynamic avalanche. The failure mechanism of power diodes is then proposed based on these findings.
Ó 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction
The silicon power diode is one of the key components
necessary to construct power electronic systems such as
DC to AC power conversion systems. However, todayÕs
silicon power diode has several drawbacks when turning
off from forward conduction to reverse blocking. For
example, the power dissipation during turn-on of a highvoltage switching device (e.g. IGBTs, GTOs) is mainly
attributable to the diodeÕs reverse recovery current. In
addition, possible diode failure when turning off with
high dI=dt [1] and dV =dt [2] limits the power electronics
systemÕs reliability. While much of the published work
on power diodes is focused on improving the reverse
recovery characteristics, the failure mechanism of power
diodes has also attracted much attention.
*
Corresponding author. Tel.: +1-540-231-8057; fax: +1-540231-6390.
E-mail address: huang@vt.edu (A.Q. Huang).
1
Silicon Power Corporation, 3 Northway Lane North,
Latham, NY 121102, USA.
2
Present address: Chrontel Inc. San Jose, CA 95131, USA.
3
Present address: RF Integrated Corp., 15375 Barranca
Pkwy, Irvine, CA 92618, USA.
Although diode failure, which limits its reverse bias
safe operation area (RBSOA) during reverse recovery, is
generally attributed to the on-set of dynamic avalanche,
the exact failure mechanism is still not well understood.
In [3], the measured turn-off failures occur at power
densities that vary from 500 kW/cm2 for voltages around
800 V to 300 kW/cm2 for 1200 V. The peak power
density generally occurs before the turn-off failure and in
some cases can be as high as 700 kW/cm2 . Device simulations performed by [3] did not predict the turn off
failure (i.e. a sudden voltage drop and a subsequent
current increase) observed in measurements. Furthermore, the diodeÕs dV =dt decreases in simulations for
high reverse voltages, whereas in measurements dV =dt
remains large until the turn-off failure at which a sudden
voltage drop appears. The reported end result of a diode
failure is that the breakdown characteristic of the diode
is impaired permanently, probably by a local heating
during a very short time (for some measurements only
0.5 ls) when the diode is conducting the failure current.
The rise of the temperature before failure seems impossible given the short time the diode is conducting the
reverse current. The diode would have to have a very
high current crowding (or current filament) to stress the
local spot to such high temperature. The same authors
also performed measurement on a higher voltage diode
0038-1101/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved.
PII: S 0 0 3 8 - 1 1 0 1 ( 0 2 ) 0 0 3 2 8 - 3
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A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
and showed a failure power density higher than 500 kW/
cm2 [4]. However, only a small temperature increase is
seen in their simulations, indicating that a homogeneous
current distribution exists in the diode and thermal
runaway does not occur. In [5], a stable dynamic avalanche at a maximum power density of about 2.4 MW/
cm2 was measured in a small 3.3 kV silicon Pþ NNþ
power diode. Device simulations of this diode with a
shallow Nþ emitter indicate that impact ionization at the
Nþ /N junction can result in negative differential resistance (NDR) and current filamentation, whereas a deep
Nþ emitter in the experimentally studied diode suppresses NDR. It is, therefore, proposed that the deep Nþ
emitter is important for the stable dynamic avalanche.
In [6], the author concludes that the reasonable agreement between measurements and device simulations
strongly indicate that the experimentally studied diode
eventually becomes limited by current filamentation due
to the on-set of impact ionization at the Nþ /N junction.
In [3–6], a new experimental technique has also been
developed to study dynamic avalanche in a well-defined
small region of a large power diode. That was accomplished by a carrier plasma excitation in a small n-region
of the diode first with a laser pulse and thereafter reverse
biasing the diode with a high dV =dt.
Since no failure was reproduced in device simulations
by authors in [3–6], it is therefore an objective of this
study to provide a better understanding of the diode
failure mechanism, in particular, the relationship between the inhomogeneous in diodes and that of diode
failure. The concepts of thermal stability and thermal
runaway are also clarified in this study. We will show, in
this paper, that the on-set of dynamic avalanche may or
may not be the failure point of the diode. We will also
show that the on-set of dynamic avalanche is not a
stable condition. The sustain-mode dynamic avalanche,
a stable condition, will be reached at a much higher
power density of more than a few MW/cm2 .
2. Diode structure and static avalanche characteristic
Numerical simulations using MEDICI [7] were performed on a high voltage Pþ NNþ diode. The diode is
rated at 3.3 kV, 1 kA and has an active region of 15 cm2 .
Default physical models for impact ionization, field dependent mobility, carrier–carrier scattering, concentration dependent carrier lifetime, Auger recombination,
Fermi–Dirac statistics and band-gap narrowing were
used. The carrier lifetime is fixed at 3.22 ls for electrons
and 0.46 ls for holes by matching the simulated forward
I–V with the experimental device. To include self-heating effect in the simulation, a lumped thermal resistance
Rthermal ¼ 3 107 K lm/W, and a lumped junction to
case thermal capacitance Cthermal ¼ 0:5 106 J/K lm
are attached to the cathode side of the diode in the
simulation.
Before the discussion on dynamic avalanche, the diodeÕs static avalanche characteristics are analyzed. Fig. 1
shows the isothermal reverse-bias I–V when the case
temperature is 348 K. Notice the high reverse current
density range shown in Fig. 1. There are three distinct
regions of the reverse I–V curve and two critical voltage
points. Before the first avalanche point, the leakage
current is low. After the first avalanche at 2870 V, the
current rises with a positive slope (or positive resistance).
Fig. 1. First and second static avalanche breakdown of the studied diode obtained by MEDICI.
A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
The current rises to more than 100 A/cm2 when VR ¼
4810 V. After this point the slope of the current becomes
negative with a NDR. This point (4810 V) is defined as
the second avalanche point. The whole I–V curve represents a stable operating locus of the diode in the reverse direction under the isothermal and homogeneous
condition.
3. Dynamic blocking capability of the diode
3.1. On-set of the Pþ /N dynamic avalanche
When power diode is in the reverse recovery, the high
dI=dt will cause a high peak reverse recovery current and
a high current density controlled effective doping (Neff ) in
the depletion region [8]. The high Neff may result in the
on-set of dynamic avalanche well below the static
breakdown voltage. Before the on-set of dynamic avalanche, the current is mostly composed of hole current in
the Pþ /N space charge region (SCR). At the Nþ /N
side, carrier extraction of electrons also happens due to
the reverse of the current direction. Another SCR region
may exist at the Nþ /N junction side in order to maintain the high reverse recovery current JR . This SCR will
appear at the Nþ /N junction if JR is higher than the
space charge limited current Jcrit ¼ qND tsat . Between
these two SCRs, a high level of carrier plasma still exists.
Diffusion of these carriers (holes to the Pþ /N SCR and
electrons to Nþ /N SCR) forms the carrier extraction
process. In the Pþ /N SCR, the critical electrical field will
be decided by the Neff , not the N-base doping concentration ND because the mobile holes will increase the
electrical field significantly. Eq. (1) shows the relationship between Neff and J before the on-set of dynamic
avalanche.
Jp Jn
J
ND þ
Neff ¼ ND þ p n ¼ ND þ
qtsat
qtsat
ð1Þ
where Jp and Jn are hole and electron current density in
the Pþ N SCR, tsat is the hole saturation velocity. A peak
power density of 200 kW/cm2 is frequently referred as
the power density required to cause the on-set of the
dynamic avalanche. This is based on the following calculation. Assume the voltage is only supported by the
Pþ /N SCR, then it reaches a critical maximum value
when the maximum space charge region width is
W ¼
es Ec
qNeff
ð2Þ
So that we can obtain the on-set voltage for dynamic
avalanche,
1
1 es Ec
BVdy ¼ Ec W ¼ Ec
2
2 qNeff
ð3Þ
729
For large J , using equation (1), and neglecting ND , one
gets
BVdy ¼
1 es Ec2 tp
2 J
ð4Þ
And, the power density at the on-set point is
1
Pdy ¼ BVdy J ¼ es Ec2 tp
2
ð5Þ
here es ¼ 11:7 8:85 1014 F/cm. If Ec ¼ 2 105
V/cm, tsat ¼ 107 cm/s, then Pdy ¼ 206 kW/cm2 .
After on-set of dynamic avalanche, the diode is normally not in the sustain-mode dynamic avalanche, because the carriers generated by the dynamic avalanche
are not enough to form a sustainable current, hence, the
SCR region will continue to expand (although at a
slower rate due to the extra carriers generated) and the
voltage will increase at lower dV =dt.
3.2. On-set of the Nþ /N dynamic avalanche
In the diode reverse recovery process, the reverse
current could be significant, therefore the Nþ /N dynamic avalanche can also happen. In most cases the
on-set of dynamic avalanche at the Pþ /N junction happens first. A simple calculation can show that the power
density needed to create the on-set of both Pþ /N and
Nþ /N avalanche is more than 400 kW/cm2 . This is
often cited as the power density required to cause dynamic avalanche at the Nþ /N junction. Assume the
voltages are supported by the two SCRs, they reach their
maximum field values at the same time, then
BV1 ¼
1 es Ec2 tp
2 J
ð6Þ
and
1 es Ec02 tn
ð7Þ
2 J
here J is the current density, tp and tn are electron and
hole saturation velocities respectively. Therefore,
BV2 ¼
BVdy ¼ BV1 þ BV2 ¼
1 es Ec2 tp 1 es Ec02 tn
þ
2 J
2 J
ð8Þ
If tp ¼ tn ¼ 1 107 cm/s, Ec0 ¼ Ec , then Pdy ¼ BVdy J ¼
es Ec2 tp 412 kW/ cm2 .
3.3. Sustained-mode dynamic avalanche and theoretical
diode RBSOA
Even after the on-set of the Nþ /N avalanche, the
total carriers generated by the avalanche are still not
enough to form a stable current because there are still
carriers between the two SCRs. The voltage will keep
increasing to expand both SCRs until the diode enters
the sustain-mode dynamic avalanche.
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A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
In order to understand the process of dynamic avalanche and sustained mode dynamic avalanche, a set of
simulations was performed under isothermal condition.
The circuit used in the mixed mode simulation is shown
in Fig. 2. A 1 cm2 diode in the schematic is numerically
modeled by MEDICI and initially conducts a forward
current of I1 ¼ I. The current source I2 is set to zero at
the beginning of the simulation. Then the value of current source I2 rises to two times of I1 within 100 ns. After
the I2 current rise, the diode will enter the reverse conduction mode and the voltage of the cathode will increase to a value that can sustain a current I (the anode
is connected to ground).
Fig. 3 shows the cathode voltage and the cathode
current waveforms when the current source I1 is 100 A.
The cathode current is therefore )100 A/cm2 initially
and increases as the current source I2 increases. At 100
ns, the current source I2 reaches 200 A and the cathode
Fig. 2. Circuit diagram used to simulate sustained mode
dynamic avalanche voltage.
current of diode is forced to be 100 A/cm2 . After the
cathode current becomes 100 A, the cathode voltage will
increase and eventually reach a stable value. The stable
value is therefore the sustain-mode dynamic avalanche
voltage at a reverse current equal to 100 A/cm2 .
Evaluation of the initial electrons and holes concentrations in the diode ðA0 Þ and those at point A in Fig. 3
indicates that the carrier concentrations do not change at
point A due to the high dI=dt assumed for current source
I2 . This provides us a reverse conducting carrier plasma
condition the same as that of the forward conducting. It
is important to emphasis that the difference between a
practical diode reverse recovery such as that in a chopper
circuit and this simulation. In this simulation, a current
boundary condition is imposed that forces stronger
carrier extraction (much stronger than practical diode
reverse recovery where the reverse current density is selfdetermined based on carrier distribution and dI=dt).
During the cathode voltage rise, the stored carriers will
be extracted at the Pþ /N junction and Nþ /N junction.
The amount of carriers extracted by both SCRs are basically the same and DQ ¼ IDt. High electrical field regions will appear at the Pþ/N and Nþ /N junctions.
Our simulation shows that the field at the Pþ /N junction
is much higher than that at the Nþ /N SCR due to difference in the electric field slope. When the electrical field
reaches the critical value, the dynamic avalanche of the
Pþ/N junction happens first. The electrons and holes
generated by the avalanche will contribute to the current.
This is the on-set of the Pþ/N junction dynamic avalanche. The change of the voltage slope at point B in
Fig. 3 is an indication of the on-set of Pþ /N dynamic
avalanche. After point B, o2 V =ot2 < 0, as shown in
Fig. 3. The power density at point B is, however, only 50
Fig. 3. The cathode voltage and current waveforms obtained in the sustained mode dynamic avalanche simulation. Initial forward
current density is 100 A/cm2 .
A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
kW/cm2 , much lower than 200 kW/cm2 calculated earlier. The difference seems due to the fact that the calculation used a critical field of 20 V/lm while the simulator
determined critical field value is only 11 V/lm (Fig. 5).
Since the carriers generated by the Pþ /N avalanche
are not enough to maintain the constant reverse current,
the SCRs will expand and the voltage will increase. At
the same time, the electrons generated by Pþ /N avalanche will drift to the SCR1 region which makes SCR1
wider with lower field slope (Fig. 5). Eventually, dynamic avalanche happens in the Nþ /N junction and
this provides more carriers to support the current.
However, if the electrons and holes generated by the two
avalanche regions are still not enough to compose the
current, the SCRs must expand further into the middle
diode region. If the two SCRs meet in the middle before
sustain mode is reached, there will be no more carriers
left in the middle region to be extracted [9]. The voltage
rise will then become extremely fast. This is shown in
Fig. 3 after point C. The power density at point C is
about 180 kW/cm2 and on-set of both avalanches and
merging of the two SCRs have already happened. At
point D, avalanche generated electrons and holes can
provide the cathode current. Then the cathode voltage
will not increase and the diode enters its sustain mode
dynamic avalanche. The stable cathode voltage is
therefore the sustain mode dynamic avalanche voltage.
Fig. 4 shows the carrier distribution along the Y direction during the cathode voltage rising at points B, C
and D. Fig. 5 shows the electrical field distribution along
the Y direction at the three same points. At point B, the
stored carriers in the middle region have not been extracted completely, so the holes and electrons concen-
731
trations are quite large as shown in Fig. 4. The carrier
generation rate and the electrical field are small as shown
in Fig. 5. That means only a weak dynamic avalanche has
happened at the Pþ /N junction. At point C, the holes
and electrons concentration are smaller compared to
point B, but are still higher than the N region doping
concentration (1013 cm3 ) in order to maintain the current. From Fig. 5, it is clear that the dynamic avalanche
has occurred at both the Pþ/N junction and Nþ /N
junction at point C and the two SCRs have merged. The
generated electrons form the majority of the current. At
point D, the device has entered sustain dynamic avalanche and the avalanche in the Nþ /N junction has
become quite large. From Fig. 5, we can see the electrical
field has been changed. The electrical field in the middle
region becomes flat but high. That makes the avalanche
region larger in order to generate enough electrons and
holes to sustain the current.
Fig. 6 shows the calculated sustain mode dynamic
voltage at different current densities, using the circuit of
Fig. 2, compared with the static breakdown voltage. The
difference is very small. That means the sustain-mode
dynamic avalanche voltage is basically the same as the
static breakdown voltage at the same current density.
The sustain-mode dynamic avalanche is therefore a
stable situation and the diode can stay in that condition
if there is no temperature rise. The sustain-mode dynamic avalanche voltage should also be expected to be
the same as the static avalanche breakdown voltage at
other temperatures.
From the above conclusion, the failure of diode will
only occur when the reverse recovery trajectory crosses
the sustain mode dynamic avalanche curve in Fig. 6.
Fig. 4. The carrier concentration distribution along Y direction at points B, C, D in Fig. 3. The diode cathode is on the left and the
anode is on the right of the figure.
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A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
Fig. 5. The electrical field distribution along Y direction at points B, C and D.
Fig. 6. The simulated sustain mode dynamic voltage and the static breakdown voltage at 298 K.
Therefore the sustain-mode of dynamic avalanche
boundary in the J –V plane can be considered as the
theoretical RBSOA. This large RBSOA is only reached
when isothermal condition is maintained across the
whole region of the device, and no other inhomogeneity
exists in the device. For example, Fig. 6 suggests that the
ideal RBSOA is reached at a power density of more than
several MW/cm2 .
4. Large area diode failure and thermal stability
The above ideal diode RBSOA was only realizable
under isothermal and homogeneous condition. This is
almost impossible to realize in reality. As the tempera-
ture of the device will rise during turn-on or turn-off,
thermal resistance and thermal capacitance of the actual
packaged device should be added for a real case. Coupled lattice temperature methods should therefore be
used in simulations in order to calculate the dynamic
junction temperature of the device. However, to study
the failure of large area power diode under single pulse
condition, the temperature rise is small, thus the external
thermal resistance and capacitance due to a heat sink are
not important. However, if localized high power stress
exists, then the effect of internal temperature rise becomes important.
To study diode reverse recovery stress, especially the
localized high power stress exists in large area diode,
diode inhomogeneity must be included. Local differences
A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
(edge current fringing, non-uniform carrier lifetime and/
or doping etc.) between the diode segment (cells) lead to
current density inhomogeneity in the large area diode
which in turn results in local areas of higher power stress
during reverse recovery. This situation becomes worse
when the area of the diode becomes large since a larger
area diode may behave ÔuniformlyÕ while a smaller area
cell is carrying a high current filament.
4.1. Inhomogeneities in large area diode
Inhomogeneities in large area diode are caused probably by the following mechanisms. First of all, a
small area with lower breakdown voltage may be introduced due to the field crowding at the edge of the
diode. Second, in the case of devices where high level
minority carrier injection occurs, it becomes necessary to
introduce deep level recombination centers in order to
speed up or control the device characteristics. If those
recombination centers or impurities are introduced nonuniformly, non-uniform lifetime results which causes
non-uniform initial carrier distribution in the diode.
Initial carrier plasma level in the inhomogeneous area is
typically higher than those of other areas. Third, nonuniform Pþ region doping can also cause inhomogeneity
in carrier plasma because of the differences in injection
efficiency. The edges and corner regions of the diode
are both regions that can have higher initial plasma
concentration than the rest of device due to the twodimensional current spreading effect.
Above-mentioned inhomogeneities should be ideally
studied by directly simulating the large area device. The
direct modeling approach considers a device structure in
which there are small parts that are different from the
other region, for example, they have more carriers or
higher ionization rate or have higher lifetime. Between
the special region and the normal region, there also
should have a middle or joining region that connects the
special part with the normal region to make the change
of such parameters continuous. However, such a model
is difficult to realize because of the huge number of
numerical nodes needed to describe a large area device,
and the limited capability of the numerical simulator
and computer resources (memories and CPU). A simpler
approach is to use two paralleled 1-D diode structures
with different areas. The areas of the two 1-D diodes are
different; the large diode A represents the normal ÔuniformÕ portion of the diode and the small diode B represents the special region. The area ratio N determines
the final current filament density in the special region
because the worse case would be for diode B carrying all
current hence JB;max ¼ N JB;0 , where J JB;0 is the initial
current density. The inhomogeneity that causes current
filament can be introduced by changing the device parameters of the small device B. For example, the ion-
733
ization rate can be changed to obtain a lower breakdown
voltage in diode B; the lifetime can be changed to model
the lifetime difference. The doping concentration can
also be changed to make the small device having higher
initial carrier concentration. This approach is used in
our simulation of large area diode turn-off. Inhomogeneous is introduced either as a difference in avalanche
breakdown voltage, or the difference in initial carrier
distribution.
4.2. Simulation results and discussions
Fig. 7 shows the circuit diagram used to study the
large area diode reverse recovery circuit. Paralleled small
and large 1-D diodes are used. The area of the large
diode A is 15 cm2 and the area ratio N is fixed at 100.
The impact of area ratio N will be discussed later in the
report. The current source was 1000 A, resulting in an
initial forward conducting current density of 66 A/cm2 .
The voltage source V1 was set at 2500 V. The Lp is the
parasitic inductor and its value is very small, about
10 nH. The Lp is the snubber inductor to limit the dI=dt
of the diodes during the reverse recovery.
4.2.1. Inhomogeneous breakdown voltage
A small inhomogeneity was introduced by increasing
the ionization rate of the small diode. The doping profile
and initial carrier concentration in the small diode is the
same as the large diode. Only the static breakdown
voltage of the small diode is about 180 V lower. With a
large snubber inductor of 5 lH (or a dIF =dt of 500 A/ls),
no failure or current filament was observed in the simulation. Although the simulated waveforms show a very
snappy reverse recovery (sudden drop of reverse current
to zero), the current density in the small diode B remains
the same as those in the large diode A. Therefore it is
concluded that an inhomogeneous static breakdown
voltage (therefore also sustained mode dynamic avalanche voltage) does not cause a current filament in
diode B for slow dIF =dt.
When the dIF =dt of the diode increases, the reverse
peak current and the peak voltage of diode will increase.
So do the reverse recovery power density (defined as
reverse peak current times reverse peak voltage). Fig. 8
shows the turn-off waveforms when the snubber inductor decreases to 0.5 lH. Although the diode finally turns
off and hence we consider no failure happens, there are
two significant current filaments or current bumps in the
small diode during the reverse recovery. The first filament only lasts for about 150 ns and the second one lasts
longer for about 500 ns. During these two rapidly
forming filament periods, the current of the large diode
transfers to the small diode to make the current density of the small diode rise dramatically. But the trend of
the current density rising or the formation of current
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A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
Fig. 7. Paralleled 1-D diode model used in the simulation of a large diode turn-off.
Fig. 8. The reverse recovery current and voltage waveforms when the Ls ¼ 0:5 lH, showing current filament formation and disappearance.
filament in the small diode didnÕt continue. As the reverse recovery voltage keeps rising, the current goes
back to the large diode. Eventually, the current density
in the diode will become the same as the large diode
again. The diodes turn off safely with homogeneous
current sharing at the end.
The first bump region shown in Fig. 8 is enlarged in
Fig. 9 and solutions at several time points were saved to
reveal the details in the small diode. Fig. 10 shows the
electrical field in the small diode. At time point 1, the
dynamic avalanche happened only in the Pþ/N junc-
tion (which is located at distance ¼ 365 lm in the diagram). The electrical field and the generation rate in the
Pþ/N junction are much larger than the rest area. At
point 2, the dynamic avalanche begins to occur at the
Nþ /N junction (at distance ¼ 12 lm). The electrical
field and the carrier generation rate (not shown) in the
Nþ /N junction are comparable to that of the Pþ /N
junction region. At point 3, the current density of
the small diode is the biggest and the avalanche in
both junction regions is the strongest. But at point 4,
the avalanche in both junction regions ceased and the
A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
735
Fig. 9. Enlarged current waveform of Fig. 8 showing the first current bump (filament) in the small diode.
Fig. 10. Electric field corresponding to that of Fig. 9.
current density of the small diode decreases to the same
value as that of the large diode. It is clearly shown that
the inhomogeneity happened before point 2 but reaches
a critical point at point 2 because of the dynamic ava-
lanche breakdown voltage is different for the two diodes.
The dynamic avalanche of the small diode happens first
and the current of the small diode will increase. That
makes part of the large diode current transfer to the
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A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
small diode and makes the current density of the small
diode increase dramatically. The dynamic avalanche at
the Nþ /N junction region initiates the current bump in
Fig. 8. But as we mentioned before, the diode did not
reach its sustain mode dynamic avalanche and the voltage can continue to increase. As the voltage increases,
the dynamic avalanche in the large diode occurs and
draws some current back from the small diode. That is
why we observed the later decrease of the current density
in the small diode. Eventually, the current density of the
two diodes becomes equal again. The first current bump
of the small diode disappeared. The two diodes become
homogeneous again.
The second bump happens at much higher voltage.
The high voltage is induced by the snappy reverse recovery of the diode current (large diode current, not
clearly visible in Fig. 8). This can be confirmed by a
much faster voltage rise rate. This bump disappears for
the same reason as the first bump because the large
diode reaches the same condition slightly later and
draws the current back into the large diode and stable
filament does not form. Since these filaments are so
short, the temperature rise is also small and device
failure cannot be observed even with a coupled thermal–
electrical simulation of Fig. 8 case. In any case, the
power density at which the first bump (filament) is observed can be obtained in our simulation. This can be
done by repeating Fig. 8 simulation at different dIF =dt
which causes the first current bump of the small diode to
happen at different reverse recovery voltage and current.
Fig. 11 shows such points in the current density and
voltage plane and are compared with the sustain mode
dynamic avalanche voltage. The constant power density
of 400 kW/cm2 curve is also plotted. The first bump
region happens at about 400 kW/cm2 . It is the on-set
dynamic avalanche points of the Nþ /N junction calculated before. Some papers [3] have reported failures at
a reverse power density of about 400 kW/cm2 .
Based on the above discussion, it is concluded that the
only way a stable filament can be formed is that the
filament reaches the sustained mode of dynamic avalanche (Fig. 11) before the on-set of dynamic avalanche
in the large diode. To facilitate this discussion, a parameter called dynamic avalanche conductance gdynamic is
defined.
gdynamic ¼
dJ
dV
V >Von-set
ð9Þ
For the studied diode, gdynamic is estimated to be about
15 S/ cm2 . Diode failure at 400 kW/ cm2 would happen if
the following conditions are satisfied
condition (1): gdy DVon-set > Jsustain ðT Þ J0
condition (2): NJ0 > Jsustain ðT Þ
condition (3): NDR exits in sustain mode dynamic
avalanche voltage
Condition (1) means that the diode current filament
must reach a stable mode to cause failure. J0 is the
current density when the on-set dynamic avalanche of
the small device happens. Jsustain ðT Þ represents the sustain mode current density at voltage V ffi Von-set þ DVon-set .
DVon-set is the difference of the on-set dynamic breakdown voltage between the small diode and the large
diode. Since the effect of temperature rise is important, T
is included in condition (1). Condition (2) means that
Fig. 11. Simulated power density that causes the current filament in the diode.
A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
737
Fig. 12. Proposed diode failure mechanism.
there is enough current to stress the small cell. This
condition is typically always true in large diode if N is
large. Condition (3) is basically necessary for (1) to be
true, otherwise (1) can never be reached.
A proposed diode failure mechanism is then shown in
Fig. 12 based on condition (1)–(3). Isothermal, ideal
RBSOA is also shown. For the diode under study, a very
small NDR is seen. Therefore, an estimated non-isothermal NDR is constructed assuming an increased
temperature towards higher current side. Since a much
larger NDR is possible at higher temperature (or higher
dynamic temperature). For the diode to fail, the current
filament must be large enough to reach stable condition
before counter effects, such as the on-set of dynamic
avalanche in large diode happens. This requires the
small diode to move from T 1 ! T 2 ! T 3.
4.2.2. Inhomogeneous initial carrier plasma
Previous simulation models diode based on the inhomogeneous in static breakdown voltage, the initial
carrier concentration in the diode is homogeneous.
Diode failure was not observed in the simulation even at
high dIF =dt and high bus voltage. We suspect that the
on-set of dynamic avalanche of both diodes are too close
to cause the small diode to reach sustained-mode or
meet condition (1)–(3).
Fig. 13 shows a failure case during reverse recovery
simulation. Coupled thermal/electrical simulation was
Fig. 13. Turn-off waveforms when the lifetime of small diode is 10 times of that in large diode. Stable current filament is formed with
filament temperature reaching more than 1800 K.
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A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
used in this case. The lifetime of carriers in small diode is
increased to 10 times of that in large diode, which makes
the initial forward current density in small diode 4.7
times larger than that of the large diode (299.7 and 63.7
A/cm2 respectively). This results in large inhomogeneity
in initial carrier plasma. The onset of dynamic avalanche
voltage is therefore significantly changed. As the anode
voltage reaches the dynamic avalanche voltage of the
small device at about 500 V, a current bump appears
and the current is increased quickly in the small device.
Since the dynamic avalanche has not happened in the
large device, the current of the small diode takes over
100% of the total current. As the current density of the
small device increases, its sustain-mode dynamic avalanche voltage may have been reached. However, this
cannot be confirmed. At t ¼ 1:7 ls, a drop in the voltage
may indicate the reaching of the sustained-mode dynamic avalanche at a temperature already much higher
than the initial temperature. This result also confirms the
importance of including temperature effects during the
formation of the filament. Since a very large power stress
is applied to the small diode for a much longer time
(stable), the temperature eventually rises to 1800 K
about 1 ls after the current bump. Failure of turn-off
eventually occurs due to rapidly rising temperature in
the small diode. The high temperature will form hot
spots in diode and destroy the device permanently in the
form of a melted through holes. The end result of such
failure is frequently referred as thermal runaway or
thermal instability. The result in Fig. 13 shows a failure
during the second phase of reverse recovery (overall
reverse current starts to decrease after passing the reverse recovery current peak) starting at t ¼ 1:3 ls. The
failure point power density in the small device is 500
V 500 A=cm2 ffi 250kW=cm2 , however, the effective
failure power density for the overall diode is 500 V 100 A=cm2 ffi 50 kW=cm2 . This simulated failure power
density (50 kW/cm2 ) is much less than the 400 kW/cm2
predicted in Fig. 11. This is simply because the inhomogeneity in the initial carrier density (which can cause
current density of several hundred percent different and
here 4.7 higher) is a much worse situation than the
previous inhomogeneity in static breakdown.
When the difference in the lifetime of the two diodes is
five times, the strong inhomogeneous current distribution still makes the small diode fail in the turn off. But
when the difference changes to three times, both diodes
turn off successfully. These results confirm that the level
of inhomogeneity is very important in determining diode
failure.
Area ratio between these two diodes is another important factor. When the lifetime difference changes to
three times, if N increases to 1000, it was found that the
turn-off still failed. In actual large area diodes, N is a
dynamic parameter with N ðt1 Þ < N ðt2 Þ for t1 < t2 . The
size of the current filament is increasingly squeezed into
a small spot due to the positive feedback between NðtÞ
and J (small). Quantitatively it is difficult to model N ðtÞ,
but N in the range of several thousand is not surprisingly
large. Also it is feasible that the filament might move
from one location to another location. Using two paralleled diode model, this type of movement cannot be
modelled. Using three or more cells with different types
of inhomogeneities, it may be possible to model the filament formation as well as filament movement from cell
to cell.
Finally, based on all results presented in this paper,
the diode RBSOA can be expressed as:
RBSOAdiode ¼ ð250–400 kW=cm2 Þ=K
ð10Þ
where K P 1 represents the initial current density
ratio of the failure cell to the rest of the diode. This
RBSOA is reached when conditions (1)–(3) are met. If
conditions (1–3) are not met, larger RBSOA can be
observed.
5. Conclusions
Numerical analysis of the failure for 3.3-kV Si power
diodes during reverse recovery was performed. The
sustain-mode dynamic avalanche voltage was extracted
and has been proved to be the same as the static
breakdown voltage. It was found that under isothermal
and homogeneity condition, the RBSOA of power diodes is the same as the sustain-mode dynamic avalanche.
This theoretical RBSOA is very large and even exceeds 3
MW/cm2 . So the potential RBSOA of power diodes are
very large.
Because of the inhomogeneity and thermal consideration existing in the real world diode, the failure will
occur at reverse power density that is much less than
the RBSOA determined by the sustain-mode dynamic
avalanche. A simple numerical model was used to
approximate two such possible inhomogeneities. Two
paralleled diode of different size and physical parameters
were used for simplicity. After the introduction of the
inhomogeneity between the large and small devices, a
current bump occurs in the small diode. It was shown
that such current bump was the results of the on-set of
dynamic avalanche at the Nþ /N junction. Such current
bumps arise form current filament formation that is
dangerous to diode operation. Device failure will happen if the current density of the filament reaches the
sustain-mode. In some cases, counter effects exist to remove the current filament and the device becomes homogeneous again. Diode failure has been proved to be
caused by diode electrical property, not the thermal
properties of the diode. Thermal runaway is basically an
end product of current filament larger than the sustainmode dynamic avalanche RBSOA.
A.Q. Huang et al. / Solid-State Electronics 47 (2003) 727–739
Acknowledgements
This work was supported primarily by Silicon Power
Corporation and National Science Foundation Career
Award ECS-9733121.
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