572
21 Diodes
Fig. 21.56 a Large electric
fields at large curvatures in
a shallow junction.
Avoidance of regions with
large electric fields by b
deep junction and c
field-ring structure. d
shows a guard-ring
structure with circular,
low-doped n region. Grey
area denotes insulating
material, arrows indicate
field lines and the dashed
lines indicate the extension
of the depletion layers
(a)
n
+
p
(b)
n
+
p
(c)
n
+
p
n
+
(d)
n
+
p
+
p
n
n
Fig. 21.57 Breakdown
voltage (in units of the
breakdown voltage V B of a
plane junction) for
cylindrical and spherical
junctions as a function of
the curvature radius (in
units of the depletion layer
width at breakdown W B for
a plane junction). Data
from [1774]
breakdown voltage increases with the temperature (Fig. 21.55). This behavior is opposite to tunneling
diodes and the two processes can be distinguished in this way.
In planar structures (Fig. 21.56a), high electric fields as present in high power devices will occur
at the parts with large curvature. At these sites breakdown will occur first and at much lower voltages
than expected for a perfectly planar (infinite) structure [1777, 1778]. For devices that require high
breakdown voltage, design changes have to be made. These include deep junctions (Fig. 21.56b) with
a smaller curvature, a field-ring structure (Fig. 21.56c) in which an additional depletion layer is used
to smooth the field lines and the often used guard ring (Fig. 21.56d) for which a circular region of low
doping (and thus high breakdown voltage) is incorporated.
The decrease of breakdown voltage in a junction with cylindrical and spherical geometry has been
numerically calculated as a function of curvature [1779] (Fig. 21.57). Analytical formulas in terms of
the ratio of radius of curvature and the depletion layer width at breakdown for a plane junction r/w B
have been given later [1774].
Defects
In material with extended defects such as polycrystalline silicon breakdown can occur locally at lower
voltage than in the corresponding defect-free bulk material (‘pre-breakdown’) [1771]. This effect
typically occurs at certain grain boundaries and probably involves mid-gap states. It is also accompanied
with electroluminescence by which it can be detected with high spatial resolution (Fig. 21.58).
21 Diodes
Fig. 21.56 a Large electric
fields at large curvatures in
a shallow junction.
Avoidance of regions with
large electric fields by b
deep junction and c
field-ring structure. d
shows a guard-ring
structure with circular,
low-doped n region. Grey
area denotes insulating
material, arrows indicate
field lines and the dashed
lines indicate the extension
of the depletion layers
(a)
n
+
p
(b)
n
+
p
(c)
n
+
p
n
+
(d)
n
+
p
+
p
n
n
Fig. 21.57 Breakdown
voltage (in units of the
breakdown voltage V B of a
plane junction) for
cylindrical and spherical
junctions as a function of
the curvature radius (in
units of the depletion layer
width at breakdown W B for
a plane junction). Data
from [1774]
breakdown voltage increases with the temperature (Fig. 21.55). This behavior is opposite to tunneling
diodes and the two processes can be distinguished in this way.
In planar structures (Fig. 21.56a), high electric fields as present in high power devices will occur
at the parts with large curvature. At these sites breakdown will occur first and at much lower voltages
than expected for a perfectly planar (infinite) structure [1777, 1778]. For devices that require high
breakdown voltage, design changes have to be made. These include deep junctions (Fig. 21.56b) with
a smaller curvature, a field-ring structure (Fig. 21.56c) in which an additional depletion layer is used
to smooth the field lines and the often used guard ring (Fig. 21.56d) for which a circular region of low
doping (and thus high breakdown voltage) is incorporated.
The decrease of breakdown voltage in a junction with cylindrical and spherical geometry has been
numerically calculated as a function of curvature [1779] (Fig. 21.57). Analytical formulas in terms of
the ratio of radius of curvature and the depletion layer width at breakdown for a plane junction r/w B
have been given later [1774].
Defects
In material with extended defects such as polycrystalline silicon breakdown can occur locally at lower
voltage than in the corresponding defect-free bulk material (‘pre-breakdown’) [1771]. This effect
typically occurs at certain grain boundaries and probably involves mid-gap states. It is also accompanied
with electroluminescence by which it can be detected with high spatial resolution (Fig. 21.58).