AN3022
Establishing the Minimum Reverse Bias for a PIN Diode in a
High-Power Switch
Abstract
- An important circuit design parameter in a
high-power p-i-n diode application is the selection of an
appropriate applied dc reverse bias voltage. Until now,
this important circuit parameter has been chosen either
conservatively, using the magnitude of the peak RF volt-
age, or by empirical trials to determine a possible lower
value. This paper explores the reverse bias requirement
for a p-i-n diode operating in a high power microwave
environment. It demonstrates that the minimum reverse
bias voltage is equivalent to the p-i-n diode’s self-
generated dc voltage under similar RF conditions. A
concise expression for this self-generated voltage is de-
veloped and experimentally verified and will assist the
design engineer in more accurately selecting an appro-
priate minimum value for the applied reverse bias voltage
setting.
Rev. V2
It is conditionally safe region where most high-power
(greater than 1 kW) p-i-n diode switches are designed to
operate. The applied dc reverse bias voltage must be
large enough to prevent excessive conduction during the
positive portion of the RF signal. If excessive conduction
does occur, the p-i-n diode loss will increase and the
diode will be subject to failure.
In absence of any theory or analytic design guidelines,
the design engineer may choose a dc bias voltage equal
to the peak RF voltage, resulting in extremely conserva-
tive and costly designs; more frequently, however the
design is based on empirically matching a p-i-n diode to
an available voltage. This paper presents a guide for the
p-i-n diode circuit designer, similar to the forward bias
case, for selecting a minimum applied reverse bias volt-
age based on diode and circuit operating parameters.
The investigation of the relationship of the reverse bias
requirement was prompted by experimental observations
of p-i-n diode distortion under zero applied bias open
circuit conditions, using a test circuit of the type shown in
Figure 2. The 10
9
Ω
resistor was inserted in the
voltmeter line to increase the effective voltmeter internal
resistance from its nominal 10
7
Ω
value to better
approximate an open circuit across the diode. The
voltage read was then approximately 1% of the diode
voltage.
A self-generated reverse bias dc voltage was developed
across the p-i-n diode that allowed the diode to operate
in its high-impedance state with good stability. The
magnitude of the self-generated dc voltage was
influenced primarily by the peak RF voltage level, the
frequency, and the thickness of the I-region. Upon
application of an equivalent externally applied dc bias,
the distortion generated was identical to the self-
generated dc voltage. However, when the applied dc
voltage was lower than the self-generated voltage,
unstable performance would occur, manifested by large
increases in distortion signals and by heating of the p-i-n
diode, which often led to device failure. Published
experimental results by other investigators [3] show
similar device and circuit parameters that affect the
degree of forward conduction in the p-i-n diode.
An analysis of the p-i-n diode leading to a concise
expression for the safe minimum operating dc reverse
bias voltage is presented. The expression indicated how
the p-i-n diode I-region and circuit parameters such as
frequency, duty factor, and peak RF voltage affect the
magnitude of the minimum reverse bias voltage. The
derived expression is verified using experimental
measurements of the developed open-circuit zero bias
1. Introduction
A fundamental property of a p-i-n diode is its ability to
control large radio frequency (RF) and microwave signals
with much lower values of dc current and voltage. While
there are design rules for selecting a minimum level of
forward current based on allowable ohmic loss and dis-
tortion requirements [1], [2], there are no existing design
rules on which to base the selection of the minimum level
of applied dc reverse bias voltage.
The instantaneous voltage across the p-i-n diode (both
RF and dc) must never exceed its avalanche breakdown
voltage (V
BR
in Fig. 1(a)), where high reverse current
densities may cause p-i-n diode failure. Safe operation
will result if the instantaneous voltage never forces the p-
i-n diode into forward conduction or into avalanche
breakdown (Fig. 1(b)). However, this requires that the
applied dc voltage be at least equal to the peak RF volt-
age and that the breakdown voltage be at least twice the
peak RF voltage (V
RF
). In many applications, high ap-
plied reverse bias voltages are often not available or are
too expensive to implement. Frequently p-i-n diodes are
operated in the so-called conditionally safe region, where
an instantaneous excursion of voltage into the forward
conducting region may be tolerated (Fig. 1c)). If a dc
reverse bias voltage in this region is chosen, circuit per-
formance parameters such as loss, distortion, and reli-
ability must not be compromised.
1
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changes to the product(s) or information contained herein without notice.
AN3022
Establishing the Minimum Reverse Bias for a PIN Diode in a
High-Power Switch
Rev. V2
Figure 1. (a) Unsafe operating region, (b) safe operating region, and (c) conditionally safe
operating region for the reverse-biased p-i-n diode.
2
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Data Sheets contain information regarding a product M/A-COM Technology Solutions
•
North America
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Europe
Tel: +353.21.244.6400
is considering for development. Performance is based on target specifications, simulated results,
•
India
Tel: +91.80.43537383
•
China
Tel: +86.21.2407.1588
and/or prototype measurements. Commitment to develop is not guaranteed.
Visit www.macomtech.com for additional data sheets and product information.
PRELIMINARY:
Data Sheets contain information regarding a product M/A-COM Technology
Solutions has under development. Performance is based on engineering tests. Specifications are
typical. Mechanical outline has been fixed. Engineering samples and/or test data may be available.
M/A-COM Technology Solutions Inc. and its affiliates reserve the right to make
Commitment to produce in volume is not guaranteed.
changes to the product(s) or information contained herein without notice.
AN3022
Establishing the Minimum Reverse Bias for a PIN Diode in a
High-Power Switch
Rev. V2
p-i-n diode cross section. In this case no externally ap-
plied dc reverse bias voltage is necessary to prevent
forward conduction since the I-region stored charge is
never established during the positive portion of the RF
signal. The conducting state of the p-i-n diode is there-
fore never achieved.
Between these two limiting cases lies an operating re-
gion for the p-i-n diode where prevention of forward con-
duction of the diode may be achieved by reverse biasing
the diode at a voltage less than the peak RF voltage.
Experiments [7] have shown that the dc voltage devel-
oped by the p-i-n diode in its open-circuit, zero bias state
is directly related to the dc reverse bias voltage needed
to prevent significant forward conduction in the p-i-n di-
ode.
The analysis of the developed open-circuit, zero bias
voltage in p-i-n diodes is based on the existence of both
conduction and displacement currents flowing through
the p-i-n diode [8]:
Figure 2. Test set used for measurement of
the self-generated dc voltage of p-i-n diodes
voltage across a variety of p-i-n diode geometrics and
circuit operating conditions. An application example is
also presented.
2. Analysis
In the presence of an applied RF or microwave signal, an
ideal rectifier diode will instantaneously conduct when
the RF voltage places the diode into its forward bias
state. In most applications where a reverse-biased p-i-n
diode is used, forward conduction in the p-i-n diode can
be unconditionally avoided if the diode is reversed biased
such that the peak RF voltage swing remains between
the device turn-on voltage (typically 0.7 V for silicon di-
odes) and the reverse bias breakdown voltage. This
requirement is the basis for conservative “worst case” p-
i-n diode dc reverse bias point, where lV
DC
l = lV
RF
l.
In real circuit applications, however, the p-i-n diode does
not show the same instantaneous turn-on time as the
ideal rectifier diode. Rather, the RF signal must be
positive for a finite amount of time before the diode starts
conducting in the forward direction. This turn-on time is
the time required for the I-region to fill with charge
carriers (both holes and electrons from the heavily doped
end regions) during the forward cycle of the applied RF
signal. Depending on the frequency, the peak RF
voltage level (lV
RF
l), and the I-region thickness (W), the
excursion into the forward direction of the RF signal may
be too short to allow sufficient time for the carriers to
completely traverse the I-region, hence preventing the p-
i-n diode from entering its conducting state [4]-[6]. The
diode will then act as a lossy capacitor with its
capacitance dependent on the I-region thickness and
3
where
J(t)
is the total current density,
n
is the I-region
carrier density (where the density of holes equals the
density of electrons to simplify the analysis),
q
is the ele-
mental electronic charge,
v
is the drift velocity of the
charge carriers (assuming equal hole and electron drift
velocities),
ε
is the dielectric permittivity, and
E
is the
electric field. Assuming that the flux density
D
is uniform
through the diode’s cross section (A) yields
where
Q
is the sum of both the RF and dc components of
the I-region stored charge and
ρ
is the total I-region
charge density. Substituting the results of (2) into (1)
shows that the total current density,
J(t),
may be written
as
A p-i-n diode with I-region thickness W then, using (3)
has a total diode current of
where the I-region transit time,
T,
is defined as
W/2
v
[8].
If a time variation of the form
e
for all quantities is
assumed, the RF component of the total diode current
may be written as
jwt
ADVANCED:
Data Sheets contain information regarding a product M/A-COM Technology Solutions
•
North America
Tel: 800.366.2266 •
Europe
Tel: +353.21.244.6400
is considering for development. Performance is based on target specifications, simulated results,
•
India
Tel: +91.80.43537383
•
China
Tel: +86.21.2407.1588
and/or prototype measurements. Commitment to develop is not guaranteed.
Visit www.macomtech.com for additional data sheets and product information.
PRELIMINARY:
Data Sheets contain information regarding a product M/A-COM Technology
Solutions has under development. Performance is based on engineering tests. Specifications are
typical. Mechanical outline has been fixed. Engineering samples and/or test data may be available.
M/A-COM Technology Solutions Inc. and its affiliates reserve the right to make
Commitment to produce in volume is not guaranteed.
changes to the product(s) or information contained herein without notice.
AN3022
Establishing the Minimum Reverse Bias for a PIN Diode in a
High-Power Switch
and the dc component of the total diode current may be
written as
The resistance (or conductance) of the p-i-n diode can
be computed from the amount of stored charge in the I-
region [3]. The RF and dc voltages are determined from
these resistances and the corresponding currents:
where
D = T
D
/ T
P
is the RF pulse duty cycle. The dc
voltage developed across the p-i-n diode may be written
using (8), (9), and (10) as
Rev. V2
Assuming that the electronic field across the I-region of
the p-i-n diode may be approximated by
E = V
RF
/ W,
then the rms value of the electric field,
E,
may be calcu-
lated as
where
μ
is the mobility (again, assuming equal hole and
electron mobility values for simplicity). The magnitude of
the ratio of these two voltages may be written using [7]
and the definition for the transit time as
Equation (11) may be simplified if one assumes a carrier
mobility of
μ
= 0.15 cm
2
/ V-s and the previously men-
tioned value of
v
sat
:
The transit time,
T,
is a function of the carrier drift
velocity,
v
,
and, in turn, a function of the electric field. In
semiconductors such as silicon, the carrier velocity
increases approximately linearly with applied electric field
for only relatively low values of electric field (Fig. 1). At
higher electric field values, the interaction of the charge
carriers with the semiconductor lattice atoms serves to
limit the velocity of the carriers to a value termed the
saturation velocity,
v
sat
. This velocity varies with carrier
type, semiconductor material, and temperature, but is
approximately 10
7
cm/s for electrons in silicon at 290 K
[9]. An approximation of the electric field dependence on
velocity which includes the effects of velocity saturation
may be written as [10]
A further simplification may be used on (12) if the applied
RF voltage is low enough so that velocity saturation does
not occur:
where the term
μ
is the low-field carrier mobility.
The p-i-n diode is often used in high-pulsed-power
applications and is able to handle kilowatts of power
operating in this mode. The rms value of the electric field
under these conditions is needed to estimate the carrier
drift velocity (9) and may be computed assuming a half-
wave-recitified pulsed RF waveform where the carrier
frequency (
f
)
is much larger than the inverse of either
the pulse period (T
P
) or the pulse duration (T
D
).
4
At low frequency and/or for diodes with thin I-regions, the
developed dc voltage, lV
dc
l, approaches the peak RF
voltage, approximating the ideal behavior of a pn junction
diode. For higher frequencies or thicker I-regions, how-
ever, the dc voltage developed decreases as 1/
f
for a
given RF voltage. The developed dc voltage will then
decrease by increasing the I-region thickness. Increas-
ing the I-region effectively increases the transit time pro-
portionally since at high RF voltages the carrier velocity
is limited to its saturation value,
v
sat
. Fig. 3 illustrates the
dependence of the ratio lV
DC
l / lV
RF
l on the rms
value of the applied RF electric field (E
= 0.475
lV
RF
l
D
/ W) with the factor
fW
2
/
D
1/2
as a parameter. A
significant reduction in the developed dc voltage is
indicated for low peak RF electric fields (low applied
lV
RF
l), high-frequency operation, large I-region widths
(
W
), and short duty cycles. At large RF voltages, the dc
voltage developed approches the limiting factor.
ADVANCED:
Data Sheets contain information regarding a product M/A-COM Technology Solutions
•
North America
Tel: 800.366.2266 •
Europe
Tel: +353.21.244.6400
is considering for development. Performance is based on target specifications, simulated results,
•
India
Tel: +91.80.43537383
•
China
Tel: +86.21.2407.1588
and/or prototype measurements. Commitment to develop is not guaranteed.
Visit www.macomtech.com for additional data sheets and product information.
PRELIMINARY:
Data Sheets contain information regarding a product M/A-COM Technology
Solutions has under development. Performance is based on engineering tests. Specifications are
typical. Mechanical outline has been fixed. Engineering samples and/or test data may be available.
M/A-COM Technology Solutions Inc. and its affiliates reserve the right to make
Commitment to produce in volume is not guaranteed.
changes to the product(s) or information contained herein without notice.
AN3022
Establishing the Minimum Reverse Bias for a PIN Diode in a
High-Power Switch
3. Experimental Results
Experimental measurements of the dc self-generated
voltage were performed using a test set similar to that
shown in Figure 2. This test set simulates the isolating
arm (reverse bias p-i-n diode) of a SP2T p-i-n diode in
each arm. Measurements were made at power levels up
to 100 W at frequencies from 1 to 60 MHz and duty fac-
tors from 0.07 to 1.0. The p-i-n diode specimens se-
lected had I-region widths ranging from 50 to 200
μm
and
encompassed various cross sections and carrier lifetime
values. Figure 4 graphically illustrated a comparison
between experimental measurements of the ratio of the
peak RF voltage to self-generated dc voltage (lV
RF
l /
lV
DC
l) and the expression for the ratio indicated by (12).
Rev. V2
A significant experimental observation indicated that the
p-i-n diode may be operated at high RF power without
applying any external dc bias. The p-i-n diode here is
operating in a zero bias open-circuit mode where the
self-generated voltage becomes the reverse bias. To
operate in the open-circuit mode, any external resistance
across the diode must be very high, generally higher
than 10
8
Ω.
Typical levels of harmonic distortion in this
mode were approximately 20 dB below the carrier.
Upon application of an external dc reverse bias at
identical values of the self-generated dc voltage, the
distortion measured was identical. When the applied dc
reverse bias was increased slightly, often as little as 10 V
higher than the self-generated voltage, the distortion
improved significantly, by as much as 60 dB below
carrier. If the applied reverse voltage was lower than the
self-generated dc voltage, the distortion would degrade
and the loss would increase, often leading to p-i-n diode
failure. The dependence of reverse bias distortion on
increasing reverse bias is consistant with observations
and experiments previously reported by the authors [11].
It was also observed that the time it took the self-
generated voltage to reach its final value was virtually
instantaneous upon the initial application of RF power.
However, when the RF power was changed, there
appeared a time lag of as much as several seconds until
the self-generated dc voltage stabilized and reached its
new final value.
Figure 3. Graph of the magnitude of the
self-generated dc voltage vs. the magni-
tude of the peak RF voltage with the term
as a parameter
Figure 5. Calculated generated dc reverse
bias voltage vs. I-region thickness and duty
cycle for a 1 kW signal at 1 GHz
Figure 4. Comparison of measured and
theoretical values of the ratio lV
ac
l / lV
dc
l.
5
ADVANCED:
Data Sheets contain information regarding a product M/A-COM Technology Solutions
•
North America
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Europe
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is considering for development. Performance is based on target specifications, simulated results,
•
India
Tel: +91.80.43537383
•
China
Tel: +86.21.2407.1588
and/or prototype measurements. Commitment to develop is not guaranteed.
Visit www.macomtech.com for additional data sheets and product information.
PRELIMINARY:
Data Sheets contain information regarding a product M/A-COM Technology
Solutions has under development. Performance is based on engineering tests. Specifications are
typical. Mechanical outline has been fixed. Engineering samples and/or test data may be available.
M/A-COM Technology Solutions Inc. and its affiliates reserve the right to make
Commitment to produce in volume is not guaranteed.
changes to the product(s) or information contained herein without notice.
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