5
Dielectric Relaxation Frequency and Diode Capacitance
f
DR
(Dielectric Relaxation Frequency) for a PIN diode is
given by the equation
f
DR
=
1
2πρε
where…
ρ = bulk resistivity of the I-layer
ε = ε
0
ε
R
= 10
-12
F/cm
= bulk susceptance of silicon
In the case of an epitaxial diode with a value for ρ of 10Ω-
cm, f
DR
will be in Ku-Band. For a bulk diode fabricated on
very pure material, ρ can be as high as 2000, resulting in
a value of f
DR
of 80 MHz.
The implications of a low f
DR
are very important in RF atten-
uator and switch circuits. At operating frequencies below
f
DR
, reverse bias (as much as 50V) is needed to minimize
junction capacitance. At operating frequencies well above
f
DR
, the curve of capacitance vs. reverse bias is at.
For the HMPP-386x family, f
DR
is around 500 MHz, resulting
in very low capacitance at zero bias for frequencies above
1 GHz. See Figure 1.
Diode Lifetime and Resistance
The resistance of a PIN diode is controlled by the con-
ductivity (or resistivity) of the I layer. This conductivity is
controlled by the density of the cloud of carriers (charges)
in the I layer (which is, in turn, controlled by the DC bias).
Minority carrier lifetime, indicated by the Greek symbol
τ, is a measure of the time it takes for the charge stored
in the I layer to decay, when forward bias is replaced with
reverse bias, to some predetermined value. This lifetime
can be short (35 to 200 nsec. for epitaxial diodes) or it
can be relatively long (400 to 3000 nsec. for bulk diodes).
Lifetime has a strong inuence over a number of PIN
diode parameters, among which are distortion and basic
diode behavior.
To study the eect of lifetime on diode behavior, we rst
dene a cuto frequency f
C
= 1/τ. For short lifetime diodes,
this cuto frequency can be as high as 30 MHz while for
our longer lifetime diodes f
C
≅ 400 KHz. At frequencies
which are ten times f
C
(or more), a PIN diode does indeed
act like a current controlled variable resistor. At frequen-
cies which are one tenth (or less) of f
C
, a PIN diode acts
like an ordinary PN junction diode. Finally, at 0.1f
C
≤ f ≤
10f
C
, the behavior of the diode is very complex. Suce it
to mention that in this frequency range, the diode can
exhibit very strong capacitive or inductive reactance —it
will not behave at all like a resistor.
The HMPP-386x family features a typical lifetime of 300 to
500 ns, so 10f
C
for this part is 5 MHz. At any frequency over
5 MHz, the resistance of this diode will follow the curve
given in Figure 2. From this curve, it can be seen that the
HMPP-386x family produces a lower resistance at a given
value of bias current than most attenuator PIN diodes,
making it ideal for applications where current consump-
tion is important.
