VARACTOR THEORY OF DIODE

1. VARACTOR DIODE
TRIBHUWAN KUMAR

2. VARACTOR DIODE
. The Name “Varactor” means: variable
reactor (or reactance), also called “Varicap” meaning
variable capacitance. Both names: varactor and varicap are
the same form of semiconductor or a P-N Junction
Varactor or Varicap takes advantage of the fact that the
capacitance of the diode PN junction varies with the applied reverse
bias voltage.
This differs from other diodes, such as rectifying diodes and
switching diodes, which use the rectifying effect of the PN junction,
or current regulation diodes, which take advantage of zener
breakdown or avalanche breakdown.
A Varactor provides an electrically controllable capacitance, which can
be used in tuned circuits. It is small and inexpensive, which makes its use
advantageous in many applications. Its disadvantages compared to a manual
mechanical variable capacitor are a lower Q, nonlinearity, lower voltage rating
and a more limited range.

3. p-n junction
P
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N
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Semiconductor lattice
with acceptor atoms
and free holes
Density of Acceptor Atoms NA
Hole with ‘B’ atom
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Semiconductor lattice
with donor atoms
and free electrons
Density of Donor Atoms ND
5th electron of ‘P’ atom

4. Depletion layer
N
P
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Neutral charge
region
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Negative charge Positive charge Neutral charge
region
region
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“SPACE CHARGE Region” or “DEPLETION Region”

5. Electric Field
P
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E=0
N
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-Xp
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E=0
Xn
Ex toward -x
As reverse voltage increases, the peak electric field in depletion region increases.
When it exceeds a critical value (E≅ 2x105 V/cm), reverse Current increases
dramatically.

6. Built-in potentials can be expressed as:
Thus built-in voltage is large for semiconductor with higher band gap
Where:
Nc & Nv are density of stataes in conduction and valence band
respectively and NA & ND are acceptor & donor concentrations in P- and
N –region of a P-N junction.

7. Using relationship:
The expression for built-in voltage for a PN junction having
non-degenerate semiconductors can be written as

8. CURRENT_VOLTAGE Characteristics of a P-N Junction
* Under forward bias, the potential barrier is reduced, so that carriers flow
(by diffusion) across the junction
•Current increases exponentially with increasing forward bias
•The carriers become minority carriers once they cross the junction; as the
diffuse in the quasi-neutral regions, they recombine with majority carriers
(supplied by the metal contacts). “injection” of minority carriers
•Under reverse bias, the potential barrier is
increased, so that negligible
carriers flow across the junction
•If a minority carrier enters the depletion region
(by thermal generation or
diffusion from the quasi-neutral regions), it will
be,swept across the junction
by the built-in electric field “collection” of minority carriers  reverse current

9. CAPACITOR CONCEPT:
To understand how a varactor or varicap diode works, we need to know “what a
capacitor is” and what can change its capacitance. A parallel plate capacitor consists of two
plates with an insulating dielectric medium between them.
Dielectric medium (Air)
The amount of charge that can be stored
d
Plates Each of
area “A”
depends on the area (A) of the plates and
the distance (d) between them.
Capacitance depends on area “A”, Dielectric constant of medium & distance “d” between
Plates.
Sio2
Metal
+
N
P
- - - - - - - - - - +++++++++
- - - - - - - - - - +++++++++
- - ++++
---------- - +++++++++
---------- +++++++++
---------+++++
Wp
p
Wn
W
In P-N junction, depletion layer on heavily doped P-side is very small Compared to that on
lowly doped N-side (# Charges on both side is equal). Silicon is dielectric medium here.
Junction Capacitance is inversely proportional to “W = Wn+Wp , and charges in depletion.

10. Space Charge
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N
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qND
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-qNA
Distribution of NA and ND in junction (impurity profile) determines Capacitance variation

11. Parameters to vary capacitance of a
semiconductor P-N Junction:
1.The medium of Depletion Region of a silicon P-N Junction is
Silicon, so the dielectric constant of the medium is that of silicon.
2. Area of plates is area of diode, which can be decided when the
diode is fabricated. Therefore, for a given device the area can not
be varied to vary the capacitance.
3. Depletion width of a diode depends on applied voltage. This
property of a P-N junction is utilized to operate it as a Varactor.
When forward voltage is applied to a P-N junction , the
depletion decreases so junction capacitance increases.
If reverse voltage is applied the depletion width increase
and so the capacitance of the junction will decrease. Since under
reverse bias condition the diode current is negligible low, the
variation of reverse bias is employed to vary junction capacitance
in varactor diodes.

12. A P-N junction has a junction capacitance that is a function of the
voltage across the junction. An electric field in the depletion layer is
set up by the ionized donors and acceptors. A higher reverse bias
widens the depletion layer,uncovering more fixed charge and raising
the junction potential.
The capacitance of the junction is
C = Q(V)/V,
and the incremental capacitance is dC = dQ(V)/dV.
The capacitance decreases as the reverse bias increases, according
to the relation
C = Co/(1 + V/Vo)n,
Where Co and Vo are constants. Vo is approximately the forward
voltage of the diode. The exponent ‘n’ depends on how the doping
density of the semiconductors depend on distance away from the
junction.

13. Zero bias (i.e under no applied voltage bias) the depletion
width of a P-N junction depends on carrier doping in the n- and
p- regions at the junction. If doping is heavy, the depletion width
will be small to give high zero bias capacitance. For low doping,
depletion with is large and the junction will exhibits low capacitance
value at zero applied bias.
The variation of depletion width and therefore, the capacitance
on application of reverse bias depends on impurity distribution called
impurity profiles on both sides of the junction.
In practical p-n junction the impurity profile is formed according
to the device design consideration.Commonly employed profiles are:
1. Linearly graded junction: in which carrier concentration varies
linearly with distance away from the junction. It may be on both
side or only one side. Generally one side junction are used.
2. Hyper abrupt p-n junction employs very heavy doping on one side
of the junction.In this case depletion region width on heavy doping
side is negligible compared to lowly doped side.

14. For a graded junction
(linear variation), n = 0.33.
For an abrupt junction
(constant doping density),
n = 0.5.
If the density jumps
abruptly at the junction,
then decreases
(called hyperabrupt),
n can be made as high
as n = 2.
The doping on one side of
the junction is heavy, and
the depletion layer is
predominately extends on
the other side only.

15. Step or Abrupt junction:
Impurity distribution in this
type of p-n junction is shown in the
Figure.
This structure is formed by
diffusing p- type impurity in n- type
epitaxial silicon wafer. So concentration
of p- type impurity varies with
distance from the surface while in
n-type region the doping is constant
and is that of epi- layer.
Shape or slope of p- profile
depends on time and temperature of
p- diffusion
(i.e determined by technology)

16. Hyper Abrupt p-n
junction:
As shown in the figure, in a
Hyper abrupt junction first
n- type impurity is introduced
into n- epilayer followed by
p-type diffusion. Thus in this
case carrier concentration varies
With distance on both side of
the junction.
This structure is employed to
fabricate high capacitance ratio
Varactors for tuning applications

17. CAPACITANCE VARIATION of P-N JUNCTION
For ND and NA as donor and acceptor impurities
concentrations on n-side and p-side of the junction respectively,
for junction area of A at equilibrium the total charges on the two
sides of the junction must be equal

18. For an abrupt junction the depletion region widths Xn (in n-region) and
Xp (in p-region) at applied voltage ‘V’ are given by :
From above equations the depletion width “Xd” is given by
Xd = xn + xp
Xd =

19. Expressing Xd in terms of potential step Vo, where
Vo = V1 + V2
X
V1/V2

20. The total depletion layer width Xd at the junction is
Xd = Xn + Xp
Therefore
As capacitance per unit area
Therefore, the capacitance of junction of unit area is given by
Where
is zero bias capacitance of the junction obtained by
putting V=0 in above equation.

21. For an abrupt P +- N junction i.e one side (p-side) doped heavily compared
to n-region i.e (Na >> Nd) then from expression of Cj (V) we get
Thus the capacitance is dominated by carrier concentration in lowly
doped n-region.

22. Typical C-V Characteristics of tuning varactor diodes:

23. Measuring C-V characterstics of an abrupt p+-n junction and
ploting
we can estimate the values of built-in
potential and doping concentration Nd .

24. Diodes chips are separated
by scribing using a diamond
point and packaged in a
suiatable package as shown
in the figure.
Varactors in surface
mount packages exhibit
low inductance
ensuring a wide
frequency application,
and assure
environmental
endurance and
mechanical reliability..

25. Varactors are commonly used in parametric amplifiers,
parametric oscillators and Voltage Controlled Oscillators (VCO)
as part of phase –locked loops and frequency synthesizers.
Varactors are operated reversed-biased so no current flows, but
since the thickness of the depletion layer varies with the applied
bias voltage, the capacitance of the diode can be made to vary.
Generally, the depletion region thickness is proportional
to the square root of the applied voltage; and capacitance is
inversely proportional to the depletion region thickness. Thus,
the capacitance is inversely proportional to the square root of applied
voltage.The depletion layer can also be made of a MOS-diode or a
Schottky diode.This is of big importance in CMOS and MMIC
technology.

26. Planar Junction Diode
Mesa Diode

27. Internal structure of a varicap
In the figure we can see an
example of a cros-section of
a varactor with the depletion
layer formed at the p-n jn.

28. The advent of varactor diodes has made a huge
impact in many areas of electronic design, which is only too
evident in todays consumer products.
Formerly, where bulky or unreliable mechanical
methods were used, the size, reliability and excellent
tracking abilities of the varactor has led to smaller, cheaper
and more elaborate circuitry, previously impossible to
attain.
An extensive range of Variable Capacitance diodes are
processed using ion-implantation/diffusion techniques that
assure accurate doping levels, and hence produce the
exacting junction profiles necessary for high performance
devices.
An overall capacitance range of approximately 1pF to 200pF
assures a broad applications base, enabling designs
operating from kHz and extending into the microwave
region. The Hyperabrupt junctions for example, are made to

29. Equivalent Circuit of a varactor diode:
At low frequency
At high frequency
Rs
0
L
O
Rp
Quality Factor of a varactor:
The series resistance exists as a consequence of the remaining
undepleted
semiconductor resistance, a contribution due to the die
substrate, and a small lead and package component, and is foremost in
determining the performance
of the device under RF conditions.
This follows, as the quality factor, Q, is given by: Q = 1 / 2 π f c Rs
Where:
Rs = Series Resistance, f = Frequency
So, to maximise Q, Rs must be minimised. This is achieved by the use of
an

30. Q at test conditions of 50 MHz and a
relatively low VR of 3 or 4 volt ranges
100 to 450. The specified VR is very
important in assessing Q because a
significant part of series resistance
is due to the undepleted part of epitaxial
layer which is strongly dependent upon
VR as shown in the figure.
The maximum frequency of
operation depends on the required
capacitance and hence the bias voltage
(series resistance and Q).
Also the parasitic components of package has stray capacitance (~0.08pf) and
inductance ~2.8nH. These depends on size,material and construction of the
package.

31. The capacitance ratio, commonly expressed as
C(V1)/C(V2) is a useful parameter that shows how quickly the
capacitance changes with applied bias voltage
For an abrupt junction:
C(2)/ C(20) = 2.8
For a hyperabrupt junction :
C(2)/ C(20) = may be 6
This feature of the hyperabrupt capacitance variation
is important for assessing devices for battery-powered applications.
The quality factor Q at a particular biasing condition
is a useful parameter w.r.t tuned circuit.

32. Example of a Varactor circuits:
In an electronic circuit, a capacitor is replaced with the
varactor diode, but it is necessary to also ensure that the tune voltage,
i.e. the voltage used to set the capacitance of the diode can be inserted
into the circuit, and that no voltages such as bias voltages from the
circuit itself can affect the varactor diode.
Voltage controlled oscillator using a varactor diode
In this circuit D1 is the varactor diode that is used to enable
the oscillator to be tuned. C1 prevents the reverse bias for the varactor
or varicap diode being shorted to ground through the inductor, and R1 is
a series isolating resistor through which the varactor diode tuning

36. O
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