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# Varactor theory

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VARACTOR THEORY OF DIODE

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### Varactor theory

1. 1. VARACTOR DIODE TRIBHUWAN KUMAR
2. 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. 3. p-n junction P - - - - N - - - Semiconductor lattice with acceptor atoms and free holes Density of Acceptor Atoms NA Hole with ‘B’ atom + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Semiconductor lattice with donor atoms and free electrons Density of Donor Atoms ND 5th electron of ‘P’ atom
4. 4. Depletion layer N P - - Neutral charge region - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Negative charge Positive charge Neutral charge region region region “SPACE CHARGE Region” or “DEPLETION Region”
5. 5. Electric Field P - E=0 N - - - + + + + + + -Xp + + + + + + 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. 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. 7. Using relationship: The expression for built-in voltage for a PN junction having non-degenerate semiconductors can be written as
8. 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. 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. 10. Space Charge - - - - - - - + + + + + + P + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + N ρ qND x -qNA Distribution of NA and ND in junction (impurity profile) determines Capacitance variation
11. 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. 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. 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. 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. 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. 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. 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. 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. 19. Expressing Xd in terms of potential step Vo, where Vo = V1 + V2 X V1/V2
20. 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. 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. 22. Typical C-V Characteristics of tuning varactor diodes:
23. 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. 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. 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. 26. Planar Junction Diode Mesa Diode
27. 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. 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. 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. 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. 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. 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
33. 33. O O
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