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Depletion Capacitance Linearly Graded Junction zThe Poisson equation for the case is 2 d Ψ − q −W W 2 = ax ≤x ≤ dx ε s 2 2 zWhere a is impurity gradient and W is depletion width area. ulfiqar Ali32 Z1EEE 1 Figure 4-11. Linearly graded junction in thermal equilibrium. (a) Impurity distribution. (b) Electric-field distribution. (c) Potential distribution with distance. (d) Energy band diagram. EEE132 Zulfiqar Ali 2 Linearly graded junction zBuilt in Voltage for Linearly Graded Junction ⎡ W W ⎤ (a )(a ) kT ⎢ 2 2 ⎥ 2kT ⎡aW ⎤ Vbi = ln⎢ 2 ⎥ = ln⎢ ⎥ q q 2n ⎢ ni ⎥ ⎣ i ⎦ ⎣⎢ ⎦⎥ EEE132 Zulfiqar Ali 3 Depletion Capacitance The depletion layer capacitance per unit area is defined dQ Cj = dV Where dQ is incremental charge per unit area as for an incremental charge per unit voltage. EEE132 Zulfiqar Ali 4 Figure 4.13. (a) p-n junction with an arbitrary impurity profile under reverse bias. (b) Change in space charge distribution due to change in applied bias. (c) Corresponding change in electric-field distribution. EEE132 Zulfiqar Ali 5 Depletion Capacitance zWhenever voltage dv is applied. The charge filed distribution will expand. Figure shows the region bounded by dashed line. zThis increment bring increase in electric field by an amount of dQ dε = ε s EEE132 Zulfiqar Ali 6 Capacitance-Voltage Characteristic zSeparation between two plates represents the depletion width. Refer to the figure 13. zFor forward bias large current can flow across the junction corresponding to large number of mobile carrier. zThe incremental change of these mobile carriers with respect to the biasing voltage contributes an additional term called diffusion capacitance. EEE132 Zulfiqar Ali 7 Capacitance-Voltage Characteristic. Abrupt Junction case εs qε N Cj= = s B W 2VV (bi − ) ulfiqar Ali32 Z1EEE 8 Varactor z Used in many circuit applications. zCapacitance varies with frequency. zConcept: zReverse biased application depletion capacitance: −n Cj∞() Vbi +R V or −n Cj∞()R V ulfiqar Ali32 Z1EEE 9 Varactor zVoltage sensitivity with respect to capacitance is greater in abrupt junction that linear grade. zThis because of n factor which is higher in abrupt as oppose to linear grade. zFrom Poisson condition establish the relationship between the depletion region and VR. EEE132 Zulfiqar Ali 10 Varactor zBy choosing different value of m we can approximate the relationship between the voltage and junction capacitance 1 m+2 WV∞()R −1 m+2 CVj=() R zIn RF circuit you can adjust the voltage to control the capacitive value therefore you can control resonant value. ulfiqar Ali32 Z1EEE 11 Current Voltage Characteristic zA voltage applied to a p-n junction will disturb the balance diffussion and drift current. zForward bias voltage will increase the diffusion current and decrease the drift current. zReverse biased voltage will increase the drift current and reduced the diffusion current. EEE132 Zulfiqar Ali 12 Ideal characteristic. zWe based on these assumptions: zAbrupt boundaries ,outside the boundary the semiconductor assume to be neutral. zCarrier density related by potential different. zLow density carrier is smaller compare to higher density. zElectron and hole are constant throughout the depletion region. EEE132 Zulfiqar Ali 13 Figure 4-16. Depletion region, energy band diagram and carrier distribution. (a) Forward bias. (b) Reverse bias. EEE132 Zulfiqar Ali 14 Ideal characteristic. zBuilt in Voltage kT ppo n no Vbi = ln 2 q ni zThe electron density and hole density are related through the electrostatic potential different. ulfiqar Ali32 Z1EEE 51 Ideal Characteristic zForward bias cause the electrostatic potential different reduced to Vbi-VF. zReverse bias electrostatic potential increase Vbi+VR ()Vbi− V z q kT nn= n p e zWhere nn and np are non-equilibrium electron densities at the boundary. ulfiqar Ali32 Z1EEE 61 Ideal Characteristic zJs saturation current Lp and Ln are diffusion length. qD p qD n Js≡p no + n po Lp Ln zThe above equation is the ideal diode equation. ulfiqar Ali32 Z1EEE 71 Figure 4-18. Ideal current-voltage characteristics. (a) Cartesian plot. (b) Semilog plot. EEE132 Zulfiqar Ali 18 Temperature Effect zTemperature effect has an effect on the device performance. zIn reverse bias as well as forward bias the magnitude of diffusion and generation recombination depend strong on the temperature. EEE132 Zulfiqar Ali 19 Charge storage and transient behavior zUnder forward bias the electrons are injected into p-type and holes are injected into the n-type. zOnce injected across junction the minority carriers recombine with majority carrier and decay exponentially with distance. zThese lead to current flows and charge storage in the pn junction. EEE132 Zulfiqar Ali 20 Minority Carrier Storage zThe charge minority carrier can be found by integrating excess hole in neutral region. ∞ Qp= q() p − p dx ∫ n no xn qV −1 kT qL= p p no() e Lp 2 Qp =Jp()() x= τ pJp x Dp n n ulfiqar Ali32 Z1EEE 12 Figure 4-17. Injected minority carrier distribution and electron and hole currents. (a) Forward bias. (b) Reverse bias. The figure illustrates idealized currents. For practical devices, the currents are not constant across the space charge layer. EEE132 Zulfiqar Ali 22 Diffusion Capacitance zWhen the junction is forward biased the is additional significant contribution to the junction capacitance. zThis is called the diffusion capacitance denoted by Cd. A is area of a device. Aq2 Lpp qV Cd = no e kT kT EEE132 Zulfiqar Ali 23 Transient Behavior zFor switching behavior the forward to reverse biased transition must be transient time short. zUnder the forward biased condition the stored minority carrier I Qp=τ pJp = τ F p A QpA ⎛ I F ⎞ toff≅ =τp⎜ ⎟ I Rave ⎝ I Rave ⎠ ulfiqar Ali32 Z1EEE 42 Junction Breakdown zWhen large reverse voltage is applied to p-n junction, the junction breaks down and conducts a very large current. zThe important breakdown mechanism: zTunneling process and avalance mechanism. EEE132 Zulfiqar Ali 25 Tunneling Effect zHigh electric field is applied in reverse direction valence electron make transition from valence band to conduction band. zOnly occurs if the electric field is high about 106V/cm EEE132 Zulfiqar Ali 26 Avalance multiplication z This occurs under the reverse bias condition. z The thermally generated electron gain kinetic energy from the electric field. z If the field is sufficiently high it can gain enough kinetic energy to break the bond creating electron hole pair. z The newly created electron hole pair requires energy thus create more electron hole pair and this is called the avalance multiplication. EEE132 Zulfiqar Ali 27.
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