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2.1. INTRODUCTION Diodes are among the oldest and most widely used of electronic devices. A diode may be de ned as a near-unidirectional conductor whose state of conductivity is determined by the polarity of its terminal voltage. The subject of this chapter is the semiconductor diode, formed by the metallurgical junction of p-type and n-type materials. (A p-type material is a group-IV element doped with a small quantity of a group-V material; n-type material is a group-IV base element doped with a group-III material.)
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THE IDEAL DIODE
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The symbol for the common, or recti er, diode is shown in Fig. 2-1(a). The device has two terminals, labeled anode (p-type) and cathode (n-type), which makes understandable the choice of diode as its name. When the terminal voltage is nonnegative (vD ! 0), the diode is said to be forward-biased or on ; the positive current that ows iD ! 0) is called forward current. When vD < 0, the diode is said to be reverse-biased or o , and the corresponding small negative current is referred to as reverse current.
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iD Anode + D _
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Cathode
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Fig. 2-1
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The ideal diode is a perfect two-state device that exhibits zero impedance when forward-biased and in nite impedance when reverse-biased (Fig. 2-2). Note that since either current or voltage is zero at any instant, no power is dissipated by an ideal diode. In many circuit applications, diode forward voltage drops and reverse currents are small compared to other circuit variables; then, su ciently accurate results are obtained if the actual diode is modeled as ideal. The ideal diode analysis procedure is as follows: Step 1: Assume forward bias, and replace the ideal diode with a short circuit. Step 2: Evaluate the diode current iD , using any linear circuit-analysis technique. Step 3: If iD ! 0, the diode is actually forward-biased, the analysis is valid, and step 4 is to be omitted. 30
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CHAP. 2]
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SEMICONDUCTOR DIODES
iD + infinite impedance zero impedance
LD 0
_ Forward-biased
iD = 0
LD < 0
_ Reverse-biased
(a) Terminal characteristics
(b) Circuit models
Fig. 2-2
Ideal diode
Step 4: If iD < 0, the analysis so far is invalid. Replace the diode with an open circuit, forcing iD 0, and solve for the desired circuit quantities using any method of circuit analysis. Voltage vD must be found to have a negative value.
Example 2.1. Find voltage vL in the circuit of Fig. 2-3(a), where D is an ideal diode. The analysis is simpli ed if a Thevenin equivalent is found for the circuit to the left of terminals a; b; the result is vTh
RS +
R1 v R1 RS s
iD D +L _ D
ZTh RTh R1 kRS
R1 RS R1 RS
a iD D RL + LL _
RTh + LL _ +
R1 _ b (a)
_ b (b)
RTh +
D LD _ + RL
_ b (c)
+ LL _
Fig. 2-3 Step 1: After replacing the network to the left of terminals a; b with the Thevenin equivalent, assume forward bias and replace diode D with a short circuit, as in Fig. 2-3(b). Step 2: By Ohm s law, iD Step 3: If vS ! 0, then iD ! 0 and vL iD RL RL v RL RTh Th vTh RTh RL
Step 4: If vS < 0, then iD < 0 and the result of step 3 is invalid. Diode D must be replaced by an open circuit as illustrated in Fig. 2-3(c), and the analysis performed again. Since now iD 0, vL iD RL 0. Since vD vS < 0, the reverse bias of the diode is veri ed.
(See Problem 2.4 for an extension of this procedure to a multidiode circuit.)
SEMICONDUCTOR DIODES
[CHAP. 2
DIODE TERMINAL CHARACTERISTICS
Use of the Fermi-Dirac probability function to predict charge neutralization gives the static (nontime-varying) equation for diode junction current: iD Io evD =VT 1 A where VT  kT=q; V vD  diode terminal voltage, V Io  temperature-dependent saturation current, A T  absolute temperature of p-n junction, K k  Boltzmann s constant 1:38 10 23 J/K) q  electron charge 1:6 10 19 C   empirical constant, 1 for Ge and 2 for Si
Example 2.2. Find the value of VT in (2.1) at 208C. Recalling that absolute zero is 2738C, we write VT kT 1:38 10 23 273 20 25:27 mV q 1:6 10 19
2:1
While (2.1) serves as a useful model of the junction diode insofar as dynamic resistance is concerned, Fig. 2-4 shows it to have regions of inaccuracy:
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