CHARACTERISTICS
A pn junction can be viewed as isolated ptype and ntype materials brought into intimate contact (Fig. 1.2). Being abundant in ntype material, electrons diffuse to the ptype material. The same process happens for holes from the ptype material. This flow of charges sets up an electric field that starts to hinder further diffusion until an equilibrium is struck. The energyband diagram under equilibrium is shown in Fig. 1.2(b). (Notice that when NA * Np, where Ј, crosses Ep does not coincide with the metallurgical junction.) Since the overall charge has to be conserved, it follows that for an abrupt (step) junction,
as shown in Fig. 1.2(c). An important parameter is the builtin potential y/bi. According to Fig. 1.2(b), it is the sum of y/Bn and y/Bp, given by
2 In./ 
Vbi = y’Bn+y’Bp = q 
(1.2)
which is the total band bending at equilibrium by definition.
Under bias, the following can be obtained using the Poisson equation with appropriate boundary conditions,
(1.3)
(1.4) 
m 
Equation (1.5) can be interpreted as the area under the fielddistance curve in Fig. 1.2(d). The partition of band bending and depletion width between the n — and /7regions can be related by
(1.6)
It can further be shown that
(1.7)
In practical devices, one side usually has a doping concentration much higher than the other, and the junction can be treated as a onesided junction. The depletion width and potential variation in the heavily doped side can then be neglected.
Figure 1.3, which shows the energyband diagram and the carrier concentrations under bias, is used to derive the 1V characteristics. The forward current of a pn junction under bias is determined by diffusion of injected minority carriers. The carrier concentration at the edge of the depletion region is given by
(1.8)
Combining the continuity equation with the current equation, assuming steady state, zero generation rate and zero drift current, one gets
(1.9)
where x = 0 now corresponds to the edge of the depletion region. (Notice the xcoordinate in Fig. 1.3(c).) Solving these differential equations gives the minoritycarrier profiles
(a) 
i — qVf 
FIGURE 1.3 Energyband diagram showing a pn junction (a) under forward bias (positive voltage applied to ptype material and (b) under reverse bias, (c) Minoritycarrier concentration profiles under forward and reverse bias. 
(b) 
(c) 
FIGURE 1.4
/^characteristics of a pn junction in (a) linear current scale and (b) logarithmic current scale.
qIf kT, 
exp 
n„ (*) = » p po po 




exp 
xL pj 
qh kT 
exp 


qnwd 
qVj akT, 
1 
exp 
2t 
D n no n po +— 
qh kT, kT, 
F’* 
J = q 
exp 
D » P W 
D 
— 1 
exp 
qn, 
L Nn ■ p D 
(1.12) At each side of the junction the diffusion current is a function of distance. It maximizes at x = 0 where Eq. (1.12) is obtained. Since the current has to be continuous, the diffusion current is supplemented by the majoritycarrier drift current. This equation is also valid for reverse bias when Vjis negative. In cases where the thickness of the ptype or ntype material is less than the diffusion length Lp or L„, the latter parameter should be replaced by the corresponding thickness in Eq. (1.12) and thereby increasing the current. The IVcharacteristics described by Eq. (1.12) is shown in Fig. 1.4. In both the linear current scale and the logarithmic current scale, additional features at high forward bias and reversed bias are to be noticed. In the forward direction, currents rises exponentially with Vj until the slope becomes more gradual. This can be due to highlevel injection of carriers such that the applied voltage is no longer totally developed across the depletion region. Series resistance, Rs, can also cause the same effect. At high reverse bias, breakdown can occur due to impact ionization (see Appendix B3) or Zener tunneling. These mechanisms can be separated by temperature dependence. At higher temperature, the ionization rate decreases and the breakdown voltage due to avalanche multiplication increases. The opposite dependence holds for Zener breakdown. Normally avalanche multiplication occurs first, with breakdown voltage shown in Fig. B3.3. An additional current component besides Eq. (1.12) is due to recombination/generation through midgap states within the depletion region (see Appendix B2). This mechanism gives rise to a current described by 




If the term qntWJ2T is comparable to or larger than the preexponential factor in Eq. (1.12), the current for small Vf as well as the reverse current will be increased.
A common use of the pn junction requires it to switch between the onstate and the offstate. Because of minoritycarrier storage under forward bias, the immediate response to reverse bias is shown in Fig. 1.5, with Ir =
(1.14) 
t.«r In 1 +
erf 
t, r exp (rttJ r)
(1.15) 
= 1 + 0.1 —
This reverse recovery limits a pn junction to about 1 GHz operation. In order to increase the frequency response, the carrier lifetime r can be intentionally shortened by introducing impurities for recombination. The penalty for this is an increased leakage current. An alternative approach is to use a steprecovery diode (Section 1.5.2).
The equivalent circuit for a pn junction is shown in Fig. 1.6. Since capacitance is defined by dQldV, the depletionlayer capacitance Cj is associated with the depletionlayer charge, while the diffusion capacitance CD is related to injected carriers. The CD is significant only under forward bias conditions and is proportional to the forward current, given by
,(! Ur 
q I ■/ Vf
(1.16) 
— (Lv + L n ) exp ‘
2kT F no n P°
The Cd is determined by the depletion width and for a onesided step junction,
qeN
(1.17)
where N is from the lightly doped side. A measurement of 1/C2 vs. Vn as shown in Fig. 1.7, can extrapolate j/bj and its slope can determine the doping
FIGURE 1.5
Transient current characteristics of a pn junction when switched from forward to reverse direction. td and tir are called delay time and transition time, respectively.
concentration (or area). This technique can be extended to obtain nonuniform doping profile,
(1.18) 
dcj
dV qe N (x)
1. Because it is the most common rectifier, a pn junction has many circuit applications. See Appendix ClApplications of Rectifiers.
2. Many devices are special forms of pn junction. Examples are LED, laser, solar cell, and photodiode. A pn junction also serves as a building block for many other devices such as the bipolar transistor, MOSFET, junction FET, etc.
3. Due to the nonlinear, exponential nature of the current, the pn junction can be used as a varistor.
4. The variable depletion capacitance at reverse bias can be utilized as a varactor.
5. A pn junction is a very common protection device for electrostatic discharge (ESD). It discharges a voltage surge when it exceeds a certain value comparable to the builtin potential.
6. A pn junction is a robust device and is a good choice for a diode required in power electronics.
7.
Rs 
The pn junction can be used to isolate devices or regions of semiconductors. An example can be found in the tub isolation for CMOS circuits.
FIGURE 1.6 FIGURE 1.7 Equivalent circuit of a pn junction. A is the A plot of capacitance (I/C2) under reverse bias area of the diode. yields y’i/ and doping concentration (or area). 
8. The wellbehaved forward characteristics of a pn diode enable it to be used as a temperature sensor. In operation, a constant current is applied and the voltage is monitored. This forward voltage drop is a fairly linear function of temperature. GaAs diodes can be good sensors in a wide temperature range from a few degree K to « 400 K, and Si diode from « 20 K.
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