A p-n junction can be viewed as isolated p-type and n-type materials brought into intimate contact (Fig. 1.2). Being abundant in n-type material, electrons diffuse to the p-type material. The same process happens for holes from the p-type material. This flow of charges sets up an electric field that starts to hinder further diffusion until an equilibrium is struck. The energy-band 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 built-in potential y/bi. According to Fig. 1.2(b), it is the sum of y/Bn and y/Bp, given by




Подпись: 2 In./

Vbi = y’Bn+y’Bp = q

Подпись: 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,




Подпись: (1.4)


Подпись: m«NAWdp ^DWCn

Equation (1.5) can be interpreted as the area under the field-distance curve in Fig. 1.2(d). The partition of band bending and depletion width between the n — and /7-regions can be related by



CHARACTERISTICSIt can further be shown that


In practical devices, one side usually has a doping concentration much higher than the other, and the junction can be treated as a one-sided junction. The depletion width and potential variation in the heavily doped side can then be neglected.

Figure 1.3, which shows the energy-band diagram and the carrier concentrations under bias, is used to derive the 1-V characteristics. The forward current of a p-n junction under bias is determined by diffusion of injected minority carriers. The carrier concentration at the edge of the depletion region is given by



Combining the continuity equation with the current equation, assuming steady state, zero generation rate and zero drift current, one gets



where x = 0 now corresponds to the edge of the depletion region. (Notice the x-coordinate in Fig. 1.3(c).) Solving these differential equations gives the minority-carrier profiles




Подпись: (a)

-i — qVf



Energy-band diagram showing a p-n junction (a) under forward bias (positive voltage applied to p-type material and (b) under reverse bias, (c) Minority-carrier concentration profiles under forward and reverse bias.



Подпись: (b)


Подпись: (c)FIGURE 1.4

/-^characteristics of a p-n junction in (a) linear current scale and (b) logarithmic current scale.




n„ (*) = »

p po po


6XP|f nJ














qVj akT,




D n

no n po +—





J = q


D » P



— 1



L Nn ■ p D


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 majority-carrier drift current. This equation is also valid for reverse bias when Vjis negative. In cases where the thickness of the p-type or n-type 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 I-Vcharacteristics 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 high-level 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 mid-gap states within the depletion region (see Appendix B2). This mechanism gives rise to a current described by

The two diffusion currents give a total of





If the term qntWJ2T is comparable to or larger than the pre-exponential factor in Eq. (1.12), the current for small Vf as well as the reverse current will be increased.

A common use of the p-n junction requires it to switch between the on-state and the off-state. Because of minority-carrier storage under forward bias, the immediate response to reverse bias is shown in Fig. 1.5, with Ir =



Подпись: (1.14)t.«r In 1 +


Подпись: erft, r exp (rttJ r)


Подпись: (1.15)= 1 + 0.1 —

This reverse recovery limits a p-n 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 step-recovery diode (Section 1.5.2).

The equivalent circuit for a p-n junction is shown in Fig. 1.6. Since capacitance is defined by dQldV, the depletion-layer capacitance Cj is associated with the depletion-layer 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



Подпись: ,(! Ur q I ■/ Vf


Подпись: (1.16)— (Lv + L n ) exp ‘

2kT F no n P°

The Cd is determined by the depletion width and for a one-sided step junction,



CHARACTERISTICSwhere 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


Transient current characteristics of a p-n 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,


Подпись: (1.18)dcj-

dV qe N (x)


1. Because it is the most common rectifier, a p-n junction has many circuit applications. See Appendix Cl-Applications of Rectifiers.

2. Many devices are special forms of p-n junction. Examples are LED, laser, solar cell, and photodiode. A p-n junction also serves as a building block for many other devices such as the bipolar transistor, MOSFET, junction FET, etc.

3. Due to the non-linear, exponential nature of the current, the p-n junction can be used as a varistor.

4. The variable depletion capacitance at reverse bias can be utilized as a varactor.

5. A p-n junction is a very common protection device for electro-static discharge (ESD). It discharges a voltage surge when it exceeds a certain value comparable to the built-in potential.

6. A p-n junction is a robust device and is a good choice for a diode required in power electronics.



Подпись: Rs The p-n junction can be used to isolate devices or regions of semiconductors. An example can be found in the tub isolation for CMOS circuits.



Equivalent circuit of a p-n 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 well-behaved forward characteristics of a p-n 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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