Fundamentals-of-Microelectronics-Behzad-Razavi.pdf

Br wileyrazavi fundamentals of microelectronics

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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 25 (1) Sec. 2.1 Semiconductor Materials and Their Properties 25 to the hole density, . Thus, (2.4) We return to this equation later. Recall from Fig. 2.2 that phosphorus (P) contains five valence electrons. What happens if some P atoms are introduced in a silicon crystal? As illustrated in Fig. 2.5, each P atom shares Si Si Si Si Si Si P e Figure 2.5 Loosely-attached electon with phosphorus doping. four electrons with the neighboring silicon atoms, leaving the fifth electron “unattached.” This electron is free to move, serving as a charge carrier. Thus, if phosphorus atoms are uniformly introduced in each cubic centimeter of a silicon crystal, then the density of free electrons rises by the same amount. The controlled addition of an “impurity” such as phosphorus to an intrinsic semiconductor is called “doping,” and phosphorus itself a “dopant.” Providing many more free electrons than in the intrinsic state, the doped silicon crystal is now called “extrinsic,” more specifically, an -type” semiconductor to emphasize the abundance of free electrons. As remarked earlier, the electron and hole densities in an intrinsic semiconductor are equal. But, how about these densities in a doped material? It can be proved that even in this case, (2.5) where and respectively denote the electron and hole densities in the extrinsic semiconductor. The quantity represents the densities in the intrinsic semiconductor (hence the subscript ) and is therefore independent of the doping level [e.g., Eq. (2.1) for silicon]. Example 2.2 The above result seems quite strange. How can remain constant while we add more donor atoms and increase ? Solution Equation (2.5) reveals that must fall below its intrinsic level as more -type dopants are added to the crystal. This occurs because many of the new electrons donated by the dopant “recombine” with the holes that were created in the intrinsic material. Exercise Why can we not say that should remain constant? Example 2.3 A piece of crystalline silicon is doped uniformly with phosphorus atoms. The doping density is
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 26 (1) 26 Chap. 2 Basic Physics of Semiconductors atoms/ . Determine the electron and hole densities in this material at the room tempera- ture. Solution The addition of atoms introduces the same number of free electrons per cubic centimeter. Since this electron density exceeds that calculated in Example 2.1 by six orders of magnitude, we can assume (2.6) It follows from (2.2) and (2.5) that (2.7) (2.8) Note that the hole density has dropped below the intrinsic level by six orders of magnitude. Thus, if a voltage is applied across this piece of silicon, the resulting current predominantly consists of electrons.
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