Before at an electron breaks away from bond number 2

Info icon This preview shows pages 48–50. Sign up to view the full content.

Movement of electron through crystal. before . At , an electron breaks away from bond number 2 and recombines with the hole in bond number 1. Similarly, at , an electron leaves bond number 3 and falls into the hole in bond number 2. Looking at the three “snapshots,” we can say one electron has traveled from right to left, or, alternatively, one hole has moved from left to right. This view of current flow by holes proves extremely useful in the analysis of semiconductor devices. Bandgap Energy We must now answer two important questions. First, does any thermal energy create free electrons (and holes) in silicon? No, in fact, a minimum energy is required to
Image of page 48

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 24 (1) 24 Chap. 2 Basic Physics of Semiconductors dislodge an electron from a covalent bond. Called the “bandgap energy” and denoted by , this minimum is a fundamental property of the material. For silicon, eV. The second question relates to the conductivity of the material and is as follows. How many free electrons are created at a given temperature? From our observations thus far, we postulate that the number of electrons depends on both and : a greater translates to fewer electrons, but a higher yields more electrons. To simplify future derivations, we consider the density (or concentration) of electrons, i.e., the number of electrons per unit volume, , and write for silicon: (2.1) where J/K is called the Boltzmann constant. The derivation can be found in books on semiconductor physics, e.g., [1]. As expected, materials having a larger exhibit a smaller . Also, as , so do and , thereby bringing toward zero. The exponential dependence of upon reveals the effect of the bandgap energy on the conductivity of the material. Insulators display a high ; for example, eV for dia- mond. Conductors, on the other hand, have a small bandgap. Finally, semi conductors exhibit a moderate , typically ranging from 1 eV to 1.5 eV. Example 2.1 Determine the density of electrons in silicon at K (room temperature) and K. Solution Since eV J, we have (2.2) (2.3) Since for each free electron, a hole is left behind, the density of holes is also given by (2.2) and (2.3). Exercise Repeat the above exercise for a material having a bandgap of 1.5 eV. The values obtained in the above example may appear quite high, but, noting that silicon has , we recognize that only one in atoms benefit from a free electron at room temperature. In other words, silicon still seems a very poor conductor. But, do not despair! We next introduce a means of making silicon more useful. 2.1.2 Modification of Carrier Densities Intrinsic and Extrinsic Semiconductors The “pure” type of silicon studied thus far is an example of “intrinsic semiconductors,” suffering from a very high resistance. Fortunately, it is possible to modify the resistivity of silicon by replacing some of the atoms in the crystal with atoms of another material. In an intrinsic semiconductor, the electron density, , is equal The unit eV (electron volt) represents the energy necessary to move one electron across a potential difference of 1 V. Note that 1 eV J.
Image of page 49
Image of page 50
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern