3.12 Interpretation of Energy Band Diagrams Six different silicon samples mainta

Question

3.12 Interpretation of Energy Band Diagrams Six different silicon samples maintained at 300 K are characterized by the energy band diagrams in Fig P3.12. Answer the questions that follow after choosing a specific diagram for analysis. Possibly repeat using other energy band diagrams. (Excessive repetitions have been known to lead to the onset of insanity) (a) Do equilibrium conditions prevail? How do you know? (b) Sketch the electrostatic potential (V) inside the semiconductor as a function of x (c) Sketch the electric field (E) inside the semiconductor as a function of x (d The carrier pictured on the diagram moves back and forth between x m o and x L without changing its total energy. Sketch the KE. and PE, of the carrier as a function of position inside the semiconductor. Let E be the energy reference level. (e) Roughly sketch nand p versus x On the same set of coordinates, make a rough sketch or the electron drift-current den. sity (UNrasn) and the electron diffusion-current density (J inside the Si sample as a function of position. Be sure to graph the proper polantyorthe current densities at all points and clearly identify your two current componenti. Also briefly explain how you arrived at your sketch.

Explanation / Answer

Continue the study of semiconductor devices by looking at the material used to make most devices

• The energy band diagram is a representation of carrier energy in a semiconducting material and will be related to an orbital bonding representation

• Devices require materials with tailored characteristics, obtained through doping, the controlled introduction of impurities

• Will discuss electrons and holes, as well as intrinsic, n-type and p-type materials.

Movement within a band is not difficult due to continuum of energy levels.

• Movement between bands requires acquisition of difference in energy between bands (in pure crystal, can’t exist in between)

• Main features of interest for first order device analysis are – top of valence band (Ev) – bottom of conduction band (Ec) – difference in energy between Ec and Ev, energy gap Eg.

At room temperature, very few electrons can gain energy Eg to move to the conduction band ( 10^10 cm-3 at 300K = 23°C)

In pure silicon at 300K, most valence band orbitals ( 10^22 cm-3 ) are full, most conduction band orbitals are empty

Conduction of current occurs through electron movement

• Two mechanisms of electron movement are possible: – movement within the nearly empty conduction band orbital structure – movement within the nearly full valence band orbital structure

• Conduction in the valence band structure is more conveniently modeled as the “movement” of an empty orbital

• Model this empty valence band orbital as a positively charged pseudo-particle called a hole

• Density of electrons in conduction band is n (cm-3)

• Density of holes in valence band is p (cm-3)

Intentional addition of impurities during manufacture or in specialized fabrication steps is termed doping

• Doped material is called extrinsic

• Ability to change the electrical characteristics of the material through selective introduction of impurities is the basic reason why semiconductor devices are possible

• Later lectures will outline the processes used to introduce impurities in a controlled and repeatable way.

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