n-type Semiconductors - 15

We seem to have developed a rather complete description of conduction in semiconductors without discovering any properties that might be useful in constructing a diode, or a transistor.  If semiconductors could only be produced in the pure state discussed so far, computers might still be using vacuum tubes and taking up an entire room.  All of the incredible electronics inside the computer on which this page is being typed are due to the particular properties of "doped" semiconductors.  A doped semiconductor has "impurities", atoms of a different type, scattered throughout the primary semiconductor.  For example, in phosphorus-doped silicon, phosphorus atoms have been added in place of silicon atoms occasionally throughout the material.  "Occasionally" here means very infrequently.  Substantial effects on the conductive behavior of silicon can be achieved with as little as one phosphorus atom for every million silicon atoms!

To understand exactly what the effects of doping are, we turn again to band diagrams.  Remember that atoms tend to form bonds that fill the energy states in the outermost energy level.  The Discussion Questions page asked you to look up silicon and phosphorus in the periodic table.  Phosphorus, with atomic number 15, lies just to the right of silicon in the periodic table.  Ten of its fifteen electrons will be in filled shells corresponding to n=1 and n=2.  The other five are in its unfilled valence shell.  Substituting an atom of phosphorus, with its five valence electrons, in the place of a silicon atom, with four valence electrons, results in one electron being "left over" once the eight valence energy states of silicon are filled (by four electrons from silicon and four electrons from phosphorus).  The fifth phosphorus electron is only loosely bound since it doesn't fit in the filled valence band, but it is not quite  in the conduction band.  (Its ground state is in the valence shell of the phosphorus atom, so it does not quite have the energy of an excited state of silicon.)  The energy of this extra electron falls somewhere in the band gap - at an energy forbidden in pure silicon.  This energy is much, much closer to the energy of the empty conduction band than to the energy of the filled valence band and exists only at the location of the phosphorus atom, yielding an energy diagram (at absolute zero) looking something like the second frame of the animation in Figure (a) below.  Be aware that the drawing understates the number of silicon atoms corresponding to each phosphorus atom (the "real" ratio is around 106:1) for purposes of illustration and simplicity.  Figure (b) below shows the motion of this extra electron using a lattice diagram.  Notice the similarities and differences in the two ways of representing the same effect.
 



(a)


The fifth valence electron from the phosphorus atom can be represented as an additional line in the lattice diagram.  It is only loosely bound and can move through the lattice.  When it does so, however, a charge separation arises between the now positively-charged phosphorus core and the negatively charged electron.
(b)

The "extra" electron contributed by phosphorus can easily jump into the conduction band, becoming a conduction electron and greatly increasing the conductivity of the silicon.  "But," the diligent student protests, "How can one extra conduction electron for every million silicon atoms make a difference?"  The diligent student is advised to reflect upon Another Word of Warning a few pages back.  Included in that warning was the information that pure silicon at room temperature has one conduction electron (plus, the diligent student may recall, one hole) for every ten trillion sillicon atoms.  The effects of even a minute amount of phophorus are great indeed!  The influence of doping is not limited to the magnitude of the conductivity - doping also determines the nature of the conductivity.  Both holes and electrons contribute equally to electrical conduction in pure silicon; conduction in phosphorus-doped silicon is due almost entirely to the motion of electrons.  (The "extra" electron does leave behind a hole when it jumps into the conduction band, but the hole is not in a band with electrons around, so it does not move.)  Electrons provide most of the current and are called the majority carrier.  When the majority carrier is negative, the material is known as an n-type semiconductor.  Since the phosphorus atom has "donated" an electron to the conduction band, phosphorus is called the donor material.   Any element with five valence electrons could theoretically serve as a donor for silicon and produce n-type behavior, but the number of valence electrons is not the only factor to consider.  The size of the donor core, and how it fits into the lattice, has practical implications, as does the chemical properties of the donor.  Finally, the distance between the donor energy level and the conduction band of the base material will determine how significant an effect the donor has on conductivity.  Phosphorus and arsenic are used most commonly to dope silicon..

In practical applications, it is the ability to control conductivity through doping that defines a semiconductor.  Some of the materials which are among the best insulators when in pure form, such as diamond, are being used in semiconductor applications through doping.
 

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Copyright © 2003 Doris Jeanne Wagner and Rensselaer Polytechnic Institute.  All Rights Reserved.