4.3 Extrinsic Semiconductor

The intrinsic semiconductor may be an interesting material，but the real power of semiconductors is realized by adding small，controlled amounts of specific dopant，or impurity，atoms. The doped semiconductor，called an extrinsic material，is the primary reason we can fabricate the various semiconductor devices.

Fig.4.3 shows three basic bond representations of a semiconductor. Fig.4.3（a）shows intrinsic silicon，which is very pure and contains a negligibly small amount of impurities. Each silicon atom shares its four valence electrons with the four neighboring atoms，forming four covalent bonds. Fig.4.3（b）shows an n-type silicon，where a substitutional phosphorous atom with five valence electrons has replaced a silicon atom，and a negative-charged electron is donated to the lattice in the conduction band. The phosphorous atom is called a donor . Fig.4.3（c）similarly shows that when a boron atom with three valence electrons substitutes for a silicon atom，a positive-charged hole is created in the valence band，and an additional electron will be accepted to form four covalent bonds around the boron. This is p-type，and the boron is an acceptor .

Fig.4.3 Three basic bond pictures of a semiconductor.（a）Intrinsic Si with no impurity.（b）n-type Si with donor（phosphorus）.（c）p-type Si with acceptor（boron）.

We can calculate the approximate distance of the donor electron from the donor impurity ion，and also the approximate energy required to elevate the donor electron into the conduction band. This energy is referred to as the ionization energy .

Adding donor or acceptor impurity atoms to a semiconductor will change the distribution of electrons and holes in the material. Since the Fermi energy is related to the distribution function，the Fermi energy will change as dopant atoms are added. If the Fermi energy changes from near the midgap value，the density of electrons in the conduction band and the density of holes in the valence hand will change. These effects are shown in Fig.4.4 and 4.5. Fig.4.4 shows the case for EF＞EFi and Fig.4.5 shows the case for EF＜EFi. When EF＞EFi，the electron concentration is larger than the hole concentration，and when EF＜EFi，the hole concentration is larger than the electron concentration. When the density of electrons is greater then the density of holes，the semiconductor is n type；donor impurity atoms have been added. When the density of holes is greater than the density of electrons，the semiconductor is p type；acceptor impurity atoms have been added. The Fermi energy level in a semiconductor changes as the electron and hole concentrations change and，again，the Fermi energy changes as donor or acceptor impurities are added.

In an n-type semiconductor，n0＞p0，electrons are referred to as the majority carrier and holes as the minority carrier. Similarly，in a p-type semiconductor where p0＞n0，holes are the majority carrier and electrons are the minority carrier.

As we will see，the Fermi level changes when donors and acceptors are added，as the Fermi level changes from the intrinsic Fermi level，n0 and p0 change from the nivalue. If EF＞EFi，then we will have n0＞ni and p0＜niOne characteristic of an n-type semiconductor is that EF＞EFi so that n0＞p0. Similarly，in a p-type semiconductor，EFni and n0n0.

Fig.4.4 Density of states functions. Fermi-Dirac probability function，and areas representing electron and hole concentrations for the case when EF is above the intrinsic Fermi energy.

Fig.4.5 Density of states functions，Fermi-Dirac probability function，and areas representing electron and hole concentrations for the case when EF is below the intrinsic Fermi energy.

We can see the functional dependence of n0 and p0with EF in Figures 4.4and 4.5. As EF moves above or below EFi，the overlapping probability function with the density of states functions in the conduction band and valence band changes. As EF moves above EFi，the probability function in the conduction band increases，while the probability，1－fF（E），of an empty state（hole）in the valence band decreases. As EF moves below EFi，the opposite occurs.

For the semiconductor in thermal equilibrium，

n0p0＝n2i （4.9）

Equation（4.9）states that the product of n0and p0 is always a constant for a given semiconductor material at a given temperature. Although this equation seems very simple，it is one of the fundamental principles of semiconductors in thermal equilibrium.