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Extra electron Figure 2.1; Donor atom in Si matrix A group 5 atom replaces a group 4 atom and uses up 4 of its valence electrons for covalent bonding, The spare electron will now no longet be tightly bound to its nucleus as in a free group 5 atom since the outer shell is now fully occupied. Thus this electron is not tightly bound but the parent atom still has enough net positive change to distinguish it from neighbouring silicon atoms and so the electron still has some affinity for its parent. So that band structure is as shown in figure (2.3) below Figure 2.2: Extrinsies band structure with donors This phenomenon is usually described as an electron donated by the impurity atom. Thus Ep is called the donot level. The group 5 atom is called a donot impurity (or donor) Impurity Ge Si Antimony(Sb) 0.0096 | 0.039 Phosphorous(P) 0.0120 | 0.045 Arsenic(As) 0.0127 | 0.049 Table 2.1; Selected donor ionization energies Acceptor impurities If instead of a group 5 impurity we have some group III atoms. E.g. In, Al there would be an electron missing from one of the covalent bonds and thus we have a hole, A wandering electron will thus be welcome to help out, or the impurity nucleus 8 ight get an electron from the next site. In other words there is a low energy at the host atom but low enough to come into consideration when an electron has acquired some extra energy and feels an urge to jump somewhere. Thus the energy levels due to group III impurities are just above the valence band. These atoms ate called acceptors impurities ( or just acceptors) and the corresponding energy levels are called acceptor levels. n-type and p-type semiconductors In practice a material will contain both donor and acceptor impurities. Usually one type will exceed the other and we talk of semiconductots as n-type (negative carrier) or p-type (positive cartier) depending on the dominant charge carriers. For example if we had ~ 10” indium atoms per cubic metre of silicon then it would be p-type. If on the other hand we had ~ 10?! phosphorus atoms per cubic metre of silicon then we would have n-type silicon, The addition of impurities to a semiconductor material is called doping Usually group III and V elements form what are known as shallow states because these are near the band edges. Deep states are formed by imputity atoms that are difficult to ionize and so would form states close to the middle of the forbidden gap Impurity Ge Si Indium(In) 0.0112 | 0.160 Gallium(Ga) 0.0108 | 0.065 Boron(B) 0.0104 | 0.045 Aluminium(Al) 0.0102 | 0.057 Table 2.2: Selected acceptor ionization energies CARRIER DENSITIES IN EXTRINSIC SEMICONDUCTORS For an extrinsic semiconductor the equations for carrier concentration are the same as those for intrinsic materials so long as the assumptions that 1. Only electrons at the bottom of the conduction band and holes at the top of the valence band are responsible for electrical conduction 2. The bottom of the band is many times kT away from the Fermi level in energy : 11 concentration. Moreover assuming that conductivity is also dominated by the majotity carrier we can use the relation. b= lo. ee EE (2.5) to determine the carrier mobility where [1 is the mobility and o is the conductivity. NON - EQUILLIBRIUM PROCESSES The foregoing theory of semiconductors was given with the assumption that there is thermal equilibrium. Some of the ways of disturbing this equilibrium are (a) Shine electromagnetic energy (usually in the visible range) upon the semiconductor material. One thing that may happen is photoemission as occurs in metals. Secondly, and this is the process of interest here, is that the number of charge carriers (and hence electrical conductivity) may increase. This is called photoconduction. (b) Apply an electric fied (c) Bombardment with high energy particles such as electrons There are various non equilibrium processes as outlined below Figure 2.4: Processes that may cause photoconduction. 1. Band to band transitions producing an electron hole pair. In this process, an electron is excited to move from the valence band to the conduction band to create the electron hole pair. The process of creation of electron hole pairs by band to band transitions is called generation As electrons and holes drift along they encounter other electrons and holes. An electron in the conduction band can fall into empty states in the valence band, resulting in loss of an electron-hole pair. This process which is the reverse of generation is called recombination. 2. Ionization of donor atoms i. e. exciting an electron from a donor level to the conduction band 3. Ionization of acceptor atoms i. e. exciting an electron from the valence band to an acceptor impurity level. 4. Recombination through traps. Direct recombination is unlikely because they are both moving very rapidly and they would both have to be at the 14 rectifiers If a negative voltage is applied to the p-region and a positive one to the n-region then the potential difference between them is incteased and the p-n junction is said to be teverse biased. Now practically no electrons can climb the potential energy hill and the recombination current is the only current that can cause a current flow. On the other hand if the opposite of the above voltages is applied then a large current will flow and the p-n junction is forward biased. Effectively then the p-n junction will allow a significant current to flow in only one direction. If an alternating voltage is applied then only when the junction is forward biased will a current flow. The alternating current will thus have been rectified. infrared detection If electromagnetic energy of frequency @ falls on a semiconductor whose band gap is less than f@ in energy then this energy will cause an electron to jump from the valence band to the conduction band. This absorption increases the number of carriers and may be detected as an increase in electrical conductivity. This is called photoconduction and is used in infra-red detection. solar cells and photovoltaic detectors If light falls on an unbiased p-n junction photons ate absorbed and so form an electron hole pair. When these two diffuse to the junction, the built in electric field sweeps them down the energy barrier. The separation of the carriers creates a forward voltage across the batrier. The voltage is forward because the electric field of the excited carriers is opposite to the built in field of the junction, The appeatance of a forward voltage across an illuminated junction is called the photovoltaic effect. The illuminated p-n junction can therefore deliver powet to an external circuit. References 1, Introduction to solid state physics 
