1. 1 EE 2 Fall 2007 Class 9 slides

2. 2 Outline 1.Review of last class 2.Extrinsic semiconductors 3.Donor and acceptor impurities 4.Majority and minority carries in extrinsic semiconductors 5.Thermal equilibrium carrier densities 6.Law of mass action 7.Compensated semiconductor

3. 3 Extrinsic semiconductors Extrinsic semiconductors are those in which controlled (and trace) amount of specific impurities are incorporated in the semiconductor lattice to increase the electron density or the hole density. Depending on the type of impurity the electron or the hole density will be increased by the number of impurities added. Whereas in an intrinsic semiconductor the electrons and holes arise due to thermal excitation of electrons from the valence band to the conduction band, in an extrinsic semiconductor electrons (or holes) will be excited to the conduction band (or to the valence band) from the impurity atoms with energy levels in the band gap close to E c for increasing the electron density (or E v for increasing the hole density). The material is called extrinsic since its properties depend on the externally added impurities.

4. 4 Extrinsic semiconductors The impurities are said to be substitutionally added since the impurity atoms substitute the original atoms in the material. For example in silicon an impurity atom will sit in the site previously occupied by a silicon atom. If you recall the discussion in an earlier class the semiconductors crystallize in diamond structure because in such a structure each atom say silicon is surrounded by four nearest neighboring silicon atoms The s 2 p 2 electron configuration in silicon gives rise to the covalent bond whereby each atom shares an electron with the four neighbors forming the diamond structure.

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6. 6 Extrinsic semiconductors

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8. 8 Elements of group V of the periodic table have five valence electrons. When one of these impurity atoms is substituted for silicon in the crystal lattice, four of the five electrons complete the four covalent bonds and the fifth electron is not participating in the covalent bond and is weakly bound to the site of the impurity atom. It takes very small amount of energy to break the fifth electron from this site and make the electron free to move in the crystal i.e., we have now an electron in the conduction band. The impurity atom contributes (or donates) an electron to the conduction band and hence the impurity atom is called a donor atom. We have an electron in the conduction band for each ionized donor atom. Each ionized donor atom has a localized positive charge. In a piece of extrinsic semiconductor we have an electron in the conduction band for each ionized donor atom.

9. 9 Extrinsic semiconductors

10. 10 Extrinsic semiconductors In an extrinsic semiconductor with donor impurities, electrons arise in the conduction band due to two processes one due to thermal excitation from the valence band and the other due to ionization of donor atoms. It takes a very small amount of energy to ionize the donor atom and thus even at moderate temperature such as room temperature most of the donor atoms are ionized.

11. 11 Extrinsic semiconductors Typical donor type of impurities used in silicon and germanium are phosphorous (P), arsenic (As), antimony (Sb) and bismuth (Bi) all from column V of the periodic table. The ionization energy in silicon and germanium for these impurities are given in the bottom of page 53 in the course reader material. The donor is modeled as a hydrogen atom with a central charge of +q coulomb and the fifth electron as the single electron in the hydrogen atom. The ionization energy is the same as the ionization energy of the hydrogen atom as corrected for the permittivity of the silicon material by dividing the value of ionization energy in hydrogen atom by the square of the dielectric constant of the semiconductor material. It is customary to approximate the ionization energy as 0.05 eV for all the donor atoms in silicon material.

12. 12 Extrinsic semiconductors Elements of the third column of the periodic table have only three valence electrons and when they are used as substitutional impurity in the site of semiconductor atom say silicon, the three valence electrons are able to complete the covalent bond with only three of its neighbors and the bond with the remaining (fourth) neighbor remains incomplete. An electron from a covalent bond in a neighboring silicon site breaks away generating a hole and jumps into the site where the bond with the impurity atom is incomplete and the four covalent bonds are completed for the impurity atom. The site of the impurity atom is negatively charged. Each ionized impurity atom accepts so to say an electron and these impurities are called acceptors and there is a hole in the valence band for each ionized acceptor atom. The holes in a semiconductor with acceptor impurities arise from thermal excitation from the valence band as well as from ionized acceptor atoms/

13. 13 Extrinsic semiconductors

14. 14 Extrinsic semiconductors The acceptor impurity atom can be modeled also as a hydrogen atom with a central charge of -q coulomb with a hole orbiting around it and the ionization energy can be modeled as was done for the donor atom. The typical trivalent atoms that are uses as acceptors in silicon and germanium are boron (B), gallium (Ga), Aluminum (Al), and Indium (In) and the ionization energy is given in page 54 of the course reader. It is customary to think the ionization energy of all acceptor atoms in silicon as.05 eV.

15. 15 Extrinsic semiconductors

16. 16 Extrinsic semiconductors We will discuss the semiconductor physics using silicon as the material although our discussion is valid for any semiconductor A semiconductor with donor type of impurity is called n-type semiconductor since there are more electrons than holes. Similarly, a semiconductor with acceptor type of impurity is called p- type semiconductor since there are more holes than electrons. We denote the carrier density in the two types of semiconductors with a subscript n or p, such as n n or n p for electron density and p p or p n for hole density. We use a second subscript 0 to denote thermal equilibrium densities such as n n 0 or n p 0 for electron density and p p 0 or p n0 for hole density.

17. 17 Extrinsic semiconductors Neutral n-type semiconductor: Total positive charge in the semiconductor per unit volume is equal to q ( p n 0 + N D + ) where N is the density of donor atoms and the superscript + denotes ionized donor atoms. Total negative charge per unit volume is equal to –q n n0 In thermal equilibrium, there is no net charge and hence these two must be equal in magnitude. p n 0 + N D + = n n0 n n0 > p n 0 Hence electrons are called majority carriers and holes are called minority carriers

18. 18 Extrinsic semiconductors Neutral p-type semiconductor: Total negative charge in the semiconductor per unit volume is equal to -q ( n p0 + N A - ) where N A is the density of acceptor atoms and the superscript - denotes ionized acceptor atoms. Total positive charge per unit volume is equal to q p p 0 In thermal equilibrium, there is no net charge and hence these two must be equal in magnitude. p p 0 = n n 0 + N A - p p 0 > n n 0 Hence holes are called majority carriers and electrons are called minority carriers

19. 19 Extrinsic semiconductors Thermal equilibrium career densities: n n0, p n0 in n-type material and p p0 and n p0 in p-type material. We can determine the electron and hole densities in extrinsic semicondcutors the same way we did for intrinsic materials,

20. 20 Extrinsic semiconductors Non-degenerate semiconductor is one in which E F is less than E c by more than 3 kT and above E v by more than 3 kT. In this case the expression for the density of electrons and holes will be the same as what we got in the case of intrinsic material. Therefore the law of mass action will be valid i.e., n n0 x p no = n i 2 and p p0 x n po = n i 2 The non-degenerate assumption is valid as long as the majority carrier density is less than 10 19 cm -3. If the majority carrier density is above this value, then the material is called degenerate and the law of mass action is not valid

21. 21 Extrinsic semiconductors

22. 22 Extrinsic semiconductors Similarly it can be shown that in the case of a non-degenerate p-type semiconductor, p p0 is approximately equal to N A - The thermal equilibrium minority carrier density can be written as p no = n i 2 / N D + in n-type material and n po = n i 2 / N A - in p-type material

23. 23 Extrinsic semiconductors

24. 24 Extrinsic semiconductors Compensated semiconductors are those in which both donor and acceptor impurities are present and the material will be n-type or p- type depending on which impurities are larger in number. It will be determined by the net impurity type.. For example in a semiconductor with N D larger than N A, the net impurity will be donor type with a net concentration of N D – N A and will be n-type. In order to fabricate semiconductor devices we need to make layers of n and p type material and we use compensated material to make alternately n and p type layers.