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Chapter 10: Q63E (page 470)

As a crude approximation, an impurity pentavalent atom in a (tetravalent) silicon lattice can be treated as a one-electron atom, in which the extra electron orbits a net positive charge of 1. Because this "atom" is not in free space, however, the permitivity of free space, 蔚0. must be replaced by 魏蔚0, where魏 is the dielectric constant of the surrounding material. The hydrogen atom ground-state energies would thus become

E=鈭�me42(4蟺魏蔚0)2鈩�21n2=鈭�13.6eV魏2n2

Given 魏=12for silicon, how much energy is needed to free a donor electron in its ground state? (Actually. the effective mass of the donor electron is less than , so this prediction is somewhat high.)

Short Answer

Expert verified

The amount of energy is needed to free a donor electron in its ground state is鈭�0.094eV.

Step by step solution

01

Given data

k=12- dielectric constant

The energy of hydrogen atom innstate is,E=鈭�13.6eVk2n2.

02

Formula of energy of hydrogen

The energy of hydrogen atom in n state is, E=鈭�13.6eVk2n2.

03

Step 3:Determine the amount of energy required to free a donor electron 

The dielectric constant for silicon atom is,k=12.

Substitute 12 forkand 1 fornin equationE=鈭�13.6eVk2n2.

E=鈭�13.6eV(12)2(1)2=0.094eV

The amount of energy is needed to free a donor electron in its ground state is 鈭�0.094eV.

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Most popular questions from this chapter

A string wrapped around a hub of radius Rpulls with force FT on an object that rolls without slipping along horizontal rails on "wheels" of radiusr<R. Assume a massmand rotational inertia I.

(a) Prove that the ratio ofFTto the object's acceleration is negative. (Note: This object can't roll without slipping unless there is friction.) You can do this by actually calculating the acceleration from the translational and rotational second la was of motion, but it is possible to answer this part without such a "real" calculation.

(b) Verify thatFTtimes the speed at which the string moves in the direction of FT (i.e., the power delivered byFT) equals the rate at which the translational and rotational kinetic energies increase. That is.FTdoes all the work in this system, while the "internal" force does none. (c) Briefly discuss how parts (a) and (b) correspond to behaviors when an external electric field is applied to a semiconductor.

The resistivity of the silver is 1.6脳10-8鈥�惟鈰�mat room temperature of (300 K), while that of silicon is about10鈥�惟鈰�m

(a) Show that this disparity follows, at least to a rough order of magnitude from the approximate 1 eV band gap in silicon.

(b) What would you expect for the room temperature resistivity of diamond, which has a band gap of about 5 eV.

The accompanying diagrams represent the three lowest energy wave functions for three "atoms." As in all truly molecular states we consider, these states are shared among the atoms. At such large atomic separation, however, the energies are practically equal, so anelectron would be just as happy occupying any combination.

(a) Identify algebraic combinations of the states (for instance, 5+11/2+11/2 ) that would place the electron in each of the three atoms.

(b) Were the atoms closer together, the energies of states 1.11, and III would spread out and an electron would occupy the lowest energy one. Rank them in order of increasing energy as the atoms draw closer together. Explain your reasoning.

Section 10.6 notes that as causes of resistance, ionic vibrations give way to lattice imperfections at around 10 K. A typical spring constant between atoms in a solid is or order of magnitude103鈥�Nm and typical spacing is nominally10-10鈥�m . Estimate how much the vibrating atoms locations might deviate, as a function of their normal separations, at 10 K.

By the 鈥渧ector鈥� technique of example 10.1 , show that the angles between all lobes of the hybridsp3states are 109.5掳..
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