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Chapter 10: Q53E (page 470)

In diamond, carbon鈥檚 four full (bonding) s and p spatial states become a band and the four empty(anti bonding) ones becomes a higher energy band. Considering the trend in the band gaps of diamond, silicon, and germanium, explain why it might not be surprising that 鈥渃ovalent鈥� tin behaves as a conducting metallic solid.

Short Answer

Expert verified

The number of electrons are large in the conduction band and it makes the time behaves like metallic solid.

Step by step solution

01

Determine the formulas

Consider the formula for the energy of the electron as:

E=hc位

Here,位 is the wavelength, h is the plank鈥檚 constant, and c is the speed of light.

02

Determine the answer for the question:

Consider the energy gap of the diamond is 5.4 eV and the energy gap of the silicon is 1.1 eV and 0.7 eV in the germanium. In the same way the energy gap of the covalent tin is small and same is at the room temperature. Thus, the number of electrons are large in the conduction band and it makes the time behaves like metallic solid.

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Most popular questions from this chapter

Question: - For a small temperature change. a material's resistivity (reciprocal of conductivity) will change linearly according to

p(dT)=蚁0+d蚁=蚁0(1+伪dT)

The fractional change in resistivity, 伪also known as the temperature coefficient, is thus

伪=1蚁0d蚁dT

Estimate for伪 silicon at room temperature. Assume a band gap of 1.1 e v .

Formulate an argument explaining why the even wave functions in Fig 10.1 should be lower in energy than their odd partners.

Starting with equation (10-4), show that if 螖苍 is-1 as a photon is emitted by a diatomic molecule in a transition among rotation-vibration states, but 螖鈩�can be卤1 . Then the allowed photon energies obey equation (10-6).

Question: Referring to equations(10-2), lobe I of the hybrid states combines the spherically symmetric s state with the state that is oriented along thez-axis. and thus sticks out in the direction (see Exercises 28 and 33), If Figure is a true picture, then in a coordinate system rotated counterclockwise about they-axis by the tetrahedral angle, lobe II should become lobe. In the new frame. -values are unaffected. but what had been values in the 2x -plane become values in the -plane. according tox=x'cos伪+z'sin伪 and z'cos伪-x'sin伪, where伪=109.5o iscos-1(-13) , or .

(a) Show that lobe II becomes lobe I. Note that since neither the 2s state nor the radial part of the p states is affected by a rotation. only the angular parts given in equations (10-1) need be considered.

(b) Show that if lobe II is instead rotated about thez-axis by simply shifting 蠁by卤1200 . it becomes lobes III and IV.

Carbon(diamond) and silicon have the same covalent crystal structure, yet diamond is transparent while silicon is opaque to visible light. Argue that this should be the case based only on the difference in band gaps roughly 5 eV for diamond in eV is silicon.
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