Question

1. Discuss how a missing atom at a lattice side contributes to the conductivity of a semiconductor     

2. Estimate the energy of a photon of X rays. (Answer: 12 keV)

3. On the one hand, we say that electrons in atoms have discrete energies; on the other hand, we say that there is inherent uncertainty in our ability to measure energies. Is there a conflict here?

4. You have just calculated the number density of p-carriers in undoped germanium, a semiconductor, at room temperature. Is it necessary to make a second calculation to find the number density of free electrons?

5. Estimate the energy of a photon of visible light. (Answer: 2.4 eV)

Answer 1

1. When a particle is missing at one or more lattice sites we get a vacancy. If these vacancies are occupied by some other material´s atom, then the conductivities will change abruptly. Semiconductors are very sensitive to impurities. The conductivity of silicon or germanium can be increased by a factor of up to 10⁶ by adding as little as 0.01% of an impurity. The conductivity of a semiconductor is given by:

are the mobilities of electron and holes, q is the charge of the carriers, p and n are the density of hole and electrons in semiconductor. A doped semiconductor, majority carriers greatly outnumber minority carriers, so that the equation above can be reduced to a single term involving the majority carrier.

2. Typical X-ray wavelength is about 1 Angstrom. Energy of a X-ray photon is expressed

3. Nevertheless, the general meaning of the energy-time uncertainty principle is that a quantum state which exists for only a short time cannot have a definite or discrete energy. The reason is that the frequency of a state is inversely proportional to time and the frequency connects with the energy of the state, so to measure the energy with good precision, the state must be observed for many cycles. Another important fact is that the multiplication of uncertainties of energy and time is about 10^-34. If you say that electron have discrete energy means it is rotating in a particular defined orbit. But, according to quantum mechanics, the electron in an atom form a cloud like structure around the nucleus. According to uncertainty principle, you can see the energy of an electron is slightly different from the previous measurement. That is why you will see a spectral width of an emission from an atom though it is very small.

4. Semiconductor materials are normally in crystalline form with each valence electron shared by two atoms. The semiconductor is said to be intrinsic (like undoped germanium) if it is not contaminated with impurity atoms. The thermal energy stored in a semiconductor crystal lattice causes the atoms to be in constant mechanical vibration. At room temperature, the vibrations shake loose several valence electrons which then become free electrons. When an electron is shaken loose from an atom, an electron vacancy is left which is called a hole (positive carrier). The parent atom then becomes an ion. The constant mechanical vibration of the lattice can cause the ion to capture a valence electron from a neighboring atom to replace the missing one. When such a transfer takes place, the position of the hole moves from one atom to another. This is equivalent to a positive charge +q moving about in the semiconductor. Therefore, in an intrinsic semiconductor, the hole concentration must equal the electron concentration. There is no need to make a second calculation to find the number density of free electrons if you have just calculated the number density of p-carriers (hole) in undoped germanium, a semiconductor, at room temperature.

5. Visible light has a wavelength range from ~400 nm to ~700 nm. If you consider wavelength in the middle of this range , then the wavelength is about 550 nm. Energy of a visible photon is expressed