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Chapter 29: Problem 21

(II) The energy gap \(E\)g in germanium is 0.72 eV. When used as a photon detector, roughly how many electrons can be made to jump from the valence to the conduction band by the passage of an 830-keV photon that loses all its energy in this fashion?

Short Answer

Expert verified
The photon can excite approximately 1,152,778 electrons.

Step by step solution

01

Convert Energy Units

First, convert the energy of the photon from kilo-electronvolts (keV) to electronvolts (eV). Since 1 keV equals 1000 eV, \[830 \text{ keV} = 830 \times 1000 \text{ eV} = 830,000 \text{ eV}.\]
02

Determine Electrons Generated

To find out how many electrons can be excited from the valence band to the conduction band, divide the photon energy by the energy gap:\[\text{Number of electrons} = \frac{830,000 \text{ eV}}{0.72 \text{ eV}}.\]
03

Calculate Result

Perform the division to find the number of electrons:\[\text{Number of electrons} = \frac{830,000}{0.72} \approx 1,152,778.\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Energy Conversion
Energy conversion involves transforming energy from one form to another. In semiconductor physics, this process is crucial in the functioning of devices like photon detectors or solar cells.
When a semiconductor absorbs a photon, it converts the photon's energy into electrical energy by moving electrons. In the given exercise, an 830-keV photon has its energy transformed into exciting electrons within germanium. This transformation is vital in detecting photons, as it determines the number of free electrons available to conduct electricity.
  • Photon energy is commonly measured in electronvolts (eV), a convenient unit for the tiny energy levels involved in atomic scale processes.
  • The energy gap plays a significant role in determining how effectively a material can convert photon energy into free electrons.
This efficiency of energy conversion is critical in the design of efficient photodetectors and energy harvesting devices, where optimizing the number of excited electrons can improve performance.
Valence Band
In semiconductor physics, the valence band represents the highest range of electron energies in which electrons are normally present at absolute zero temperature.
The valence band is filled with electrons that are tightly bound to atoms and are unable to move freely. This band forms part of the electronic structure of a material.
  • Electrons in the valence band are bound to the material's atoms and cannot conduct electricity.
  • The energy levels of the valence band are lower than those of the conduction band.
For a semiconductor to conduct electricity, electrons must be excited out of the valence band. This occurs when energy, such as from an incoming photon, is absorbed and exceeds the material's band gap.
Conduction Band
The conduction band, contrasting with the valence band, is the range of electron energy levels that is typically empty unless energy is added to the system.
Electrons in the conduction band are free to move within the material, enabling them to conduct electricity. This movement forms the basis for semiconductors' electrical conductivity.
  • When electrons jump from the valence band to the conduction band, they become mobile charge carriers.
  • The ability of electrons to move freely in the conduction band allows semiconductors to conduct electrical current efficiently.
Understanding the dynamics of the conduction band and how electrons transition into it is essential for designing semiconductor devices like transistors, diodes, and photon detectors. In applications such as the photon detector in the exercise, maximizing the number of electrons reaching the conduction band is key to its functionality.

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Most popular questions from this chapter

Use the uncertainty principle to estimate the binding energy of the molecule by calculating the difference in kinetic energy of the electrons between (i) when they are in separate atoms and (ii) when they are in the molecule. Take \(\Delta x\) for the electrons in the separated atoms to be the radius of the first Bohr orbit, 0.053 nm, and for the molecule take \(\Delta x\) to be the separation of the nuclei, 0.074 nm. [\(Hint\):Let \(\Delta p \approx \Delta p_x\).]

When EM radiation is incident on diamond, it is found that light with wavelengths shorter than 226 nm will cause the diamond to conduct. What is the energy gap between the valence band and the conduction band for diamond?

(II) An ac voltage of 120-V rms is to be rectified. Estimate very roughly the average current in the output resistor \(R\) (= 31 k\(\Omega\)) for (\(a\)) a half- wave rectifier (Fig. 29-31), and (\(b\)) a full-wave rectifier (Fig. 29-32) without capacitor.

(III) Suppose that a silicon semiconductor is doped with phosphorus so that one silicon atom in 1.5 \(\times\) 10\(^6\) is replaced by a phosphorus atom. Assuming that the "extra" electron in every phosphorus atom is donated to the conduction band, by what factor is the density of conduction electrons increased? The density of silicon is 2330 kg/m\(^3\), and the density of conduction electrons in pure silicon is about 10\(^{16}\) m\(^{-3}\) at room temperature.

Must we consider quantum effects for everyday rotating objects? Estimate the differences between rotational energy levels for a spinning baton compared to the energy of the baton. Assume the baton consists of a uniform 32-cm-long bar with a mass of 230 g and two small end masses, each of mass 380 g, and it rotates at 1.8 rev/s about the bar's center.
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