Department of Electrical and Electronic Engineering Electronic Devices and Circuits ELEC2306/ELEC3346 Tutorial 1: Introduction to Quantum Theory 1.1. The Photoelectric Effect: Photons and photon flux ( [1] Q3.1) a) Consider a 1 kW AM radio transmitter at 200 kHz. Calculate the number of photons emitted from the antenna per second. b) The average intensity of sunlight on Earth’s surface is about 1kW m-2. The maximum intensity is at a wavelength around 800 nm. Assuming that all the photons have an 800 nm wavelength, calculate the number of photons arriving on Earth’s surface per unit time per unit area. What is the magnitude of the electric field in the sunlight? c) Suppose that a solar cell device can convert each sunlight photon into an electron, which can then give rise to an external current. What is the maximum current that can be supplied per unit area (m2) of this solar cell device? 1.2. The Photoelectric Effect: Photoelectric effect ([1] Q3.3) A photoelectric experiment indicates that violet light of wavelength 420 nm is the longest wavelength radiation that can cause the photoemission of electrons from a particular multialkali photocathode surface. a) What is the work function of the photocathode surface, in eV? b) If a UV radiation of wavelength 300 nm is incident upon the photocathode surface, what will be the maximum kinetic energy of the photoemitted electrons, in eV? c) Given that the UV light of wavelength 300 nm has an intensity of 20 mW/cm2, if the emitted electrons are collected by applying a positive bias to the opposite electrode, what will be the photoelectric current density in mA cm-2? 1.3. The Photoelectric Effect: Photoelectric effect and quantum efficiency ([1] Q3.4) Cesium metal is to be used as the photocathode material in a photoemissive electron tube because electrons are relatively easily removed from a cesium surface. The work function of a clean cesium surface is 1.9 eV. a) What is the longest wavelength of radiation which can result in photoemission? b) If blue radiation of wavelength 450 nm is incident onto the Cs photocathode, what will be the kinetic energy of the photoemitted electrons in eV? What should Prepared by Barry Mok. Aug 2013 (Revision: 06) [1] Reference: S. O. Kasap. Principles of Electronic Materials and Devices, Third Edition, Boston: McGraw-Hill, 2002.
be the voltage required on the opposite electrode to extinguish the external photocurrent? c) Quantum efficiency (QE) of a photocathode is defined by,
Quantum e±ciency =
Number of photoemitted electrons Number of incident photons
QE is 100 percent if each incident photon ejects one electron. Suppose that blue light of wavelength 450 nm with an intensity of 30 mW cm-2 is incident on a Cs photocathode that is a circular disk of diameter 6 mm. If the emitted electrons are collected by applying a positive bias voltage to the anode, and the photocathode has a QE of 25%, what will be the photoelectric current? 1.4. De Broglie Relations: Wavelength of an electron beam ([1] Example 3.4) Electrons are accelerated through a 100 V potential difference to strike a polycrystalline aluminum sample. The diffraction pattern obtained indicates that the highest intensity and smallest angle diffraction, corresponding to diffraction from the (111) planes, has a diffraction angle (2µ) of 30.4±. From X-ray studies, the separation of the (111) planes is 0.234 nm. a) Use Bragg diffraction condition to calculate the wavelength of the electron. b) Use wave-particle duality nature of electrons ( ¸ = h=p and p = h=¸ ) to calculate the wavelength of the electron. 1.5. De Broglie Relations: Diffraction by X-rays and an electron beam ([1] Q3.5) Diffraction studies on a polycrystalline Al sample using X-rays gives the smallest diffraction angle (2µ) of 29.5± corresponding to diffraction from the (111) planes. The lattice parameter a of Al (FCC) is 0.405 nm. If we wish to obtain the same diffraction pattern (same angle) using an electron beam, what should be the voltage needed to accelerate the electron beam? Note that the interplanar separation d for planes (h; k; l) and the lattice parameter a for cubic crystals are related by d = a=(h2 + k2 + l2)1=2. 1.6. Infinite Potential Well: Electron confined within atomic dimensions ([1] Example 3.5) Consider an electron in an infinite potential well of size 0.1 nm (typical size of an atom). a) What is the ground energy of the electron? b) What is the frequency of the electron associated with this energy? c) What is the energy required to put the electron at the third energy level from the ground level? Prepared by Barry Mok. Aug 2013 (Revision: 06) [1] Reference: S. O. Kasap. Principles of Electronic Materials and Devices, Third Edition, Boston: McGraw-Hill, 2002.
d) How can this energy be provided? 1.7. Potential Box: Three Quantum Numbers (Number of states with the same energy) ([1] Example 3.12) How many states (eigenfunctions) are there at energy level E443 for a square potential energy box? 1.8. Quantized electron Energy (Electron excitation and photon absorption) What is the wavelength of the light required to excited an electron in the hydrogen atom (Z=1) from the ground state (n=1) to the third energy level (n=3)?
Prepared by Barry Mok. Aug 2013 (Revision: 06) [1] Reference: S. O. Kasap. Principles of Electronic Materials and Devices, Third Edition, Boston: McGraw-Hill, 2002.
Appendix Constants and Useful Information
Prepared by Barry Mok. Aug 2013 (Revision: 06) [1] Reference: S. O. Kasap. Principles of Electronic Materials and Devices, Third Edition, Boston: McGraw-Hill, 2002.
