Question: This question is related to a charge-coupled device (CCD). Students are expected to provide a definition of quantum efficiency of a pixel.
Mark Scheme: ratio of the no. of electrons produced to no. of photons (of a particular energy) incident on the pixel.
Comments:
The question can be improved by at least two ways. Firstly, the question could be rephrased as “define the quantum efficiency of a charge-coupled device’s pixel.” This is to distinguish from the quantum efficiency of a solar cell. For example, the quantum efficiency of a solar cell can be defined as the ratio of the number of charge carriers collected by the solar cell to the number of photons of a specific range of wavelength absorbed. Secondly, there could be an interesting context such as a selfie or how a photograph can be taken by using a smartphone. That is, the question can be related to the photo-sensors of the smartphone.
On the other hand, the definition specified in the marking scheme is slightly different from the textbook’s definition. In Physics for the IB diploma, the quantum efficiency of a pixel is defined as “the ratio of the number of emitted electrons to the number of incident photons (Tsokos, 2008, p. 466).” The mark scheme uses the phrase “electrons produced” instead of “emitted electrons.” It should be noted that electron-holes pairs are produced instead of only an electron. Next, the marking scheme uses the phrase “number of photons” instead of “incident photons.” However, the mark scheme could include physical requirements such as “normal lighting conditions.” Physics teachers should explain that intense photons emitted from a laser may damage the photo-sensors.
Feynman’s insights?:
In general, quantum efficiency is a measure of the photoelectric sensitivity of a device. Interestingly, Feynman opines that the photoelectric effect is not simply about how photons eject electrons from a classical view. In Feynman’s (1942) words, “one attempts to list those phenomena which seem to indicate that light is quantized, the first type of phenomenon which comes to mind are like the photoelectric effect or the Compton effect. One is however, struck by the fact that since these phenomena deal with the interaction of light and matter their explanation may lie in the quantum aspects of matter, rather than requiring photons of light. This supposition is aided by the fact that if one solves the problem of an atom being perturbed by a potential varying sinusoidally with the time, which would be the situation if matter were quantum mechanical and light classical, one finds indeed that it will in all probability eject an electron whose energy shows an increase of hν, where ν is the frequency of variation of the potential (pp. 3-4).” Importantly, the probability of ejection of the electron should be related to the work function of the matter from a quantum mechanical view.
In The Feynman Lectures on Physics, Feynman does not explicitly discuss the photoelectric effect. From a perspective of classical physics, Feynman explains that “it turns out that in a piece of metal, electrons are attracted to the ions, or to atoms, of the metal. They are attracted, if we may say it crudely, to the metal. In order to get an electron out of a piece of metal, it takes a certain amount of energy or work to pull it out. This work varies with the different kinds of metal (Feynman et al., 1963, section 42–2 Thermionic emission).” In addition, Feynman defines the work function as follows: “W is equal to qeϕ, where ϕ is the so-called work function, or the voltage needed to pull an electron off the surface (Feynman et al., 1963, section 42–2 Thermionic emission).” In other words, the work function is related to an electric field or potential difference that can remove the electron from the metal’s surface.
More importantly, Feynman elaborates that “it turns out that the behavior of electrons in a metal is not correctly described by the classical theory, but by quantum mechanics, but this only changes the factor in front a little. Actually, no one has ever been able to get the thing straightened out very well, even though many people have used the high-class quantum-mechanical theory for their calculations. The big problem is, does W change slightly with temperature? (Feynman et al., 1963, section 42–2 Thermionic emission).” Essentially, it is possible that the work function of the metal varies with its temperature. From a perspective of quantum mechanics, the probability of emission of electrons from the metal’s surface is dependent on the temperature of the metal.
Note:
1. Based on the classical Maxwell’s theory of light, if the intensity of incident light rays is increased, the kinetic energy of photoelectrons ejected from the metal can be increased. However, this does not happen in the single-photon photoelectric effect. This photoelectric effect experiment illustrates the particulate nature of light rays and the increase in intensity of light rays does not increase the kinetic energy of photoelectrons. Strictly speaking, an increase of light intensity can increase the maximum of kinetic energy of photoelectrons emitted. For example, a more intense light source such as a laser of a particular wavelength can produce the multiple-photon photoelectric effect in which the maximum kinetic energy of photoelectrons can be increased (Georges, 1995). That is, an electron at the surface of a metal could absorb energy from more than one photon such that it can leave the metal’s surface with more kinetic energy.
2. In the famous paper titled On a Heuristic Point of View Concerning the Production and Transformation of Light, Einstein (1905) writes that “it seems to me that the observations of ‘blackbody radiation,’ photoluminescence, production of cathode rays by ultraviolet light, and other related phenomena associated with the emission or transformation of light appear more readily understood if one assumes that the energy of light is discontinuously distributed in space. According to the assumption considered here, in the propagation of a light ray emitted from a point source, the energy is not distributed continuously over ever-increasing volumes of space, but consists of a finite number of energy quanta localized at points of space that move without dividing, and can be absorbed or generated only as complete units (p. 178).”
References:
1. Einstein, A. (1905). On a Heuristic Point of View Concerning the Production and Transformation of Light. In J. Stachel (ed.), Einstein’s Miraculous year: Five papers that changed the face of physics. Princeton: Princeton University Press.
2. Feynman, R. P. (1942). Feynman thesis: A New approach to Quantum Theory. Singapore: World Scientific.
3. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.
4. Georges, A. T. (1995). Theory of the multiphoton photoelectric effect: A stepwise excitation process. Physical Review B, 51(19), 13735.
5. Tsokos, K. A. (2008). Physics for the IB Diploma (5th ed.). Cambridge: Cambridge University Press.
Mark Scheme: ratio of the no. of electrons produced to no. of photons (of a particular energy) incident on the pixel.
Comments:
The question can be improved by at least two ways. Firstly, the question could be rephrased as “define the quantum efficiency of a charge-coupled device’s pixel.” This is to distinguish from the quantum efficiency of a solar cell. For example, the quantum efficiency of a solar cell can be defined as the ratio of the number of charge carriers collected by the solar cell to the number of photons of a specific range of wavelength absorbed. Secondly, there could be an interesting context such as a selfie or how a photograph can be taken by using a smartphone. That is, the question can be related to the photo-sensors of the smartphone.
On the other hand, the definition specified in the marking scheme is slightly different from the textbook’s definition. In Physics for the IB diploma, the quantum efficiency of a pixel is defined as “the ratio of the number of emitted electrons to the number of incident photons (Tsokos, 2008, p. 466).” The mark scheme uses the phrase “electrons produced” instead of “emitted electrons.” It should be noted that electron-holes pairs are produced instead of only an electron. Next, the marking scheme uses the phrase “number of photons” instead of “incident photons.” However, the mark scheme could include physical requirements such as “normal lighting conditions.” Physics teachers should explain that intense photons emitted from a laser may damage the photo-sensors.
Feynman’s insights?:
In general, quantum efficiency is a measure of the photoelectric sensitivity of a device. Interestingly, Feynman opines that the photoelectric effect is not simply about how photons eject electrons from a classical view. In Feynman’s (1942) words, “one attempts to list those phenomena which seem to indicate that light is quantized, the first type of phenomenon which comes to mind are like the photoelectric effect or the Compton effect. One is however, struck by the fact that since these phenomena deal with the interaction of light and matter their explanation may lie in the quantum aspects of matter, rather than requiring photons of light. This supposition is aided by the fact that if one solves the problem of an atom being perturbed by a potential varying sinusoidally with the time, which would be the situation if matter were quantum mechanical and light classical, one finds indeed that it will in all probability eject an electron whose energy shows an increase of hν, where ν is the frequency of variation of the potential (pp. 3-4).” Importantly, the probability of ejection of the electron should be related to the work function of the matter from a quantum mechanical view.
In The Feynman Lectures on Physics, Feynman does not explicitly discuss the photoelectric effect. From a perspective of classical physics, Feynman explains that “it turns out that in a piece of metal, electrons are attracted to the ions, or to atoms, of the metal. They are attracted, if we may say it crudely, to the metal. In order to get an electron out of a piece of metal, it takes a certain amount of energy or work to pull it out. This work varies with the different kinds of metal (Feynman et al., 1963, section 42–2 Thermionic emission).” In addition, Feynman defines the work function as follows: “W is equal to qeϕ, where ϕ is the so-called work function, or the voltage needed to pull an electron off the surface (Feynman et al., 1963, section 42–2 Thermionic emission).” In other words, the work function is related to an electric field or potential difference that can remove the electron from the metal’s surface.
More importantly, Feynman elaborates that “it turns out that the behavior of electrons in a metal is not correctly described by the classical theory, but by quantum mechanics, but this only changes the factor in front a little. Actually, no one has ever been able to get the thing straightened out very well, even though many people have used the high-class quantum-mechanical theory for their calculations. The big problem is, does W change slightly with temperature? (Feynman et al., 1963, section 42–2 Thermionic emission).” Essentially, it is possible that the work function of the metal varies with its temperature. From a perspective of quantum mechanics, the probability of emission of electrons from the metal’s surface is dependent on the temperature of the metal.
Note:
1. Based on the classical Maxwell’s theory of light, if the intensity of incident light rays is increased, the kinetic energy of photoelectrons ejected from the metal can be increased. However, this does not happen in the single-photon photoelectric effect. This photoelectric effect experiment illustrates the particulate nature of light rays and the increase in intensity of light rays does not increase the kinetic energy of photoelectrons. Strictly speaking, an increase of light intensity can increase the maximum of kinetic energy of photoelectrons emitted. For example, a more intense light source such as a laser of a particular wavelength can produce the multiple-photon photoelectric effect in which the maximum kinetic energy of photoelectrons can be increased (Georges, 1995). That is, an electron at the surface of a metal could absorb energy from more than one photon such that it can leave the metal’s surface with more kinetic energy.
2. In the famous paper titled On a Heuristic Point of View Concerning the Production and Transformation of Light, Einstein (1905) writes that “it seems to me that the observations of ‘blackbody radiation,’ photoluminescence, production of cathode rays by ultraviolet light, and other related phenomena associated with the emission or transformation of light appear more readily understood if one assumes that the energy of light is discontinuously distributed in space. According to the assumption considered here, in the propagation of a light ray emitted from a point source, the energy is not distributed continuously over ever-increasing volumes of space, but consists of a finite number of energy quanta localized at points of space that move without dividing, and can be absorbed or generated only as complete units (p. 178).”
References:
1. Einstein, A. (1905). On a Heuristic Point of View Concerning the Production and Transformation of Light. In J. Stachel (ed.), Einstein’s Miraculous year: Five papers that changed the face of physics. Princeton: Princeton University Press.
2. Feynman, R. P. (1942). Feynman thesis: A New approach to Quantum Theory. Singapore: World Scientific.
3. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.
4. Georges, A. T. (1995). Theory of the multiphoton photoelectric effect: A stepwise excitation process. Physical Review B, 51(19), 13735.
5. Tsokos, K. A. (2008). Physics for the IB Diploma (5th ed.). Cambridge: Cambridge University Press.
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