Radiation Sensors: Photoelectric Effect, Work Function - PDF

## Unit - IV ### Radiation Sensors: The sensors which are developed to detect the emissions from matter. The fundamental law on which some of these sensors are based is the photoelectric effect. Radiation energy propagating through space in quanta when it collides with matter, a certain integral n...

## Unit - IV ### Radiation Sensors: The sensors which are developed to detect the emissions from matter. The fundamental law on which some of these sensors are based is the photoelectric effect. Radiation energy propagating through space in quanta when it collides with matter, a certain integral number of quanta called photons are emitted, reflected, and absorbed depending on the material characteristics. If the photon energy $hv$ (where $h$ is Planck's constant and $v$ is the frequency of radiation), then $hv = \frac{1}{2}mv^2 + \phi e$ Where: * $\frac{1}{2}mv^2$ is the energy of the electron emitted from the atom of the matter by the impact of a photon. * $\phi e$ is the energy required to release the electron (where $e$ is the charge of election, and $\phi$ is the work function of material). The kinetic energy of the photo election is dependent only on the incident photon energy which is transmitted to the electron. When the photon energy hits the electron, two situations arise: * If the incident energy is sufficient to transfer the electron into a vacant conductivity level and not beyond, this process leads to increased photoelectric conductance. * If the incident energy $hv$ is high enough, it causes the electron to be detached and emitted from the material. Radiation sensors are also called photosensors or photosensistors, optical or photonic sensing. The types of radiations known are infrared, ultraviolet, visible, photon-type, X-rays, and nuclear radiations such as $\beta$- and $\gamma$-rays The earlier classification of radiation sensors are: (i) The photoelectric cell such as a photoemissive cell. (ii) The photoemf cell such as photovoltaic cell. (iii) The photoconductive cell such as light sensitive resistors. \* The photosensistor is a combination of two electrodes in an electrolyte, and according to radiation ranges, frequency, or wavelength, the electrodes change in size and shape and the electrolyte changes to gas, liquid, or solid. ### Basic Characteristics: The important characteristics that are needed to be considered for photodetectors are: (i) Work function (ii) Quantum yield and quantum voltage (iii) Spectral sensitivity and spectral threshold (iv) Time lag (v) Drift, fatigue (vi) Static and dynamic responses (vii) Linearity **(i) Work function:** The work function is a physical constant for a given material and is usually expressed in electron volts, denoted by $\phi$. The energy $E$ which is spent in overcoming the surface attractive forces is given by: $E = \phi e$, where $e$ is the electronic charge. For metallic elements, the work function is observed to be smaller for higher atomic numbers, like for caesium, which has the smallest value, 1.54 eV. So, for photodetectors, alkali metals make a good choice, where alkali metals are electropositive and lose electrons easily. This makes them vulnerable to the atmospheric state that contains electronegative oxygen or hydroxyl ions. These are only as surface layers on metal plates of higher work functions. Thus, Na, K, Rb, Cs layers are laid on Ag, Be, Ta, Ni, Al, Cu, Ca, Zr, W plates. The alkali metals have a single electron on the outermost orbit, so a low work function is enough to dislodge it from an atom. When the number of electrons on the outermost orbit increases, then the metal has a higher work function. **(ii) Quantum yield and quantum voltage:** It is the ratio of the number of electrons emitted by the sensistor cathode to the number of photons it receives for the purpose. At any wavelength $\lambda$, the number of electrons emitted can be given by a number $6.242 \times 10^{18} \xi$, where $\xi$ is the sensitivity and a flow of $6.242 \times 10^{18}$ electrons is required to produce 1A current. To free an electron, an energy of $E_\lambda = \frac{12395}{\lambda} eV = \frac{1.9857 \times 10^{-8}}{\lambda} ergs$ is required, and one watt ($10^7 ergs/s$) of power would release $\frac{10^7\times 10^8}{1.9857} \lambda = 5.036 \times 10^{14} \lambda$ electrons/s, producing a current of $\frac{(5.036 \times 10^{14})}{(6.243 \times 10^{18})} A/W$. The quantum yield is, however, $Q_y = \frac{6.242 \times 10^{18} \xi}{5.036 \times 10^{14} \lambda} = \frac{12395 \xi}{\lambda}$ The energy that a photo election acquires by the impact of a photon is expressed as quantum voltage. The maximum kinetic energy it can have after escape from the surface is $E_m = E_\lambda - \phi$. The threshold wavelength is then defined as the one for which $E_m = 0$. The value of the quantum voltage is: $E_\lambda = \frac{hv}{e} = \frac{hc}{\lambda e} = \frac{1.2395}{\lambda} eV$ The photoelectric effect occurs at $E_\lambda > \phi$, indicates the color of the radiation, for visible light, for green radiation $\lambda = 0.546 \mu m$. | Element | work function (eV) | Ionization potential | | :------ | :----------------- | :------------------- | | Cs | 1.54 | 3.87 | | K | 1.8 | 4.32 | | Na | 1.94 | 5.12 | | Rb | 2.15 | 4.16 | | Li | 2.21 | 5.37 | | So | 2.3 | 5.67 | | Ca | 2.51 | 6.09 | **(iii) Spectral Sensitivity and Spectral Threshold:** When the electron velocity is zero, V=0, which occurs at absolute zero from the product value of $hv$, then the electron escape from the metal surface is possible with radiation if $hv>\phi e$ and a threshold frequency is obtained as $v_0>= \frac{\phi e}{h}$ and the wavelength is $\lambda_0<=\frac{hc}{\phi e}$ $c$ is the velocity of light, then $\lambda_0=\frac{1.2395}{\phi} \mu m.$ for caesium $\lambda_0$ = 0.8045 µm. The photoelectric emission from the metal surface occurs if the wavelength of incident radiation is less than the threshold frequency wavelength. The amount of emission is proportional to the intensity of incident radiation. The spectral sensitivity of photosensistors is higher than the threshold frequency is a function of incident radiation. | Element | Atomic weights | $\lambda_p (µm)$ | | :------ | :------------- | :--------------- | | Li | 6-94 | 0.4050 | | Na | 22.997 | 0.4190 | | K | 39.096 | 0.4400 | | Rb | 85.48 | 0.4730 | | Cs | 132.91 | 0.5390 | **iv) Time lag:** Time lag for photosensistors obviously varies over a wide range. It is very small, of the order of 10-8 s in photo-emissive cells and quite large, of the order of 5 x 10-2 s in light-sensitive resistors. For gas-filled photocells, the time lag is of the order of 10-5 s. The time response characteristics of the photosensistor becomes $Y= Y_0(1-e^{-\alpha t})$ $Y_0$ and $\alpha$ are constants. $\alpha$ is large for photoemissive cells, and small for photoresistor types. **v) Drift, fatigue:** When the incident radiation is fluctuating at a frequency larger than 100Hz, the response of the detector does not follow the fluctuations faithfully. This is prominent in LDRS, and it is called as dynamic fatigue. For a steady high energy incidence, the photodetector output is not always with respect to input and it is called as static fatigue. Drift is the transient response change during a short period after the cell is irradiated, is more common in photovoltaic cells. **vi) Static and Dynamic Response:** The static response is the ratio of the output to the input for steady illumination. it is called as Static Sensitivity. $S_{st} = \frac{I_a}{\phi_1}$ where $I_a$ is anode current. The dynamic response is given by dynamic sensitivity: $S_{dy} = \frac{\partial I_a}{\partial \phi_1} = \frac{\partial I_a}{\partial t} / \frac{\partial \phi_1}{\partial t}$ **vii) Linearity:** The linearity in response of a photosensistor is not ideal particularly in a loaded condition. The photovoltaic cell produces a voltage and the linearity between this voltage $V$ and incident light flux $\phi_1$is ideal. However, for photoemissive cells, the linearity is much better at $R = R_0 e^{-\beta L}$. ### Types of Photosensors/ Photodetectors: (i) Photoemissive cells and photomultipliers. (ii) Photovoltaic cells including photodiodes. (iii) Photoconductive cells and light detecting resistors. **(i) The Photoemissive cell and the photomultiplier:** This type of radiation sensor shows an external effect when a photoelectric cell consists of a pair of electrodes separated by a rare gas or vacuum, as shown in the image. The image displays a basic photoemissive cell. The cathode electrode is labeled 'photocathode'. The anode electrode is labeled 'Anode'. Light is made to fall on a properly coated photocathode to have a very low work function which releases electrons which are attracted towards the anode. The external circuit is connected with a resistance so that the change in current indicates the intensity of optical radiation falling on the cathode. The current with a single pair of electrodes is very small and the photomultiplication process is incorporated at large current output. The technique takes advantage of secondary emission of elections and for this, a number of electrodes called dynodes are used, which are secondary emitters of electrodes. The diagram depicts a photomultiplier consisting of seven dynodes with "+++'' indicating each dynode. Light shield protects the surface. Optical Ray goes from light shield to "P" which references photocathode. The image illustrates the layout of electrodes in a photomultiplier. All electrodes are kept at a higher potential for electrons to be attracted by it. The use of nine to eleven such dynodes is shown in above figure. The light shield is actually a grill connected to the photocathode and in this way the electrode assembly is electrostatically completed. Optical radiation reaches the photocathode P through this shield, and elections liberated from the cathode are first attracted to dynode 1. These elections by impact on dynode 1 release a number of secondary elections. Like this successive impacts occur on other dynodes increasing elections exponentially and at the end this stream of elections are collected by the anode. A and an external load may now be connected to it to produce the output current I given by $I = I_p k^n$ where $I_P$ is the initial primary photoelectric current, $K$ is a constant dependent on the dynode, and n is the number of stages. The potential difference applied between successive stages is about 100-130 volts. A mica shield is provided between photocathode and subsequent multiplying stages for isolation to prevent spurious election emission. The typical current sensitivity/amplification characteristics of a photomultiplier are show in the image of the figure. The vacuum photoemissive cell has a variation when it is filled with an inert gas at a very low pressure. With a potential between cathode and anode exceeding a certain critical value for filling gas, the photo election emitted, gets accelerated and ionizes a gas atom into another election and a positive ion. The positive space charge close to the photocathode may induce secondary election emission from it which partly neutralizes