 So and welcome to a lecture on optical detectors part 2. Learning outcome by the end of the session student will be able to derive the performance parameters of photo detecting materials. These parameters will be applicable to all the photo detecting materials. Here you may pause the video and try to find out the answer to this question. How is the energy of a photon related to its frequency? We know the formula for energy of a photon is E equals to hf, where h is Planck constant, f is the frequency of a photon. So, we can say that energy of a photon E is directly proportional to the its frequency f or in terms of wavelength that is lambda, E equals to hc by lambda, where c is the speed of light, lambda is the wavelength of the photon, quantum efficiency. The first parameter quantum efficiency is one of the most important parameters used to evaluate the quality of the photo detecting materials. Quantum efficiency quantifies the photon absorption ability of the photo detecting materials. Quantum efficiency is nothing but it is a major of electrical power generated per unit incident optical power. Quantum efficiency is denoted by letter eta and it is defined as it is the ratio of number of electron whole pairs generated that contributes to photo current to the number of incident photons. So, we will derive the equation for quantum efficiency. Suppose we have a photo detecting material with width w and absorption coefficient alpha at a specific wavelength lambda and suppose we are incidenting optical power p 0 on this photo detecting material and we get the converted optical power as p 0 times e raise to minus alpha w, where w is a width of photo detecting material. Here we are not considering the frictional reflection constant which is nothing but the amount of photons reflected back at this interface. So, the optical power absorbed in the depletion region would be 1 minus r times p 0 times 1 minus e to the power minus alpha w, where p is incident optical power r is frictional reflection coefficient. So, this whole term 1 minus r gives the amount of light incident on the material between on the interface at air and photo detecting material. So, the number of photons absorbed by the materials becomes this optical power absorbed divided by the energy of a single photon which is nothing but H f. So, the total number of photon incident we can calculate by this formula incident optical power p 0 by H f. So, if we divide this number of photons absorbed by the total number of incident photons, then we will get the quantum efficiency. So, here the term in the numerator is nothing but the total number of photons absorbed and this is nothing but in the denominator we have total number of photon incidents. So, this H f term gets cancelled p 0 term get cancels and we get quantum efficiency equals to 1 minus r times 1 minus e to the power minus alpha w, where r is frictional reflection coefficient, alpha is absorption coefficient of photo detecting material and w is a width of photo detecting material available for absorption of the photons. From this equation it is clear that if we want to increase the quantum efficiency we have to reduce the value of r that is Fresnel's reflection coefficient or by having higher absorption coefficient alpha as well as by increasing the width available for absorption of the photon we can increase the quantum efficiency. Here point to note is that quantum efficiency is sometime specified in terms of percentage 75 percent of quantum efficiency means 75 out of 100 incident photons are absorbed for generation of photo current. Also quantum efficiency and absorption coefficient alpha are specified at specific wavelength. So, the photon current is given by the formula 1 minus r times into p 0 times 1 minus e raise to minus alpha w into electron charge e by H f unit of photo current will be amperes. We can increase the photo current by once again reducing the Fresnel's reflection coefficient or by increasing the absorption coefficient alpha or having wider width available for absorption of photons. The next parameter is responsivity. Responsivity gives the transfer characteristics of photo detecting materials or in simple words it gives the input output gain of a photo detecting materials. Responsivity is defined as it is a ratio of photo current to the incident optical power. Previously we have seen the expression of photo current and incident power is given by H f. Here we are calculating photo current generated to per unit incident optical power. So, here we are taking just H f which is nothing but a energy of a single photon. We know this 1 minus r times 1 minus e to the power minus alpha w is nothing but quantum efficiency eta. So, we get responsibility as quantum efficiency eta times electron that is e by H f. Responsivity can be increased by increasing the quantum efficiency. Responsivity of photo detecting material is directly proportional to the quantum efficiency of photo detecting material. Here figure 2 shows the characteristics graph of responsivity versus wavelength. The unit of responsivity is ampere per watt as it is a ratio of photo current to the incident optical power. The straight line is for ideal photodiode with quantum efficiency of 100 percent and this curve is for silicon photodiode available commercially. Here the point to note is that the responsivity suddenly drops to 0 after specific wavelength. This wavelength is referred as long wavelength cutoff. The next performance parameter is long wavelength cutoff. We know the condition for absorption of photon is the incident photon energy should be greater than or equal to the band gap energy of the photo detecting materials. So therefore, we can write the equation as the energy of a photon which is nothing but H f should be greater than or equal to band gap energy of the material. If we rewrite this equation in rearrangement we can write H c by lambda should be greater than or equal to E g. So, once again we can rearrange the equation as lambda should be less than or equal to H c by E g where H is playing constant C is speed of light and E is energy band gap in electron volts. So, this equation clearly indicates that there is threshold for absorption of photon in terms of wavelength which could be given as lambda c equals to H c by E g. This equation clearly states that if the photon with wavelength greater than this lambda c incident on a photo detecting materials it would not get absorbed. These are the references. Thank you.