 Hello everyone. In the previous lecture, I discussed the detectors for gamma gamma ray counting based on scintillation detectors and mainly the sodium alder thallium detector which we discussed in details also some of the more advancements in the scintillation technology. Today I will discuss one of the most advanced detector systems for gamma spectrometry that is based on semiconductor detectors. So, as you know, the semiconductors are materials which have the bandgap range of around few electron bolts. They are between metals and insulators and these detectors were developed in the 1960s and are mainly based on the two semiconductor materials like silicon and germanium. They have a lot of advantages over the detectors that we have discussed so far. Namely, they have the excellent energy resolution. They have the fast timings. Of course, the efficiency for detection for gamma ray is not that high because of the low atomic number of these materials like silicon is 14, germanium is 32, but the overall the detectors are one of the best detectors for the spectroscopy of gamma rays. The basic principle of the detectors is similar to the gas field counters like ionization chambers. In the ionization chambers the incoming radiation ionizes the gas medium creating positive ions and electrons. Whereas in the case of semiconductors, the radiation when it falls on the detector material generates electron hole pairs. So, electron hole pairs are analogous to the positive ion and electron ion pair in a gas detector. So, the basically the semiconductor detectors function upon collection of electrons and holes at their respective electrodes. So, this is a schematic of the semiconductor material. We have the valence band and we have the conduction band. In a semiconductor, the bulk of the electrons will be in the valence band, but because of certain temperatures even at room temperature you will find there will be a significant quantity of electrons in the conduction band. So, that is the there are electron hole pairs generated thermally in a semiconductor material and the probability per unit time that an electron hole pair will be generated depends upon the band gap is the band gap and the temperature. So, even at room temperature there will be a sizeable number of electron hole pairs in the conduction band and therefore, when you want to use the detectors for counting of different types of radiations, we will need to take care of this particular task. So, the band gaps of this main detector material silicon and germanium are given here. Silicon is 1.115 electron volt, germanium is 0.65 electron volt and the W value as I mentioned earlier also W values are higher than the band gaps or the ionized putting cells in the gaseous media. Again, because every interaction may not lead to electron hole pair formation. Many a times this electrons and hole will get trapped and so, they are not really useful for the collection of the charge. So, germanium being higher Z is used mainly for the gamma ray spectroscopy, gamma ray counting, whereas silicon being the lower Z is used for alpha counting or even the other charge particles like protons and heavy ions. Both these detector materials in fact have been widely used for charge particle spectroscopy or gamma ray spectroscopy. I will discuss mainly the germanium based detectors and little bit touch upon the silicon based ones. Now, what is the basic principle of these detectors? Any of these semiconductor materials you have, in fact, you cannot have a pure germanium crystal, 100 percent pure or pure silicon crystal, but there will be by the by the process of manufacturing, they will be always associated with some impurity. So, if you have a electron rich impurity doped in these materials like tetravalent material silicon and germanium, this pentavalent impurities like phosphorus and antimony, then we call it n-type because over the tetravalent there is a pentavalent. So, there is an excess electron to these impurity centers and so, they are called electron rich centers or n-type synconductors. On the other hand, if there are electron deficient impurities like boron and aluminium, trivalent ones with respect to the tetravalent, silicon and germanium, then they are electron deficient with respect to the bulk material and we call them as p-type synconductors. So, how do we make use of this p-type or n-type materials for detection of radiation that I try to explain in this next slide. So, basically what we need to have is a semiconductor diode. So, how do you make a diode? You take a n-type and take a p-type and join them electronically. So, you have what when you say n-type material means it is rich in electrons, when we have p-type material it is rich in holes or electron deficient material. So, when you join them then depending upon the type of biasing that you invoke, you can have different scenario. So, I try to explain based on what way we bias this diode. Please say two electrode system n-type and p-type materials are there connected to the anode and cathode of detectors and the biasing system. So, when you do a forward biasing, what do you mean by forward biasing? That means that electrons are going across the junction to the anode and the holes are going across the junction to cathode. So, when we join the n and p-type of semiconductor materials and if there is a forward biasing then you will find there is a flow of electrons and holes across this junction and there will be a large amount of current generated even without any radiation falling on the detector system. So, this is called the forward biasing and this mechanism results in a large amount of leakage current. That means inherently the system there is a lot of current flowing through the circuit in the system in the forward bias mode. So, this forward bias mode is not utilized for using this as a radiation detectors. On the other hand, let us see the reverse biasing mode. The reverse biasing mode the n-type semiconductor is connected to the anode. So, you have the electrons going towards anode and you have the the neutron deficient side connected to the cathode. So, what is happening now when you apply the reverse bias to this diode junction diode material you will find the electrons are going to anode the holes are going to cathode and so there is a net no net flow of electrons and holes across the junction. So, there is a very very small leakage current. Of course, there will be some electrons on the p side which will go towards the if you cross the junction there will be some holes in the n side which will cross the junction. So, there will be a small leakage current anyway, but the bulk leakage current that was flowing in the forward biasing case which not flowing in the reverse biasing. So, the detectors the semiconductor materials if you want to use them as detectors we use them in the reverse biasing. So, I hope the concept of reverse biasing is clear by reverse biasing we decrease the leakage current significantly by connecting the n side to the anode and the p side to the cathode. In fact, it was the case earlier when we did not have the semiconductor materials of very high purity. So, you have inherently a high concentration of impurities like n-type or p-type and if you want to make a detector then we have to necessarily compensate for the impurity concentrations by making a diode. But nowadays the technology of semiconductor detectors has become so good that the whatever pure materials that you have the concentrations of impurities are of the order of 10 atoms per cc or even less than that. People are talking about 13 n purity when you say 39% 99.99999 and so on total there will be 13 nines. So, that is called 13 n purity they are highly pure materials. So, the impurity concentrations become 10 atoms per cc or so. So, such a detector material like germanium or silicon then there are very very few impurities and this is called as the intrinsic detector material. That means the number of electrons and holes is very very low. So, there will be very very less leakage current flowing through the the diode junction. Now, to make this as a detector anywhere you have to need a p junction. So, what you do you create a n-type layer on one side and you create a p-type layer on the other side. So, you may have a n inherent it is called the intrinsic detector material. So, nip. So, essentially if you have this reverse bias you are actually creating a intrinsic region which is which where there are no excess electrons or holes. And so, you can take a pure material relatively pure material and then if this is a pure material then you can you need to create n-type n p type layers on both sides. So, how do you create n-type layer or n-type layer likely to take a germanium crystal you can take you can diffuse the lithium from one side lithium will go in the interested positions and you generate the n-type. Or you can implant osforus or a pentavalent impurity by ion implantation. Similarly, the p-type you can create a surface barrier like in you you can edge the surface. So, there will be an oxide layer and oxide layer becomes a surface barrier and then you have a gold coating to protect it to make it like to make a little electrode contacts. So, you can create n-type layer or p-type layer of a few microns on both sides and the bulk material is intrinsically pure. So, there again n-side you connect to the anode and p-side to the cathode and now you have the detector system ready for operation. So, the germanium detector that are now available with highly pure crystals are called HPGE high quality germanium detector is the particular photograph of a detector. So, you have the crystal here germanium crystal which is in the vacuum because you should not come to room temperature. So, germanium detectors when you are using them for gamma spectroscopy to further reduce the leakage current they need to be kept at liquid nitrogen and so liquid nitrogen if you are having a old finger connected to the cryo state then you need to have a detector at vacuum otherwise it will start sweating and then you have the system for different geometry to keep the samples at different distance and you have the pre-amplifier all inside this casing. So, we have a field FET system field effective transistors to take care of the shaping of the pulse. So, this is the typical a 30 liter diva containing liquid nitrogen to pool the detector when it is in operation. So, the HPGE detector has concentrations of infinity less than 10.10 atoms per cc and depending upon whether you can take n-type or p-type you can have the germanium detector based on them. If it is a p-type germanium crystal then you can prepare n-contact by lithium evaporation on to lab surface or if it is a p-type then you can make it if it is an n-type you can make a p-type contact. So, you can make the p-type contact by a surface barrier means you etch this with the then acid and then expose to air you get upside layer. So, that is how you can make n-type and p-type junctions on both sides of a intrinsic germanium detector. Of course, these earlier times you know people did not have high purity germanium. So, you have the you diffuse lithium they call lithium drifted germanium detectors, but once you drift a lithium in germanium it has to be always kept at liquid nitrogen otherwise this lithium will keep on drifting at liquid nitrogen. So, there were there was a drawback of germanium lithium drifted germanium detectors, but now we do not need the jelly detectors we have the intrinsic germanium only when you want to operate them for gamma spectrometry you need to take you can have them to reduce the leakage. Okay. So, let us consider the discuss the properties of germanium detector how it mentioning about the energy resolution. The energy resolution of germanium is one of the best resolutions. So, we have excellent resolution in germanium detectors. Let us just typically do a calculation if we have a 1 mV gamma ray and the W value that is the energy required to produce one electron whole pair then for 1 mV gamma ray you have 10 power 6 upon 3 3 10 power 5 electron whole pairs and if we assume that all of them are collected at the respective electrodes then the resolution is 2 upon root n into 100 percent that is a percentage. So, if you calculate this number 2.35 is the capital HM for a Gaussian 2.35 sigma and so, it becomes 1 upon root n. So, in terms of percentage so, it becomes about 0.43 percent is the resolution. Compare this with sodium iodide thalium which was about 6 to 7 percent. But this is the calculated resolution and the experimental values are of the order of 0.15. Typically you know at 1332 keV of 60 cobalt we have the resolution FWHM equal to 2 keV. So, 2 upon 1 3 3 2 into 100 equals to 0.15 percent or so. So, this is the kind of resolutions that we are getting with the germanium detector. So, this is even better than the what you expect based on the statistical fluctuation in the number of electron whole pairs. And that is why a concept of FANF factor has been introduced to to take care of the decreased resolution or rather the improved resolution up to what we expect based on the Poisson's distribution. So, the FANF factor actually is the reduction in the resolution in the value of FWHM from this statistical value. So, that is 2.35 root F upon N when N is the number of ion pairs that are produced. And for semiconductors the FANF factor is less than 1, you will see here 0.15 upon 0.43 that will be the kind of FANF factors that we are getting. In fact, we did not talk about the different factors that are responsible for the resolution of the detector because inherently the detector was not having good resolution. But in case of germanium, the resolution is so good that we will start taking care of the different factors that contribute to the absorption of the gamma Dp. So, we have the statistical fluctuation in the full width at half maximum because of the number of ion pairs of electron whole pairs that we collect that is the statistical factor plus the noise. So, when you have a few volts of noise, few volts of signal, then you will find the noise of 2 millivolts 10, 20 or 30 millivolts will also start affecting the resolution. So, the FWHM due to the noise that will add up. And the drift over a period of time the system may drift the amplifiers, the multitalented analyzers, different electronic circuits will have a small drift. So, the overall FWHM is actually a resultant of the statistical fluctuation in the FWHM, the noise and the drift in the electronic system. So, when you set up a germanium digital system, you need to reduce the noise, you need to see that there is no drift in the pulsates and anyway the statistical fluctuations are taken care because of the FANF factor being less than 1, the resolution is anyway etc. So, these are the kind of state-of-the-art digital systems that people use for gamma spectrum. The FANF factor in case of germanium is less than 1, there are other detector systems where FANF factor can be more than 1. So, FANF factor is nothing but observed variance upon Poisson predicted variance f into n. So, if you expect n ion pairs, then the observed variance is less than n by a factor of f, where f is less than 1. So, excellent resolution for germanium detectors for gamma spectrum, gamma rays. Second part is the detection efficiency and the detection efficiency of a system depends upon the atomic number because the photo section will be high. For sodium agate thallium iodine I equal to Z equal to 53, for lanthanum bromide lanthanum Z equal to 57 and so on. So, high Z of a material will lead to high photo fraction. For germanium atomic number 32 and so the photo fraction is less and therefore, we will find that inherently the detection efficiency for the photopy is less than sodium agate thallium iodine. Otherwise also in general in the case of the gamma detection the efficiency for detection decreases with the increasing energy because the photoelectric effect probability decreases with the increasing energy of the gamma. So, typical efficiency you can see here 1.5 minus 4 and so in that range it can be minus 4 minus 3 and so on. So, when you are doing the efficiency calibration for the gamma ray you need to take the source of multiple gamma energy and calculate the efficiency by this formula. So, here when you do assay of activity so what you do in the peak area you will see a peak area you will see a gamma spectrum like this. So, you take the peak area so divide by the time will be counts per second and this counts per second divide by the efficiency of detection the branching intensity of gamma ray to get the absolute activity. In other words to want to get efficiency to take a source of known activity measure the counts per second intensity of the gamma ray is known branching it is so you can determine the efficiency that is what is plotted here as a function of gamma ray. Now as I mentioned already detection efficiency of germanium detector is much less than sodium agate thallium why because of the low atomic number of germanium distance and the efficiency decreases with the increasing energy of the gamma ray because the photoelectric absorption decreases with the increasing energy of the gamma ray. Now let us see how a gamma spectrum is appearing in the case of gamma spectrum between with semiconductors. So, I will take that case two to three cases one is a large volume detector. So, I will take a case of a large volume detector and you can even take a well type. So, you can take this one you take a well type germanium it is like a sphere and the gamma ray comes it interacts by photoelectric effect. So, it will give you an electron and the photon is absorbed. So, this electron with the positive energy detector material another gamma ray comes and undergo the Compton scattering and then the detector is large in volume. So, Compton scattered photon also may get other undergo photoelectric effect and deposit all energy. Similarly, you can have a gamma ray going for pair production. So, electron positron is produced and this positron may annihilate with another electron to give to 511 keV gamma ray. So, all these 511 keV photons also may get absorbed because the volume of detector is large. So, because of this large volume detector all three processes photoelectric effect counter-skating and pair production. So, this is the gamma ray energy and this is the bounce you will find you will have the full energy position in the detector and so, gamma ray spectrum will have a single peak. So, for large volume detectors you get a single peak in the gamma spectrum, but that is a little bit hypothetical case you may not be possible to have a such a large volume detector. Let us discuss about the small detector. So, you have a small detector whereby you have again the gamma ray undergoing photoelectric effect in generating an electron and the photon is absorbed. So, in this particular process we give to full energy deposition. Now, you have the Compton scattering electron and the h nu dash and because the detector is very small in size the Compton photon may scatter. Similarly, the pair production electron positron pair this may annihilate and give to 511. This 511 keV gamma rays may escape the detector volume because it is a small. So, only the photon the photoelectric effect photoelectron that is depositioning energy. So, as a result of these processes you will see counts you will have a full energy deposition and you will have a Compton scattering. So, Compton scattered photon are escaping you get a Compton h and since the 511 keV are escaping. So, you will see here single escape and double escape of 511 keV escaping. This is a scenario for a small tip. Now, let us see for the intermediate volume that is the practical size detectors that we will be using. So, you have a slightly bigger detector now compared to the small one. You have here the photoelectric effect the photoelectron depositioning energy in the detector volume. You have the Compton scattering electron is depositioning and the photon is there. This photon may further undergo photoelectric effect giving rise to electron and some part of h nu double dash may escape. After second one more scatter and the pair production of course, it is possible that the electron-phototron pair is produced. One part 511 may escape but other may not escape. So, the net result of these three processes you will see in now the intermediate volume detector is gamma. So, you have the photoelectric peak, photoelectric absorption and now whatever was there earlier the photo the Compton scattering there will be now multiple Compton scattering. So, there will be now a value will getting filled here and you may have a single escape peak of 1 pi. So, this is the typical gamma spectrum that you get with the practical detectors. You have the full energy peak, you have the Compton edge, you have the escape of one of the analysis gamma. So, these are the kind of features that you get with a germanium detector when you are doing gamma rays. Just to compare the gamma ray spectra with the sodium iodide thallium for the germanium detectors, you can see here the blue one is for the sodium iodide thallium. You can see to 511 to 2 gamma rays of over 60, 1172 and 1332 and this is the cesium 137, 662 PV and over the same spectrum which is superimposed a gamma spectrum due to germanium detector. You can see here 662, 1172 and 1332. The resolution due to germanium is much, much better compared to that of the sodium iodide 10. So, this whenever if you are doing gamma spectroscopy always go for germanium detectors. Of course, germanium detectors are little costly. The typical cost of a germanium detector will be about 20 to 20 lakhs whereas the sodium iodide thallium will cost anywhere between 2 to 3 lakhs. So, one has to decide the kind of information that you want. If you want the high resolution you have to go for germanium detector systems. Now, so detectors based on germanium are widely used for gamma ray spectroscopy but in addition to that there are detectors based on silicon or there are also called lithium drifted silicon that is called silly detectors. In fact, see for if you want to do for x-ray counting you cannot use germanium because the germanium will have its own x-ray and that x-ray may escape from the germanium system. So, if you use a small germanium system for x-ray counting then you may have problem of germanium x-ray escape whereas in the case of silicon the x-ray is very small energy and so x-ray escape probabilities are much lower. So, if you are doing x-ray counting go for lithium drifted silicon. Now, why lithium drifted silicon because silicon alone you may not be able to have a big size silicon. So, you would as you compensate for the p-type impurity by diffusing lithium and in silicon in fact, the lithium does not diffuse add to the pressure. So, once you diffuse the system at high temperature it remains in the silicon at exposure. So, for x-ray spectroscopy or x-ray fluorescence experiments if you use x-ray counting you use lithium drifted silicon detectors. Advantages of these silly detectors are many they have they are less prominent x-ray escape compared to germanium. So, the problem is not there then the greater transparency of silicon for high energy gamma. So, suppose there is a background of high energy radiations high energy gamma rays they will not impact the spectrum because most of the high energy gamma will pass through the silicon system. Then similarly, less escape of electron from it at a surface in case of beta count you can afford use for beta counting also. So, the escape of electron from the surface is much less in the case of silicon. And lastly the resolution of these detectors is about 150 electron volt for the high point 9 3 V of iron 55. So, you will find the silicon detectors based on the lithium drifted silicon are ideal for x-ray counting. Then if you want to do alpha spectroscopy for alpha counting you can use gas based counters, but if you want to do alpha spectroscopy use silicon detectors based on silicon you can have surface barrier. So, you have a you have a detector of this type silicon very thin you can you don't need to maybe few millimeter thick silicon and you have this on the surface you have the gold coating you have a source here and you put the whole thing in a vacuum because alpha will get attenuated in the air. So, surface barrier silicon detectors where you need a p-type barrier layer on this silicon crystal to make a p-type junction or you can even have an implanted if you take a p-type silicon then you can have an implanted as porous layer on the surface to make a NP junction. So, these silicon detectors for high for alpha counting you do only the germanium detector you can use a thin silicon crystal because their engines are very small. So, if you are doing type particle spectroscopy alpha alpha spectroscopy the counting actinides for their for you have mixture of plutonium and americium they have different alpha energy if you want to resolve them you use silicon based detectors. And the typical resolution of this surface barrier silicon or an implanted silicon is 15 kV at 5.486 kV of rather it is not kV it is mEV 5.486 mEV. So, 5000 kV and 15 kV you can see the kind of resolution that you get for alpha alpha spectra in silicon detector. So, you can or if you are counting mixtures of actinides plutonium americium or alpha counting you can simultaneously count alpha plutonium in the shunt silicon detector and you can determine their activity. So, this is what we the I had not discussed much about but this the basic principle remain the same in the case of silicon based detectors for alpha counting, silicon based lithium lithium drifted silicon for x-ray counting and the germanium detectors for gamma. So, today if you are doing the spectroscopy or charge particles of gamma you go for silicon detector detectors. So, I will stop here. Thank you very much.