Hey guys how's it going? In today's video I'll show you how to perform the experiment to study the variation of resistivity of a germanium crystal with temperature by a 4 probe method and hence we'll be determining the band gap of germanium. To perform the experiment we need a thin germanium crystal with a smooth surface, 4 probe arrangement, a digital voltmeter, a constant current source and oven with its power supply and a thermometer that can measure temperature between 0 to 200 degree Celsius. Now in my case the apparatus that I had at my college we already had the germanium crystal in place in the 4 probe arrangement. Also we had this 4 probe arrangement setup in which we already had the digital voltmeter and also the current source in it and we just connected our oven to this setup and to power our oven and to heat up the germanium crystal. So we'll be using these apparatus however if you have a different kind of arrangement at your college you will probably want to refer to your manual. Now the first thing that you need to do is you need to take your 4 probe arrangement right here and place it in the oven provided for it which looks somewhat like this. Then what you need to do is you need to put the thermometer in the hole provided for it to measure the oven temperature. Next what you need to do is you need to connect your oven to the power supply. As you can see in my case it was this black cable right here that goes into the power supply. Also your 4 probe arrangement will have 4 wires coming out of it so you need to connect two of those wires to the constant current source and the other two to the digital milli volt meter and you might have to refer to your manual for the 4 probe arrangement setup that your college has to find out which of the two wires going to the constant current source and which of the two going to the digital volt meter. So just find that out and make the proper connections as shown in the figure. Now once you have made the necessary connections turn on your 4 probe setup and turn this oven on. I have turned it on into a high mode so that it heats up faster. Then what you need to do is you need to try to set the constant current source as some value safe 5 milliampere then switch over to the digital volt meter mode and measure the voltage as well as the temperature at that point. So I'm getting approximately 25.5 volts and I'll note down the temperature at that point. It's approximately 56 degrees Celsius I guess so just note down the temperature as well as the voltage at that point. Now as your germanium keeps getting warmer and warmer the voltage reading keeps on decreasing so what you need to do is you need to keep on taking the voltage for different temperatures up till the temperature reaches 200 degrees Celsius. So it's going to be a while it took me at least like 45 minutes or an hour to reach 200 degrees Celsius so just keep noting down the voltage for different temperatures. And once the temperature reaches 200 degrees Celsius what you need to do is you need to turn off your oven and then you will need to start noting the voltage for different temperatures as your sample cools down. And the helpful tip to keep in mind is that you should try to note down the voltage for temperatures that you noted while you are heating the sample that way you will have two voltage readings for us for the same temperature so it would be easier to take the mean and get a better result. And keep another thing in mind that is that the sample takes a lot more time to cool than it took you to heat it. So it is a pretty lengthy experiment and it might take you like three hours I guess at the very least to complete it. Now once you have taken the readings what you can do is you can use a table like this to tabulate them so you can have the temperature in this column right here then the voltages while heating as well as cooling then you can take the mean of those voltages. Then in this column right here you need to calculate the resistivity given by rho is equal to v by i into d. Now this d here as you can see right here is 2 pi s by f of t by s where f is a correction divisor. And if you are wondering what d is or what might be the correction divisor that is f then I'm sorry but I can discuss that right now as it is quite beyond the scope of this video it is just for the practical purposes for the experiments that you will be performing in your college but I will add up some links in the description down below so that you can visit that page to find out more about the theory behind this total four probe apparatus and this setup. So moving on what you need to do is you need to find out these resistivity values and fill in this column right here. Another thing that I forgot to tell you is this distance between the probes that is denoted by s here so this distance between the probes as well as the thickness of the crystal denoted by t. Now in order to find those out you will need to refer to the manual that came with your apparatus. I can just tell you that as they differ from manufacturer to manufacturer so you will have to find that out by yourself. Then the next thing that you need to do is you will need to find out the value of t by s that is the ratio of the thickness of the crystal to the distance between the probes and then you will need to find out the correction divisor. Now I have this table right here that is being shown on your screen and you can find out the value of the correction divisor corresponding to the t by s ratio that you got from your manual or the apparatus. So you can either use this and well probably you know the manual that you get from the manufacturer of your predators. They will also have you know given a table for the correction divisor corresponding to the t by s value that they provided in their instrument. So you can just either you know look that up from the manual or you can find out the value of the correction divisor from this table right here. Now once you have the value of t s and f then it is quite easy to find out the value of d then you can substitute that in this expression right here to find out the resistivity corresponding to different temperatures. Then there is this column here for writing down the inverse temperatures and multiplied by 1000 and then there is another column to note down the log of the resistivity to the base 10. So just fill in these values and then we will move on to the next step. Now once you have filled out these values in the table you can plot a graph of log of resistivity to the base 10 versus the inverse temperature multiplied by the 1000. So basically it is just a plot of these two columns right here. So just plot them out and you should get a curve looking like something like this. Now once you have this curve what you need to do is you need to find out this slope right here and you can maybe use least square curve fitting to find out the slope of this line. Then you will need to use this formula right here and substitute the value of slope to find out the energy band gap and that's it. Now when I perform this experiment I got a graph that looks like this and I used least square curve fitting to obtain a linear fit for this graph with a slope of 1.955. Now if you substitute this value of slope into that equation that I showed you a while before then we get the energy band gap to be somewhere 0.77 electron volts and the actual value of the band gap of germanium crystal is actually 0.67 electron volts. So I had an error of about 15% in my result. Well that's it that's how you perform this experiment to study the variation of resistivity of semiconductor crystal with temperature and we also studied that how to find out the energy band gap of such a crystal using the 4 probe method and these are some precautions make sure that you go through them before it performs the experiment so that you can minimize the error and thanks for watching and have a great day ahead.