WEBVTT 00:22.320 --> 00:29.320 So, now that we are familiar with the crystal structure of silicon and also we have seen 01:34.090 --> 01:40.610 what are that common defects which are possible to be in a practical crystal, it is time to 01:40.610 --> 01:47.610 see how this single crystal can be grown in practice. Because as you know, the starting 01:47.770 --> 01:54.770 point in any integrated circuit fabrication is we must have a silicon wafer, a single 01:55.470 --> 02:01.479 crystal silicon wafer. So, we must get the substrate material. In order to get the substrate 02:01.479 --> 02:08.479 material, we must grow a single crystal of silicon. As I have already mentioned, silicon 02:08.840 --> 02:15.340 is one of the most abundant material in the world. It is formed, it is found in nature 02:15.340 --> 02:22.340 as silicon dioxide. So, first the silicon dioxide is reduced in order to obtain silicon. 02:23.730 --> 02:30.320 It is purified further in order to get very high purity semiconductor grade silicon that 02:30.320 --> 02:37.320 is 6N purity or 99.9999% purity. Once we have obtained this highly pure semiconductor grade 02:42.799 --> 02:49.799 silicon, we can use it as the starting material to obtain a single crystal. 02:49.799 --> 02:56.799 So, that brings us to the unit process step of crystal growth and the crystal growth can 02:59.889 --> 03:06.889 be broadly classified as Bridgman technique and Czochralski technique. Let me on the onset 03:09.540 --> 03:15.540 tell you that most of the silicon that is grown today, that is available, commercially 03:15.540 --> 03:22.540 available today, are grown by Czochralski technique and sometimes further purified. 03:23.549 --> 03:30.549 But for historical significance, I would like to discuss the Bridgman technique first and 03:33.510 --> 03:40.449 then I will also tell you why the Czochralski technique is preferred for growth of single 03:40.449 --> 03:47.449 crystal silicon over Bridgman. So, let us begin our discussion with the Bridgman system 03:47.859 --> 03:54.859 of crystal growth. The Bridgman system of crystal growth is a very simple process. It 03:56.500 --> 04:03.500 is very simple, can be very easily achieved. But of course, there is a catch; there will 04:05.239 --> 04:09.979 be some problems associated with this Bridgman grown crystal. 04:09.979 --> 04:16.979 Let us look at the system, where a single crystal can be grown by using the Bridgman 04:19.350 --> 04:26.350 technique. What we have here, it is a quartz ampoule, a quartz tube. The mouth of the tube 04:29.229 --> 04:36.229 is sealed. It is evacuated and sealed. So, first of all a quartz ampoule and inside this 04:38.450 --> 04:45.450 ampoule, you have a quartz boat. This is the outline of the boat. In this boat, a seed 04:49.830 --> 04:56.830 crystal, a small single crystal is placed and the rest is filled with the charge. What 04:58.800 --> 05:05.800 do I mean by charge? I mean the high purity silicon which is poly crystalline or powdered. 05:09.070 --> 05:16.070 That is called the silicon charge. So, the charge along with the seed crystal is placed 05:17.170 --> 05:24.170 in the quartz boat inside an evacuated quartz ampoule and then the charge is heated. Charge 05:27.410 --> 05:34.410 is heated to its melting point, but make sure that the seed crystal is not molten. 05:36.780 --> 05:43.780 Therefore, the temperature profile of the furnace has to be something like this - temperature 05:45.880 --> 05:52.880 versus x. So you see, the seed end is kept at a lower temperature, while the charge, 05:56.240 --> 06:03.240 the melt is at high temperature and therefore it is in the molten condition. This has to 06:04.870 --> 06:10.310 be very critically maintained. Therefore, the temperature profile in a Bridgman furnace 06:10.310 --> 06:17.280 has to be very accurate. Care must be taken, so that the seed crystal is not molten and 06:17.280 --> 06:24.280 then, once the charge is in molten condition, the heater can be moved in this direction. 06:25.210 --> 06:32.120 What is going to happen when the heater is moving in this direction? That means the end 06:32.120 --> 06:38.080 of the melt which is in contact with the seed crystal is now becoming progressively cooler. 06:38.080 --> 06:45.080 It is coming in the low temperature zone of the furnace. Therefore, that end is going 06:46.060 --> 06:53.030 to solidify and since this is in contact with the seed crystal, it will take the orientation 06:53.030 --> 07:00.030 of the seed crystal and the solidification will take place as a single event. That is 07:00.800 --> 07:03.230 I am going to realize a single crystal. 07:03.230 --> 07:10.050 So, as progressively the heater is moved in this direction from this end that is from 07:10.050 --> 07:16.970 the seed end, the melt is going to get solidified and I am going to realize a single crystal. 07:16.970 --> 07:23.970 Alternately, you could also move the quartz ampoule in this direction, same purpose will 07:24.320 --> 07:29.160 be served. Instead of moving the heater, you could just move the quartz ampoule in this 07:29.160 --> 07:34.889 direction. Even in that case, the seed end of the melt will come into the low temperature 07:34.889 --> 07:40.290 zone and therefore, it will get solidified. In contact with the seed crystal it will get 07:40.290 --> 07:47.290 solidified as a single event and will realize a single crystal. So you see, essentially 07:50.389 --> 07:57.360 this is what the Bridgman crystal growth system is all about. All you need to have is a quartz 07:57.360 --> 08:04.360 ampoule and a quartz boat, both of which is readily available and you just have to evacuate 08:04.889 --> 08:11.889 the sample before, after placing the charge and the seed crystal in it and have a very 08:13.620 --> 08:20.620 good furnace with an accurate temperature profile and maintain a relative motion, either 08:20.860 --> 08:27.860 move the heater or move the quartz ampoule and you will have your single crystal. 08:28.530 --> 08:35.530 In principle, this is what Bridgman crystal growth is all about. But, as we have already 08:36.250 --> 08:43.250 mentioned, silicon is a material which expands on solidification. So, in a Bridgman crystal 08:46.040 --> 08:53.040 growth that is the greatest drawback, because the charge is kept in a quartz boat. The confining 08:57.010 --> 09:04.010 boundary of the quartz boat is going to create a lot of stress during the solidification 09:04.790 --> 09:11.790 of the charge. Because the charge is in the molten condition, the solidification is taking 09:12.520 --> 09:17.830 place at the seed end where the charge is in contact with the boat, so the surface of 09:17.830 --> 09:24.830 the boat is going to act as a confining barrier. It is going to create a lot of stress on the 09:26.010 --> 09:31.520 crystal and therefore you know, whenever there is a lot of stress, dislocations will be formed. 09:31.520 --> 09:38.520 Therefore, Bridgman growth single crystals have a lot of dislocations in them. In fact, 09:40.070 --> 09:47.070 that is one of the reasons, a major reason, why, in spite of the inherent simplicity of 09:47.950 --> 09:54.950 the Bridgman crystal growth technique, people go for Czochralski system of crystal growth. 09:57.450 --> 10:04.450 Czochralski system of crystal growth is actually a much more complicated system, compared to 10:05.910 --> 10:12.910 a Bridgman system. It is a much more sophisticated, much more difficult system to handle. You 10:14.500 --> 10:21.500 will have to control a large number of parameters, but you can grow single crystals which have 10:22.210 --> 10:29.100 much less dislocations, much less defects. That is the greatest advantage of a Czochralski 10:29.100 --> 10:36.100 system. So, a Czochralski system is also known as a liquid solid mono component growth system, 10:40.170 --> 10:47.170 liquid solid mono component growth system. What do we have in a Czochralski system? 10:49.140 --> 10:56.140 Essentially the Czochralski system on a liquid - solid mono component system that is Czochralski, commonly referred to as the Cz, Cz crystal 11:23.560 --> 11:30.560 that is the Czochralski grown crystals. We have basically four subsystems in this Czochralski 11:33.649 --> 11:36.990 crystal growth system. 11:36.990 --> 11:43.990 First is a furnace, second is known as the crystal pulling mechanism, third is the ambient 12:07.180 --> 12:14.180 control 12:17.750 --> 12:24.750 and finally we have the control systems. So, these are the four subsystems of a Czochralski 12:29.300 --> 12:36.300 crystal growth system - furnace, crystal pulling mechanism, ambient control and a control system. 12:38.130 --> 12:45.130 Now, let us take a look at the Czochralski crystal growth system. 12:45.260 --> 12:52.260 What I have here is a quartz envelope, big quartz chamber with gas inlets, gas outlets, 12:58.330 --> 13:04.209 may be even some pumps, which I have not shown in the figure, some pumps in order to maintain 13:04.209 --> 13:11.209 the requisite pressure in it and you have another opening through which a pull rod is 13:11.680 --> 13:18.680 passed. This quartz envelope may be water cooled. The most important part in this furnace 13:27.470 --> 13:34.470 is the crucible that is a cup in which the charge is going to be placed and this is usually 13:37.420 --> 13:44.420 made of quartz. See, quartz is nothing but silicon dioxide. So, there is less chance 13:44.770 --> 13:51.770 of contamination through a quartz crucible, because it is also comprised of silicon. But, 13:52.020 --> 13:58.029 it is actually silicon dioxide, therefore some oxygen may come from the crucible to 13:58.029 --> 14:05.029 the single crystal. We will investigate that later, what happens if oxygen comes into it 14:05.339 --> 14:12.339 and usually the crucible is made of quartz and it is actually a single, you can use it 14:12.370 --> 14:19.240 only once usually, because after the crystal growth when you are cooling down the system, 14:19.240 --> 14:24.670 then because of the thermal mismatch usually the quartz crucible is going to crack. So, 14:24.670 --> 14:31.670 you cannot reuse the crucible and this quartz crucible is usually placed inside a graphite 14:35.970 --> 14:37.580 susceptor. 14:37.580 --> 14:44.580 A susceptor is, you can view it as an outer jacket. That is I have a bigger cup of graphite 14:44.750 --> 14:50.279 in which I am going to place the quartz cup. The quartz cup is called the crucible, the 14:50.279 --> 14:57.279 graphite cup is called the susceptor and the graphite susceptor is placed on a heater, 15:01.600 --> 15:08.600 graphite heater usually, very high purity graphite heater and the heating is done by, 15:08.730 --> 15:15.730 usually by RF. These signifies the RF heating. Sometimes for large charges, resistance heating 15:17.450 --> 15:24.450 is also employed, but mostly it is RF heating. So, these are the things inside the furnace. 15:32.390 --> 15:39.390 You have a quartz crucible, a graphite susceptor, a heater and the cooling for the outer quartz 15:42.190 --> 15:49.190 chamber, quartz envelope. Then, we have the crystal pulling mechanism. I have already 15:51.760 --> 15:58.760 mentioned that through this a pull rod is passed and at the end of the pull rod, a small 16:00.649 --> 16:03.200 seed crystal is fixed in a ..... 16:03.200 --> 16:10.200 It is like you have this pull rod and at this end a small seed crystal is fixed, it is held 16:12.260 --> 16:19.260 in a ...... and as can been seen from the figure, the pull rod is pulled up during the 16:19.630 --> 16:26.630 crystal growth and then of course, we have the ambient control. See, the ambient is very 16:29.890 --> 16:35.730 important in a crystal growth system. First of all realize that I am using a graphite 16:35.730 --> 16:42.730 susceptor and graphite heaters. Therefore, there must not be any oxygen inside the system. 16:43.230 --> 16:50.230 The whole thing will just go up in smoke, so to speak. It will just form carbon dioxide 16:51.420 --> 16:58.420 and there will be no susceptor, no heater, nothing left. The other thing is of course, 16:59.700 --> 17:04.880 it should not react with silicon. I want to have high purity single crystal silicon. If 17:04.880 --> 17:10.699 I have oxygen in it, oxygen is going to react with silicon to form silicon dioxide; I cannot 17:10.699 --> 17:16.419 allow that. Therefore, beware of oxygen. That is why the usual practice, even though I have 17:16.419 --> 17:23.419 not shown it in the figure, is first of all to evacuate the quartz chamber. After you 17:23.789 --> 17:30.789 have put the charge in it, first of all evacuate the quartz chamber and then fill it up with 17:30.960 --> 17:37.960 an inert ambient - argon or helium or nitrogen, something like that. You can do it in, you 17:40.970 --> 17:46.830 can fill it up and maintain atmospheric pressure or sometimes even reduced pressure. 17:46.830 --> 17:53.830 Now, let us see how exactly the crystal growth is achieved? What do you do? So, we have put 17:56.940 --> 18:03.059 in the charge, we have created the requisite ambient condition inside and we are heating 18:03.059 --> 18:10.059 the assembly. So, what happens? The charge gets molten. I have a melt inside the crucible. 18:15.399 --> 18:22.399 Remember, all this while the seed crystal was not, I repeat, not in contact with the 18:23.820 --> 18:30.820 melt. It was held somewhere up there, while the charge was below. After the charge is 18:34.999 --> 18:41.999 molten, it is uniformly in the liquid state, then the pull rod is gradually lowered till 18:44.789 --> 18:48.899 the seed crystal touches the melt surface. 18:48.899 --> 18:55.899 This is the point till the seed crystal touches the melt surface and then, very slowly the 18:59.769 --> 19:06.769 pull rod is pulled up. So, what will happen? The melt that is in contact with the seed 19:10.539 --> 19:17.539 crystal will get solidified and as we pull up, we are going to pull up the solid crystal. 19:21.580 --> 19:28.580 Care must be taken, very accurate control is necessary, so that instead of growing the 19:29.679 --> 19:36.679 crystal you do not melt down the seed crystal itself. The pull rate must be carefully adjusted, 19:38.429 --> 19:44.299 so that I get a single crystal. I do not melt down the seed crystal, because you see the 19:44.299 --> 19:50.289 seed is in contact with the melt. If the pull rate as well as the thermal conditions are 19:50.289 --> 19:57.289 not carefully adjusted, the reverse can also happen. The seed can also, can get melted. 19:57.940 --> 20:04.940 Therefore, therefore you can appreciate that the Czochralski crystal growth technique is 20:05.739 --> 20:12.739 a much more complicated process, but the quality of crystal would be very good, which brings 20:14.559 --> 20:21.559 us to the question of how the pull rate should be adjusted. Pull rate should be adjusted 20:25.470 --> 20:30.580 very carefully. If you draw it too fast you may not get a single crystal. If you draw 20:30.580 --> 20:37.580 it too slow, you may even get the seed crystal melted. Therefore, the pull rate must be very 20:37.779 --> 20:44.779 carefully adjusted which brings me to the second card, where we discuss how the pull 20:45.389 --> 20:52.340 rate should be carefully adjusted. 20:52.340 --> 20:59.340 I have written down an equation there, L dm dt plus K L dT dX 1 A 1 is equal to K S dT 21:04.249 --> 21:11.249 dX 2 A 2, where L is the latent heat of solidification, latent heat of fusion or latent heat of solidification, 21:15.659 --> 21:22.659 dm dt that is the mass solidification rate. K L is the thermal conductivity of the liquid, 21:26.369 --> 21:33.369 K S is the thermal conductivity of the solid, dT dX 1 is the thermal gradient in the melt, 21:35.379 --> 21:42.379 dT dX 2 is the thermal gradient in the solid that is in the crystal and A 1 and A 2 are 21:43.539 --> 21:50.539 the area of the isotherms in the melt and in the solid. So, basically what I have written 21:51.169 --> 21:58.169 is a heat transfer equation. Now, from this equation you can very easily see that if I 22:02.759 --> 22:09.759 assume that the thermal gradient in the melt is zero, that is the entire melt is in the 22:09.769 --> 22:16.429 constant temperature that is at the melting point, it is maintained at the melting point, 22:16.429 --> 22:23.429 so if dT dX 1 can be made equal to zero, then L dm dt is going to be equal to K S dT dX 22:50.389 --> 22:52.570 2 times A. 22:52.570 --> 22:59.570 L, I have already said is the latent heat of solidification, dm dt is the mass solidification 23:00.440 --> 23:07.440 rate. So, what is dm dt really? I can write it as L, can I not? L times area into rho, 23:17.419 --> 23:24.419 rho that is the density into dx dt. This is actually equal to the dm dt term, rate of 23:34.049 --> 23:41.049 change in volume times the density. That is the rate of change in mass. So, if I consider 23:44.479 --> 23:51.479 that the thermal gradient in the melt is zero, then this is equal to, this dx dt is nothing 24:19.229 --> 24:25.659 but my pull rate. This is the rate at which I am pulling the crystal. 24:25.659 --> 24:32.659 So, from this equation I can say that dx dt 24:51.609 --> 24:58.609 K S by L into rho times dT dx, it is dx 2; this we prefer. This is the maximum attainable 25:04.599 --> 25:11.599 pull rate, maximum attainable that is when I am assuming that the thermal gradient in 25:12.639 --> 25:16.239 the melt is going to be zero. 25:16.239 --> 25:23.239 In practice, the pull rate is kept less than the maximum pull rate. In a practical system 25:29.840 --> 25:36.840 what happens is that there will be a small change in the temperature of the melt. Because 25:36.859 --> 25:41.419 we are pulling out the crystal, the thermal conditions, they are continuously changing. 25:41.419 --> 25:48.419 So, in a practical system actually, a feedback system is used, a feedback control is used. 25:50.309 --> 25:55.759 That feedback control is used to supply the heat to the melt, so that the temperature 25:55.759 --> 26:02.759 is maintained within plus minus half degree centigrade or so and now you can understand 26:05.440 --> 26:12.440 that this heat loss, the heat needed to be supplied in the system, heat input minus heat 26:12.519 --> 26:18.109 output, the heat loss is almost entirely taken off by the latent heat of solidification, 26:18.109 --> 26:24.629 no other path of heat loss. Almost entirely this thing is going to be taken by the latent 26:24.629 --> 26:29.440 heat of solidification, if the temperature gradients are considered to be very small. 26:29.440 --> 26:36.440 So you see, in a practical system the difference between the heat input and the heat output 26:41.159 --> 26:48.159 will be almost totally taken off by this. 26:51.729 --> 26:58.729 This is the heat transfer. This is taken off almost totally by L dm dt or ..... Actually, 27:09.539 --> 27:16.539 this H i minus H naught should be small. So you see, in this equation L is a constant. 27:24.489 --> 27:30.889 I cannot do anything about L, same is for rho. Latent heat and the density, these are 27:30.889 --> 27:37.889 the material properties. So, the only variables are the area and the pull rate. So you see, 27:38.570 --> 27:45.570 actually therefore, the pull rate is going to vary inversely with the area for a given 27:47.929 --> 27:54.929 H i minus H naught. In other words, the larger your crystal, the smaller should be the pull 28:00.749 --> 28:07.749 rate. Now, this pull rate, it has a lot of effect on the defects. The defect finally 28:15.099 --> 28:22.099 in the crystal, it is going to depend quite significantly on the pull rate. How? See, 28:28.499 --> 28:35.499 as the crystal is cooling, from its mere melting point as it is cooling, the thermal point 28:37.429 --> 28:44.429 defects will try to coalesce into dislocation groups. It will try to agglomerate, it will 28:45.700 --> 28:52.700 try to, all of them will come together and form a dislocation group and form an array 28:53.539 --> 29:00.539 agglomerate. This is seen to happen at a temperature around 950 degree centigrade. 29:04.070 --> 29:11.070 Now, if the pull rate is larger, if the pull rate is say, greater than 2 millimeters per 29:12.840 --> 29:19.840 minute, then you can quench this defect formation. That is when you are pulling it very quickly, 29:20.529 --> 29:27.529 you are forcing it to cool quickly, so you can quench this defect formation. But again, 29:32.269 --> 29:39.269 as I said, if you have large diameter crystal, then you cannot afford to use a very large 29:42.469 --> 29:45.460 pull rate. They are inversely proportional. 29:45.460 --> 29:52.460 In fact, the pull rate you can plot, if this is the diameter of the crystal and if this 29:55.309 --> 30:02.309 is the pull rate, it actually varies something like this and this is about 1.5 mm per minute 30:11.599 --> 30:18.599 when the diameter is about 75 centimeters or so,75 millimeters or so. 75 millimeter 30:19.700 --> 30:26.700 that is about 7.5 centimeter that means about 3 inch diameter wafer. Funnily enough, for 30:29.999 --> 30:36.129 measuring silicon wafer diameter we still use inches. That is the common way of referring 30:36.129 --> 30:41.669 to the wafer as 2 inch dia or 3 inch dia or 4 inch dia or 6 inch dia. Now you can even 30:41.669 --> 30:43.769 get 12 inch diameter wafer. 30:43.769 --> 30:49.450 Now, the point I am trying to make is this. Therefore you see, it is relatively easier 30:49.450 --> 30:56.450 to grow a smaller diameter single crystal with very low defect density, isn't it? Because 30:58.149 --> 31:03.820 for a smaller diameter crystal, you can afford to use a large pull rate and when you use 31:03.820 --> 31:10.419 a large pull rate, the problem of this dislocation forming is less severe. That is the reason 31:10.419 --> 31:16.659 why 10 years back, the silicon crystals that were grown were almost exclusively 2 inch 31:16.659 --> 31:23.659 or 3 inch diameter; 10 years or 15 years back. At the beginning of the integrated circuit 31:24.049 --> 31:30.830 evolution, the silicon wafers available were only of 2 inch or 3 inch diameter. As the 31:30.830 --> 31:37.830 system became perfect, more perfect, technologically more advance was made, it was, it became possible 31:40.859 --> 31:46.509 to grow large diameter crystal with low defect density. 31:46.509 --> 31:51.869 Obviously, more stringent control is needed on the pull rate, more stringent control on 31:51.869 --> 31:58.869 the thermal control system, all that is required if you want to grow larger diameter crystal 31:59.529 --> 32:06.529 with low defect density. So, you will appreciate that it is difficult to grow a bigger diameter 32:06.859 --> 32:13.859 crystal. That is why they came later in the market. Now, it is even possible to grow a 32:13.940 --> 32:20.659 12 inch diameter crystal like a big plate. It was not possible 10 years back, because 32:20.659 --> 32:27.659 of the technological limitations. So, this is about the pull rate. 32:29.909 --> 32:36.909 Now, the next interesting point is, of course, how about the dopant, dopant incorporation 32:40.139 --> 32:46.119 in the crystal. Suppose I want to grow a p-type crystal or an n-type crystal, how can I do 32:46.119 --> 32:53.119 that? More importantly, suppose I want crystals of a particular doping concentration, how 32:56.769 --> 33:02.309 do I maintain that? That is inadvertently if something else comes inside, suppose I 33:02.309 --> 33:07.519 wanted to grow an n-type crystal, but I find that it is p-type because of some unintentional 33:07.519 --> 33:14.519 dopants, how do I control that? How are the dopants incorporated during the crystal growth 33:14.929 --> 33:21.929 process itself? 33:24.509 --> 33:31.509 The dopant incorporation during crystal growth is actually a very interesting thing. You 33:31.519 --> 33:38.519 see, any impurity it will have a solid solubility in the crystal and it will also have an equilibrium 33:42.379 --> 33:49.379 solubility in the melt and these two are not necessarily same. There is a different solubility 33:51.559 --> 33:56.710 in the crystal and in the melt. 33:56.710 --> 34:03.710 So, this is given by the segregation coefficient, this difference is given by the segregation 34:09.280 --> 34:16.280 coefficient, usually referred to as K naught and K naught is given as the ratio between 34:28.599 --> 34:35.599 C S and C L, where C S is the solid solubility in solid silicon, solid solubility of the 34:38.149 --> 34:45.149 dopant in silicon and C L is the equilibrium solubility in the melt. Now, usually for most 34:51.179 --> 34:58.179 common impurities this K 0 is less than 1; for most common impurities K 0 is less than 34:59.550 --> 35:06.550 1. What is the implication? The implication is that the solid solubility is less than 35:06.880 --> 35:13.880 the equilibrium solubility, equilibrium solubility in melt. That means as you grow the crystal, 35:19.650 --> 35:26.650 these impurities are preferentially left inside the melt, they do not come into the solid. 35:27.610 --> 35:34.610 They are rejected by the solid, they prefer to be in the melt. That is because C S by 35:34.990 --> 35:41.990 C L is less than 1. That means as you are drawing the crystal, the melt is becoming 35:42.930 --> 35:49.930 progressively richer in the impurity. So, when you grow a crystal, we will find that 35:53.130 --> 35:58.350 the doping concentration will vary from one end to the other. 35:58.350 --> 36:05.350 The top end will have relatively less dopant concentration and the bottom end will be relatively 36:10.450 --> 36:17.450 more doped. That is true for most common impurities with the notable exception of oxygen. That 36:33.650 --> 36:40.650 is oxygen will have a segregation coefficient greater than 1. That is oxygen will come preferentially 36:41.470 --> 36:48.470 into the crystal, it will try to come preferentially into the crystal. That is a cause for concern, 36:53.600 --> 37:00.310 because you know in the furnace itself we have a source of oxygen. We are using quartz 37:00.310 --> 37:04.960 crucible, we are using quartz envelopes. Although the envelope is water cooled, but the crucible 37:04.960 --> 37:11.960 is heated. So, there is a possibility of oxygen incorporation during the crystal growth, oxygen 37:13.800 --> 37:20.620 incorporation into the silicon during the crystal growth. Is it detrimental? What are 37:20.620 --> 37:25.170 effects of oxygen in the single crystal silicon? 37:25.170 --> 37:32.170 Usually in a Czochralski grown crystal, the amount of oxygen will vary from 5 into 10 37:48.210 --> 37:55.210 to the power 17 to about 10 power 18 per centimeter cube; 5 into 10 to the power 17 to about 10 37:57.710 --> 38:04.710 to the power 18 per centimeter cube. Now, this oxygen in the silicon will have three 38:09.840 --> 38:16.840 possible defects. First of all within a limit this oxygen, 95% of it, will be in the interstitial 38:25.460 --> 38:32.460 sites, 95% will stay in the interstitial sites. That is it will find the space in between 38:32.900 --> 38:39.900 the regular array of silicon atoms and go and sit there. The rest 5%, however it can 38:41.620 --> 38:48.620 form a complex like SiO 4 and that complex will be donor like. This complex will be electronically 39:10.900 --> 39:17.900 active, it will be donor like, therefore it will affect the resistivity of the grown crystal 39:19.000 --> 39:26.000 and the formation temperature of these complexes are around 450 to 500 centigrade. 39:42.630 --> 39:49.630 So, when the crystal is being cooled, this SiO 4 complexes will be formed. They will 39:57.580 --> 40:04.580 make the silicon n-type, donor like complexes. One possible remedy to reduce this is, you 40:08.940 --> 40:15.940 form the crystal, you cut them into wafers that is thin slices and then you heat these 40:16.110 --> 40:23.110 slices to temperature above 600 degree centigrade and then, when you heat it above 600 degree 40:25.090 --> 40:31.630 centigrade, these complexes are dissolved, because the formation temperature is only 40:31.630 --> 40:37.590 around 450 to 500 degree centigrade. You heat it above that and the complexes separate, 40:37.590 --> 40:44.590 it dissolves and then, when you cool it down, see, a wafer is going to cool much faster 40:46.070 --> 40:52.510 than the entire single crystal. It has got a much smaller thermal mass, it is going to 40:52.510 --> 40:58.330 cool much faster. So, when you are cooling down the wafer, the complexes have less time 40:58.330 --> 41:03.770 to form. Therefore, their concentration is going to be reduced. It is much easier to 41:03.770 --> 41:10.770 cool down a wafer than cooling down the entire large single crystal. So, this is a common 41:11.780 --> 41:18.780 practice in order to reduce the donor complexes due to oxygen is after the crystal is grown, 41:20.020 --> 41:27.020 the wafer slices are cut, do a thermal treatment on these wafers; heat them up and then cool 41:27.130 --> 41:32.200 them down, so that the complexes are dissolved at the high temperature and they do not have 41:32.200 --> 41:36.320 sufficient time to form back when the wafer cools quickly. 41:36.320 --> 41:43.320 This is one effect of oxygen. Remember, this is only the 5% of oxygen that is not there 41:47.170 --> 41:54.170 in the interstitial site. 95% of the oxygen that is incorporated, that is incorporated 41:54.670 --> 42:01.670 in the interstitial sites. So, these oxygen in the interstitial site actually is, you 42:04.110 --> 42:11.110 could say, beneficial to silicon. It improves the mechanical properties of silicon, it improves 42:26.080 --> 42:33.080 its yield strength. But, all this is true when I have relatively less amount of oxygen 42:55.820 --> 43:01.240 incorporated during crystal growth. That is when I am at the, towards the lower limit 43:01.240 --> 43:08.240 of the oxygen concentration, up to 6.4 into 10 power 17. 43:08.610 --> 43:15.610 If the oxygen concentration in silicon is greater than 6.4 into 10 power 17, then we 43:20.170 --> 43:27.170 come to the third problem and that is the problem of oxygen precipitate. Remember what 43:40.330 --> 43:47.330 we said about precipitate formation. The solubility is going to reduce with decrease in temperature. 43:49.940 --> 43:54.820 Therefore, when the crystal is being pulled down, if the oxygen concentration is greater 43:54.820 --> 44:01.820 than 6.4 into 10 power 17 per centimeter cube, this is going to be precipitated in silicon 44:04.640 --> 44:09.560 and once it precipitates, you have all kinds of problem, because this precipitates will 44:09.560 --> 44:16.560 give rise to compressive strength. That will stress the crystal and will start shooting 44:17.990 --> 44:22.510 off dislocations from that site. 44:22.510 --> 44:27.450 So, the precipitate formation, you know, generally it is highly undesirable, because it will 44:27.450 --> 44:34.450 give rise to dislocations in the crystal. However, they can sometimes be used to our 44:35.440 --> 44:42.440 advantage. That is you know the precipitates will attract the metallic impurities. It can 44:45.260 --> 44:52.260 be made to act as a sink for metallic impurities. They are also called as the gettering centers, 44:57.910 --> 45:04.910 gettering. Only thing you have to make sure is that these gettering centers are not coming 45:16.430 --> 45:21.680 in the active region. That is this is not where your devices are found. If they are 45:21.680 --> 45:26.930 found lowered down in the bulk of the material, you do not mind, because there it is going 45:26.930 --> 45:33.170 to act as a sink for metallic impurities, leaving your active region free from metallic 45:33.170 --> 45:40.170 contamination. So, they can be used to your advantage, can be used as gettering center. 45:41.490 --> 45:48.490 So, oxygen concentration in the Czochralski grown crystal is quite a problem. It has three 45:53.490 --> 45:58.380 effects. Some of them are beneficial, some of them are not so. 45:58.380 --> 46:05.380 So, particularly if you are very keen on the performance of the device like for example, 46:06.100 --> 46:11.100 if you are making power devices where the break down voltage needs to be very high, 46:11.100 --> 46:17.940 the leakage voltage has to be very low, then this oxygen concentration in silicon may not 46:17.940 --> 46:24.940 be acceptable, because you know, dislocations are generally going to deteriorate the device 46:26.000 --> 46:31.700 performance. Particularly it is going to lower the breakdown voltage and it is going to increase 46:31.700 --> 46:38.700 the leakage. So, in that case we may have to resort to further processing, further refining 46:39.890 --> 46:46.890 in order to remove the oxygen from the Czochralski grown crystal. 46:49.680 --> 46:56.680 So, essentially if we try to sum up what we have done so far, as far as the crystal growth 47:00.680 --> 47:07.680 technique is concerned, the Bridgman technique is a simpler process. But, since during Bridgman, 47:08.110 --> 47:14.770 during Bridgman growth, the crystal is in contact with the boat and therefore is subjected 47:14.770 --> 47:21.770 to a lot of stress, there will be a lot of dislocations present in Bridgman grown crystal. 47:22.800 --> 47:29.800 In contrast, in Czochralski the crystal is not hampered by any confining surface. It 47:30.080 --> 47:37.080 is pulled out of the melt by the seed crystal. The crystal when it is growing is not constricted 47:37.740 --> 47:44.740 by any confining surface. Therefore, the amount of defects present in this crystal will be 47:45.750 --> 47:47.350 much less. 47:47.350 --> 47:54.350 However, because of the quartz crucible there will be some oxygen present in the silicon 47:55.420 --> 48:00.880 and the problem is more aggravated, because oxygen has a segregation coefficient greater 48:00.880 --> 48:07.880 than 1, so that it will preferentially come inside the silicon. This oxygen may cause 48:08.400 --> 48:15.190 some detrimental effects, may have some detrimental effects, in the final device performance, 48:15.190 --> 48:20.550 particularly in lowering down the break down voltage and increasing the leakage current. 48:20.550 --> 48:27.550 Therefore, further refining may be necessary if one is very, very particular about the 48:30.400 --> 48:37.400 device performance requirements. I will stop here today.