Looking at a variety of key power devices we'll start off with diodes. And first we'll compare the idealist diode versus a real diode. Under reverse bias when the voltage is less than 0, the idealized diode has absolutely no current. Whereas for any kind of voltage under forward bias for any given diode current, the voltage would be 0. The idealized diode is also assumed to have no resistance and no capacitance. In the case of a real diode as shown on the right we first of all do have a reverse bias current. So there will be a current as a functional voltage even when the diode is turned off. And then under forward bias, there is a certain on voltage before the current starts increasing. In the case of silicon we'll see that this is around 0.7 volt. Beyond that point as the current is increased even more, we find that there is a finite series resistance of this diode. And then finally we'll have to include the actual parallel capacitance as well as the transit and reverse recovery time of a diode. Let's now take a look at two different diode structures. Now, the diode is a two terminal device containing a positive terminal, the anodes and the negative terminal, the cathode. Here we are comparing p-n diode which is a bipolar device since it contains a p-n n region. As well as a Schottky diode which is a unipolar device since it only contains in this example n-type regions. An n-type region is a region where the current is carried by electrons. Whereas the p-type region, that's where the current is due to holes which are effectively missing electrons but acting as a positively charged particle when we apply a field. Taking a closer look at the p-n diode, we find that a typical construction is one where you have a heavily doped substrate which is labeled here as an n substrate with the back contact on the cathode side. Typically there is a low doped n-type region. And then I've shown here a p-type region inside of that n-type region where the region within the dotted box is the actual active device. Then part of the construction is one where we need to have a contact on the an anode side. And then what is shown also is a bond wire and a ball bond connecting the front of the diode. In the case of the Schottky diode, the structure is almost identical. We also have an n-type substrate, lower doped n-type region in order to ensure a high breakdown voltage. But then we simply have a Schottky metal making contact to the load up the n-type region and again, having a contact made with a bond wire. There is a small difference in the circuit symbol between the p-n and diode and the Schottky diode as you can see here in the case where you're assimilating this with spice or drawing it on a circuit diagram. Taking a first look at the IV characteristics. What is shown here is first of all the diode current on a linear scale in red, where you see that effectively, there is hardly any current to be seen under reverse bias. And then yes the current started rising quickly around 0.7 volt and then from there on becomes almost linearly indicating that there is a serious resistance. On a logarithmic scale which is shown here as the blue curve, we see that indeed there is a small but measurable reverse bias current. What is shown here is the absolute value of the current on a logarithmic scale, add 0 volts, the current becomes 0 as well which means the current dips down to minus infinity on a logarithmic scale. And we can see that under forward bias, the current is to first order exponentially increasing as a function of the applied voltage but then eventually flattens out due to the serious resistance. Let's now take a closer look at the circuit model that we'll be using. And that circuit model is then linked to also the SPICE model that we use for device simulation. Taking a look at the diode current first we find that the diode current is modeled as being exponentially dependent on the applied voltage divided by the thermal voltage and a factor theta which is referred to as an ideology factor. In order to satisfy the condition that the drain current is 0 at 0 volts, there is a -1 term which ensures that that is the case. This first term is referred to as the ideal diode current and the value of Vt which is the thermal voltage and equals kT over Q. Where k is the Boltzmann constant, T is the temperature and Q is the electronic charge, that thermal voltage equals at room temperature which I take here as being 300K = 25.86 millivolts. In addition to the current voltage relationship, we also have a capacitance of the diode which is identified based on the capacitance at 0 volts. And then separately the voltage dependence of the diode which then involves two more parameters, namely first of all the building potential which is related to the on voltage of the diet but not identical. And then a factor m the capacitance profile parameter which can take on values between two and three. The corresponding circuit diagram is one where I do have, then the diode with that particular relationship between current and voltage. In parallel with the junction capacitance, C sub j and then the combination with two in series with the series resistance R sub s. So that the external value VD would be the internal value visa bay plus the voltage drop across the series of resistance. Looking at the table on the right, we can now identify for each of the parameters in the model, the corresponding parameter of the SPICE model. And you can easily map them to each other. One distinction is that in this case they're shown as being all capitalized because SPICE does not distinguish between upper and lower case characters. And first of all we have the IS as being the ideal diode saturation current and and as being that ideality factor so thus being the series resistance. And then for the capacitance we have CJO the junction capacitance at zero bias within M the capacitance profile parameter that I've mentioned before as well as the building potential. In order to model the recombination current which is that second term of the current equation, we then identify the corresponding saturation current ISR and the corresponding ideality factor NR. And then finally in this simple model, I've also had the breakdown voltage, which is listed as a positive value even though it occurs under reverse bias. Here is then a first simulation example for diode and the intent here is to then generate the current voltage characteristics of a particular diode. It also means that if you take a diode from a certain manufacturer and use their circuit model for the diode, you can then visualize what the current versus voltage would look like for this particular device. In order to do so we have here a dc simulation statement .dc simulation inspires. Where we let the voltage V1 of the power source vary from -12 to 2 volt in steps of 10 millivolts. In addition, I also need a model for the diode which is specified here below with the dot model statement. Referring to this particular diode which is labeled as being diode whereas it still has a separate number of the diode as being D2 and then linked to the building spice model D for diodes in general. And you can see here, I have included the saturation current series of resistance. Incidentally the default value for the ideality factor would be 1. And then I have the breakdown voltage as you can see you're a positive number as well as the recommendation current saturation value of one nanoamp and then also a corresponding ideality factor in this case I've chosen 2. And then displaying the corresponding current and voltage on both the linear and logarithmic scale you can see them here. Where the difference being that the range and voltage on the left hand side is only from -1 to 1 volt. Where has been expanded on the right hand side so we can also see the corresponding breakdown behavior, where on a linear scale the red curve, the current then dips down. But we can see on a logarithmic scale that it then rapidly increases in magnitude and even would become comparable to the current under four bias. Let's now take a closer look at each of these regimes in more detail. First of all, we have the forward bias diode analysis, and there we can recognize as we look closer that indeed we recognize each of these exponential terms. One with an ideality approximately equal to one which refers to the ideal diode equation. And then we have one related to the recombination current. And as you will have to do in the assignment, as you identify two points on this graph. You can then draw a line the dotted line through these points and then find based on the intercept with the vertical axis, the corresponding saturation current. Whereas the slope would be linked to the ideality factor. So for an actual measurement, the ideality factor can be described based on the equation as being based on the log 10 of e, divided by the thermal voltage and the slope that we measure on a semi logarithmic graph. So the slope has units of volts per decade. We can then also rearrange this using the values for Vt and the logarithm of e and identify this as being about 60 millivolts per decade in the denominator whereas the numerator contains the measured slope in units of also volts per decade of current. And then looking on the linear scale, this is here the red curve fitting it to a straight line in the region where the diode is turned on. That would be linked to the change in voltage with current, in the case of a linear resistance, we end up with a straight line. Looking now at the reverse bias behavior, [COUGH] let's first take a look at the red curve which is on on a logarithmic scale, showing the magnitude of the diode current. Where we see that initially yes, there is some variation in the reverse bias current. But at the point where we reach breakdown, the current rapidly increases. And then eventually would saturate although that is based on whatever values are put into the model. Of course in the case where we have a series resistance, it would limit the current. In terms of power dissipation once you reach breakdown, the voltage will be larger in magnitude than 10 volt. And if the current indeed reaches a value around 10 amps that would be a high power dissipation of 100 Watts on advice which is to be avoided. Looking also at the blue curve which is the reverse bias current on a linear scale. And here we can see that it is a negative current as we apply a negative voltage. We find that initially that current indeed keeps increasing with the voltage and then rapidly increases at the point where breakdown occurs. And then finally let me talk about some of the LTSPICE detail that is going to be useful for the assignment. And I've shown it here for the Mac version because the Mac version doesn't readily give you a variety of choices but you kind of have to know where you need to go in order to find the corresponding item. The particular item I'm looking at here is to export the data. So once you've done a simulation, you then get the plot window where you can already plot a graph. But in order to get to numeric values, you need to export the data to an SQ file. So in order to do this on the Mac and it is very similar in the Windows environment, is that you first have to select the plot window and then identify the hammer icon as you click on this item here. You then get the window that I've shown here where you have to then select the data export tool and once you click on this button, you get a window where you can identify particular variables that you'd like to download into an SQ file. What you can see also here in this case that there is no model statement and this is a default diode. And the default for a saturation current is 10 to the -12 1 pickle amp. Whereas the ideality factor is one and then the defiled diode by itself does not have a series resistance, but there is a separate one included here as being one million. In order to then show the behavior that indeed the current is no longer exponentially dependent on voltage.
