In the previous lecture, we have derived a simple formula for the drain to source current in weak inversion and we have shown that this current is due to diffusion. The formula that we derived was as follows, Ids is given by W by L into average electron mobility at the surface multiplied by thermal voltage square into the depletion capacitance multiplied by exponential of VGS minus V dash T by NVT into 1 minus exponential of minus VDS by VT where the average surface mobility of electrons was given by this formula, okay. Let me show the structure and biasing arrangement so that we get the meanings of all the terms here, source, drain, this is the gate, you are applying a drain to bulk voltage, source to bulk voltage, gate to bulk voltage, this is the bulk which is grounded. In weak inversion regime, your depletion width is constant from source to drain. So, this term CD is the depletion capacitance where the potential drop is psi s naught and depletion width is XD. So, this CD is equal to epsilon s by XD and this is the potential psi s naught, okay, here across this. Now, the voltage VGS is the difference between VGB and VSB. The voltage VDS is the difference between VDB and VSB, okay and this is your inversion layer which is very weak, it is concentration of electrons inversion varies from source to drain, okay and the mobility of these electrons is this average surface, mobility of these electrons here is this average surface mobility, okay. In this lecture now let us derive the model for strong inversion that is VGB greater than VHB, okay. So, this is your IDS versus VGB in a semi-lock plot and this is VHB, okay. So, we are talking about this is the strong inversion region that is where we want to derive this current, this is on a lock scale. So, the step one of this derivation is as follows, approximate the surface potential base 3 by 2 power law model, given here as a surface potential based square law model. So, you are going to approximate the 3 by 2 power law model by a square law model. This is the milestone we want to achieve, we will discuss how to get this. What you find here is that this VFB has been replaced by VTB, this term remains as it is and these 2 terms have been reduced to this square law term and in addition of course some thing from here has gone into this brackets and therefore this VFB has become VTB. In step 2, so we are first laying out the milestones we will then do the detailed derivation. What we will do is we will replace psi S0 by the saturation value VSB plus phi T of the surface potential where phi T is twice 5 plus 6 VT and we will replace psi SL by VDB plus phi T for VDB less than VDB sat and by VDB sat plus phi T for VDB greater than VDB sat. So, that would be our square law model. Let us see how do we go about doing it. Now, the origin of the 3 by 2 power terms in this expression, this is the basic expression for the drift current in the surface potential based model. It is a square root term gamma square root psi S in this expression for QI. So, this formula, this inversion charge here has the following formula in the surface potential based model where you have a gamma square root psi S term. When you integrate this term in this expression, then you get the 3 by 2 power term. Hence, to get the square law model approximate the square root term by a linear function. This is our methodology. Let us look at that linear approximation. So, here we have sketched gamma into square root psi S as a function of psi S. The shape is nonlinear as shown here. Now, what is interesting however to note that if I take a segment of this nonlinear function, I could approximate this by a straight line. Now, in practice in a MOSFET, what would be the segment of interest? In MOSFET, at the source your surface potential is psi S0, at the drain your surface potential is psi SL. So, this is the regime of interest. Corresponding to psi S0, I have gamma square root psi S as gamma square root psi S0. Corresponding psi SL, I have gamma square root psi S as gamma square root psi SL. So, let us see what is the linear approximation we can do in this regime. So, the linear approximation we can write as follows. Gamma square root psi S minus gamma square root psi S0 by psi S minus psi S0 is given by this formula. Let us explain this formula. So, you take any point, any general point here. Then this is gamma square root psi S. Now, compare the value with this value here. This is gamma square root psi S0. So, we take this difference, that is this difference and divide it by psi S minus psi S0. This is psi S. So, psi S minus psi S0 is this difference. So, ratio. Now, this we can write as alpha minus 1. Like we defined a slope n or rather 1 by n for the psi S versus VGB plot in the linear portion. We are now defining a slope for gamma square root psi S versus psi S plot in the approximation of the linear function. So, this slope is same as the slope obtained using this triangle, using similar triangles. That is what is written here. Gamma square root psi S L minus gamma square root psi S0. That is this difference and denominator psi S L minus psi S0. That is this difference. So, we are defining it as alpha minus 1. Now, why do we call it alpha minus 1 and not alpha? We will find that if you call it alpha minus 1, the final expression will turn out to be simple. So, we can use this and write gamma square root psi S as shown here. So, you take this part equate it to alpha minus 1. What you get is this. Now, why have we given this? So, this tells you how you can actually evaluate alpha minus 1, okay, based on values of psi S L psi S0 and so on. So, that part we will see later. Now, if you substitute this expression for gamma square root psi S in the Q i as a function of psi S expression in the surface potential based model, that is this expression, you are replacing this gamma square root psi S by this entire quantity, okay. Then you will end up getting Q i psi S as minus of C ox into V GB minus V TB minus alpha into psi S minus psi S0. Let us see how we get that. So, this part gamma square root psi S is gamma square root psi S0.  So, alpha minus 1 can be written as alpha into psi S minus alpha into psi S0 minus psi S plus psi S0, okay. Now, you have a minus psi S term here. So, when I subtract this quantity, okay, from this, so this minus psi S term and this minus psi S term will cancel. So, this goes off. Alpha psi S term will however remain and that is why you are getting this alpha psi S here. Similarly, alpha psi S0 term will also remain and that is what you are getting here. What you are left with is psi S0 and this gamma square root psi S0 here, okay. You recognize that V FB plus psi S0 plus gamma square root psi S0 is nothing but this threshold voltage with respect to bulk, okay, V TB. So, that is how you are getting this expression. V TB is V FB plus phi T plus V SB plus gamma into square root phi T plus V SB. So, this is actually the so called psi S0. This is also the psi S0. So, let us put that expression here and create some space. You have to substitute this QI into this expression here and do the integration. Clearly now, we have only linear terms in psi S. So, it is a straightforward integration and you will end up getting V GB minus V TB into psi S L minus psi S0 because this is a constant. When you integrate with respect to psi S, you will get a psi S term and you take the limits, you will get this. Then take this alpha into psi S term, you will get a psi square by 2. When you take the limits, you will end up getting minus alpha by 2 into psi S L minus psi S0 whole square, okay. This is also straightforward, just integration of this. Let us put that expression here on the top and create some more space for further manipulation. As we have said in step 2, we replace psi S0 by its saturation value, V SB plus phi T. Psi S L by its saturation value is given here. I want to remind you about those saturation values. So, this is psi S versus V, this is saturation value. When I put V DB here, I get psi S L. Now, the exact saturation value do not know but very close to that, this value is actually V DB plus phi T. And if I replace this V DB by V SB, all that I have to do is replace this by V SB and this will be psi S0, okay. So, similarly you can talk about the other saturation values. Now, so when you do that, you are going to end, when you do that, you are going to end up with this expression for the square law model. What has happened is the V DB minus V SB has been put here as V DS, okay. And this term here is same as this term. Now, for V DS greater than V DS sat, you have to use the same expression. All that you do is replace V DS by V DS sat. That is what is written here. Now, let us create some further space so that we can manipulate this. What about the average value of electron surface mobility? That is given by this formula, which we have derived already in the context of surface potential based model. The one thing that you should do as a part of assignment is that show that this EY effective 0 for N plus polysilicon gate, okay, can be simplified to V GS plus V T by 6 T ox. So, this quantity if you replace by various expressions terms and then simplify, you can show that the inversion charge and depletion charge you put in terms of the biases. It will reduce to the simple formula. To give you some support or help, you should use this fact that for N plus poly gate, flat band voltage plus 5 T is much less than V T, okay. Flat band voltage plus 5 T is much less than V T. So, when you replace this by expression in terms of bias, you will get this term V F B plus 5 T and you will also have V T. So, you will neglect this term compared to V T. Now, why is V F B plus 5 T much less than V T? You will have to draw the energy band diagram, okay. There for N plus poly and P substrate. So, if this is your vacuum level, this is your gate and this is your substrate, P type substrate. So, your Fermi level in the P type substrate will be here and N plus poly gate, your Fermi level coincide with EC, sorry E F is equal to EC. This is your EC, this is EV and you will have to use this fact. So, this is your phi M S. This is the intrinsic level and this is phi F. So, you will have to use this band diagram, okay and then you can write the expression for V F B. So, your V F B is equal to phi M S minus Q F minus Q F by C ox. Now, in most MOSFETs, modern MOSFETs, Q F does not matter. So, you can take V F B as approximately phi M S. So, this is your phi M S and you will have to then show that if you take phi T, phi T is twice phi F plus 6 V T. So, these two quantities will be of opposite polarity. V F B is this because you are neglecting the Q F but it has a negative polarity because Fermi level in the metal is or poly is above the Fermi level in the semiconductor. This is your phi M, Q times phi M and this is your Q times phi S. So, phi M S is negative whereas phi T will be positive and almost of the same value as V F B. So, that is how this whole quantity will be much less than V T and you will also need to show that the V DS sat that is being used here. It will be obtained using this formula. It is a value of V DS when D I DS by D V DS goes to 0. So, differentiate this with respect to V DS and when you do that please remember that a V DS term comes in the average mobility expression also. So, not only that you have V DS here you will also have V DS in the denominator of this particular expression that is this. So, when you differentiate you take that into account. This is also an assignment you have to show this expression for V DS sat. Now, let us summarize the threshold voltage based model both for the diffusion component as well as the drift component. So, the diffusion component of the threshold based model is given by this formula where this V dash T is threshold voltage based on the twice phi F criterion. The drift model is however valid for V G S more than V H. The diffusion expression is valid for V G S less than V dash T. Now, note that V dash T and V H are different values ok. They are not the same values. So, there is a regime between V dash T and V H where you do not have any model here really ok. Now, I DS for drift is given by this formula which we just derived the square law formula. So, we have put that in the slide that this model leaves a gap in the moderate inversion range between V dash T and V H. Now, although the expression for V G S greater than V H works right down to V G S equal to V T its estimates are accurate only for V G S greater than V H. Now, this is important because you find that there is a V T here which is different from V dash T ok. So, we have said this expression is used for V G S greater than V H ok. Somebody may say, but here you have V T. So, actually you can use this V G S until V G S equal to V T and V T is less than V H. Let me show you those values or those partitions this V G S, this is V H, this is V dash T and this is V T ok. This is the strong inversion ok. This is weak inversion and this is moderate inversion. So, your V T lies here. So, what we are saying is that when you take your ID versus V G S graph. So, it goes like this and it goes like that. Now, when you take the square law segment here it will go like this. This we showed with a dash line. So, what we are saying here? What this statement is saying is this dash line exists for V G S greater than V T here. So, it will give you some value. This expression will give you some value even if you go below V H, but this current will be inaccurate. This is the current you will get instead of this current. To complete the model the V D S sat is given by this formula where this EC is the critical electric field for velocity saturation. For diffusion current here the average electron mobility for the surface is given by this formula and for the drift current it is given by this formula ok. So, this L into EC is same as this. Now, before proceeding further though we have not derived this expression for V D S sat let me give you a feel for this expression ok, because it is somewhat lengthy expression and it is very different from what you would have used in a first level course with the square law model. So, you might recall that you use the saturation drain to source voltage value as V G S minus V T ok. So, as compared to that what are the changes here? So, one thing is the V G S minus V T has been divided by alpha ok. And what is alpha? Alpha is the straight line approximation for the square root function right. So, this function goes like this and you are going to use it only between psi S naught and psi SL. So, here we will approximate it by straight line and the slope of the straight line is alpha minus 1. So, that is how you get this ok. So, you can find out the slope expression by taking value of psi SL psi S naught right and then taking the slope of this triangle ok. In addition to this division by alpha you have a factor 2 here and something coming in the denominator. Why is this occurring? Because we are using a velocity saturation model ok and in the velocity saturation expression you have the critical electric field for breakdown. So, let us try to check this expression for limiting cases. You know we have said whenever we get a complicated expression we should verify whether all the terms have been taken care of by using a simple test ok. See whether this expression reduces to the simpler expression that you are familiar with for some limiting cases. So, this factor 2 is coming because in the denominator you have this one and this other thing. Now, let us try to reduce this expression to the expression V G S minus V T for V D S sat you have under what condition this will reduce. So, first thing is you must remove the velocity saturation effect. How do you remove that? If I make my E C infinite this is your velocity versus field curve where this is your E C. So, if I make this E C very large then my curve will go on increasing linearly then there will be no velocity saturation. Now, you will recall that the formula V D S sat equal to V G S minus V T is obtained using the pinch off condition there was no velocity saturation there. So, if you remove the velocity saturation we should get that expression. So, the way to remove it is to put E C infinity when I put E C as infinity this whole quantity becomes 0 and you are left with just one here. So, this 1 plus 1 is 2 and this coming the denominator this 2 will cancel with this 2 you will get V G S minus V T by alpha. Now how do you remove alpha? So, what is alpha doing really? So, if you carefully see this the linear approximation of square root psi S versus psi S is nothing but physically it amounts to getting an approximate expression for the varying depletion width from source to drain. So, you are replacing this varying depletion width by a constant depletion width which is some sort of an average value from source to drain. So, how do you get that average value? So, this average value is more than the value at the source, but less than the value at the drain. So, this averaging is obtained by using this factor alpha.  So, if you use the depletion width to be constant equal to the value at the source then you get the V G S minus V T relation for V D S sat. You will recall that that square law model assume the depletion width to be constant from source to drain equal to the value at the source. So, if your depletion width is a little larger which is actually the correct thing to do right because the depletion width is increasing from source to drain then your value of the threshold voltage will reduce a little bit that is what this factor alpha is doing alpha is more than 1. So, if you want to set if you want to set the depletion width equal to the value at the source then you have to set alpha equal to 1 and then that is how you will get your first level course approximation for V D S sat. Now finally, L denotes that part of the source to drain channel over which the channel voltage V varies from VSB to V D B for V D B less than V D B sat and to V D B sat for V D B greater than V D B sat. Remaining part of the channel delta L near the drain accommodates the voltage variation from V D B sat to V D B. So, this interpretation of channel length is also very important is analogous to what we discussed in the surface potential based model. So, this is your picture in the MOSFET. So, what we are saying is that the channel voltage is VSB here and it would be V D B if your V D B is less than V D B sat at this point but if your V D B exceeds V D B sat then your V D B sat will come here and this point will be V D B. So, the difference between V D B and V D B sat will fall across this delta L and this is your L that is what we are saying here interpretation of channel length. So, with that we have completed our module on surface potential based and threshold based model expressions. So, let us do a summary of this module. So, we will summarize the module as follows. First we will list out the learning outcomes which we laid out at the beginning of this module. So, at the end of this module you should be able to explain the surface potential and threshold based solutions of the drain to source current as a function of gate bias, drain bias and source bias with respect to bulk. Explain where and how do the above solutions differ and estimate critical quantities associated with carrier concentration N and P, current densities J N and J P, electric field and potential. Then estimate quantities related to energy bands and finally current voltage characteristics. Let us compare the equations of the surface potential and threshold based models. Surface potential based models the key features are as follows. The IDS expression consists of an average mobility integral evaluated numerically. Please recall the average mobility integral okay. So, what was that? So, if you recall we said the average mobility at the surface is average of the reciprocal. So, you are taking 1 by mu NS and taking the average over the channel length 0 to L and then taking the reciprocal of this. So, this was possible, this integration was possible only numerically because mu NS depends on both vertical field as well as horizontal field. You have closed form function for psi S0, psi SL and VGB rather you have a closed form function. The next point is the drain current expression is a closed form function of surface potential at the source, surface potential at the drain and gate to bulk voltage which have square root linear and 3 by 2 power and square log terms of psi S0 and psi SL which are obtained by integrating the X dimensional current equation. So, you have the term square root psi S, you have the term psi S, you have the term psi S power 3 by 2 and you have psi S square that is what is meant here. Another feature of the model is that the IDS expression consists of implicit relations for surface potential at the source in terms of VGB and VSB and surface potential at the drain in terms of VGB and VDB. Giving a saturating behavior for psi S0 and psi SL as a function of VGB or VSB or VDB obtained from the bi-dimensional surface potential equation. Now, it is this saturating behavior of the psi S as a function of bias which gives you the saturating behavior for current as a function of voltage. So, what was the implicit relation? For psi S, let me write it here. So, psi S is VGB minus BFB minus gamma square root psi S plus VT exponential of psi S minus V plus twice phi F by VT. So, this is the implicit relation because psi S comes here on the left hand side, it comes on the right hand side at these two places. When you replace V by VDB, you get psi SL. When you replace V by VSB, you get psi S0, okay. Now, this has a saturating behavior. Finally, the channel end modulation region where GCF fails is represented by delta L. So, the IDS expression consists of a channel end modulation region, right. So, interpretation of the channel length is that is the region over which the surface potential varies up to the saturation value so that anything excess of that that is applied to the drain falls across delta L. The channel end region is the region where gradual channel approximation is varied. Now, compare these features with those of a threshold based model. One-to-one correspondence letter C, right. So, this expression consists of closed form average mobility expression. For the case of the surface potential based model, you had an average mobility expression which was evaluated numerically. Here you have a closed form expression. Then, your expression for IDS as a function of psi SO, psi SL and VGB, okay. That is split up into two parts. Exponential approximation for VGB less than V dash TB and square law approximation for VGB greater than VHB. So, one of the issues with this threshold based model is that there are several partitioning voltages, right. So, you can see here the V dash TB is one partitioning voltage, VHB is another partitioning voltage and so on. Compare this with the corresponding feature of the surface potential based model. That is this closed form function. So, IDS consists of closed form function of this thing but which consists of root, that is square root, linear 3 by 2 power and square law terms, okay. Whereas, here you have exponential approximation for VGB less than V dash TB and square law approximation for VGB greater than VHB. Now, as far as the surface potential expression is concerned, in surface potential based model, this was an implicit expression which you have to solve numerically. Whereas, here we have expressed psi SO and psi SL as linear function of VGB for VGB less than V dash TB and the psi SO is saturating to phi T plus VSB and psi SL saturates to phi T plus VDB when VDB is less than VDB SAT and it saturates to phi T plus VDB SAT for VDB greater than VDB SAT for VGB greater than VHB, okay. So, let me show this. So, psi S versus VGB. This is your flat band voltage. This is your behavior. So, what we are saying is we are approximating this behavior by a straight line here and a constant, okay. So, these constant values are psi S naught equal to phi T plus VSB if you are at the source and phi T plus VDB if you are at the drain and this is the linear function, okay for VGB less than V dash TB. So, here you are using a linear function. But beyond this, this VHB or VHB rather you are using the so called saturating function. So, this is a 2 piece model. In between however you have a problem because this is a moderate inversion region. Then your channel length modulation region is where the channel voltage exceeds VDB SAT. What is the difference between the two models in as far as the interpretation of channel length is concerned? In the surface potential base model, L denotes that part of the source to drain channel over which the gradual channel approximation is valid. Remaining part of the channel delta L near the drain accommodates the potential variation from psi SL to psi naught plus VDB where psi naught is the built in potential of the drain to bulk voltage. So, let us say this is your MOSFET. This is delta L. What we are saying here is variation of psi SL if you sketch here. So, it will be like this. So, this delta L portion. So, your psi S varies from psi S naught to psi SL over this channel. And from psi SL to this value is psi naught plus VDB when you apply VDB here. This falls across delta L. The corresponding picture in the kind of threshold base model is that L denotes that part of the source to drain channel over which channel voltage or quasi-formal level difference varies from VSB to VDB. So, in surface potential base model, the validity of gradual channel approximation is a criterion for the channel length. Whereas in the threshold base model, your channel voltage varies from VSB to VDB for VDB less than VDB SAT and when it is in saturation, it varies from VSB to VDB SAT for VDB greater than VDB SAT. So, all that will happen is that this psi S naught will be replaced by VSB, psi SL will be replaced by VDB SAT in the threshold base model. Remaining part of the channel delta L near the drain accommodates the voltage variation from VDB SAT to VDB. So, you will not have this psi naught term because in threshold base model, you are not considering voltages with respect to bulk but voltages with respect to source. Now, this lays the foundation for improving the model because we have said that this threshold base model does not have an expression for moderate inversion region whereas what do we want in practice when you want to simulate a circuit? A model that is suitable for circuit simulation is called compact model. We have explained these parts, we have explained this definition of the compact model clearly in one of the earlier modules. For most analog applications, the device is typically biased just above threshold that is for VGS greater than VT and less than VT plus 0.6 volts where the VT is approximately 0.4 volts. So, this is where you are biasing the model. Hence, the use of regional models is no longer justified. So, we cannot use the threshold base models that we discussed for this case. Let me explain this. If I take the ID S versus VGS on a linear scale, so what we are saying is this. Suppose this is your 0.4 volt threshold and you are going up to VT plus 0.6. So, 0.4 plus 0.6 may be here. This is 0.4 plus 0.6. It is about 1 volt. So, how will your ID VGS curve look like? So, it would look something like this. So, what we are saying is that there is a significant non-linear portion that you will have to model properly if you want to simulate your circuit accurately for this bias range. As against this, in olden days the same curve would look like this. Your bias VGS bias would have gone up to much higher voltages like 5 volts. This is VGS and your threshold voltage is one-fifth of this, say about 1 volt. This is 2.5 and you divide this into, so this is about 1 volt. So, in earlier days your curve IDS versus VGS curve would be something like this. So, you have a significant portion which is not non-linear and this non-linear portion here is reduced a lot as compared to the overall biasing range in this overall biasing range whereas because biases have reduced but threshold has not scaled down as much. So, here this maximum value has reduced from 5 to 1, but threshold voltage has not gone from 1 to 0.2. It has not reduced by a factor of 5. So, it has come down only to 0.4. So, that is why this non-linear regime is now significant. That is why we cannot use regional models. So, if I use a model such as saying IDS equal to 0 here and IDS varies in a straight line fraction, it would not work. You will miss this part. Whereas, olden days I could say this one segment and this another segment and still most of this regime I would be working the model would work very well. So, in the light of this the modeling goal is the following in compact modeling. You need a single expression description of ID from sub-threshold to strong inversion as well as from linear to saturation regions where which is C infinity continuous for all VGS, VDS and VBS bias conditions. And we need a similar expression for IB and IG. Finally, let us summarize at this end of this module the role of each of the approximations in the solution. So, so far we have considered what is the difference between the surface potential based model and threshold based model. We summarized all the features of the two models and then showed the differences. Since approximations are very important in device modeling, let us summarize the various approximations we have made in this MOSFET modeling and what were their roles. These approximations can be seen in the background of the basic equations for device analysis, the drift diffusion equations. So, you know that there are 6 equations, 2 current density equations, 2 continuity equations and 2 electrostatic equations. So, all the approximations we are discussing will pertain to those equations. Let us start with approximations related to current density. We assume J P Y and J N Y are 0. So, the Y direction is the vertical direction. This is Y and this is X. In the Y direction, whole and electron currents were 0. What did this approximations allow us to do? Now, first why did we make these approximations? Because we said we neglect the gate current and bulk current and there is an insulator. So, between gate and bulk, we assume no current can flow. Similarly, there is no bulk current also. We neglect leakage and all that. Now, these approximations allow us to express carrier concentrations P and N in the space charge expression of the Poisson's equation in terms of psi using the Boltzmann relations and they therefore helped us to get the Poisson Boltzmann equation. So, these exponential terms here are because of these approximations. The consequence of these approximations because this is where we are using the Boltzmann relation. I just want to point out here that when you want to derive this factor K, it is better to plot the N and P on a linear scale. So, K times P0 and N0 in exponential minus V by VTR values at the edge of the space charge layer. The above equation is written under gradual channel approximation and its integration gives you the total silicon charge Qs as a function of psi s and channel voltage. Very important approximation was pertinent to the continuity equation divergence of Jn is equal to 0. In other words, we assume the generation decombination and tunneling currents to be absent. Now, what do we achieve using this approximation? This leads to the simplification of the current Inx as a function of x. Now, what is Inx as a function of x? That is the electron current in the MOSFET in the x direction that is what this suffix x stands for and this current in general varies with x. However, because of divergence of Jn equal to 0 approximation, we could assume that this is constant along the channel equal to its terminal value that is we could use this expression. The negative sign being due to the flow of ideas in the negative x direction. While ideas is the terminal current which is positive, Inx flows from drain to source whereas your x axis is from source to drain. So, that is why that negative sign is there. Now, this approximation plus the charge sheet approximation leads you to the current equation given here. Then another important approximation we made is the gradual channel approximation. What did we achieve out of this? So, first let us state what this approximation is. So, it says dou square psi by dou x square is much less than dou square psi by dou y square. The variation of the potential along the channel is much more gradual than that in the perpendicular direction. So, x is along the channel is x and y is this from gate to bulk. So, we are saying that variations along the channel are much slower than variation in the y direction. Now, this is understandable because you see how much is the channel length. So, we have considered a structure of the MOSFET right in one of the earlier modules. So, you would recall channel length was of the order of about 30, 40 nanometers in our structure that we considered right. Modern MOSFETs have even shorter channel lengths. Anyway, let us look at that structure and get a feel for why the gradual channel approximation works. So, this distance from drain to source is about let us say 40 or 30 nanometers okay. Now, how much is oxide thickness? So, you will recall it was much smaller just a few nanometers right. In fact, today we are going down to as low as 1 nanometer right. So, in the vertical direction the distances are very small as compared to the horizontal directions, horizontal direction. But the applied voltage is of the same order between drain and source and between gate and bulk. So, which means the field in the vertical direction is going to be several times more than field in the horizontal direction because this drain to source distance is more than the gate to bulk distance okay. Now, this is the reason why variations in the horizontal direction are much slower than variations in the vertical direction because of this distance issue. Now, the gradual channel approximation can also be stated in terms of the electric field in which case dou Ex by dou X is much less than dou Ey by dou Y. The variation of the field along the channel is much more gradual than that in the perpendicular direction. What did we achieve out of this? The simplifies the two-dimensional Poisson's equation as dou square psi is replaced by del square psi is replaced by dou square psi by dou Y square only one term okay that is what we have achieved or it simplifies the Gauss law where divergence of is replaced by dou Ey by dou Y. Next directed variations are removed. Now it yields the silicon charge Qs as a function of psi s and channel voltage by integrating the Poisson Boltzmann equation that is where its utility lies the utility of the gradual channel approximation. Some more advantages of gradual channel approximation this is used extensively it allows us to write psi ox equal to minus of Qs x plus Qf by C ox okay using the one-dimensional capacitor formula. In the surface potential equation Vgb equal to psi ox plus psi s plus phi ms we neglected the poly potential drop even when the quantities in the equation vary with x. So the MOSFET is two-dimensional we are writing the oxide potential drop in terms of the one-dimensional capacitor formula which relates the potential to charge even though you have variation in the x direction or along the channel okay. So this is what is the advantage of gradual channel approximation and ultimately this yields Qs in terms of psi s in this formula which is then used in the current equation. Then let us look at the charge sheet approximation. The inversion charge Qi due to the distribution of electrons is compressed into a sheet or delta function at Y equal to 0 that is what this approximation means that is you are writing N of xy as Qix by Q into delta y where Qi of x is the integral of the distribution of electrons. So what this means is the following in your MOSFET your electron concentration in the y direction goes like this in the inversion layer. We are taking the area under this and putting this entire charge as a delta function at the interface right charge sheet that is this charge sheet approximation. The consequence of this is that various layers of Qi distribution over y experience the same values of mu n, E x and psi. This is the great simplification that results if your entire inversion charge is compressed in a sheet okay. Then the mobility, the exaggerated electric field and the potential psi right that is experienced by all the electrons would be the same whereas if you have a distribution something like this evidently your E x value at the interface and E x value little bit inside will not be the same. So different layers of inversion charge will experience different values of E x. Similarly different values of mobility also okay if the electron distribution is assumed to be you know over a distance. Now consequently the charge sheet approximation allows conversion of the equation for current density J N x which is in terms of the volume charge Q times N x okay as in this form. So this is your actual current density expression. So this gets converted into an equation for I N x in terms of the sheet charge. This is current density in terms of the volume distribution of charge. This is a more complicated situation. It is simplified to the current in terms of the sheet charge Q i okay that is the advantage of the charge sheet approximation and the same mobility value will be valid for all the inversion charge right whereas here you can see the mobility varies in x and y direction right and so different layers of electrons experience different mobilities. Another consequence of charge sheet approximation is that no potential drop across Q i because inversion charges compressed into a sheet and that is the entire potential size drops across the depletion charge. So the charge sheet approximation when combined with depletion approximation and gradual channel approximation allow us to write the formula for Q B which is given by this simply as shown here even when the quantities in the equation vary with x that is even when the quantities vary along the channel you are using the one-dimensional capacitor formula in the vertical direction to write the expression for Q B. This Q B formula allows us to derive a closed form relation for Q i in terms of psi s in the form shown here then we come to the depletion approximation. The space charge due to reduction in whole concentration that is the term Q times P minus N A on the right hand side of the Poisson equation or Goss law can be approximated as follows. This is the statement of the depletion approximation. What is the advantage of this approximation? This approximation plus the charge sheet approximation and the gradual channel approximation allow us to write the depletion charge in this way where you can see that we are assuming that the entire psi s is falling across the depletion charge though part of psi s in practice does fall across the inversion layer because inversion layer is compressed into a sheet so that is the charge sheet approximation. Therefore you are putting the entire psi s in the across Q B and that Q B you are not considering the mobile charge at all. You are only considering the ionized acceptor charge so that you can write it in this form. This Q B formula allows us to derive a closed form relation for Q I in terms of psi s. This was one of the major steps in MOS modeling right that is because we cannot evaluate Q I from the basic definition of integral of the distribution of electrons. We cannot get an analytical expression for Q I based on that basic definition of area under the electron distribution. Therefore we are writing that inversion charge as difference between the total silicon charge and the depletion charge which can individually be expressed in terms of simple expression of psi s. Now with that we have come to the end of this module.


The study found that the prevalence of episiotomy was 73.9 percent, which is much higher than the recommended rate of 10 percent set by the World Health Organization. Additionally, the study also revealed that perineal trauma was associated with factors such as age, parity, and birth weight. Furthermore, it was found that episiotomy was a risk factor for vaginal tear. Based on these results, we recommend further research to inform the development and implementation of restrictive episiotomy policies to reduce and prevent occurrences of perineal trauma.


Sometimes theorcistity is cruel and unfair to you. When they engage in wicked and immoral behaviour. In an attempt to hurt you or cause misfortune. The narcissist will usually do this in the discard phase. When they are preparing to discard you, why should you be careful with what you are sharing with the narcissist? You cannot confide in someone like that. a ddiddordeb i'r ddweud o gollun o'r ddweud o drefn i'r gael. Narcissaethau yn cyfrifio ar gyfer o'r ddweud. Ddod oedd yn cyfrifio o gael i'r ddweud. Mae'r ddweud yn edrych i ddweud a ddweud. Yn gwneud ar y ddweud o ddweud i ddweud o'r ddweud o'r ddweud. Ac mae'r ddweud o'r ddweud o'r ddweud. Mae'n ddweud o'r ddweud o'r ddweud. The make mole hills into mountains. When they see that you're doing well, they're never there to congratulate you or to give you praise. If you do one thing wrong, they will be there to give you their opinions. But you never see them when you're doing something well. It's only when you do something that's not good. That's the only time that you see them. ac mae'n gofynu ei wneud hynny yw'r rhaid. Byddwch yn hollu'n meddwl am yma. Rwy'r byd, ac yn ymddiwyll. Rwy'r byd yn cael ei ymddiwch i chi. Yma'n gwybod i'w gwneud yma yma o'r cyfle o'r gwestiynau. Rwy'r gwestiynau, rwy'n gwybod i chi. Rwy'r gwestiynau, rwy'n gwybod i chi. Rwy'r gwestiynau i chi. pan fwrdd tlu dod i ni'n ddweud i gael ei weld yn ddweud gyda gwas croelol. Mae yna ni'n ben bwysigio. Mae yna ni'n dweud eich lleolol, ond petrwch bod felly mae'n nhw ddweud yn ei ddweud. Mae maen nhw'n ddweud ymgy ролol, cael mae'r cyfnwysig o fewn iawn. Mae'r hynny, bod yna y gallu bod wedi'n gweithio'r hynny'n ddweud ar eich fetid. Mae bwysigio'r cydym yn ni'n gweithio'r cyfnwysgol o fewn. ..wyd gan rhaid e opod yr hyn sydd e'i gweinwysuüyoron. Ac yw'r rhaid i wonwyo ar y dyfodol cyflymol ar hynny. Er sefydlu iaeth ac yn ysgol ymweld a'r ddarparu... ..reinwys hefyd, i fi'n ynchydeg ar y ddesod. I baen i'n dweud y cyflenwyr nad yw'r ysgol ac rhaid i ni eu gwelio eich ffynol... ..er i ni'n dweud i'r dyfodol i mi. Mae hwnnw ysgol, ac i'n dweud i ni... .. Hollyf, ac rydw i ni'n dweud eu mynd i chi. ac mae'n gwybod i chi... Mae'n gwybod i chi ddweud ymlaen nhw... Mae'n gwybod i chi ddweud ymlaen nhw... Ond nifedwch yn ei ddweud. Dwi'n ddweud, mae'n ddweud a bwyl i chi ddweud. felly mae'n ddweud. Mae'n ddweud yn y ddweud. Mae'n ddweud yma i chi ddweud yma. Mae'r ddweud yn ddweud yma. Fel ydy'r gyfnod, dyf yn siŵn yn cael ei wneud. Dyf yn cael ei fawr ein fawr i chi. Roedd ydych chi'n gwiswma ar hyn am gwnod i chi o'n gwneud i chi. Rydw i'n ddim gyflaen. Cyflaen i chi ar gweithio i chi, ac roedd chi chi wedi gondol gwybod. Wahdwch chi'n rai'r gwmwysgol i chi'r lleig, ac yw'n siŵn ei gweithio i chi'n gwneud i chi o chwell pan-mapio. There's really nothing they won't do when they are planning to be cruel and unfair to you. They will side with people who are already an option to you. They will cooperate with them so that they can get to you. And they will already know all of the wicked and immoral things. Those are the people did to you. But they will still associate themselves with them. Because it's designed to hurt you. It's designed to show you that they don't care about what anyone did to you. They know what they're doing. They know the effect of what they do. They know that it is hurtful and unfair. But they will use these things to affect you. They will use it to make fun of you. And then they will come back to you the next day and apologise to you. Because they want to give you time to go through it on your own. They want you to soak in these feelings of hurt. They want to dismiss you as something unimportant. They want to dehumanise you. Because they get a kick out of it. They get off on your pain. They get off on your anger. They enjoy seeing people hurt. They enjoy making people feel less than human. They like to see people worrying about something that they caused. Because it makes them feel like they have power over that person. The more hurtful and unfair it is, the better. Because then it puts you in a state of shock. Where you can't believe that they would say or do something like that. It puts you in a state of confusion. They want to show you how far they're willing to go. Where you may be thinking that you could just move on. But then they come along and do all of these things to you. They try to break you down. Because they're very bitter and resentful people. So they will seek to harm you in return for their perceived injury. Which is why you need to monitor people. You need to check if they're really supporting you. Because narcissists can be very envious. They may desire to take something from you. And that's what fuels them to be that way. Because they may have been envious from the day they met you. They couldn't stand you. But they stayed with you because they believed they could get something from you. Which is why they eventually got what they wanted. And then they got themselves out of there. But they had to destroy everything in the process of doing that. It's done to put you in a state of shock. It's done to hurt you. To bring you down. And if someone is willing to go that far out of their way to hurt you. You shouldn't feel bad for them. You have to check that you have reliable and respectable people around you. People who have put in the work to earn that position in your life. People who have proved themselves with their actions. Rather than just their words. When you're involved in a difficult situation. Who is in it with you. Who's still by your side. Who's still supporting you and defending you. Because if a person goes that far to build you up. They're not going to destroy you. If they were the ones who built you. The narcissists will try to break you down. No matter what you do. They will try to destroy everything you have. Because they never invested anything into you. All they ever did was take from you. So they don't care if they ruin everything. Because they never supported you anyway. They were never on your side to begin with. Thank you for watching. I hope this video resonate with you. Please like, comment, share and subscribe. If you would like to donate. My PayPal link is in the video description. Coaching inquiries. You can email me at coaching.naugsurviver.co.uk. Thank you for watching and I'll talk to you soon.


Radioactive materials, called sources, have many beneficial uses for our society. To protect public health, they are used to sterilize medical supplies, kill harmful organisms in foods and spices, and sterilize harmful insects that could damage crops. In manufacturing, they are used in fixed gauges to measure a wide variety of processes, including maintaining the proper fill on your bottled water and soda. Other gauges are used to measure moisture and density of soil, metal, and concrete to ensure structural integrity of roads, buildings, and bridges. In medicine, sources are used to treat cancer and other diseases. They can also be used to detect smuggled contraband, including other radioactive materials. While radiation sources provide many benefits, they can be dangerous if not handled properly. The possibility that these materials could be used by terrorists to expose people to radiation or spread radioactive contamination with a dirty bomb is a national security concern. The Nuclear Regulatory Commission works with other federal agencies, state regulators, and international partners such as the UN's International Atomic Energy Agency to help ensure the safety and security of the most risk-significant radiation sources at home and abroad. First line of defense is licensing. The NRC and state governments license and regulate the use of radioactive materials. This oversight ensures that only qualified people use these materials for proper uses. Background checks confirm the trustworthiness and reliability of personnel granted access to the most risk-sensitive sources. Three web-based information platforms, the web-based licensing system, the license verification system, and the national source tracking system form an integrated source management portfolio. Together these systems help authorities know who has what sources and where. In the second line of defense, licensees are required to have security plans or procedures to detect, assess, and respond to unauthorized attempts to access radiation sources. They are required to have security barriers to discourage and prevent theft of devices that contain radioactive material. They must also coordinate with local law enforcement to ensure an adequate response should a security event occur. Finally, the NRC cooperates with other federal agencies and state partners to identify potential security threats. If the threat comes from mother nature such as a flood or hurricane, we check with licensees to ensure their radioactive materials remain secure. And when a large source is no longer used or needed, the NRC requires that the source be safely stored or disposed of. In many cases, the NRC has worked with the Department of Energy and state regulators to collect and dispose of radioactive material that is no longer in use. The NRC's security requirements for radioactive materials are consistent with international recommendations in the IAEA's Code of Conduct for the Safety and Security of Radioactive Sources. We work internationally through the IAEA to help other countries improve their security programs and prevent theft of radioactive material overseas that could pose a threat to the United States. Because ensuring that our society can benefit from radioactive materials safely and securely is a 24-7 responsibility and a worldwide mission.


one of the components of the section that I am actually not terribly familiar with. Okay, fair enough. Let's see, who else? The library may have an opinion on that. Sure. So first of all, I think with respect to red flag knowledge, I think the courts have interpreted it correctly. The office acknowledges that it's by changing the red flag knowledge standards as they're suggesting, it could very well require notice and stay down, i.e. filtering of some sort. So that would move towards an EU model that really would have very serious First Amendment issues. So this is an area where just utter changes could have, as you suggest, very serious unimportant consequences. And again, the report itself acknowledges that changing the red flag knowledge standards could very well lead to, as a practical matter, a filtering of requirements. For the bigger platforms, that's not a big problem. For the smaller platforms, that could be very serious issues. Certain libraries, if they needed to start doing that, that would be very costly. But also it could have various impacts on users. I see my time's up and I have a lot of other questions. I want to thank the Copyright Office for the work it's put in. And just note that I do think copyright modernization is going to advance the cause of compensation for artists. It's not going to solve all the problems, but it is going to be a huge help for artists and creators in getting paid for their work. And I will defer other questions to my written opportunity and thank each and every one of the witnesses for being with us today and sharing their perspective. I yield back.


Hi, everyone. I'm here with Nia from the podcast log off already She's known as queer money on Twitter and she is a real life economist And she's here to answer some of our burning questions about the economy currently and the current state that we're in Nia. Welcome to the show Yeah, it's it's good to talk to you again I was recently on log off already with Cole James Cash great show everyone. So definitely check that out Okay, so I really want to pick your brain about a lot of things that are being discussed But I don't necessarily feel like I'm qualified to talk about them So we've been hearing a lot about inflation and supply chain issues. So break it down for me What exactly is the cause of? Inflation currently because my understanding is that it is because of supply chain issues So can you kind of break that down and explain why that's the case? Sure. So, yeah You know, when we think about the supply chain, what is that exactly? Well supply chain is people ultimately and the issue of the supply chain is again people Then the problem right now is that You know, we have had this historic pandemic. That's really disrupted the way we do things It's disrupted the way we work and also it's really Put a lot of people in danger So a lot of these jobs are a lot more dangerous to do and a lot of people feel like they should be compensated better And that their working conditions are not good enough for them to do their jobs so You're seeing a lot more labor of militancy a lot more workers who are willing to Quit their jobs look for a better one try and bargain for better working conditions and for better wages and As a result, you're seeing the pushback You're seeing you know Management refusing to pay for those higher wages and refusing to spend on making these jobs safer so you're seeing increasing quits and labor stoppages, you know labor strikes You know earlier you mentioned that What why is it that these supply chains are only arising now? Supply chain issues. I mean and why did it take so long? Well Part of it is that it took a while to shift for consumption to shift in a way that really started to impact our Storage of things our storage of goods But a large part of it is also that when the pandemic hit there was a historic low in labor militancy There was a historic low in labor strikes the total work stoppages in 2020 I think was the third lowest on record and that's because you know People didn't have the ability to really do that at the time the economy was crashing Now as the economy is getting better as there's you know, we had those economic relief programs that held our economy together And caused really a historic recovery if you look at the charts, I can send you some charts to show actually This has been the fastest recovery and I don't know maybe since the 80s And the depth of the recession is so deep that To say that I actually understates how how good of a recovery it was so in 2021 as a result We're having more work stoppages than we've seen in decades We can say something Yeah, I wanted to ask You know, what is it about currently? Do you think that the pandemic fueled these work stoppages because you know I've talked about on the show the worker strikes. We see the Kellogg strike in the way that they're trying to bring in scabs and they're You know permanently laying off workers and then we saw strike tober What is it about right now? Is it the pandemic that it was kind of like the final Straw that broke the camel's back. What is it about this moment in your opinion? That has led to these historic work stoppages because I've never seen anything like this Yeah, I think it is basically the pandemic plus our actual You know decent economic response or stimulus response because Workers feel like they can do this sort of thing when they have at least a little bit of room economically, you know This this comes after decades though of just stagnant wages Worsening working conditions. So it really was like the the needle that broke the camel's back and set it all off Yeah, that's really interesting because This is something that I've been trying to figure out like why now of all times And you know, I I think about it not necessarily in economic terms but socially maybe it's the case that because Workers see other workers rising up and you know opting for unionization Maybe that's it, but I think that it's kind of like the culmination of a lot of different things in the pandemic Really being like the primary one What you mentioned the recovery effort Um Do you have any insight into the recovery effort? You know because of the pandemic the 2021 stimulus package and all the reforms and uh are not reforms that all the like stimulus bills passed in 2020 in comparison like with the 2008 economic crash because I feel like people till this day haven't fully recovered And there's an article that I believe david sirota wrote about this in jack been kind of explaining how everything still kind of goes back to 2008 and how it's still hurt people till this day like what's your insight on that? Yeah, that's that's pretty much it, you know our response to the greater session was pretty horrible um the obama stimulus The it was about half the size of what was recommended and even what was recommended in my opinion would probably have been a little bit too small um I can't remember who was I think was christina roemer who's in charge of that who basically she made came up the estimate and then once She was going to present to the obama. I think larry summers Forced her to just cut it in half. Um, of course Yeah, it's always it's always going to be larry. Come on larry summers. Motherfucker Great feeling of economics But yeah, so they they literally just cut it in half and It just did not fill the hole and it was a pretty conventional, uh, kanesian stimulus as well um, the crash we faced then is pretty different from the crash we faced the pandemic because you know, economic recessions aren't all the same that was a financial crisis and It was caused by the housing market. There are a lot of dynamics here that aren't Don't exactly line up with what happened with the pandemic but the pandemic response was just much better much more effective and It's it's funny because we actually, you know the early response was it was still pretty bad Because it was you know, it was just like a giveaway to corporations Right, it's a big businesses, but it still was structured in a way that was much better And what we saw was despite This historic crash really the the biggest crash of our lifetimes The property rate fell after the stimulus and Uh, if you look at household wealth for those at the bottom it grew by historic amounts. So it was Is great even though we did badly at it Yeah, yeah, so uh, here's what I wanted to ask you because you know, a lot of this, uh The recovery effort has led to people kind of realizing that You know, they're they're getting a bad deal. The pandemic has led to that as well Um, what do you say to people like Joe Manchin who have this idiotic argument that we've heard a thousand times About how you know right now of all times is really when you don't want to authorize Newspending because that's going to make matters even worse like how do you respond to that because I think that's probably the predominant mindset I'm not sure if you'd agree with that but in dc at least like that's like the main mindset Uh, how do you respond to that and how do we shift away from this? Mindset that it just feels like we're on loop and it's the same response To every single crisis and it's the wrong response. So like what's your take on that because it's driving me nuts Yeah, I mean Joe Manchin I It's hard for me to take him in good faith. I don't think that he would explain anything Yeah, right, right but basically the issue is that they have you know, this um The mainstream view of money basically that's Uh, there's this quantity quantity theory of money. I don't know if you've ever heard that term before I have I've not so that's like the mainstream view. Um, actually so Oh, I love this got like The mainstream view is this uh, yeah quantity theory. So mv equals p p y where m is money uh v is velocity and then So you have that and then p and y that's your price level times your uh output so Their idea is that this is how the economy works and I think this is wrong but I'm gonna explain it So like inflation is reflected by changes in the price level And output is total production the total production of goods and services in our economy Uh, velocity is this idea of like How much how many transactions occur in the economy and most mainstream models hold this constant And so what you have is then the money supply Um That can change based on government spending, right? And if the government just starts to spend more money then m goes up Right And but these have to hold constant. They have to hold equal So if this v is constant and m goes up and these are equal then this has something over here has to change and since Their idea is that if you spend money, there is no increase in output. That means an increase in prices It's like a mechanical relationship and this Doesn't make any sense. It's completely ridiculous and it's it's like most economists would not want to just Deride it like that because it's the mainstream theory, but the central bank of Both the united states and of europe has admitted that this is not a functioning theory of inflation. It makes no sense um this sort of Mechanical relationship. It's just There's no way to make sense of it in real life because imagine if the government went to We're simply to print dollars and spend them Covertly on some sort of projects somewhere They don't they don't tell anybody else about it This says that At least in the long run You know Prices would go up everywhere But how would anybody for stuff? How would anybody know? And secondly like What is the long run? Is it one year? Is it five years? Is it 10 years? Like This you don't really see this relationship if you try and look at the data. It doesn't hold up And part of that is that this assumption that if you spend more money The output doesn't increase so therefore Prices have to increase That doesn't make any sense because what are you spending the money on right? If the government is spending money on let's say like a program to house homeless people or To build infrastructure or all these other things It's not creating nothing. Right. Those are that that's output That those things have value So those things add value to the economy So you don't necessarily have to have an increase in prices even in the mainstream theory in the mainstream framework I I don't really subscribe to the mainstream view anyways. I follow mmt, which is modern monetary theory and Under modern monetary theory basically We disregard the idea that demand can drive inflation that all inflation comes down to supply to the actual constraints and constraints in the economy are our real resources so If you spend money to create something you're not getting fewer resources, right? I mean this goes back to this other idea that Resources are becoming that's a quote. I think from Fred Lee that Resources are not this static thing that we just have this. We don't just have a stock of resources resources Are created by by production, you know the inputs to all things are the outputs of something else If I You know want to write a paper An essay or something and I do it by hand. I need a pencil I need the paper Those are both the outputs of another form of production so And when I when I produce a paper it also creates some other, you know Some other product that people consume. So these things are all much more circular or much There's feedback loops you know, so Yeah, and when you explain this it it makes so much sense and it clicks in a way that makes me frustrated because Why has this mentality stayed the same? I mean, I I mean I could come, you know, it's kind of a rhetorical question, but you know We know this we we know the way that the economy functions We know that when you spend money it doesn't just vanish. We know that it goes back into the economy I mean if you spend money on working people They're not going to be like rich people and hoard that money put it in overseas bank accounts It goes right back in so it's really it's frustrating to me that this mentality hasn't shifted and as an economist Who and I'm also a huge fan of mmt And I think it just it clicks it makes sense You know, what is it for you anyways in your opinion that's keeping everyone in dc including a lot of Not necessarily progressives more but more liberal minded politicians in the democratic party who ostensibly Shouldn't subscribe to these, you know ask backwards austerity minded views of the world Like what is it in your opinion that keeps them stuck on this antiquated view of the economy? Well part of it is that they've been living in this world forever, you know Right, we've been indoctrinated to have this sort of tax to spend mentality pretty much our whole lives Even if you're not an economist, you've probably been exposed to that repeatedly through the news or Uh, even you know in books you read and even on the left or people ostensibly on the left they use rhetoric that reinforces this idea And you know, I have a lot of love for Bernie Sanders, but he does this often or he talks about You know taxing certain people to pay for certain things It sounds good But if you think of it that way that's the sort of frame your framework you're working in so you reinforce that view Now for other people who aren't doing it subconsciously and you know, they just are Corrupt basically they don't want to admit that that we could pay for all these things because they don't want to Yeah, yeah, you know, I noticed that like just to to kind of demonstrate how brainwashed we are as a society Um, you know, I noticed that too. I would always use that point imagine if we didn't spend the social money on the military We could take that and put those dollars towards, you know healthcare free education when in actuality, I mean Taxes don't fund spending I think that modern monetary theory has proven that and honestly one thing that I've noticed Is that it seems as if republicans when they're in power at least They kind of govern as modern monetary theorists and that they spend money, but they don't pay for it Um So there's this double standard and this is one thing that I think really makes it a greatest Whenever it comes to, you know, a social safety net program something that benefits people It's always how are we going to pay for that? We got, you know, we've got to balance the budget when it comes to Blowing people up in the middle east and north africa Not a peeve. I mean, I don't think I've heard a single person except for bernie sand or sarcastically asking How are we going to pay for that with this latest spending bill? Um, so how do we get out of this mindset? Yeah, because it's driving me nuts and I noticed that I'm part of the problem because I keep using the same rhetoric But again, like you said, like we're almost conditioned to it So it's hard to break out of the I we could use this money for that when it doesn't work that way in actuality like literally That's not how it works. So how do we get out of this mindset? That's a good question. I think spreading modern monetary theory to people Spreading these ideas is a big part of it challenging politicians And and news media and other people When they say things like that I think that's important. It's hard to say what will really break through to people ultimately, but I think A labor movement is absolutely necessary. We're already seeing that Breeda, you know build up um And that's because the labor movement will make demands that aren't going to be based on Politicians desires and you're going to have the ability to force those demands And once people see that like we can do this sort of thing On a small scale here and there they start to get a sense of what is more is possible Yeah Yeah, yeah, that perfectly said it's for the first time. I think in a really long time I feel a little bit of hope um, which is dangerous. I know because you know, it's america But uh, you know seeing the strike till we're seeing people workers for the first time Stand up it really is Great to see I mean I've worked at really shitty retailers like wal-mart and subway and the thought of unionization Was really difficult because when I worked at wal-mart, you know We were shown an anti-union propaganda video and I was triggered immensely by that and I I spoke to my co-workers about it I'm like, did you see the same union video and they didn't know what unions were So it really felt inconceivable to me that we'd be at this place currently where starbucks employees, for example Are forming unions and you know warehouse workers in alabama get a second vote, thankfully on Unionizing their amazon warehouse So it feels like there's been a little bit of a paradigm shift and maybe if things are going to change at the mentality will shift Perhaps this is the start of it But then again, there's this cynicism inside of me that makes me think This is america. So maybe in a year things will just go back to normal. What what's your take? Do you have any hope young to offer us? What's like the practical economic stone like cold view just the practical perspective like what do you think about all of this? Yeah, I'm pretty hopeful. I think that this strikes We've been seeing which I was reading off the timeline of them earlier just to myself and On wikipedia to the page here. There's just so many of them That that gives me a lot of hope My fear is that the political situation will turn south I worry about a civil war brewing at this point with I mean an increasing Fascist movement, you know, there's no other thing to call it. So It comes down to I guess if that is held off you know long enough for a labor movement to finally start affecting people's lives in a way that they They really feel and that can cause sort of a widespread calming effects You know, hopefully we can we can avoid that civil war, but Yeah, I am a bit fearful of that and more fearful fearful of the political situation than the economic one at this point Yeah, yeah, there's there's definitely reason to be fearful if only we had a single politician that was You know wanting to jump on this labor wave and compete with fascism Maybe I just think bernie should run a third time. I'm not sure but either way like it does it's nice to hear You know here an economist confirmed that the left has kind of been right all along and it's not like it's that Like I feel like when when you break it down like when you break out the whiteboard It's it's very easy to see why their worldview is flawed and it's just a matter of waking enough people up So, yeah, this is this is all very fascinating. Nia. Thank you so much before you go Can you please tell people where we can find you how we can support your work? Uh, yeah, my twitter is at queer underscore money And I also am on the log off already show on twitch, which is just twitch.tv slash log off already And um, that's the best way to support me. I don't have a patreon anymore. Just stopped using it. So I closed it down um Yeah, also check out money on the left. I've written an article for them at least one So it's it's a very good publication Excellent. Well, thank you so much. Nia. We'll be in touch You'll be my uh one of my go-to economic advisors here on the show because this stuff goes over my head But you break it down in a way that makes me understand it Which is very impressive because I'm not a numbers person. So thank you. I really appreciate it. Well, thank you Thank you for having me


The Southern Maine Conservation Collaborative is a new organization designed to increase effectiveness of its member organizations in Cumberland and York Counties. They recently held an event to illustrate the impact a working farm has on the environment and Roger Burley was there. This is Roger Burley at the Broadturn Farm in Scarborough. This is an event sponsored by the Southern Maine Conservation Collaborative, a new organization in its pilot year of 2012 drawing together now nine land conservation organizations in Cumberland and York Counties. We are witnessing and experiencing what a working farm does within the context of land preservation and land trust work. I'm now standing with Jeremy Winterstein of the Scarborough Land Trust and Jeremy is the vice chair of the Southern Maine Conservation Collaborative and so you're involved with this work and at least two levels but I suspect a whole lot more. So please tell us about this preservation project Jeremy. We're at Broadturn Farm right now and this is a 430 acre property owned by the Scarborough Land Trust. We bought it in 2004 with help from a lot of people and public agencies. The town of Scarborough through their land bond contributed to it. The land from Maine's future board contributed to it. The Maine Department of Agriculture and the U.S. Department of Agriculture and a lot of private donors contributed to this project. So we purchased it in 2004 and it's the land trust's biggest property. We've conserved about a thousand acres to date in Scarborough and we were founded in 1977 and it's just been a great, great project to the land trust to figure out how does the land trust own and manage a farm because our core competency is in protecting land and looking after trails and managing forests and things like that. We now have John Bliss and Stacy Brenner who were formerly a turkey hill farm in Cape Elizabeth and before that they were in Cumberland. They've been on the farm for over five years. We've recently signed a 30-year lease with John and Stacy which was a really big milestone for both us and John and Stacy. It gave us a, it gave both of us a long-term vision for the property or a long-term chance at the property. It gives John and Stacy as farm managers the opportunity to invest in the property, buy a tractor, invest in the irrigation, make the soils better, put money into the buildings and so for them to have a long-term lease has really been helpful. And for us, we couldn't ask for better farmers. They are really good members of the community, they're one of the most more well-respected young farmers in the state in the organic farming community and they're just great ambassadors for both land conservation and farming. Now I'm standing with Paul Austin for the Southern Maine Conservation Collaborative but Paul, you are the president of Scarborough Land Trust so tell me about your personal interest in making this a success, obviously it's a land trust coup but what are the challenges, what are the benefits, what excites you most about this? When this property was first purchased, the president of the Land Trust at the time called me one day and said, I think we could make this a real farm and I said in your dreams I had no dream at all that she could possibly find farmers to work on this and we had one false start with some farmers and now we've found I think almost the perfect farmers for this project. They're very community oriented, they're really great farmers, they're very smart businessmen and they're really nice people. I think we're fortunate that we're saving farm soil above anything. Once this was 200 houses it would never be a farm again, there's not a prayer. I think we're really fortunate that it didn't happen on this property but we've been involved with another small farm in Scarborough. I think we're really fortunate now to have Maine Farmland Trust because we're concerned about open space, saving land from development and they're concerned about farming so the combination of the two of us is perfect. There's a conservation easement on the land now or will be and in most ultimate terms if the farm drives up and disappears and everyone leaves the farm buildings ultimately nothing else can happen to this land beyond what the terms of the conservation easement are so that the soil will always be here. You buy this and you protect it and you have it forever and we're never going to have less people around here at least I'd be surprised if we do and there will always be more pressure and you know there needs to be a certain percentage of open space and I don't know what that is but I know that once it's gone it's gone probably forever.


You guys see it right there. Randall was my quarterback when I won the belt in Madden 17. Let's see how he does in Madden 22 Boys we got the new Randall cutting him you guys know he won me a belt He led my team back in Madden 17. So every time he comes out we got to try him I'd be lying to if I told you I wasn't disappointed that he's wearing number seven Which you wore in Minnesota, you know in Philadelphia Eagles to Jersey. I got hanging behind me over here He wore number 12. He was the ultimate weapon. He was Lamar before Lamar He was cam before cam. He was almost big before Vic, but pretty close. So he was great He was electrifying back in the late 80s early 90s for the Eagles Then went to Minnesota probably had his best passing years with Randy Moss and Chris Carter and the boys up there. So I Still think he should be in the 12 from the Eagles still should be in a eagle green But he's number seven. It looks a little awkward Especially in the usual it looks like Vic but not Vic it look He should be number 12 But let's take a look at my team boys if you guys want to watch me play live twitch.tv slash dub dot you guys know that link Is below check-in. Let me know you're from YouTube man. This is the team. I'm rocking right now 50 50 jets as you guys know from my team team video a couple videos ago If you missed that make sure you check that out why we're running jets and what we like about it but There you see him right there Randall cutting him and people ask me all the time What do you what do you put on them? What do you put on them? What do you put on those gunslinger? I don't know I mean Roaming might be cool right boys. I don't know. I'm not a big roaming guy. It might be great might be good I used it man 20. I think we're kind of people kind of stuck on it for man 20 This game is a man 20. I think it's a lot more pocket passing You don't really need to be running for your life all the time, but all I have one is gunslinger. You see him right there 94 speed Fastest quarter now. I don't know if he's the fastest in the game. Definitely the fastest gunslinger He's got that 92 throwing the pressure It comes down to do you want to spend another ap your salary cap on that gunslinger costs five for him? So, you know the biggest weakness of josh allen is the throwing the pressure So will Randall cutting him make every throw Yeah, so far. He's been really good the new car some people believe when the new quarterback comes out They patch the old ones. I don't believe that but Randall does look pretty geeked as you know, we have Alvin Kamara backfield master We got key Sean Johnson in the slot route tech and deep out elite Robbie Anderson as deep out elite and then Brandon Marshall has matchup nightmare. Does it work? It doesn't not work put it that way. It's he's been catching everything We got the new Kyle Pitts. We put deep out elite on him as well Deep out elite is glitched this year pretty much any pass over 20 yards. He's going to catch automatically So that's why we do that. You see him 94 speed. He's an absolute monster So you'll definitely be seeing him in action first as well And then we have one post up now. You guys know, I like two post-ups on my guards But right now because of the more ap de Randall cutting him We only got or we got one post up, which I I'm not in love with I'm not in love with it I do like two And part of me feels like if you don't have two why I might as well not have any But I've seen one post up on the center actually do a lot of work and do really well So that's why I have it. We'll see how it goes this week here big tournament this weekend So gotta get a little gotta figure out the team and exactly what we want to do But that's our offense defense Jet steam team. I gotta figure out who I want at corner right now I used The new Derwin James last night. You say he's on the bench actually But we have ed read Justin Simmons up top who's going to get replaced Let me know below. Who are you guys rocking at safety and corner? Who are you guys rocking? Ronnie lie at corner Nickerson doesn't play. He's my slot. I think we got Jamal Adams and cam chance their linebacker Abraham Jason Taylor and Lawrence Taylor. We're going to put it at the end So the D line is cool. The ed read is a lock Ronnie lot is a lock It's really just the other three guys or four guys. I have in the secondary Like I said, I have The new Derwin. I'm gonna try him out. He's got to be a beast, right? But Not in love with Justin Simmons not in love with Marcus may Perry Nickerson's ratings aren't good enough to play for real for other than slot So my secondary that's that's the biggest that's the biggest question mark going forward Like I said, we have the ultimate wild card tournament this weekend. So I got to figure out. Who's my secondary Who are you guys running in your secondary? Who do you got? I love ed read. I love Ronnie lot. Those two guys are studs Other than that, there's new certane comes out might try him and I do have a lot I do like safeties. I feel like they hit a little bit better I like if you're not playing man, why not have safeties, you know That's kind of how I feel. So that's something that keep my mind. I mean the certane is great. I'm sure you guys like jc horn Woodson and Haynes were always good and raiders theme team.  Like I said check in the twitch Let me know you're from youtube Um, we also made the Super Bowl as well. There's two games. Check them out boys.  What? What defense am I in now?  Was I in that the whole time?  There's no way you're that bad Pick pick.   We will love to know Good good work here. Good work. Good work.  Good play. I'll try to get a free first down right there Yo, derwin can bro cuz It ain't no way good playing punch him in the face. Come on man Derwin, these are your plays to make out here, man. Nobody fumbles, dude I've come to conclusion in this game. If you fumble you just you're unlucky Speaking of unlucky, can we get some pressure?  Oh, come on, man Sack him. Come on the Quinn and Williams.  Oh, good play You got no line abilities, bro. Maybe this is kind of Oh, there we go. Good. Jason Taylor. That's what I need you to do Oh pick. Oh my god. Like, what are you even throwing that for? Like, why even throw that pass? Oh, no way. I just gave that up. Oh my god Oh my god I just didn't believe it. I just didn't believe it. He had to was fourth down It's just a stoop. Everybody in the world kicks right there.   He's gonna eventually go right up the middle. That's my lurk That's actually a great pass. Come on, man. That can't be that many yards my quick snap verts here Oh, no way Simmons. You don't just get walked by like that.  I need one of these passes. Oh, Jesus Christ, dude Just hold on. We're going home, dude. All right. Now we go back to his struggle drive. Here we go All right, dude, three plays where it ends on Palamalu.  I don't know if he flips here How do you break that tackle? He might he might fake he might fake take that out on snap He's a crab So there's just no way he can just roll out so easily man god I blissed everybody to prevent that. I blissed that I should have just contained I blissed the extra person. I thought it would get it done, but it didn't play Bro, the amount of throwaways we have to get after the quarterback here boys Throw it in a blind hardflap, man 29 throws, dude Oh Too much too fast, huh? Would I go for two for two would be calling the game It would be the way to get the game go for two here That's nasty. I could do the way defense have been though the way we've been playing defense We get a stop eventually, right? We got to get a sack Intentional grounding somebody make a play I mean, we got to pick this off, please Oh, that's been a rough one here boys. It's been a rough one I mean just off his back foot just Just this is just jesus christ Oh my god cam and he just put your hands like Out of balance, you jeez. Let's go. It's been real. It's been real Sorry, you guys didn't get to watch me play offense too much this game Just pray that nothing bad happens Okay, Derwin his first pick of the day He had 33 completions Or 33 of the pass attempts quarterback comparison there boys, man. I am mine. Let's tell you play bad But super bowl with Randall Cunningham. Let's go dude. Jalen reyger.   It's your like fifth option It's irrelevant, but when he drops two two touchdowns to win the game. That's rough. That's rough And we couldn't match to that.  Oh my god, man. There's no way Hey Simmons might get cut out of that one. I thought he missed that throw up I can't give that up. What do I think of cutting him? He's good enough, man We run cover six the first play you nasty That's how we almost took it Almost P. I thank you ouch Let's go Kamara Good drive. Good drive. Good drive. How do I like the new quarterback? It seems pretty tough flip Wait, actually Good hit Jamal Pick. Oh, come on there. When I can't lie his corner played that I guess because I I backed him up He runs here. He runs here. I'm ready. I'm ready for the run ready for the run Oh Good job.  He's just like, I don't know. I explain it boys Boys we gotta get home Hmm good play good play good play. Oh kamara Yeah, nice noise that looked really nice right there boys Easy pickings. Let's go get up And this game right now cam and this game right now cam. Let's go Oh, that's a good tackle Randall Into the end zone man his first Super Bowl. Let's go, man. Is it worth spending AP? One more AP for might be Yeah, it's Josh Allen, but I thought Josh Allen is like I'm telling you Josh Allen's high key wash if that makes sense for real Dan is good. I ain't gonna doubt.  That's what you got to say noise to boys. What do you got post-ups here? What are these post-ups that I like I like that I like that call nothing open. Let's go. Let's go. Let's go Oh, he's getting cheated. I gotta pay attention Oh one second. Oh, come on man Almost got me almost got me right there. Can't lie almost got me almost got me Oh, that's just you don't see dots like that too often. You don't You don't see dots like that too often.  He's in trouble boys This is fourth and quit right here. Does this man have a dot for these situations? Oh, this is so bad. I'll have running backs wide open. How I mean, I ran cover six I didn't expect my deep half because my deep half went down and matched on an in route Which I mean which was it bagged it, but I didn't expect it. We just got blurred. Oh, do I have Omaha? Yeah, tell me it works. Okay Nice nice. I mean we gotta call bench. We gotta call this right Omaha in the Super Bowl Omaha in the Super Bowl Oh Nine for nine. Wow. Okay, put that guy. Okay. Okay. Make some adjustments. Okay Okay Freestyle guy. Oh, he got a lot of yellow zones If you got oh, I got the leg. That's why I hate this. Why I hate this All right. What's he got going on? All right. What are you doing? What are you doing the soft squat? Okay, put him okay Maned up there. Okay. Is he gonna yellow zone some more people again? Okay yellow zone Well, you put him in a deep. Okay. Okay. Let's go That's why they watch your boys. That's why you get Omaha.  You can't go out there putting flat putting Oh, that's gonna end the game right there. Oh, kiss him. Good night. I appreciate you It's a hell of a way to go out there in the Super Bowl GGs Super Bowl champion


We are now seeing upwards of 100,000 new COVID-19 cases per day, and it is the worst it's ever been. Contrary to what Donald Trump and the Republicans said, it's not going to go away after the election.  Like whoever thought that this worldwide pandemic would suddenly go away after the election. Like it's a worldwide conspiracy all to make Joe Biden look better and Donald Trump look worse. Like this type of thinking is idiotic, but nonetheless, it's getting worse. Contrary to, I hope, not popular belief, but contrary to what some imbeciles were saying. However, finally, we got a little bit of good news, a little bit of a glimmer of hope that maybe we're starting to see the light at the end of the tunnel, because vaccine trials are showing very promising results. So as Sam Meredith of CNBC reports, Pfizer and BioNTech announced Monday their coronavirus vaccine was more than 90% effective in preventing COVID-19 among those without evidence of prior infection, hailing the development as a great day for science and humanity. I think we can see the light at the end of the tunnel. Pfizer chairman and CEO Dr. Albert Borla told CNBC's Meg Terrell on Squawk Box. I believe this is likely the most significant medical advance in the last 100 years. If you count the impact this will have in public health, global economy. The announcement comes as drug makers and research centers scramble to deliver a safe and effective vaccine to help bring an end to the coronavirus pandemic that has claimed over 1.2 million lives worldwide. Scientists are hoping for a coronavirus vaccine that is at least 75% effective, while White House coronavirus advisor Dr. Anthony Fauci has said one that is 50 or 60% effective would be acceptable. Pfizer's results were based on the first interim efficacy analysis conducted by an external and independent data monitoring committee from the Phase 3 clinical study. The independent group of experts oversees US clinical trials to ensure the safety of participants. The analysis evaluated 94 confirmed COVID-19 infections among the trials, 43,538 participants. Pfizer and the United States pharmaceutical giants German BioNTech partners said the case split between vaccinated individuals and those who received a placebo indicated a vaccine efficacy rate of above 90% at seven days after the second dose. It means that protection from COVID-19 is achieved 28 days after the initial vaccination, which consists of a two-dose schedule. The final vaccine efficacy percentage may vary, however, as safety and additional data continue to be collected. So this is incredible news, obviously, really, really good news. And it comes at a time when we are seeing spikes in cases, more deaths, a thousand people dying per day, a thousand plus people dying per day. And we need some hope at this moment. The question, however, remains, how long will this immunity last? That is yet to be determined because we don't know. We don't have a long-term analysis of this vaccine. Another question is how long will it take until it's widely available and will it be affordable? These are all questions that are important because this will determine whether or not this virus or this vaccine, rather, is going to be able to effectively wipe out this virus. Now, in terms of the latter question, it does seem as if it will be affordable, at least for Americans, because as CNN's Caitlin Collins reports, Pfizer CEO Albert Borla tells Dr. Sanjaya Gupta, the vaccine will be available for free to all American citizens. Now, this is phenomenal news because the United States is the only developed country that does not have some sort of universal health care plan. However, when he says it's going to be free to all Americans, that worries me a little bit because I want a little bit more specificity. Is it going to just be free to all Americans or will it be free to everyone throughout the world? Because if it's only free to Americans, then we're not wiping out the virus because we're only as strong as our weakest link. So if you leave out a particular country, it's still going to be an issue. So there's a lot that we don't have answers to yet. All we know is that the preliminary results are everything that we'd hoped for better than what we'd hoped for, actually. Now, in terms of when this is going to become widely available, well, President-elect Joe Biden isn't as optimistic as I would have hoped at a COVID press briefing. He talked about this and claims that it's not actually going to be widely available until quite some time. It's clear that this vaccine, even if approved, will not be widely available for many months yet to come. The challenge before us right now is still immense and growing. And although we are not in office yet, I'm just laying out what we expect to do and hope can be done. Some of it between now and the time we were sworn in. But so the purpose of this is to let you know what we're going to do once sworn in. And so there's a need for bold action to fight this pandemic. We're still facing a very dark winter. There are now nearly 10 million COVID cases in the United States. Last week, we topped 120,000 new cases on multiple successive days. Infection rates are going up, hospitalizations are going up, deaths are going up. This crisis claimed nearly a thousand American lives a day. And nearly 240,000 deaths so far. Protecting the projections still indicate we could lose 200,000 more lives in the coming months before a vaccine can be made widely available. So we can't forego the important work that needs to be done between now and then to get our country through the worst wave yet in this pandemic. So he's correct that this isn't going to be widely available right away. First, it's going to be administered to people who are the most vulnerable individuals who are elderly with some sort of preexisting condition that is going to make the virus more deadly for them. Healthcare workers, first responders, they are all going to be the ones who get this vaccine first if this is in fact the candidate that we all go with throughout the world. But in terms of like when the average person can go out and get this vaccine, it's going to be a while, it's going to be months. And I'm not banking on anything before mid 2021. And I think that's kind of a more optimistic prediction. And I don't know, I'm not an expert. I'm just saying that it's going to take some time and we have to be cognizant of that fact. But still, it is important that we see a really promising vaccine that could be available. That's that's great news. And I think that we allow ourselves the opportunity to celebrate, be a little bit optimistic. Don't inject too much hope into your veins just yet, but acknowledge that this is some good news. The pandemic isn't going to be with us forever. And we're starting to see that there is a little bit of hope, a little bit of hope. Now, in that same press briefing, Joe Biden, I think, made the most important point when he said that right now, the best tool that we have to combat the spread of this virus is masks. And I hope that once he becomes president, more people are going to want to wear masks if we have someone who is, you know, in power, the most powerful person who's trying to reinforce the importance of masks. But who knows, we don't necessarily know about that. We already see Donald Trump basically make it seem as if the announcement of this vaccine trials results is political because it happened after the election. I mean, this is all to be expected. One thing that's interesting is Mike Pence basically broke his public silence after losing this election and tried to claim credit for this vaccine. Honestly, even though neither administration gets credit for this, because this isn't anything that they've done personally, part of me wants to let Mike Pence take credit for this, as word as that may sound, because what we're dealing with now is the situation where Trump supporters and Republicans may not feel inclined to take a vaccine that they think comes from Joe Biden, even if it does get FDA approval. So the way to get them to take this vaccine possibly is to get them to think that this is something that Trump delivered to them. If we can get them to think that, then maybe they'll be more inclined to take the vaccine. I don't know, but whatever is going to get them to take the vaccine, that's really important because we've talked through, you know, when is this going to be widely available? Additionally, how much will it cost? And these are all important questions, but another factor is the political factor, the social factor that we haven't even begin to contemplate. How many people are going to want to take this vaccine? That, again, is going to be key because if we have this vaccine that's highly effective available, even if it's cheap and widely available, if people don't take it, it's not going to do anything. So there's still a lot that we have to consider. There's a long road ahead of us and lots of destruction and deaths until we get to this point where we get this under control. But still, it's a tiny, tiny little glimmer of hope for now that we desperately need. And it's nice to feel a little bit of hope again, even if I am cautiously optimistic.