Dc model of a large uniformly doped bulk MOSFET - lecture 46
- 1. DC Model of a Large Uniformly Doped Bulk MOSFET-Lecture 46 M.GIRITHARAN ECE – 17D123
- 2. DC Model of a large uniformly doped bulk MOSFET : Qualitative Theory Spatial distribution of energy band with x and x, y Summary of the module
- 3. Plot of energy bands with x We sketch the energy bands versus x at y=0, in saturation and sub- threshold(bias points 2 and 3) 1. Non-Saturation 2. Saturation 3. Sub-Threshold
- 4. Energy bands versus x at y=0
- 5. Energy bands versus x at y=0 The bias point VGB greater than VFD but less than the threshold voltage. This corresponds to the Weak inversion condition. In this case, you will have a depletion region controlled by the gate and this is the edge of the depletion region shown by the red line. The potential drop in this direction is Psi S in other words Psi S is the potential of the surface with respect to bulk.
- 6. Energy bands versus x at y=0 the space charge region controlled by the drain near the interface this has also got expanded from the blue line to the red line. Now effect of that will be the potential drop across this depletion region controlled by the drain will be more. So that is what is shown here by the red line. the potential drop was shown by this blue line now the depletion region as expanded and this is the new conduction band edge.
- 7. Energy bands versus y near the channel mid-point that the quasi Fermi level for holes is located at the same place as the Efp corresponding to the case VDB = 0. the band diagram of a p n junction we first show the quasi Fermi levels for majority carriers. we add the minority carrier quasi Fermi level later. Now there is, however no such problem in showing in this Efp region because here the n+ region is grounded p region is grounded and therefore this particular junction is under equilibrium and therefore the Fermi level would continue to be the same throughout for this junction.
- 8. Energy bands versus x at y=0 we can conclude that from any point in the substrate when I move to the surface along this line the Efp will be constant. I consider the vertical line away somewhere here, here also when I move along this line perpendicular interface Efp should be constant. all points in this neutral p region the Fermi level for the hole should be at the same point. The split between Efp and Efn that is this distance is equal to the applied bias that is Q time VDB.
- 9. Energy bands versus x at y=0 let us change our bias. We will not go beyond threshold VGB greater than VTB And if you do that for the VDB condition we will be reaching saturation. The result of that would be expansion of the depletion width from the source to drain. because now once your VGB is greater than VTB you have a strong inversion reason here at the interface though inversion charge is varies from source to drain it decreases.
- 10. Energy bands versus x at y=0 1. Non-Saturation 2. Saturation 3. Sub-Threshold
- 11. Energy bands versus x at y=0 The variations in 𝜀c and 𝜀fn with x reveal thee importance of diffusion current in saturation(2) and sub-threshold(3) At point 3, 𝜀c flat over most of the channel ⟹ small drift ⟹ Jn due to diffuse rather than drift We sketched the energy bands versus x(at y=0) in saturation and sub- threshold to highlight the following 1. the contributions of drift and diffusion to Ids 2. the behaviors of n, p, Jn E, 𝜑 all in a diagram
- 12. Plot of E and 𝜑 with (x, y) We correlate the x-dimensional distributions of 𝜑, Ex and Ey over the surface y=0 to their y- dimensional distributions near the channel mid-point to highlight 1. inherent 2D nature of the MOSFET 2. worsening of GCA towards the drain
- 13. Plot of energy bands with (x, y) 2-D energy band diagram highlights the inherent 2D nature of the MOSFET. Now let us plot the energy bands with x, y. That is the 2 dimensional energy bands diagram. The 2 dimensional energy bands diagram highlights the inherent 2 dimensional nature of the MOSFET. Here is the device, source and drain L is the channel length, W is the width of the channel.
- 14. Contd.. The source and bulk are shorted also they are grounded; you apply VGB to the gate with respect to the bulk and VDB to the drain with respect to bulk. Next direction is from source to drain along the interface y direction is perpendicular to the silicon-silicon dioxide interface. Now we are going to plot the energy levels E as a function of y and x. First, we identify the depletion regions controlled by their source and by their drain, then we sketch the quasi Fermi levels. In a 2 dimensional band diagram the quasi Fermi levels and other energy levels would be surfaces.
- 15. Variables, constants and parameters of the model
- 16. MOSFET Biasing The first important point to note in this module is that while the device is bias with respect to source in practical applications for device modelling purposes. it is more useful to consider the biasing arrangement with respect to the bulk. After we have derived the equations for this biasing arrangements in which we derive the expression for ID, IB as a function of VDB, VSB and VGB. we can then express the same model in terms of the voltage with respect to source using these equalities.
- 17. MOSFET with VGB≠ 0, VSB =0 and VDB=0
- 18. Contd… The regions to be identified here are the depletion region which is between the Flat-band point and the point at which the surface concentrations of electrons which is = Ni, that is the depletion region. when you increase the VGB further your surface concentration of electrons at the interface becomes equal to the hole concentration in the bulk and this boundary now is a boundary of so called Weak inversion region. So between Ns = Ni and Ns = Pp0 you can have the weak inversion. Now at the point when inversion charge becomes equal to the bulk charge, this is the charge per unit area that is the area under the electron distribution
- 20. Factors responsible for creation and continuity of Jn, Jp and E the electric field is created by voltages applied to the gate, source and bulk and this electric field causes several things. one is an inversion layer is created near the interface and this inversion layer then transports current. The generation can really increase in the space charge region near the drain at the interface because of high electric fields here which causes impact ionization shown by this red lines.
- 21. Id – Vds characteristic of a large bulk MOSFET This was done to emphasis the sub- threshold region of operation where the saturation voltage is constant independent of the gate voltage and it is at value at approximately 3 times Vt. A log plot the current appears to increase linearly with VGS, in other words ID VGS is exponential. This is in the sub-threshold region.
- 22. Ib – Vgs characteristic of a large bulk MOSFET the IB VGS curves for a device operating saturation near the breakdown. So what we said is for VGS less than Vt there is no inversion charge and there is no IDS. Therefore there is really no subset current because subset current is the consequence of multiplication of the drain to source current because of impact ionization. So this current depends on 2 factors the amount of electric field available to the impact ionization.
- 23. Id – Vds characteristic of modern MOSFET the variations of the breakdown voltage as a function of VGS which follows from the IB. the ID VGS reason there is a slope of the characteristics these are short channel affects corresponding to small geometry devices. A modern MOSFET is a small geometric device, whereas we are considering large geometry device here.
- 25. Contd… The boundaries we considered were silicon-silicon dioxide interface that is boundary 1, boundary 2 silicon dioxide poly interface, boundary 3 between the device and the ambient, boundary 4 a device. The ambient there are 2 parts one is between silicon and the ambient and the other is between silicon dioxide and the ambient that is 4 and 5 is the electrodes. At these boundaries the conditions on these quantities are decided by the dielectric constant of silicon The dielectric constant through a walk side, dielectric constant of the ambient, fixed charge, surface recombination velocity, the potential applied at the electrodes and thermionic emission and tunnelling currents which are negligible perpendicular to the interfaces for the conditions considered.
- 26. Flow lines for Jn, Jp, E and equi- potential line for 𝜑
- 28. The Jnx that is the current density in the x direction as a function of y was something like this showing that the current is restricted to the inversion layer. In y direction, Jn and Jp are 0 that is current perpendicular to the interface that is 0. Then we emphasis the depletion approximation of the charge controlled by the gate, and the charge sheet approximation of the inversion layer. Similarly, you have depletion approximation of the charge controlled by the gate in the n+ poly region also.
- 35. Variables, constants and parameters of the model
- 36. Thank you…