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--- nnp:mosfet_in_2d [2020/08/03 01:30]
daryoush.nosraty-alamdary [Appendix: MOSFET]
+++ nnp:mosfet_in_2d [2024/01/03 16:01]
stefan.birner removed
@@ Line 432: / Line 432: @@
 \end{equation}
 which would be straight line with respect to $V_{\rm DS}$, and $V_{\rm GS}$.
-===== Comparison of different mobility models =====
+===== Comparison of Different Mobility Models =====
 The effect of the correct mobility model for the simulations of such devices as MOSFETs cannot be overstated.
 It is an established fact, that the best mobility models used for simulating the current transport in the channel are those that are field dependent, and therefore are modified along the channel as a result of the perpendicular (and also parallel) field.
@@ Line 467: / Line 467: @@
 </figure>
 As the curves suggest, the difference is negligible for very high and very low gate voltages. The difference becomes significant only for $ 1.5 \leq V_{\rm GS} \leq 2.5 \ \mathrm{V}$.
+Furthermore, it is worth mentioning, that a good mobility model for the inversion layer in the MOSFET should have two field dependencies, one being the perpendicular field originating from the gate, and the other one the parallel field coming from the source-drain bias. The velocity saturation method, which has recently been implemented would only have one of these components, namely the parallel field dependency, and since it is still at the experimental level, we did not put any results simulated with that. However the implementing velocity saturation would have a distinguishable effect on the output characteristics of the short channel MOSFET.
 =====Channel Length Modulation and Pinch-Off Effect =====
@@ Line 578: / Line 580: @@
 The calculated mobility from the simulation is once again $933 \ \rm cm^2/Vs$ in the substrate, however it is $576  \ \rm cm^2/Vs$ at $y=0$ coordinate.
 ===== Appendix: MOSFET =====
-In the last section we found out, from the comparison of the input characteristics at high drain-source voltage $V_{\rm DS} = 2 \ \rm V$, that the MOSFET device with a gate length of smaller than $L \leq 400 \ \rm nm$, would suffer from the punch-through effect. However, if we further shorten our gate length below $100 \ \rm nm$, the situation would even be worse. Namely the leakage current would be so high, that even at very low source-drain voltages $V_{\rm DS} = 0.2 \ \rm V$, the MOSFET would conduct, even at gate-voltages below the threshold voltage $V_{\rm GS} < V_{\rm Th}$, and therefore the switching capability of the MOSFET would be diminished and eliminated. Figure illustrates this phenomenon:
+In the last section we found out, from the comparison of the input characteristics at high drain-source voltage $V_{\rm DS} = 2 \ \rm V$, that the MOSFET device with a gate length of smaller than $L \leq 400 \ \rm nm$, would suffer from the punch-through effect. However, if we further shorten our gate length below $100 \ \rm nm$, the situation would even be worse. Namely the leakage current would be so high, that even at very low source-drain voltages $V_{\rm DS} = 0.2 \ \rm V$, the MOSFET would conduct, even at gate-voltages below the threshold voltage $V_{\rm GS} < V_{\rm Th}$, and therefore the switching capability of the MOSFET would be diminished and eliminated. Figure {{ref>fig32}} illustrates this phenomenon:
-<figure fig7>
+<figure fig32>
 {{ :nnp:mosfet_extreme-short-channel-leakage_input-char.png?550 |}}
 <caption> ** The comparison of input characteristics of the N-Ch MOSFET calculated quantum mechanically with the Masetti mobility, showing the leakage current in the input characteristics. **
 </caption>
 </figure>
-As the above input characteristics cures show, for gate-length below $100 \ \rm nm$ there is basically no valid switching function possible, as the drift current has already started at $V_{\rm GS} = 0 \ \rm V$ for $L_G = 75 \ \rm nm$. This is basically to say that, at higher drain-source voltages the leakage curremt is actually more dominant to the channel inversion layer current, which can be switched on and off. It is also worth noting that the leakage current takes place inside the bulk of the MOSFET at the bottom of source drain doped region as figure shows:
+As the above input characteristics cures show, for gate-length below $100 \ \rm nm$ there is basically no valid switching function possible, as the drift current has already started at $V_{\rm GS} = 0 \ \rm V$ for $L_G = 75 \ \rm nm$. This is basically to say that, at higher drain-source voltages the leakage curremt is actually more dominant to the channel inversion layer current, which can be switched on and off. It is also worth noting that the leakage current takes place inside the bulk of the MOSFET at the bottom of source drain doped region as figure {{ref>fig33}} shows:
-<figure fig7>
+<figure fig33>
 {{ :nnp:mosfet-lg75nm-leakage.png?600 |}}
 <caption> ** The norm of the leakage current in $L_G = 75 \ \rm nm$ MOSFET, at zero gate-voltage $V_{GS}=0$, flowing within the bulk. **
@@ Line 614: / Line 616: @@
 </code>
-But to be able to see the quantum mechanical effects, lets us first take a look at the classical energy resolved densities in the channel and the source-drain doping regins (for that the //only_quantum_regions// flag has to be set to //no// in the //energy_resolved_density// group)
+But to be able to see the quantum mechanical effects, lets us first take a look at the classical energy resolved densities in the channel and the source-drain doping regions (for that the //only_quantum_regions// flag has to be set to //no// in the //energy_resolved_density// group). The classical energy resolved densities are shown in figure {{ref>fig34}}:
+<figure fig34>
-In the above input characteristics curve, however, the drift and diffusion parts are hard to distinguish from each other without the logarithmic scale.
+{{ :nnp:mosfet_class_erd.png?550 |}}<caption> ** The classical energy resolved density in the $L_{\rm G} = 25 \ \rm nm$ MOSFET at three different energy levels. **
-This could be enhanced using a ''shift'' parameter in the ohmic contact of the drain:
-<code>
- ohmic{
-      name = Drain_Contact
-      shift = 0.40  # [eV] used to increase (or decrease)
-                    #      the resistivity of the ohmic contact
-      bias = $SourceDrainVoltage
-   }
-</code>
-Basically the shift of the band structure using the shift parameter in the ohmic contact leads to the change of the resistivity of the ohmic contact (see  [[https://www.nextnano.de/nextnanoplus/software_documentation/input_file/contacts.htm|contacts{}]]).
-This has the advantage of bringing the I-V curve into a better form, distinguishing the drift and diffusion even without the logarithmic scale, and therefore consequently, making the determination of the threshold voltage $V_{\rm Th}$ easier.
-However the price to pay is that the output current will be significantly less in terms of [A/cm] (in our case close to 1 order of magnitude less).
-Without the shift in the drain contact the input I-V characteristics look somewhat differently, as shown in figure {{ref>fig7}}:
-<figure fig7>
-{{ :nnp:modelocking.gif?550 |}}
-<caption> ** The input characteristics of the N-Ch MOSFET calculated classically with the Masetti mobility, both in normal and logarithmic scales, without the effect of the shift of the ohmic drain contact. **
 </caption>
 </figure>
+Now let us look at the same energy resolved densities in the MOSFET source and drain region, obtained using the quantum mechanics alone:
+<figure fig35>
+{{ :nnp:mosfet_qm_erd_qm-confinement.png?580 |}}
+<caption> ** The quantum mechanical energy resolved density in the MOSFET source and drain regions, showing spacial quantum confinement at discrete energy levels. **
+</caption>
+</figure>
+In the above figure we can clearly see that compared to the classical density, the quantum mechanical density indicate quantum confinement in the source drain doping regions. Furthermore, as we shall see in figure {{ref>fig36}}, also the density in the inversion layer shows quantum confinement for different discrete energy levels:
+<figure fig36>
+{{ :nnp:mosfet-lg25nm_qm-confinement-in-channel_2d.png?550 |}}
+<caption> ** The quantum mechanical energy resolved density in the inversion layer of the MOSFET-channel, at two different energy levels, showing the standing wave pattern, which indicates quantum confinement. **
+</caption>
+</figure>
+As we can see there is clearly two different quantum confined modes in the inversion layer of the channel for this MOSFET.
-With regards to the issue of convergence for the output characteristics, relevant, since for the wrong set of parameters, the simulations may very well never converge and if so might take a significant amount of time.
-The key parameter to keep in mind is the ''alpha_fermi'' parameter in [[https://www.nextnano.com/nextnanoplus/software_documentation/input_file/run.htm | current-poisson{}]] calculations, which would decide the fate of the calculations.
+With regards to the issue of convergence for the output characteristics, the convergence parameters become very relevant, since for the wrong set of parameters, the simulations may very well never converge and if so might take a significant amount of time. The key parameter to keep in mind is the ''alpha_fermi'' parameter in [[https://www.nextnano.com/nextnanoplus/software_documentation/input_file/run.htm | current-poisson{}]] calculations, which would decide the fate of the calculations. This parameter needs to be chosen corrently, and also since it will be dynamically reduced, the //alpha_scale// parameter also need to be set appropriately, with a relatively small //alpha_iterations// (default is 1000, which is very high!!!), so that a quick adjustment can be achieved if the parameter is too large. One also needs to significantly increase the number of iterations from the default 100, to a few thousand. This so called under-relaxation parameter for the quasi-Fermi level is important due to the fact that it decides the volume of the search for the solutions.
-One also needs to significantly increase the number of iterations from the default 100, to a few thousand.
-This so called under-relaxation parameter for the quasi-Fermi level is important due to the fact that it decides the volume of the search for the solutions.
 If the solution somehow is located outside of this volume
-------------------
-f
---------------------
---------(In development)------

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