nnp:mosfet_in_2d
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nnp:mosfet_in_2d [2020/08/03 01:41] daryoush.nosraty-alamdary [Appendix: MOSFET] |
nnp:mosfet_in_2d [2020/08/03 14:53] daryoush.nosraty-alamdary [Comparison of Different Mobility Models] |
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| \end{equation} | \end{equation} | ||
| which would be straight line with respect to $V_{\rm DS}$, and $V_{\rm GS}$. | 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. | 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. | 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. | ||
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| </figure> | </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}$. | 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}$. | ||
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| + | 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 ===== | =====Channel Length Modulation and Pinch-Off Effect ===== | ||
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| <figure fig34> | <figure fig34> | ||
| - | {{ :nnp:modelocking.gif?550 |}} | + | {{ :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. ** |
| - | <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> | </caption> | ||
| </figure> | </figure> | ||
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| - | |||
| In the above input characteristics curve, however, the drift and diffusion parts are hard to distinguish from each other without the logarithmic scale. | In the above input characteristics curve, however, the drift and diffusion parts are hard to distinguish from each other without the logarithmic scale. | ||
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