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MIT Virtual Source Model By Saurav Thakur Parameters on which MIT VS model depends β’ πΆππ₯ , ππ , πΏ, π£π ππ‘ , π, πΏ are physical parameters which are pretty much known although ππ is not very well defined so we use apparent mobility and π£π ππ‘ is also replaced by π£πππ in this model and hence little tweaking is done by parameters like π½ which is used for velocity tweaking due to ππ·π and πΌ which is introduce to account for the variation of ππ in subthreshold and above threshold as bands changes a little bit in both the regimes β’ We have Resistances too between extrinsic and intrinsic terminals and that too is included in this model Description of Charge model of MVS β’ When the size of the channel decreases to the order where 1D electrostatics canβt be easily applied there we use can this model with few parameters(most of them are physical) and we can model that problem too using familiar 1D electrostatics although with few tweaks β’ When size of transistor is reduced then πΌ = πππ£ here I changes due to Q being given by π = βπΆππ₯ (ππΊπ β ππ ) and as ππ is given by ππ = ππ0 β πΏππ·π where πΏ is DIBL. Velocity doesnβt depends on the size of the channel although it depends on ππ·π in this model which is semi-empirical relation with π½ parameter Description of Charge model of MVS β’ As metal contacts at the terminals introduce resistances hence the values of ππ·π is less than extrinsic applied voltage. This correction is included in this model. This tends to reduce the charges(as current or flux is reduced) although as no current is drawn by gate terminal so it doesnβt requires any correction β’ VS model is based on identifying the top of the barrier and there we are applying 1D electrostatics to determine the charge β’ Dependency of πππ with ππΊπ is exponential at low voltage(ππΊπ βͺ ππ ) and converts to linear at high voltage(ππΊπ β« ππ ) so an empirical relation can be formed MVS Model 2.0.0 β’ In this model we assume that Resistances arenβt constants and depend on πΌπ·π with a function given by πΉπ ππ‘ = 1 πΌπ 1β πΌππ ππ‘ π½ 1/π½ . This relation introduces the decrease of ππ as seen at high current. β’ In this model we also account for the sub bands and we subtract π10 from fermi level along with applied surface potential(to calculate the band gap) which is the first energy sub band in the conduction band. β’ We consider non parabolicity of conduction band in this model and account the DOS accordingly MVS Model 2.0.0 β’ The charge ππ₯0 is calculated by integrating DOS*fermi-dirac function from π10 β ππ to β(entire conduction band) β’ For small channel we 1have to1 consider1 quantum capacitance too while calculating Gate channel capacitance = + πΆππ πΆπππ πΆππ (π₯ππ£ ) β’ πΆπππ = π/π‘πππ and πΆππ π₯ππ£ = π/π₯ππ£ here π₯ππ£ is the separation between channel charge centroid and semiconductor-insulator interface β’ π₯ππ£ is given by empirical parameters and due to the above relations the surface potential is defined at centroid of the charge not at the interface as πΆππ value is now reduced due to quantum capacitance and to account for it we assume that the length is increased MVS Model 2.0.0 π β’ The charge ππ₯0 is given by β π£ ( 2 β π πΉπ + ππΉπ) here T is transmission, π‘ Fs is flux or current entering from source and Fd is flux from drain. These flux are dependent on πππ and πππ which accounts energy gaps at source and drain respectively β’ If we include 2D electrostatics then ππ is dependent on πΆπβππ (which is equal to πΆππ ), πΆπβππ , πΆπ βππ and ππ₯0
