1. EE466: VLSI Design Lecture 02 Non Ideal Effects in MOSFETs

2. Outline Junction Capacitances –Parasitic capacitances Velocity Saturation Channel length modulation Threshold Voltage –Body effect –Subthreshold conduction

3. Junction Capacitances The n + regions forms a number of planar pn-junctions with the surrounding p-type substrate numbered 1-5 on the diagram. Planar junctions 2, 3 and 4 are surrounded by the p + channel stop implant. Planar junction 1 is facing the channel while the bottom planar junction 5 is facing the p-type substrate with doping N A. The junction types will be n + /p, n + /p +, n + /p + n + /p + and n + /p.

4. Junction Capacitances The voltage dependent source-substrate and drain- substrate junction capacitances are due to depletion charge surrounding the source or drain diffusion regions embedded in the substrate. The source-substrate and drain-substrate junctions are reverse biased under normal operating conditions. The amount of junction capacitance is a function of applied terminal voltages

5. Junction Capacitances All junctions are assumed to be abrupt. Given that the depletion thickness is xd we can compute the depletion capacitance of a reverse biased abrupt pn-junction. Where NA and ND are the n- type and p-type doping densities respectively, V is the negative reverse bias voltage. The built-in junction potential is:

6. Junction Capacitances The junction is forward biased for a positive voltage V and reverse biased for a negative voltage V. The depletion region charge stored in this area in terms of x d is A stands for the junction area. The junction capacitance associated with the depletion region is defined as: If we differentiate the equation describing Q j with respect to the bias voltage we get C j.

7. Junction Capacitances We can write the junction capacitance If the zero bias capacitance is: in a more general form as m is the gradient coefficient and is 0.5 for abrupt junctions and 1/3 for linearly graded junction profiles The value of the junction capacitance ultimately depends on the external bias voltage applied across the pn- junction.

8. Junction Capacitances The sidewalls of a typical MOSFET source or drain diffusion region are surrounded by a p + channel stop implant having a higher doping density than the substrate doping density N A. The sidewall zero bias capacitance is C j0sw and will be different from the previously discussed junction capacitance. The zero-bias capacitance per unit area can be found as follows: Where N A(sw) is the sidewall doping density,  0(sw) is the built- in potential of the sidewall junctions. All sidewalls in a typical diffusion structure have approximately the same junction depth x j. The zero bias sidewall junction capacitance per unit length is:

9. MOS Capcitances Beyond the steady state behavior of the MOS transistor. In order to examine the transient (AC) response of MOSFETs the digital circuits consisting of MOSFETs we have to determine the nature and amount of parasitic capacitances associated with the MOS transistor. On chip capacitances found on MOS circuits are in general complicated functions of the layout geometries and the manufacturing processes. Most of these capacitances are not lumped but distributed and their exact calculations would usually require complex three dimensional nonlinear charge- voltage models. A lumped representation of the capacitance can be used to analyze the dynamic transient behavior of the device. The capacitances can be classified as oxide related or junction capacitances and we will start the analysis with the oxide related capacitances.

10. MOS Capacitances These are C gs and C gd respectively. If both the source and drain regions have the same width (W), the overlap capacitance becomes: C gs =C ox WL D and C gd =C ox WL D. These overlap capacitances are voltage dependent. C gs, C gd and C gb are voltage dependent and distributed They result from the interaction between the gate voltage and the channel charge. C gb G D B S C db C gd C sb C gs Masks result in some regions having overlaps, for example the gate electrode overlaps both the source and drain regions at the edges. Two overlap capacitances arise as a result.

11. MOS Capacitance Model Simply viewed as parallel plate capacitor Gate-Oxide-Channel C = C g =  ox WL/t ox = C ox WL Define –Cpermicron = C ox L =  ox L/t ox

12. MOS Oxide Capacitances The gate-to-source capacitance is actually the gate-to-channel capacitance seen between the gate and the source terminals. The gate-to-drain capacitance is actually the gate-to-channel capacitance seen between the gate and the drain terminals. In Cut-off mode the surface is not inverted and there is no conducting channel linking the surface to the source and to the drain. The gate-to-source and gate-to- drain capacitances are both equal to zero (C gs =C gd =0). The gate-to-substrate capacitance can be approximated by: C gb =C ox WL In linear mode the inverted channel extends across the MOSFET between the source and drain. This conducting inversion layer on the surface effectively shields the substrate from the gate electric field making it C gb =0.

13. MOSFET Oxide Capacitance In linear mode the distributed gate-to-channel capacitance maybe viewed as being shared equally between the source and the drain leading to: C gs =C gd =0.5C ox WL If the MOSFET is operating in saturation mode the inversion layer on the surface does not extend to the drain, but is pinched off. The gate-to-drain capacitance in therefore zero (C gd =0). The source is however still linked to the conducting channel. It shields the gate from the channel leading to C gb of zero. The distributed gate-to-channel capacitance as seen between the gate and the source is approximated by: C gs  2/3C ox WL.

14. MOS Gate Capacitances CapCutoffLinearSaturation CgbC000 Cgs0C0/22/3C0 Cgd0C0/20 Cg=Cgs+Cgd+CgbC0 2/3C0

15. Velocity Saturation Ideal carrier velocity relation: – v = mE –E = Vds/L In reality velocity does not increase forever with applied field For high values of Applied field, E ~ 10000V/cm –v= mE/(1+E/Esat)

16. Velocity Saturation and Mobility Degradation Recall ideal current equation With velocity saturated at v=vsat

17. Velocity Saturated Current Modeling Cutoff –Ids = 0: Vgs<Vt Linear –Ids = IdsatVds/Vdsat: Vds<Vdsat Saturation –Ids = Idsat: Vds>Vdsat Modeling with empirical parameters –α between 2(ideal) to 1(compeletely velocity saturated

18. Velocity Saturation The critical E-field at which scattering effects occur depends on the doping levels and the vertical electric field applied. Velocity saturation effects are less pronounced in pMOS devices. By increasing V DS the electrical field in the channel ultimately reaches the critical value and the carriers at the drain become velocity saturated. Further increasing V DS does not result in increased I D. The current saturates at I DSAT The behavior of the MOS transistor is better understood by analysis of the I- V curves.