lecture_05_MOS_modeling_II

lecture_05_MOS_modeling_II - Handout #5 EE 214 Winter 2009...

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Unformatted text preview: Handout #5 EE 214 Winter 2009 Winter 2009 MOS Transistor Modeling for Analog Design Part II B. Murmann and B. A. Wooley Stanford University Corrections: 1/23/09: Fixed p2 expression on slide 32; see also text p. 641 Re-cap Subthreshold Operation Operation Transition to ? Strong Inversion What causes the discrepancy between 2/V OV and 0.18 m NMOS in strong inversion? B. A. Wooley, B. Murmann EE214 Winter 2008-09 2 strong inversion? Short Channel Effects Velocity saturation due to high lateral field Mobility degradation due to high vertical field V t dependence on channel length and width V t = f(V DS ) r o = f(V DS ) We will limit the discussion in EE214 to the first two aspects of the above list, with a focus on qualitative understanding B. A. Wooley, B. Murmann EE214 Winter 2008-09 3 Velocity Saturation (1) In the derivation of the square law model, it is assumed that the carrier velocity is proportional to the lateral E-field, v= E Unfortunately, the speed of carriers in silicon is limited At very high fields (high voltage drop across the conductive channel), the carrier velocity saturates Approximation: c c E (E) E f o r E E 1 d scl v E = = > > c 1 E + 1 2 d c scl v (E ) v = B. A. Wooley, B. Murmann EE214 Winter 2008-09 4 Velocity Saturation (2) It is important to distinguish various regions in the above plot Low field, the long channel equations still hold Moderate field, the long channel equations become somewhat inaccurate inaccurate Very high field across the conducting channel the velocity saturates completely and becomes essentially constant (v scl ) To get some feel for latter two cases, let's first estimate the E field using simple long channel physics In saturation, the lateral field across the channel is 6 OV V 200 E e.g. 1 11 10 0 18 mV V . L . m m = = B. A. Wooley, B. Murmann EE214 Winter 2008-09 5 Field Estimates In 0.18 m technology, we have for an NMOS device 5 1.73 10 v m V Therefore 6 scl c 2 v E 11 5 10 150 V s . cm m Vs = = 6 6 c 1 11 10 E 0 1 E 11 5 10 V . m . V . m = Therefore m This means that for V OV on the order of 0.2V, the carrier velocity is somewhat reduced, but the impairment is relatively small The situation changes when much larger V OV are applied, e.g. as the case in digital circuits B. A. Wooley, B. Murmann EE214 Winter 2008-09 6 Short Channel I D Equation A simple equation that captures the moderate deviation from the long channel drain current can be written as (see text) 2 1 1 2 1 D o x O V OV c W I C V L V E L + ( ) 1 2 c O V ox OV c O V E L V W C V L E L V + Think of this as a parallel combination" 6 E L 11 5 10 0 18 2 1 V m V = = Minimum-length NMOS c 6 c E L 11 5 10 0 18 2 1 E L 28 75 10 0 18 5 25 . . m . V m V . . m . V m = = = = Minimum length NMOS: Minimum-length PMOS: B. A. Wooley, B. Murmann B....
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lecture_05_MOS_modeling_II - Handout #5 EE 214 Winter 2009...

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