Fundamentals-of-Microelectronics-Behzad-Razavi.pdf

Is doubled it is as if two transistors carrying equal

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is doubled, it is as if two transistors carrying equal currents are placed in parallel, thereby dou- bling the transconductance. The reader can show that this trend applies to any type of transistor. There is some resemblance between the second column and the behavior of . If the bipolar transistor width is increased while remains constant, then both and increase linearly.
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 303 (1) Sec. 6.2 Operation of MOSFET 303 W L V TH V GS Constant Variable g m I D g m V TH V GS g m I D g m W L W L V TH V GS Variable Constant g m g m W L W L V TH V GS Variable Constant V TH V GS 1 Table 6.1 Various dependencies of . V V DS GS V DS V GS Figure 6.27 Equivalence of a wide MOSFET to two in parallel. Exercise How do and change if only and are doubled? 6.2.5 Velocity Saturation Recall from Section 2.1.3 that at high electric fields, carrier mobility degrades, eventually lead- ing to a constant velocity. Owing to their very short channels (e.g., 0.1 m), modern MOS devices experience velocity saturation even with drain-source voltages as low as 1 V. As a result, the I/V characteristics no longer follow the square-law behavior. Let us examine the derivations in Section 6.2.2 under velocity saturation conditions. Denoting the saturated velocity by , we have (6.48) (6.49) Interestingly, now exhibits a linear dependence on and no dependence on . This section can be skipped in a first reading. Of course, if is increased substantially, while remains constant, then the device experiences less velocity saturation and (6.49) is not accurate.
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 304 (1) 304 Chap. 6 Physics of MOS Transistors We also recognize that (6.50) (6.51) a quantity independent of and . 6.2.6 Other Second-Order Effects Body Effect In our study of MOSFETs, we have assumed that both the source and the sub- strate (also called the “bulk” or the “body”) are tied to ground. However, this condition need not hold in all circuits. For example, if the source terminal rises to a positive voltage while the substrate is at zero, then the source-substrate junction remains reverse-biased and the device still operates properly. Figure 6.28 illustrates this case. The source terminal is tied to a potential with respect to ground while the substrate is grounded through a contact. The dashed line added to the transistor symbol indicates the substrate terminal. We denote the voltage difference between the source and the substrate (the bulk) by . n + n + p substrate + p V G V G V S V D V D V S Substrate Contact Figure 6.28 Body effect. An interesting phenomenon occurs as the source-substrate potential difference departs from zero: the threshold voltage of the device changes . In particular, as the source becomes more positive with respect to the substrate, increases . Called “body effect,” this phenomenon is formulated as (6.52) where denotes the threshold voltage with (as studied earlier), and and are technology-dependent parameters having typical values of 0.4 and 0.4 V, respectively.
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