University:
Massachusetts Institute of Technology
Course:
6.012 | Microelectronic Devices and Circuits
Academic year:

2019
Views:

44

Pages:

6
Author:

Ismael Edwards

Recitation 10 MOSFET VI Characteristics II 6.012 Spring 2009 Recitation 10: MOSFET VI Characteristics Channel Length Modulation & Back Gate Eﬀect Yesterday we discussed two more aspects in MOSFET IV characteristics. • Channel length modulation • Backgate eﬀect Here is the n-MOS IV characteristic (ideal, no channel length modulation) What about the IV characteristic for a p-MOS? 1 Recitation 10 MOSFET VI Characteristics II Channel Length Modulation NMOS What happens when VDS = VGS − VT ? |Qn (L)| = Cox (VGS − VDS − VT ) = 0 IDS = w μn Cox (VGS − VT )2 2L L ↓ IDS ↑ PMOS When VSD = VSG + VTp , |Qp (L)| = Cox (VSG − VSD + VTp ) = 0 2 6.012 Spring 2009 Recitation 10 MOSFET VI Characteristics II 6.012 Spring 2009 As a result, To model it, we have: ID (or − IDp e.g. λ = w μn Cox (VGS − VT )2 (1 + λVDS ) 2L w μp Cox (VSG + VTp )2 (1 + λVSD )) 2L 0.1 μm −1 V L The ideal case is the ideal current source, now we have a current source with some internal resistance (will talk about this later). Note: pinch-oﬀ region does not impede current ﬂow near drain (high lateral E-ﬁeld near drain makes them go fast) 3 Recitation 10 MOSFET VI Characteristics II Backgate Eﬀect NMOS When VBS = 0, 1 2s qNa (−2φp ) Cox = −(φgate − φbody )) VT = VFB − 2φp + (VFB When VBS < 0, VT (VBS ) = VFB − 2φp + 1 Cox 2s qNa (−2φp − VBS ) Backgate eﬀect parameter: 1 2s qNa Cox VT (VBS ) = VTO + γ( −2φp − VBS − −2φp ) γ = PMOS When VBS = 0, VTp (VFB 1 2s qNd (+2φn ) Cox = −(φgate − φbody )) = VFB − 2φn − When VSB < 0, or VBS > 0 VTp (VSB ) = VFB − 2φn − 1 2s qNd (2φn − VSB ) Cox 1 2s qNd Cox VTp (VSB ) = VTpo − γ( 2φn − VSB − 2 φn ) γ = 4 6.012 Spring 2009 Recitation 10 MOSFET VI Characteristics II 6.012 Spring 2009 Exercise NMOS, channel doping Na = 1017 cm−3 VGS vary from 0 → 5 V, VBS = 0, −5 V. VTn = 10 V when VBS = 0; VTn = 2 V when VBS = −5 V. What is γn ? What is Cox ? γn = VTn (VBS ) = 2V = Cox = = 1 2s qNa to ﬁnd γn , need to know Cox Cox VTno + γn ( −2φp − VBS − −2φp ) φp = −0.42 V √ √ 1 1 V + γn ( 0.84 V + 0.5 V − 0.84 V) =⇒ γn = 0.67 V 2 1 1 2s qNa = 2 × 1times10−12 F/cm × 1.6 × 10−19 C × 1017 cm−3 1 γn 0.67 V 2 2.7 × 10−7 F/cm2 When VGS = 3 V, VDS = 0.1 V, VBS = 0 V, what is the channel electron charge density at 5 Recitation 10 MOSFET VI Characteristics II 6.012 Spring 2009 the drain? |Qn (L)| = Cox (VGS − VTno − VDS ) = 2.7 × 10−7 F/cm2 × (3 − 1 − 0.1) V = When VDS = 0.1 V, VGS = 3 V, VBS = −5 V, what is the channel electron charge density at the drain? |Qn (L)| = Cox (VGS − VTn (VBS ) − VDS ) = 6