L28: I-V Characteristics (Cont.): Channel-Length Modulation, Sub Threshold Regime

6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-1 Lecture 28 - The ”Long” Metal-Oxide-Semiconductor Field-Effect Transistor (cont.) April 18, 2007 Contents: 1. Second-order and non-ideal effects Reading assignment: del Alamo, Ch. 9, §9.7 Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-2 Key questions • The potential of the inversion layer increases along the channel. This should change the local threshold voltage. Does this affect the I-V characteristics of the MOSFET? • What happens to MOSFET I-V characteristics if we apply a bias to the body with respect to the source? Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-3 1. Second-order and non-ideal effects in MOSFETs Introduce four significant refinements to model: • Body effect (impact of y-dependence of VT ) • Back bias (impact of VBS ) • Channel length modulation (impact of VDS > VDSsat ) • Subthreshold regime (channel conduction for VGS < VT ) Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-4 � Body effect In a MOSFET biased in linear or saturation regimes, channel voltage V (y) depends on position: ⇒ voltage difference between channel and body V (y) ⇒ VT (y) (increases along y) V VDS VDSVT ID G n+ S 0 D n+ L 0 y n+ inversion� layer VBS=0 depletion� region VGS-V(y) p 0 L VGS y B VDS local gate� overdrive no body effect VT L 0 y VGS-V(y) VGS VDS local gate� overdrive with body effect Vth(y) VTo 0 L y Dependence of VT (y) further debiases transistor: ⇒ ID lower than ideal ⇒ VDSsat lower than ideal Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-5 Voltage dependence of VT : � � VT (V ) = VT o + γ( φsth + V − φsth) VT o is VT for VSB = 0. Charge control relation becomes: � � Qi = −Cox (VGS −V −VT ) = −Cox [VGS −V −VT o−γ( φsth + V − φsth)] Insert into current equation: � � dV dV Ie = W µe Qi = −W µe Cox [VGS −V −VT o−γ( φsth + V − φsth)] dy dy Integrate from y = 0 to y = L ⇒ MOSFET current in linear regime: � W 1 2 ID = µe Cox {(VGS −VT o+γ φsth− VDS )VDS − γ[(φsth+VDS )3/2 −(φsth)3/2 ]} L 2 3 Note new terms multiplied by γ ⇒ if γ → 0, body effect → 0. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-6 To get VDSsat , look at Qi at y = L: � � Qi(y = L) = −Cox [VGS −VDSsat −VT o−γ( φsth + VDSsat − φsth)] = 0 Solve for VDSsat : VDSsat � � γ2 � 4 � = VGS − VT o + γ φsth − [� 1 + 2 (VGS − VF B ) − 1] 2 γ � MOSFET saturated current: plug VDssat into current equation in linear regime: IDsat � W 1 = µe Cox {(VGS − VT o + γ φsth − VDSsat )VDSsat L 2 2 − γ[(φsth + VDSsat )3/2 − (φsth)3/2 ]} 3 Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-7 Three noticeable features: • for all values of VGS and VDS , body effect reduces ID • for given VGS , body effect reduces VDSsat • body effect goes away as transistor is turned off Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-8 Key observations for model simplification: • VDSssat dependence on VGS remains roughly linear: • IDsat dependence on VGS remains roughly quadratic: Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-9 Linearize dependence of VT on V (V � φsth): γ VT (V ) = VT o + γ( φsth + V − φsth) � VT o + √ V 2 φsth � � Solve again differential equation to get MOSFET current in linear regime: ID � W m µe Cox (VGS − VT o − VDS )VDS L 2 with: γ m=1+ √ >1 2 φsth VDSsat becomes: VDSsat � 1 (VGS − VT o) m Current in saturation regime: IDsat � W µe Cox (VGS − VT o)2 2mL Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-10 Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-11 m is body-effect coefficient (m > 1): γ m=1+ √ 2 φsth m has same dependences as γ: • xox ↓⇒ γ ↓⇒ m ↓ (less severe body effect) • NA ↑⇒ γ ↑⇒ m ↑ (more severe body effect) m and γ represent relative electrostatic influence of gate and body on inversion layer; if γ = 0 → m = 1 (negligible impact of body). In circuit CAD, m used as fitting parameter. Typically m ∼ 1.1−1.4. Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-12 � Back bias If bias applied to body with respect to source (VSB > 0): ⇒ VT shifts positive ⇒ for constant VGS and VDS , ID reduced Model in absence of body effect ⇒ just replace VT in first order model by: � � VT (VSB ) = VT o + γ( φsth + VSB − φsth) Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-13 Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-14 I-V characteristics of n-channel MOSFET (L = 1.5 µm) � Output characteristics (VGS = 0 − 3 V , ΔVGS = 0.5 V ): Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-15 � Transfer characteristics (VDS = 4 V ): Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-16 � Output characteristics vs. back bias (VSB = 0, 2 V ): Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-17 � Transfer characteristics vs. back bias (VDS = 4 V , VSB = 0− 2 V , ΔVSB = 0.5 V ): Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-18 � Backgate output characteristics (VSB = 0 − 3 V in 0.5 V incre­ ments, VGS = 1.5 V ): Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 28-19 Key conclusions • ”Body effect” arises from spatial dependence of VT : local gate overdrive reduced. • Main consequences of body effect: – ID lower than ideal, – VDSsat lower than ideal. • Simple formulation of body effect is fairly accurate: IDsat � W µe Cox (VGS − VT o)2 2mL with m ≥ 1. • m captures relative electrostatic influence of gate and body (want m → 1). • Application of back bias shifts VT positive and reduces ID . Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].