Lecture 8 February 2 2001 EECS 105 Microelectronics Devices and Circuits Spring 2001 Andrew R Neureuther Topics F MOS threshold voltage Reading HS 3 7 3 9 Light on math of the MOS capacitance 3 9 2 Analog Integrated Circuits Overview and Circuit Value Added Version 2 5 01 MOS Details N d 10 20 N a 1017 n E gap 2 1 1V 550mV 2 1017 p 0 026V ln 10 10 420 mV VFB n p 550 420mV 970mV Analog Integrated Circuits Overview and Circuit Value Added MOS like Case Revisited Mobile Electrons Analog Integrated Circuits Overview and Circuit Value Added Charge MOS Prototype Equal area For charge neutrality Has both a boundary and a distributed charge density GATE Analog Integrated Circuits OXIDE SUBSTRATE Overview and Circuit Value Added MOS Case Depletion VGB 0 25V VFB 970 mV VGB VTn 0 6V n VGB 550 250 800 mV Discontinuity by factor of 3 9 11 7 Change in slope by factor of 3 9 11 7 Parabolic shape Xd increases as sqrt VB Analog Integrated Circuits Overview and Circuit Value Added MOS Cases Set by VGB Accumulation 0 x tox VGB VFB Thin layer of mobile holes VFB 970 mV Flatband 0 x tox VTn 0 6V VGB VFB No charge or electric field x x Depletion VTn VGB VFB Inversion 0 x tox Negative lattice charge 0 x tox x Analog Integrated Circuits Overview and Circuit Value Added VGB VTn Thin layer of mobile electrons xd max x MOS Case Inversion VGB VTn 0 6V Maximum bending of the potential is p as n x makes layer of mobile electrons s max p 420 mV x 1 5 V VT n n 1 V Vo x 500 m V VT n VF B p to x 2 p 0 84V 0 Mobile electrons Analog Integrated Circuits 500 m V Overview and Circuit Value Added Xd max p x V B max p 0 n ni MOS Case Flatband VGB VFB 0 x n p 970 mV No Charges x Eo x No E field No charges x 0 x No change in potential x Potential p 420 mV Analog Integrated Circuits Overview and Circuit Value Added MOS Case Accumulation x VGB VFB 970 mV QG accumulated holes t ox charge density x 0 QG E x tox electric field 0 x Mobile holes Eox QG ox x tox potential 0 x 250mV V G B n V GB VFB 500mV 750mV 1 0V 1 25V Analog Integrated Circuits E field is from right to left Overview and Circuit Value Added n VFB 550 970 420 mV MOS Case Inversion VGB VTn 0 6V Maximum bending of the potential is p as n x makes layer of mobile electrons s max p 420 mV x 1 5 V VT n n 1 V Vo x 500 m V VT n VF B p to x 2 p 0 84V 0 Mobile electrons Analog Integrated Circuits 500 m V Overview and Circuit Value Added Xd max p x V B max p 0 n ni Carrier Density vs Position x no x ni exp o x VTH 1 5 V p p ni2 Na n ni2 p ni2 p ni2 Na Na Lots of electrons VT n n 1 V s max p 420 mV Vo x 500 m V VT n VF B 0 n ni Reference level p p Na Xd max to x 0 500 m V n ni2 Na Analog Integrated Circuits Overview and Circuit Value Added x V B max p Gate Charge vs Gate Voltage Accumulation Depletion Inversion Gate Charge Flatband 0 97V Threshold 0 6V Capacitance VGB Analog Integrated Circuits Overview and Circuit Value Added Threshold Voltage VTn VTn VFB 1 2 p Cox Start from no charge Make mobile electron density equal hole density in substrate VFB n p C ox s t ox Analog Integrated Circuits 2q s N A 2 p Account for extra potential due to E field across oxide that terminates on lattice charge QB max qN a xd max 2q s N A 2 p Overview and Circuit Value Added QB max is Boron lattice charge and is negative NMOS Example QB max 2q s N a 2 p Example pp 139 Na 1017 tox 150A n 550 mV p 420 mV QB max 2 1 6 x10 19 11 7 8 85 x10 14 1017 0 84 1 67 x10 7 C cm 2 Cox Voxide 3 9 8 85x10 14 Fcm 1 150 x10 8 cm1 2 3x10 7 Fcm 2 230aF m 2 1 67 x10 7 1 2q s N A 2 p 0 725V Cox 2 3 x10 7 Analog Integrated Circuits Overview and Circuit Value Added NMOS Example cont VTn 1 V FB 2 p Cox 2q s N A 2 p VTn 970mV 840mV 725mV 0 595V Any excess gate voltage i e voltage above VTn creates additional mobile electrons For each volt excess gate voltage QMobile 2 3 x10 7 Fcm 2 1V 2 3x10 7 C cm 2 This is 1 4x1012 electrons cm2 Analog Integrated Circuits Overview and Circuit Value Added n type substrate PMOS Analog Integrated Circuits Overview and Circuit Value Added Threshold Voltage VTp VTp VFB 1 2 n Cox 2q s N D 2 n Example pp 144 Nd 1017 tox 150A n 550 mV n 420 mV COX 2 3 x 10 7 F cm2 QB max 2q s N D 2 n 2 1 6 x10 19 11 7 8 85x10 14 1017 0 84 1 67 x10 7 C cm 2 VTp 550 420 2 420 Analog Integrated Circuits mV 1 695V 1 67 x10 7 10 3 2 3x10 7 Overview and Circuit Value Added
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