Lecture 21 OUTLINE The MOS Capacitor Electrostatics Reading Course Reader Spring 2003 EE130 Lecture 21 Slide 1 MOS Capacitor Structure Typical MOS capacitors and transistors in ICs today employ MOS capacitor cross sectional view heavily doped polycrystalline Si poly Si film as the gateelectrode material GATE n type for n channel transistors NMOS p type for p channel transistors PMOS xox VG Si SiO2 as the gate dielectric band gap 9 eV r SiO2 3 9 Si as the semiconductor material p type for n channel transistors NMOS n type for p channel transistors PMOS Spring 2003 EE130 Lecture 21 Slide 2 1 Bulk Semiconductor Potential B q B Ei bulk E F p type Si kT B ln N A ni 0 q Ec EF n type Si kT B ln N D ni 0 q Spring 2003 EF q B Ei Ev Ec q B Ei Ev EE130 Lecture 21 Slide 3 MOS Equilibrium Energy Band Diagram Ef Ec 9eV P Silicon body SiO2 N polysilicon 3 1 eV 3 1 eV Ec Ev gate Ec Ev body Ev a b How does one arrive at this energy band diagram Spring 2003 EE130 Lecture 21 Slide 4 2 Guidelines for Drawing MOS Band Diagrams Fermi level EF is flat constant with distance x in the Si Since no current flows in the x direction we can assume that equilibrium conditions prevail Band bending is linear in the oxide No charge in the oxide d dx 0 so is constant dEc dx is constant From Gauss Law we know that the electric field strength in the Si at the surface Si is related to the electric field strength in the oxide ox ox Spring 2003 Si ox Si 3 Si so dEc dx 3 oxide dEc dx Si at the surface EE130 Lecture 21 Slide 5 MOS Band Diagram Guidelines cont The barrier height for conduction band electron flow from the Si into SiO2 is 3 1 eV This is equal to the electron affinity difference Si and SiO2 The barrier height for valence band hole flow from the Si into SiO2 is 4 8 eV The vertical distance between the Fermi level in the metal EFM and the Fermi level in the Si EFS is equal to the applied gate voltage qVG E FS E FM Spring 2003 EE130 Lecture 21 Slide 6 3 Voltage Drops in the MOS System In general where VG VFB Vox s qVFB MS M S Vox is the voltage dropped across the oxide Vox total amount of band bending in the oxide s is the voltage dropped in the silicon total amount of band bending in the silicon q s Ei bulk Ei surface For example When VG VFB Vox s 0 i e there is no band bending Spring 2003 EE130 Lecture 21 Slide 7 Special Case Equal Work Functions M S What happens when the work function is different Spring 2003 EE130 Lecture 21 Slide 8 4 General Case Different Work Functions Spring 2003 EE130 Lecture 21 Slide 9 Flat Band Condition SiO2 0 95 eV E0 Ec q M Ec EF 3 1 eV Si 3 1 eV Ec VFB Ef Ev Ev 9 eV N poly Si E0 Vacuum level E0 Ef Work function E0 Ec Electron affinity Si SiO2 energy barrier Spring 2003 q s Si Ec EF SiO P type Si 4 8 eV Ev EE130 Lecture221 Slide 10 5 MOS Band Diagrams n type Si Decrease VG toward more negative values move the gate energy bands up relative to the Si decrease VG Accumulation VG VFB decrease VG Depletion VG VFB Electrons accumulate at Electrons repelled from surface surface Spring 2003 Inversion VG VT Surface becomes p type EE130 Lecture 21 Slide 11 Biasing Conditions for p type Si increase VG VG VFB Spring 2003 VG VFB increase VG VT VG VFB EE130 Lecture 21 Slide 12 6 Accumulation n poly Si gate p type Si M VG VFB O S 3 1 eV qVox Ec EFM GATE Ev qVG q s is small 0 VG Ec p type Si 4 8 eV VG VFB Vox Mobile carriers holes accumulate at Si surface Spring 2003 EFS Ev EE130 Lecture 21 Slide 13 Accumulation Layer Charge Density Vox VG VFB VG VFB From Gauss Law ox GATE VG tox Qacc C cm2 Qacc SiO2 Vox t Qacc Cox ox ox where Cox SiO2 tox p type Si units F cm2 Qacc Cox VG VFB 0 Spring 2003 EE130 Lecture 21 Slide 14 7 Depletion n poly Si gate p type Si M VT VG VFB O qVox S Wd Ec GATE VG q s 3 1 eV qVG EFS Ev Ec EFM p type Si Ev 4 8 eV Si surface is depleted of mobile carriers holes Surface charge is due to ionized dopants acceptors Spring 2003 EE130 Lecture 21 Slide 15 Depletion Width Wd p type Si Depletion Approximation The surface of the Si is depleted of mobile carriers to a depth Wd The charge density within the depletion region is qN A Poisson s equation 0 x Wd d qN A dx Si Si 0 x Wd Integrate twice to obtain S s Spring 2003 qN A 2 Wd Wd 2 Si 2 Si s qN A To find s for a given VG we need to consider the voltage drops in the MOS system EE130 Lecture 21 Slide 16 8 Voltage Drops in Depletion p type Si From Gauss Law VG Qdep SiO2 GATE ox Vox Qdep C cm2 p type Si t Qdep Cox ox ox Qdep is the integrated charge density in the Si Qdep qN AWd 2qN A Si s VG VFB s Vox VFB s Spring 2003 2 qN A si s Cox EE130 Lecture 21 Slide 17 Surface Potential in Depletion p type Si VG VFB s 2 qN A si s Cox Solving for S we have s 2 qN A si 2Cox VG VFB 1 1 qN A si 2Cox qN A si s 2 2Cox Spring 2003 2 2Cox VG VFB 1 1 qN A si 2 EE130 Lecture 21 Slide 18 9 Threshold Condition VG VT When VG is increased to the point where s reaches 2 the surface is said to be strongly inverted The surface is n type to the same degree as the bulk is p type This is the threshold condition VG VT s 2 B E i bulk Ei surface 2 Ei bulk E F Ei surface EF Ei bulk E F nsurface N A Spring 2003 EE130 Lecture 21 Slide 19 MOS Band Diagram at Threshold p type Si M s 2 B 2 Wd Wdm kT N A ln q ni qVox 2 Si 2 B qN A q F O S Wdm q B q s Ec EFS Ev qVG Ec EFM Ev Spring 2003 EE130 Lecture 21 Slide 20 10 Threshold Voltage For p type Si VG VFB s Vox VFB s VT VFB 2 B 2 qN A si s Cox 2qN A Si 2 B Cox For n type Si VT VFB 2 B Spring 2003 2qN D Si 2 B Cox EE130 …
View Full Document
Unlocking...