EECS 105 Fall 1998Lecture 9MOS Capacitor in Depletion■ Now we make VGB > VFB. Note that thermal equilibrium falls into this range of applied bias.■ Surface potential at oxide/silicon interface is now positive --> n-type(slightly, ns = 1013 cm-3). ρ (x)-toxXdx-qNa-toxXdxE (x)00QG-toxXdxφ (x) 0φs = 185 mVVGB + φn+ -500 mV500 mV1 VchargedensityelectricfieldpotentialVGB9EECS 105 Fall 1998Lecture 9The Threshold Voltage VTn■ Keep increasing VGB --> surface potential keeps increasing. At some point, the surface is n-type (i.e., we say that it is inverted) ■ The gate-bulk potential at the onset of inversion is called the threshold voltage, VTn. To find the threshold voltage, we need to consider the electrostatics in depletion (no electrons at the surface at the onset of inversion) -- with the surface potential equal to the opposite of the bulk potential:φsmax,φp–=-toxXd,maxxφ (x) 0φs,max = - φp = 420 mV VTn + φn+ -500 mV500 mV1 V1.5 VVoxVB,max VTn - VFB- φpEECS 105 Fall 1998Lecture 9Threshold Voltage Expression■ We can solve for the threshold voltage:■ The drop across the depletion region is■ The drop across the oxide for VGB = VTn is■ Substituting for the bulk charge (found from the potential drop across the depletion region, we findVTVFB– Vox′ VBmax,+=VBmax,φsmax,φp– φp– φp–2φp–===Vox′ Eox′toxQ–Bmax,εox----------------------toxQBmax,–Cox----------------------== =VTnVFB2– φp1Cox---------2 q εsNa2– φp()+=EECS 105 Fall 1998Lecture 9The Inverted MOS Capacitor (VGB > VTn)■ We consider the surface potential as fixed (“pinned”) at φs,max = - 2 φp■ Inversion charge QN at SiO2 - silicon surface balances extra + charge on gate as VGB increases- toxXd,maxxφ(x) 0500 mV- 500 mV1.0 V1.5 Vφs,max = 420 mVVoxVGB - VFB−2 φpQNC–oxVGBVTn–()=EECS 105 Fall 1998Lecture 9Charge Storage in the MOS Structure■ Three regions of operation:Accumulation: qG = Cox (vGB - vFB) ... parallel plate capacitorDepletion: qG = - qB(vGB), with the bulk (depletion) charge in thesilicon being a nonlinear function of vGBInversion: qG = - qN - qB,max , where qB,max = qB(vGB = VT) is thedepletion charge at the onset of inversion and■ Sketch of the gate charge as a function of gate-bulk voltage:qG [C/cm2]VGB [V]VFBVTnEECS 105 Fall 1998Lecture 9MOS Capacitance■ The capacitance of the MOS structure is defined as■ From sketch, determine the slope and plot as the capacitanceCdqGdvGB-------------VGB=C [C/cm2]VGB [V]VFBVTnEECS 105 Fall 1998Lecture 9Physical Interpretation of MOS Capacitance■ Accumulation: parallel plate capacitor --> C = Cox■ Depletion: increment in gate charge is mirrored at bottom of depletion region, so capacitance model is Cox in series with the depletion region capacitance Cb ■ Inversion: bulk charge is no longer changing with VGB --> an increment ingate charge is “mirrored” in the inversion layer under the gate.The capacitance is therefore the same as in accumulation --> C = CoxCoxεoxtox--------=CbεsXd------=gateSi/SiO2 surfacebulkNote that Xd is a function of VGBCCoxCb=EECS 105 Fall 1998Lecture 9MOS Field Effect Transistors ,,,,,,,,,,,,,deposited oxidefieldoxiden+ drain diffusiondraininterconnect,,,,,,,,p+[ p-type ]bulkinterconnectLdiffgate contact(a),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,Adraincontactsbulkcontactn+ polysilicon gate,,,,,active area (thinoxide area)polysilicon gatecontactmetalinterconnectn+ source diffusionedge ofactive area,,sourceinterconnect(b)Ln+ polysilicon gate ,,,,,,,,,,,,gate oxidegateinterconnectsource contactsdraininterconnectsourceinterconnectAWEECS 105 Fall 1998Lecture 9MOSFET Circuit SymbolsTwo complementary devices (each with two symbols): both are very useful p-substrate (n-type channel under gate oxide) n-substrate (p-type channel under gate oxide)Four electrical terminals: source (lowest potential for n-channel, highest for p-channel), drain, gate, and bulk. Basic concept: inversion layer (called the channel) formed under gate between source and drain enables drift currentn+n+pBulk orBodyDrainSourceGate(a) n-channel MOSFET D−G−IDpBp+p+nBulk orBodyDrainGate(b) p-channel MOSFETSource+_VSGDS−G++_VGSIDnIDnBVSD > 0 VDS > 0 +_VBS+_VSBDGBSSSBDG−IDpEECS 105 Fall 1998Lecture
View Full Document
Unlocking...