1Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15Lecture 15: MOS Transistor models:Body effects, SPICE modelsProf. J. S. SmithDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithContextIn the last lecture, we discussed the modes of operation of a MOS FET:– Voltage controlled resistor model– I-V curve (Square-Law Model)– Saturation modelIn this lecture, we will:– add a correction due to the changing depletion region, called the body effect– Produce small signal models for the FET– and look at how MOS Transistors are modeled in SPICE2Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithReadingz Today, and Friday we will finish the material from chapter 4.z Then we look at the analog characteristics of simple digital devices, 5.2→5.4z And following the midterm, we will cover PN diodes again in forward bias, and develop small signal models: Chapter 6 z we will then take a week on bipolar junction transistor (BJT): Chapter 7z Then go on to design of transistor amplifiers: chapter 8Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithMOS operationz An inversion mode MOS transistor operates by producing a sheet carriers just under the oxidez The names source and drain are picked so that the inversion charge is larger at the source end z Approximate inversion charge QN(y): drain is higher than the source Æ less charge at drain end of channel3Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithGradual channel approximationz We have played pretty fast and loose, using the average charge and average velocity, etc.z A more accurate model of the physics includes the fact that the charge density under the gate and the velocity vary along the channel lengthz The current at each point along the length of the device must be independent of position in steady state (no buildup of charge)z Where IDis the drain current, y is the distance in the direction from the source to the drain, vyis the component of velocity in the source→drain direction, and QN(y) is the charge density of the electrons under the gate)()( yQyWvINyD−=Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithGradual channel approximation -2z For most FET’s the distances in y, the Source→Drain direction, are significantly larger than the distances in the x direction, (perpendicular to the oxide). z If this assumption is not true, its called a short channel device.z This means that the fields in the x direction are much stronger than the fields in the y direction.z This is in the text, section 4.3, with the main difference from the simple approximation being the back gate effect, due to the variation in the depletion width to the body (substrate).4Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithEffect of substrate voltagez What is the effect of different substrate voltages?– Depletion width W changes– Need to account for different depletion region chargePSABqNQφε220−−=SBPSABVqNQ +−−=φε22(VSB≠ 0):(VSB= 0):Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithThreshold voltage: generalz General form (with substrate bias):z Substituting the capacitance as a function of voltage:oxoxoxBPFBTCQCQVV −−−=02φ()oxSAPSBPTTCqNVVVεγφφγ2220=−+−+=+ for NMOS-for PMOSWhere:5Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithThreshold voltage, summaryz If VSB= 0 (no substrate bias):z If VSB≠ 0 (non-zero substrate bias)z Body effect (substrate-bias) coefficient:(NMOS)z Threshold voltage increases as VSBincreases. The threshold voltage will also vary along the gate. This is called the body effect, or back gate effect.oxoxoxBFFBTCQCQVV −−−=φ20()PSBPTTVVVφφγ220−+−+=oxSACqNεγ2=Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithThreshold Voltage (NMOS vs. PMOS)VSB< 0VSB> 0Substrate bias voltageVT0< 0VT0> 0Threshold voltage (enhancement devices)γ < 0γ > 0Substrate bias coefficientQB> 0QB< 0Depletion charge densityφn> 0φp< 0Substrate Fermi potentialPMOS(n-substrate)NMOS(p-substrate)6Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithBody effectz Voltage VSBchanges the threshold voltage of transistor– For NMOS, Body normally connected to ground– for PMOS, body normally connected to Vcc– Raising source voltage increases VTof transistorn+n+SDBp+LjxSDBLjxNMOSPMOSGGp-type substrateN wellp+ p+n+Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithThreshold voltage adjustmentz Threshold voltage can be changed by doping the channel region with donor or acceptor ionsz For NMOS:– The threshold voltage is increased by adding acceptor ions– The threshold voltage is decreased by adding donor ionsz For PMOS:– The threshold voltage is increased by adding donor ions– The threshold voltage is decreased by adding acceptor ionsz Approximate change in threshold voltage:– Density of implanted ions = NI[cm-2]oxITCqNV =∆07Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithChannel Length Modulationz As VDSis increased, the pinch-off point moves closer to source, shortening the channel lengthz The drain current increases due to shorter channel()()DSTNGSoxnDVVVLWCILLLλµ+−=∆−=1221'λ = channel length modulation coefficientDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithReviewCutoff0=⇒<<DTPGSTNGSIVVVVLinear()[]221,,DSDSTGSoxDTPGSDSTPGSTNGSDSTNGSVVVVLWCIVVVVVVVVVV−−=⇒−>≤−<≥µSaturation()()DSTGSoxDTPGSDSTPGSTNGSDSTNGSVVVLWCIVVVVVVVVVVλµ+−=⇒−≤≤−≥≥1,,221Note: if VSB≠ 0, need to calculate VT8Department of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithNMOSz iSlope due toChannel lengthmodulationTGSDSVVV−=VGSStepsDepartment of EECS University of California, BerkeleyEECS 105 Spring 2004, Lecture 15 Prof. J. S. SmithPMOSTGSDSVVV−=Slope due toChannel lengthmodulation9Department of EECS University of California,
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