Lecture 15The MOSFETN-Channel MOSFET StructureReview: Charge in a SemiconductorChannel Formation (Qualitative)Voltage-Dependent ResistorChannel Length & Width DependenceComparison: BJT vs. MOSFETMOS CapacitorGauss’ LawGauss’ Law in 1-DElectrostatic PotentialBoundary ConditionsMOS Capacitor ElectrostaticsMOS Capacitor: VGB = 0Flatband Voltage, VFBVoltage Drops across a MOS CapacitorVGB < VFB (Accumulation)VFB < VGB < VTH (Depletion)VGB > VTH (Inversion)Maximum Depletion Depth, Xd,maxQ-V Curve for MOS CapacitorExampleEE105 Fall 2007 Lecture 15, Slide 1 Prof. Liu, UC BerkeleyLecture 15OUTLINE•MOSFET structure & operation (qualitative)•Review of electrostatics•The (N)MOS capacitor–Electrostatics–Charge vs. voltage characteristicReading: Chapter 6.1-6.2.1EE105 Fall 2007 Lecture 15, Slide 2 Prof. Liu, UC BerkeleyThe MOSFET•Current flowing through the channel between the source and drain is controlled by the gate voltage.SubstrateGateSource DrainMetal-Oxide-Semiconductor Field-Effect Transistor:GATE LENGTH, LgOXIDE THICKNESS, ToxJUNCTION DEPTH, XjM. Bohr, Intel DeveloperForum, September 2004“N-channel” & “P-channel” MOSFETs operate in a complementary manner“CMOS” = Complementary MOS|GATE VOLTAGE|CURRENTVTHEE105 Fall 2007 Lecture 15, Slide 3 Prof. Liu, UC Berkeley•The conventional gate material is heavily doped polycrystalline silicon (referred to as “polysilicon” or “poly-Si” or “poly”)–Note that the gate is usually doped the same type as the source/drain, i.e. the gate and the substrate are of opposite types.•The conventional gate insulator material is SiO2.•To minimize current flow between the substrate (or “body”) and the source/drain regions, the p-type substrate is grounded.N-Channel MOSFET StructureCircuit symbolEE105 Fall 2007 Lecture 15, Slide 4 Prof. Liu, UC BerkeleyReview: Charge in a Semiconductor•Negative charges:–Conduction electrons (density = n)–Ionized acceptor atoms (density = NA)•Positive charges:–Holes (density = p)–Ionized donor atoms (density = ND)•The net charge density [C/cm3] in a semiconductor is•Note that p, n, ND, and NA each can vary with position.•The mobile carrier concentrations (n and p) in the channel of a MOSFET can be modulated by an electric field via VG. ADNNnpq EE105 Fall 2007 Lecture 15, Slide 5 Prof. Liu, UC Berkeley•As the gate voltage (VG) is increased, holes are repelled away from the substrate surface. –The surface is depleted of mobile carriers. The charge density within the depletion region is determined by the dopant ion density.•As VG increases above the threshold voltage VTH, a layer of conduction electrons forms at the substrate surface.–For VG > VTH, n > NA at the surface. The surface region is “inverted” to be n-type.Channel Formation (Qualitative)The electron inversion layer serves as a resistive path (channel) for current to flow between the heavily doped (i.e. highly conductive) source and drain regions.VG < VTHVG ≥ VTHEE105 Fall 2007 Lecture 15, Slide 6 Prof. Liu, UC BerkeleyVoltage-Dependent Resistor•In the ON state, the MOSFET channel can be viewed as a resistor. •Since the mobile charge density within the channel depends on the gate voltage, the channel resistance is voltage-dependent.EE105 Fall 2007 Lecture 15, Slide 7 Prof. Liu, UC Berkeley•Shorter channel length and wider channel width each yield lower channel resistance, hence larger drain current.–Increasing W also increases the gate capacitance, however, which limits circuit operating speed (frequency).Channel Length & Width DependenceEE105 Fall 2007 Lecture 15, Slide 8 Prof. Liu, UC BerkeleyComparison: BJT vs. MOSFET•In a BJT, current (IC) is limited by diffusion of carriers from the emitter to the collector.–IC increases exponentially with input voltage (VBE), because the carrier concentration gradient in the base is proportional to•In a MOSFET, current (ID) is limited by drif of carriers from the source to the drain.–ID increases ~linearly with input voltage (VG), because the carrier concentration in the channel is proportional to (VG-VTH)In order to understand how MOSFET design parameters affect MOSFET performance, we first need to understand how a MOS capacitor works...TBEVVe/EE105 Fall 2007 Lecture 15, Slide 9 Prof. Liu, UC BerkeleyMOS Capacitor•A metal-oxide-semiconductor structure can be considered as a parallel-plate capacitor, with the top plate being the positive plate, the gate insulator being the dielectric, and the p-type semiconductor substrate being the negative plate.•The negative charges in the semiconductor (for VG > 0) are comprised of conduction electrons and/or acceptor ions.In order to understand how the potential and charge distributions within the Si depend on VG, we need to be familiar with electrostatics...EE105 Fall 2007 Lecture 15, Slide 10 Prof. Liu, UC BerkeleyGauss’ Law If the magnitude of electric field changes, there must be charge!•In a charge-free region, the electric field must be constant.•Gauss’ Law equivalently says that if there is a net electric field leaving a region, there must be positive charge in that region: EQdSEVVdVdVEVQdVSVdSEdVEThe integral of the electric field over a closed surface is proportional to the charge within the enclosed volume is the net charge density is the dielectric permittivityEE105 Fall 2007 Lecture 15, Slide 11 Prof. Liu, UC BerkeleyGauss’ Law in 1-D•Consider a pulse charge distribution:dxdEEdxdE')'()()(00dxxxExExx)(xEx0)(xxdXAqN0dXEE105 Fall 2007 Lecture 15, Slide 12 Prof. Liu, UC BerkeleyElectrostatic Potential•The electric field (force) is related to the potential (energy):–Note that an electron (–q charge) drifs in the direction of increasing potential:)()( 22xdxxVddxdVE dxdVqqEFe)(xxdXAqN)(xVx00)(xEx0dXdXEE105 Fall 2007 Lecture 15, Slide 13 Prof. Liu, UC BerkeleyBoundary Conditions•Electrostatic potential must be a continuous function. Otherwise, the electric field (force) would be infinite.•Electric field does not have to be continuous, however. Consider an interface between two materials:Discontinuity in electric displacement E charge density at interface!)( 11E)( 22EinsideQSESEdSE2211x then,0 If0
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