MOSFET Device Physics and Operation

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  • 1MOSFET Device Physicsand Operation

    1.1 INTRODUCTION

    A field effect transistor (FET) operates as a conducting semiconductor channel with twoohmic contacts the source and the drain where the number of charge carriers in thechannel is controlled by a third contact the gate. In the vertical direction, the gate-channel-substrate structure (gate junction) can be regarded as an orthogonal two-terminaldevice, which is either a MOS structure or a reverse-biased rectifying device that controlsthe mobile charge in the channel by capacitive coupling (field effect). Examples of FETsbased on these principles are metal-oxide-semiconductor FET (MOSFET), junction FET(JFET), metal-semiconductor FET (MESFET), and heterostructure FET (HFETs). In allcases, the stationary gate-channel impedance is very large at normal operating conditions.The basic FET structure is shown schematically in Figure 1.1.

    The most important FET is the MOSFET. In a silicon MOSFET, the gate contactis separated from the channel by an insulating silicon dioxide (SiO2) layer. The chargecarriers of the conducting channel constitute an inversion charge, that is, electrons in thecase of a p-type substrate (n-channel device) or holes in the case of an n-type substrate(p-channel device), induced in the semiconductor at the silicon-insulator interface by thevoltage applied to the gate electrode. The electrons enter and exit the channel at n+ sourceand drain contacts in the case of an n-channel MOSFET, and at p+ contacts in the caseof a p-channel MOSFET.

    MOSFETs are used both as discrete devices and as active elements in digital andanalog monolithic integrated circuits (ICs). In recent years, the device feature size ofsuch circuits has been scaled down into the deep submicrometer range. Presently, the0.13-m technology node for complementary MOSFET (CMOS) is used for very largescale ICs (VLSIs) and, within a few years, sub-0.1-m technology will be available,with a commensurate increase in speed and in integration scale. Hundreds of millions oftransistors on a single chip are used in microprocessors and in memory ICs today.

    CMOS technology combines both n-channel and p-channel MOSFETs to provide verylow power consumption along with high speed. New silicon-on-insulator (SOI) technologymay help achieve three-dimensional integration, that is, packing of devices into many

    Device Modeling for Analog and RF CMOS Circuit Design. T. Ytterdal, Y. Cheng and T. A. Fjeldly 2003 John Wiley & Sons, Ltd ISBN: 0-471-49869-6

  • 2 MOSFET DEVICE PHYSICS AND OPERATION

    Gate

    Drain Source

    Semiconductor substrate

    Insulator Gate junction

    Substrate contact

    Conducting channel

    Figure 1.1 Schematic illustration of a generic field effect transistor. This device can be viewedas a combination of two orthogonal two-terminal devices

    layers, with a dramatic increase in integration density. New improved device structuresand the combination of bipolar and field effect technologies (BiCMOS) may lead tofurther advances, yet unforeseen. One of the rapidly growing areas of CMOS is in analogcircuits, spanning a variety of applications from audio circuits operating at the kilohertz(kHz) range to modern wireless applications operating at gigahertz (GHz) frequencies.

    1.2 THE MOS CAPACITOR

    To understand the MOSFET, we first have to analyze the MOS capacitor, which consti-tutes the important gate-channel-substrate structure of the MOSFET. The MOS capacitoris a two-terminal semiconductor device of practical interest in its own right. As indi-cated in Figure 1.2, it consists of a metal contact separated from the semiconductor bya dielectric insulator. An additional ohmic contact is provided at the semiconductor sub-strate. Almost universally, the MOS structure utilizes doped silicon as the substrate andits native oxide, silicon dioxide, as the insulator. In the siliconsilicon dioxide system,the density of surface states at the oxidesemiconductor interface is very low comparedto the typical channel carrier density in a MOSFET. Also, the insulating quality of theoxide is quite good.

    Semiconductor

    InsulatorMetal

    Substrate contact

    Figure 1.2 Schematic view of a MOS capacitor

  • THE MOS CAPACITOR 3

    We assume that the insulator layer has infinite resistance, preventing any charge carriertransport across the dielectric layer when a bias voltage is applied between the metal andthe semiconductor. Instead, the applied voltage will induce charges and counter chargesin the metal and in the interface layer of the semiconductor, similar to what we expect inthe metal plates of a conventional parallel plate capacitor. However, in the MOS capacitorwe may use the applied voltage to control the type of interface charge we induce in thesemiconductor majority carriers, minority carriers, and depletion charge.

    Indeed, the ability to induce and modulate a conducting sheet of minority carriers atthe semiconductoroxide interface is the basis for the operation of the MOSFET.

    1.2.1 Interface Charge

    The induced interface charge in the MOS capacitor is closely linked to the shape ofthe electron energy bands of the semiconductor near the interface. At zero applied volt-age, the bending of the energy bands is ideally determined by the difference in thework functions of the metal and the semiconductor. This band bending changes with theapplied bias and the bands become flat when we apply the so-called flat-band voltagegiven by

    VFB = (m s)/q = (m Xs Ec + EF)/q, (1.1)

    where m and s are the work functions of the metal and the semiconductor, respectively,Xs is the electron affinity for the semiconductor, Ec is the energy of the conduction bandedge, and EF is the Fermi level at zero applied voltage. The various energies involvedare indicated in Figure 1.3, where we show typical band diagrams of a MOS capacitorat zero bias, and with the voltage V = VFB applied to the metal contact relative to thesemiconductoroxide interface. (Note that in real devices, the flat-band voltage may be

    qVFB

    m

    Vacuum level

    V = 0

    Ec

    EFEv

    Eg

    Xs s

    V = VFB

    Metal

    Oxide

    EFm

    EgqVFB

    Ec

    EFsEv

    Semiconductor

    (a) (b)

    Figure 1.3 Band diagrams of MOS capacitor (a) at zero bias and (b) with an applied voltageequal to the flat-band voltage. The flat-band voltage is negative in this example

  • 4 MOSFET DEVICE PHYSICS AND OPERATION

    affected by surface states at the semiconductoroxide interface and by fixed charges inthe insulator layer.)

    At stationary conditions, no net current flows in the direction perpendicular to theinterface owing to the very high resistance of the insulator layer (however, this doesnot apply to very thin oxides of a few nanometers, where tunneling becomes important,see Section 1.5). Hence, the Fermi level will remain constant inside the semiconductor,independent of the biasing conditions. However, between the semiconductor and the metalcontact, the Fermi level is shifted by EFm EFs = qV (see Figure 1.3(b)). Hence, we havea quasi-equilibrium situation in which the semiconductor can be treated as if in thermalequilibrium.

    A MOS structure with a p-type semiconductor will enter the accumulation regime ofoperation when the voltage applied between the metal and the semiconductor is morenegative than the flat-band voltage (VFB < 0 in Figure 1.3). In the opposite case, whenV > VFB, the semiconductoroxide interface first becomes depleted of holes and weenter the so-called depletion regime. By increasing the applied voltage, the band bendingbecomes so large that the energy difference between the Fermi level and the bottom ofthe conduction band at the insulatorsemiconductor interface becomes smaller than thatbetween the Fermi level and the top of the valence band. This is the case indicated forV = 0 V in Figure 1.3(a). Carrier statistics tells us that the electron concentration thenwill exceed the hole concentration near the interface and we enter the inversion regime.At still larger applied voltage, we finally arrive at a situation in which the electron volumeconcentration at the interface exceeds the doping density in the semiconductor. This isthe strong inversion case in which we have a significant conducting sheet of inversioncharge at the interface.

    The symbol is used to signify the potential in the semiconductor measured relativeto the potential at a position x deep inside the semiconductor. Note that becomespositive when the bands bend down, as in the example of a p-type semiconductor shownin Figure 1.4. From equilibrium electron statistics, we find that the intrinsic Fermi levelEi in the bulk corresponds to an energy separation qb from the actual Fermi level EFof the doped semiconductor,

    b = Vth ln(

    Na

    ni

    ), (1.2)

    Ec

    Semiconductor Oxide

    Depletion region

    Ei

    EFEv

    qy qjb

    qys

    Figure 1.4 Band diagram for MOS capacitor in weak inversion (b < s < 2b)

  • THE MOS CAPACITOR 5

    where Vth is the thermal voltage, Na is the shallow acceptor density in the p-type semicon-ductor and ni is the intrinsic carrier density of silicon. According to the usual definition,strong inversion is reached when the total band bending equals 2qb, corresponding to thesurface potential s = 2b. Values of the surface potential such that 0 < s < 2b corre-spond to the depletion and the weak inversion regimes, s = 0 is the flat-band condition,and s < 0 corresponds to the accumulation mode.

    The surface concentrations of holes and electrons are expressed in terms of the surfacepotential as follows using equilibrium statistics,

    ps = Na exp(s/Vth), (1.3)ns = n2i /ps = npo exp(s/Vth), (1.4)

    where npo = n2i /Na is the equilibrium concentrat