Metal–oxide–semiconductor structure The traditional metal–oxide–semiconductor (MOS) structure is obtained by growing a layer of
silicon dioxide () on top of a silicon substrate, commonly by
thermal oxidation and depositing a layer of metal or
polycrystalline silicon (the latter is commonly used). As silicon dioxide is a
dielectric material, its structure is equivalent to a planar
capacitor, with one of the electrodes replaced by a semiconductor. When a voltage is applied across a MOS structure, it modifies the distribution of charges in the semiconductor. If we consider a p-type semiconductor (with
NA the density of
acceptors,
p the density of holes;
p = NA in neutral bulk), a positive voltage,
VG, from gate to body (see figure) creates a
depletion layer by forcing the positively charged holes away from the gate-insulator/semiconductor interface, leaving exposed a carrier-free region of immobile, negatively charged acceptor ions (see
doping). If
VG is high enough, a high concentration of negative charge carriers forms in an
inversion layer located in a thin layer next to the interface between the semiconductor and the insulator. Conventionally, the gate voltage at which the volume density of electrons in the inversion layer is the same as the volume density of holes in the body is called the
threshold voltage. When the voltage between transistor gate and source (
VG) exceeds the threshold voltage (
Vth), the difference is known as
overdrive voltage. This structure with p-type body is the basis of the n-type MOSFET, which requires the addition of n-type source and drain regions.
MOS capacitors and band diagrams The MOS capacitor structure is the heart of the MOSFET. Consider a MOS capacitor where the silicon base is of p-type. If a positive voltage is applied at the gate, holes which are at the surface of the p-type substrate will be repelled by the electric field generated by the voltage applied. At first, the holes will simply be repelled and what will remain on the surface will be immobile (negative) atoms of the acceptor type, which creates a depletion region on the surface. A hole is created by an acceptor atom, e.g., boron, which has one less electron than a silicon atom. Holes are not actually repelled, being non-entities; electrons are attracted by the positive field, and fill these holes. This creates a depletion region where no charge carriers exist because the electron is now fixed onto the atom and immobile. As the voltage at the gate increases, there will be a point at which the surface above the depletion region will be converted from p-type into n-type, as electrons from the bulk area will start to get attracted by the larger electric field. This is known as
inversion. The threshold voltage at which this conversion happens is one of the most important parameters in a MOSFET. In the case of a p-type MOSFET, bulk inversion happens when the intrinsic energy level at the surface becomes smaller than the
Fermi level at the surface. This can be seen on a band diagram. The Fermi level defines the type of semiconductor in discussion. If the Fermi level is equal to the Intrinsic level, the semiconductor is of intrinsic, or pure type. If the Fermi level lies closer to the conduction band (valence band) then the semiconductor type will be of n-type (p-type). When the gate voltage is increased in a positive sense this will shift the intrinsic energy level band so that it will curve downwards towards the valence band. If the Fermi level lies closer to the valence band (for p-type), there will be a point when the Intrinsic level will start to cross the Fermi level and when the voltage reaches the threshold voltage, the intrinsic level does cross the Fermi level, and that is what is known as inversion. At that point, the surface of the semiconductor is inverted from p-type into n-type. If the Fermi level lies above the intrinsic level, the semiconductor is of n-type, therefore at inversion, when the intrinsic level reaches and crosses the Fermi level (which lies closer to the valence band), the semiconductor type changes at the surface as dictated by the relative positions of the Fermi and intrinsic energy levels.
Structure and channel formation '': Top panels: An applied gate voltage bends bands, depleting holes from surface (left). The charge inducing the bending is balanced by a layer of negative acceptor-ion charge (right). Bottom panel: A larger applied voltage further depletes holes but conduction band lowers enough in energy to populate a conducting channel. A MOSFET is based on the modulation of charge concentration by a MOS capacitance between a
body electrode and a
gate electrode located above the body and insulated from all other device regions by a gate dielectric layer. If dielectrics other than an oxide are employed, the device may be referred to as a metal-insulator-semiconductor FET (MISFET). Compared to the MOS capacitor, the MOSFET includes two additional terminals (
source and
drain), each connected to individual highly doped regions that are separated by the body region. These regions can be either p or n type, but they must both be of the same type, and of opposite type to the body region. The source and drain (unlike the body) are highly doped as signified by a "+" sign after the type of doping. If the MOSFET is an n-channel or nMOS FET, then the source and drain are
n+ regions and the body is a
p region. If the MOSFET is a p-channel or pMOS FET, then the source and drain are
p+ regions and the body is a
n region. The source is so named because it is the source of the charge carriers (electrons for n-channel, holes for p-channel) that flow through the channel; similarly, the drain is where the charge carriers leave the channel. The occupancy of the energy bands in a semiconductor is set by the position of the
Fermi level relative to the semiconductor energy-band edges. With sufficient gate voltage, the valence band edge is driven far from the Fermi level, and holes from the body are driven away from the gate. At larger gate bias still, near the semiconductor surface the conduction band edge is brought close to the Fermi level, populating the surface with electrons in an
inversion layer or
n-channel at the interface between the p region and the oxide. This conducting channel extends between the source and the drain, and current is conducted through it when a voltage is applied between the two electrodes. Increasing the voltage on the gate leads to a higher electron density in the inversion layer and therefore increases the current flow between the source and drain. For gate voltages below the threshold value, the channel is lightly populated, and only a very small
subthreshold leakage current can flow between the source and the drain. When a negative gate-source voltage (positive source-gate) is applied, it creates a
p-channel at the surface of the n region, analogous to the n-channel case, but with opposite polarities of charges and voltages. When a voltage less negative than the threshold value (a negative voltage for the p-channel) is applied between gate and source, the channel disappears and only a very small subthreshold current can flow between the source and the drain. The device may comprise a
silicon on insulator device in which a buried oxide is formed below a thin semiconductor layer. If the channel region between the gate dielectric and the buried oxide region is very thin, the channel is referred to as an ultrathin channel region with the source and drain regions formed on either side in or above the thin semiconductor layer. Other semiconductor materials may be employed. When the source and drain regions are formed above the channel in whole or in part, they are referred to as raised source/drain regions.
Modes of operation The operation of a MOSFET can be separated into three different modes, depending on the device's
threshold voltage (V_\text{th}), gate-to-source voltage (V_\text{GS}), and drain-to-source voltage (V_\text{DS}). In the following discussion, a simplified algebraic model is used. Modern MOSFET characteristics are more complex than the algebraic model presented here. For an
enhancement-mode, n-channel MOSFET, the three operational modes are:
Cutoff, subthreshold, and weak-inversion mode Criterion: V_\text{GS} According to the basic threshold model, the transistor is turned off, and there is no conduction between drain and source. A more accurate model considers the effect of thermal energy on the
Fermi–Dirac distribution of electron energies which allow some of the more energetic electrons at the source to enter the channel and flow to the drain. This results in a subthreshold current that is an exponential function of gate-source voltage. While the current between drain and source should ideally be zero when the transistor is being used as a turned-off switch, there is a weak-inversion current, sometimes called subthreshold leakage. In weak inversion where the source is tied to bulk, the current varies exponentially with V_\text{GS} as given approximately by: I_\text{D} \approx I_\text{D0} e^\frac{V_\text{GS} - V_\text{th}}{nV_\text{T}}, where: • I_\text{D0} is the current when V_\text{GS} {=} V_\text{th}, • V_\text{T} {=} kT/q is the thermal voltage, and • n is the slope factor given by: n = 1 + \frac{C_\text{dep}}{C_\text{ox}}, where C_\text{dep} is the capacitance of the depletion layer and C_\text{ox} is the capacitance of the oxide layer. This equation is generally used, but is only an adequate approximation for the source tied to the bulk. For the source not tied to the bulk, the subthreshold equation for drain current in saturation is I_\text{D} \approx I_\text{D0} e^\frac{V_\text{G} - V_\text{th}}{nV_\text{T}} e^{-\frac{ V_\text{S}}{V_\text{T}}}. In a long-channel device, there is no drain voltage dependence of the current once V_\text{DS} \gg V_\text{T}, but as channel length is reduced
drain-induced barrier lowering introduces drain voltage dependence that depends in a complex way upon the device geometry (for example, the channel doping, the junction doping and so on). Frequently, threshold voltage
Vth for this mode is defined as the gate voltage at which a selected value of current
ID0 occurs, for example,
ID0 = 1μA, which may not be the same
Vth-value used in the equations for the following modes. Some micropower analog circuits are designed to take advantage of subthreshold conduction. By working in the weak-inversion region, the MOSFETs in these circuits deliver the highest possible transconductance-to-current ratio, namely: g_m/I_\text{D} = 1/\left(nV_\text{T}\right), almost that of a bipolar transistor. The subthreshold
I–V curve depends exponentially upon threshold voltage, introducing a strong dependence on any manufacturing variation that affects threshold voltage; for example: variations in oxide thickness, junction depth, or body doping that change the degree of drain-induced barrier lowering. The resulting sensitivity to fabricational variations complicates optimization for leakage and performance. near drain.
Triode mode or linear region (also known as the ohmic mode) Criteria: V_\text{GS} > V_\text{th} and V_\text{DS} The transistor is turned on, and a channel has been created which allows current between the drain and the source. The MOSFET operates like a resistor, controlled by the gate voltage relative to both the source and drain voltages. The current from drain to source is modeled as: I_\text{D} = \mu_n C_\text{ox}\frac{W}{L} \left( \left(V_\text{GS} - V_{\rm th}\right)V_\text{DS} - \frac{{V_\text{DS}}^2}{2} \right) , where \mu_n is the charge-carrier effective mobility, W is the gate width, L is the gate length and C_\text{ox} is the gate oxide capacitance per unit area. The transition from the exponential subthreshold region to the triode region is not as sharp as the equations suggest.
Saturation or active mode Criteria: V_\text{GS} > V_\text{th} and V_\text{DS} \geq (V_\text{GS} - V_\text{th}) . The switch is turned on, and a channel has been created, which allows current between the drain and source. Since the drain voltage is higher than the source voltage, the electrons spread out, and conduction is not through a narrow channel but through a broader, two- or three-dimensional current distribution extending away from the interface and deeper in the substrate. The onset of this region is also known as
pinch-off to indicate the lack of channel region near the drain. Although the channel does not extend the full length of the device, the electric field between the drain and the channel is very high, and conduction continues. The drain current is now weakly dependent upon drain voltage and controlled primarily by the gate-source voltage, and modeled approximately as: I_\text{D} = \frac{\mu_n C_\text{ox}}{2}\frac{W}{L}\left[V_\text{GS} - V_\text{th}\right]^2 \left[1 + \lambda V_\text{DS}\right]. The additional factor involving λ, the channel-length modulation parameter, models current dependence on drain voltage due to the
Early effect, or
channel length modulation. According to this equation, a key design parameter, the MOSFET transconductance is: g_m = \frac{\partial I_D}{\partial V_\text{GS}} = \frac{2I_\text{D}}{V_\text{GS} - V_\text{th}} = \frac{2I_\text{D}}{V_\text{ov}} , where the combination
Vov =
VGS −
Vth is called the
overdrive voltage, and where
VDSsat =
VGS −
Vth accounts for a small discontinuity in I_\text{D} which would otherwise appear at the transition between the triode and saturation regions. Another key design parameter is the MOSFET output resistance
rout given by: r_\text{out} = \frac{1}{\lambda I_\text{D}} \, . Note:
rout is the inverse of
gDS, where g_\text{DS} = \frac{\partial I_\text{DS}}{\partial V_\text{DS}}.
ID is the expression in the saturation region. If λ is taken as zero, an infinite output resistance of the device results that leads to unrealistic circuit predictions, particularly in analog circuits. As the channel length becomes very short, these equations become quite inaccurate. New physical effects arise. For example, carrier transport in the active mode may become limited by
velocity saturation. When velocity saturation dominates, the saturation drain current is more nearly linear than quadratic in
VGS. At even shorter lengths, carriers transport with near zero scattering, known as quasi-
ballistic transport. In the ballistic regime, the carriers travel at an injection velocity that may exceed the saturation velocity and approaches the
Fermi velocity at high inversion charge density. In addition, drain-induced barrier lowering increases off-state (cutoff) current and requires an increase in threshold voltage to compensate, which in turn reduces the saturation current.
Body effect showing body effect.
VSB splits Fermi levels Fn for electrons and Fp for holes, requiring larger
VGB to populate the conduction band in an nMOS MOSFET. The occupancy of the energy bands in a semiconductor is set by the position of the
Fermi level relative to the semiconductor energy-band edges. Application of a source-to-substrate reverse bias of the source-body pn-junction introduces a split between the Fermi levels for electrons and holes, moving the Fermi level for the channel further from the band edge, lowering the occupancy of the channel. The effect is to increase the gate voltage necessary to establish the channel, as seen in the figure. This change in channel strength by application of reverse bias is called the "body effect". Using an nMOS example, the gate-to-body bias
VGB positions the conduction-band energy levels, while the source-to-body bias VSB positions the electron Fermi level near the interface, deciding occupancy of these levels near the interface, and hence the strength of the inversion layer or channel. The body effect upon the channel can be described using a modification of the threshold voltage, approximated by the following equation: : V_\text{TB} = V_{T0} + \gamma \left( \sqrt{V_\text{SB} + 2\varphi_B} - \sqrt{2\varphi_B} \right), where
VTB is the threshold voltage with substrate bias present, and
VT0 is the zero-
VSB value of threshold voltage, \gamma is the body effect parameter, and 2
φB is the approximate potential drop between surface and bulk across the depletion layer when and gate bias is sufficient to ensure that a channel is present. As this equation shows, a reverse bias causes an increase in threshold voltage
VTB and therefore demands a larger gate voltage before the channel populates. The body can be operated as a second gate, and is sometimes referred to as the "back gate"; the body effect is sometimes called the "back-gate effect". == Circuit symbols ==