Mode Of Operation

MODE of Operation:

The operation of a MOSFET can be separated into three different modes, depending on the voltages at the terminals. In the following discussion, a simplified algebraic model is used that is accurate only for old technology. Modern MOSFET characteristics require computer models that have rather more complex behavior. For example, see Liu^[4] and the device modeling list at Designers-guide.org.^[5]

For an enhancement-mode, n-channel MOSFET, the three operational modes are:

Cutoff, subthreshold, or weak-inversion mode

When V_GS < V_th:

where V_th is the threshold voltage of the device.

According to the basic threshold model, the transistor is turned off, and there is no conduction between drain and source. In reality, the Boltzmann distribution of electron energies allows some of the more energetic electrons at the source to enter the channel and flow to the drain, resulting 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 calledsubthreshold leakage.

In weak inversion the current varies exponentially with gate-to-source bias V_GS as given approximately by:^[6][7]

,

where I_D0 = current at V_GS = V_th and the slope factor n is given by

n = 1 + C_D / C_OX,

with C_D = capacitance of the depletion layer and C_OX = capacitance of the oxide layer. In a long-channel device, there is no drain voltage dependence of the current onceV_DS > > V_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 V_th for this mode is defined as the gate voltage at which a selected value of current I_D0occurs, for example, I_D0 = 1 μA, which may not be the same V_th-value used in the equations for the following modes.

Some micropower analog circuits are designed to take advantage of subthreshold conduction.^[8][9][10] By working in the weak-inversion region, the MOSFETs in these circuits deliver the highest possible transconductance-to-current ratio, namely: g_m / I_D = 1 / (nV_T), almost that of a bipolar transistor.^[11]

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.^[12][13]

MOSFET drain current vs. drain-to-source voltage for several values of V_GS − V_th; the boundary between linear(Ohmic) and saturation (active) modes is indicated by the upward curving parabola.

Cross section of a MOSFET operating in the linear (Ohmic) region; strong inversion region present even near drain

Cross section of a MOSFET operating in the saturation (active) region; channel exhibits pinch-offnear drain

Triode mode or linear region (also known as the ohmic mode^[14][15])

When V_GS > V_th and V_DS < ( V_GS - V_th )

The transistor is turned on, and a channel has been created which allows current to flow 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:

where μ_n is the charge-carrier effective mobility, W is the gate width, L is the gate length and C_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^[16][17]

When V_GS > V_th and V_DS > ( V_GS - V_th )

The switch is turned on, and a channel has been created, which allows current to flow between the drain and source. Since the drain voltage is higher than the gate 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. The drain current is now weakly dependent upon drain voltage and controlled primarily by the gate–source voltage, and modeled very approximately as:

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:

,

where the combination V_ov = V_GS - V_th is called the overdrive voltage.^[18] Another key design parameter is the MOSFET output resistance r_Ogiven by:

.

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 V_GS. At even shorter lengths, carriers transport with near zero scattering, known as quasi-ballistic transport. In addition, the output current is affected by drain-induced barrier lowering of the threshold voltage.