Modes of operation

Operation of a MOSFET can be separated into 3 different modes, depending on the voltages at the terminals. In the discussion below, a simplified algebraic model is used which is accurate only for former technology. Modern MOSFET characteristics need computer models which have rather more complex behavior.

For the enhancement-mode, N channel MOSFET, the 3 operational modes are as follows:

Cutoff, subthreshold, or weak-inversion mode

When V_GS < V_th:

here 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 in between drain and source. Actually, the Boltzmann distribution of electron energies allows some more energetic electrons at source to enter the channel and flow to drain, resulting in the subthreshold current which is an exponential function of gate source voltage. While the current in between drain and source should ideally be zero when transistor is used as a turned-off switch, there exists a weak-inversion current, at times called  subthreshold leakage.

In weak inversion the current varies exponentially with gate to source bias V_GS as given approximately by

,

here ID0 = current at VGS = Vth and slope factor n can be 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 once V_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 Vth  for this mode is defined as the gate voltage at which a selected value of current ID0 occurs, for example, I_D0 = 1 μA, which may not be the same V^th-value used in the equations for the following modes.

Some of the micropower analog circuits are designed to take advantage from the 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_D = 1/ (nVT), almost that of the bipolar transistor. 

The subthreshold  I- V curve depends exponentially on the threshold voltage, introducing a strong dependence on any of the manufacturing  variation which affects threshold  voltage; for instance: variations in oxide thickness, junction depth, or body doping which change degree  of   drain-induced  barrier  lowering.  The resulting sensitivity to fabricational variations complicates optimization for the leakage and performance.

MOSFET drain current versus drain to source voltage for a number of values of V_GS - V_th; the boundary in between saturation (active) and linear modes is indicated by upward curving parabola.

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

Cross section of a MOSFET operating in the saturation region; channel exhibits pinch- off near drain 

Triode mode or linear region (also known as the ohmic mode.

When VGS > Vth and VDS < ( VGS - Vth )

Transistor is turned on, and a channel has been created which permits the current to flow in between the drain and the source. The MOSFET operates just like a resistor, controlled by gate voltage relative to the source and drain voltages both. The current from drain to source can be modeled as:

here μ_n is the charge carrier effective mobility, W is gate width, L is gate length and C_ox  is gate oxide capacitance per unit area. The transition from exponential subthreshold region to the triode region is not as sharp as equations suggest.

Saturation or active mode

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

The switch gets turned on, and a channel has been created, which allows current to flow in between the drain and source. As the drain voltage is higher than the gate voltage, the electrons spread out, and conduction is not by a narrow channel but by a broader, 2- or 3-dimensional current distribution extending away from interface and deeper in substrate. The onset of this region is also called as pinch-off to indicate the lack of channel region near drain. The drain current is now slightly dependent on drain voltage and controlled primarily by gate-source voltage, and modeled approximately as:

The additional  factor  involving  λ,  channel-length modulation  parameter, models current  dependence  on the  drain  voltage  because of  the   Early  effect,  or  channel  length modulation. According to equation, the key design parameter, MOSFET transconductance can be given by:

here the combination V_ov  = V_GS  - V_th  is called as overdrive voltage.  Another key design parameter is MOSFET output resistance r_O can be given by:

Hear r_out  is inverse of g_ds    . V_DS  is the expression in the saturation region.

If λ is taken as zero, an infinite output resistance of device results which 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 nearly linear than quadratic in VGS. At shorter lengths even, carriers transport with near zero scattering, called as quasi ballistic transport. Additionally, the output current is affected by the drain-induced barrier lowering of threshold voltage.

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