terminals. 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 When VGS < Vth: where is gate-to-source bias and 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. 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 as given approximately by: where = current at , the thermal voltage and the slope factor n is given by: with = capacitance of the depletion layer and = 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 In a long-channel device, there is no drain voltage dependence of the current once , 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: , 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