Operation of MOSFET

The operation of a metal-oxide-semiconductor field-effect transistor which is abbreviated as MOSFET can be separated into three modes, depending upon the voltages at the terminals. In the following conversation, a simplified algebraic model is used which is accurate only for old technology. Modern MOSFET characteristics need computer models that have rather much more complex behavior.

For an enhancement-mode, n-channel MOSFET, the 3 operational modes that are:

1. Cut off,
2. Sub threshold, or
3. Weak-inversion mode
   

While V_GS < V_th:

In which V_th is the threshold voltage of the device.

As per to the basic threshold model transistor is turned off and there is no conduction in between drain and source. Actually, the Boltzmann distribution of electron energies permits some of the more energetic electrons at the source to enter the channel and flow to the drain, resultant in a sub threshold current which is an exponential function of gate-source voltage. Whereas the current between drain and source should ideally be zero while the transistor is being employed as a turned-off switch, there is a weak-inversion current, occasionally termed as sub threshold leakage.

In weak inversion the current changes exponentially with gate-to-source bias V_GS as described approximately by:

I_D ≈ I_D0e ((V_GS - V_th) / n V_T),

In which I_D0 = current at V_GS = V_th and the slope factor n is described by

n = 1 + C_D / C_OX,

Along with C_D = capacitance of the depletion layer and C_OX = capacitance of the oxide layer. There is no drain voltage dependence of the current once V_DS > > V_T, in a long-channel device however as channel length is reduced drain-induced barrier lowering introduces drain voltage dependence which depends in a complex way upon the device geometry (for instance, the channel doping, the junction doping and so on). Commonly, threshold voltage V_th for this mode is described as the gate voltage at which a selected value of current I_D0 takes place, for instance, I_D0 = 1 μA, that may not be similar V_th-value employed in the equations for the following modes.

A number of micro power analog circuits are designed to take benefit of sub threshold conduction. Through working in the weak-inversion region, the MOSFETs in these types of circuits deliver the highest possible trans conductance-to-current ratio, that are: 

g_m / I_D = 1 / (nV_T), almost that of a bipolar transistor.