MOSFET Analysis

 

 

Voltage characteristics of an MOS transistor

 

Principal regions of voltage characteristic

                 

                  Linear region (triode region) (V_D < V_G - V_T)

                        Transistor acts as a resistor

 

                                                  L ... Length of the channel

                                                  W ... Width of the channel

                                                  μ_n ... Mobility of the electrons in the channel

                                                  Q_n ... Charge density of the electrons in the channel

 

                        Resistance R is controlled by V_G as Q_n is depending on V_G

 

                  Saturation region (active region) (V_D ≥ V_G - V_T)

                        Drain saturation voltage V_Dsat = V_G - V_T         

                        Drain current I_D ~ independent of V_D

C_ox ... Capacitance per unit area of the oxide layer

 

                  Channel-length modulation

                        Increase of the drain current with channel length reduction

                        Approximation of the preceding formula:

 

 

                                                  l ... device constant depending on L, doping concentration, ...

                                                           for L ~ 10 μm,  l  ~ 0.03 V -1

                                                          

                                                            usual abbreviations:          

 

 

Body effect

Key limitation of MOSFETs used as analogue circuit elements

Assumption v_SB = v_S - v_B = 0 is not valid (v_B ... bulk (substrate) voltage)

Threshold voltage of an n-channel transistor:

V_T0 ... threshold voltage for  v_SB = 0

g ... device constant (often called as body-effect constant)

 

e_S = e₀ K_S   ...  permittivity of silicon (K_S ≈ 11.7)

q                 ...  electron charge (q = 1.6 10-19C)

N_imp           ...  density of the impurity ions in the bulk

                         (N_imp = N_a for NMOS, N_imp = N_d for PMOS)

C_ox             ... oxide capacitance

F_p               ... material constant of the bulk ~ 0.3 V