3.3. Body Effect and Threshold Voltage

In Fig. 3.4 is shown an example of a circuit in which the body and source cannot be at the same voltage. We now use the four-terminal symbol for the NMOS, which includes the body contact. In most applications, the body would be tied to the lowest potential in the circuit (NMOS), in this case, V_SS (e.g., V_SS = –5 V). But by the nature of the circuit, the source voltage is V_S = V_SS + I_DR_S, such that the source-body voltage is V_SB = I_DR_S.

In MOSFET devices, the threshold voltage depends on V_SB and in SPICE is modeled according to (NMOS)

Equation 3.14

SPICE parameters contained in the equation are V_tno (VTO), γ_n (Gamma), and 2Φ_F (Phi) (Table 3.1). Typically, γ_n ≈ 0.5 V^1/2 and 2Φ_F ≈ 0.6 V. Therefore, for example, for V_SB = 5 V, the body effect adds 0.8 V to V_tno.

In the case of the CMOS array ICs of our lab projects (CD4007), the body effect for the PMOS is significantly less pronounced than for the NMOS (γ_p < γ_n), but the parameter for the channel-length-modulation effect is much smaller for the NMOS than for the PMOS (λ_n < λ_p). The combination suggests that the chip is a p-well configuration; that is, the NMOS devices are fabricated in “wells” of p-type semiconductor that are fabricated into an n-type substrate. The PMOS devices reside directly in the n-type substrate material. As far as our measurements are concerned, the extremes in parameters are an advantage, as we are interested in observing the effects of the various parameters.

In Project 4, a number for γ_n is obtained by measuring V_tn as a function of V_SB. The results are plotted as V_tn versus . LabVIEW calculates the X variable. The data plotted should give a straight line with slope γ_n. The effectiveness of SPICE modeling for representing the behavior of the transistor in a circuit is investigated in Project 4. The transfer characteristic, V_GS versus I_D, is measured for a circuit of the type shown in Fig. 3.4, where the circuit has V_SB = I_DR_S. In the project, V_SS is swept over a range of values to produce a range of I_D of about a decade. From (3.14), the threshold voltage characteristic that includes the body effect is

Equation 3.15

The input circuit loop equation (Fig. 3.4) is

Equation 3.16

Including the body effect, V_GS is now [from (3.12)]

Equation 3.17

where, for this special case, V_DS = V_GS (V_D = 0, V_S = 0).

A solution is obtainable through combing (3.14), (3.16), and (3.17) for I_D and V_GS. These equations contain every parameter from this discussion of MOSFET SPICE parameters along with R_S. In a project Mathcad file, Project04.mcd, a solution is obtained to provide a comparison with the measured V_GS versus I_D for the circuit. The Mathcad iteration formulation is, from (3.16),

Equation 3.18

and, from (3.15) and (3.17),

Equation 3.19

I_D and V_GS are found for the range of V_SS corresponding to that used in the measurement, which is 2.5 < |V_SS| < 10 V.