Internal Capacitances of MOSFET and High Frequency Model

Internal Capacitances of MOSFET and High Frequency Model

• High frequency response of MOSFET affects due to internal capacitances.

• There are two types of internal capacitances in the MOSFET :

• Gate capacitance : It is a parallel-plate capacitance formed by a gate electrode with the channel, with the oxide layer acts as a capacitor dielectric. It is denoted as C_ox.

• Junction capacitances (Source-body and drain-body depletion layer capacitances) : These capacitances are due to the reverse-biased pn junctions formed by the n + source region and the p-type substrate, and the n + drain region and the p-type substrate. These are denoted as source diffusion capacitance and drain diffusion capacitance, respectively.

1. Gate Capacitances

There are three gate capacitances : C_gs, C_gd and C_gb"

Values of gate capacitances

• In triode region, the channel has uniform depth and hence we have

C_gs, = C_gd  = 1/2 WL C_ox   (Triode region)

• In saturation region, the channel has a tapered shape and is pinched off at or near the drain. Therefore, we have

• In cut-off region, the channel disappears and thus

C_gs, = C_gd  = D (cut-off)

However, gate-body model capacitance is given by

C_gb = W L_ov C_ox (cut-off)

• Due to the fact that the source and drain diffusions extend slightly under the gate oxide we need to add the capacitive component (C_ov) to the Cgs and Cgd in the above formulas. The component Cov is known as overlap capacitance and is given by

C_ov =  W L_ov C_ox

where L_ov is the overlap length and is typically 0.05 L to 0.1 L. 

2. Junction Capacitances

• Source diffusion capacitance is given by

where C_sb0 is the value of Csb at zero body-source bias, VSB is the magnitude of the reverse-bias voltage, and V0 is the junction built-in voltage, typically 0.6 V to 0.8 V.

• Similarly, drain diffusion capacitance is given by

3. High-Frequency MOSFET Model

• Fig. 7.6.1 shows the high frequency equivalent circuit model for MOSFET. In this model, capacitance Cdb can be neglected to simplify the analysis. The resulted model is shown in Fig. 7.6.1 (b).

4. Unity-Gain Frequency (f_T)

• The f_T is the frequency at which the short-circuit current gain of the CS MOSFET amplifier becomes unity.

• Fig. 7.6.2 shows the modified high-frequency equivalent circuit to determine the short-circuit current gain. Here, the input is fed with a current-source signal Ii and the output terminals are shorted.

• The short circuit current Io is given by

I_o = g_m V_gs – s C_gd V_gs

• The second term in the above equation is very small and can be neglected at the frequencies of interest and thus

I_o = g_m V_gs   ... (7.6.3)

• The Vgs m terms of Ii can be given by

V_gs = I_i / s (C_gs V_gd )  ...(7.6.4)

• Substituting the values of Ii and Io from equations (7.6.3) and (7.6.4) we have

• For physical frequencies S = j rn From equation (7.6.5) it can be seen that the magnitude of the current becomes unity at the frequency.

• From equation (7.6.7) we can say that fT is proportional to gm and inversely proportional to the internal capacitances.

Ex. 7.6.1 For n-channel MOSFET, L = 1.0 µm Lgv = 0.05 µm W=10µm C_ox =3.45 × 10-3 F / m2, I_D = 200 µA and K_n = 150 µA/ V². Find the fT if MOSFET is operating in the triode region.

Sol. : C_ox = 3.45 × 10^-3 F/m²