PHT.301 Physics of Semiconductor Devices




Electrons in crystals

Intrinsic Semiconductors

Extrinsic Semiconductors


pn junctions




Bipolar transistors




Exam questions

Html basics

TUG students

Student projects


High frequency response of MOSFETs

The maximum speed at which a MOSFET can operate can be estimated from the formulas derived in the gradual channel approximation. Consider a MOSFET that has an AC current $\tilde{i}_{in}$ applied to its gate. The AC gate voltage will be $\tilde{v}_G = \tilde{i}_{in}/(2\pi f ZLC_{\text{ox}})$ where $f$ is the frequency of the AC signal, $Z$ is the width of the gate, $L$ is the length of the gate, and $C_{\text{ox}}$ is the specific capacitance. The output drain current will be given by the transconductance,


where the transconductance in the saturation regime is,

$$g_m= \frac{dI_D}{dV_G}=\frac{Z}{L}\mu C_{\text{ox}}(V_G-V_T).$$

There will be gain if $\tilde{i}_{in}\lt \tilde{i}_{out}$. This results in the condition,

$$f\lt f_T=\frac{g_m}{2\pi ZLC_{\text{ox}}}=\frac{\mu (V_G-V_T)}{2\pi L^2},$$

where $f_T$ is called the transit frequency. This formula seems to imply that the transit frequency increases as the size of the transistor decreases like $1/L^2$. However, the voltages are typically scaled down with $L$ to hold the electric field constant. The characteristic electric field is on the order of $E\approx V_DL \approx V_GL$ so the transit frequency is approximately,

$$f_T=\frac{\mu E}{2\pi L}.$$

The average electron velocity is $\mu E$ for low electric fields and saturates at a saturation velocity $v_s$ for high electric fields. If the MOSFET operates at high electric fields (which is typical) the transit frequency is approximately, $$f_T=\frac{v_s}{2\pi L}.$$

Here $t_T= L/v_s$ is the transit time for an electron travelling at the saturation velocity to cross the gate of length $L$. The maximum frequency at which a MOSFET exhibits gain is approximately one over the transit time.