PHT.301 Physics of Semiconductor Devices

## n-MESFET

The expression for the drain current of a n-channel MESFET is:

$$$I_{D}=I_p\left[\frac{V_D}{V_p}-\frac{2}{3}\left(\frac{V_{bi}-V_G+V_{D}}{V_p}\right)^\frac{3}{2}+\frac{2}{3}\left(\frac{V_{bi}-V_G}{V_p}\right)^\frac{3}{2}\right]$$$

Where the drain voltage $V_D$ and gate voltage $V_G$ are measured with respect to the source. The pinch-off voltage $V_P$ and pinch-off current $I_P$ are defined as,

$$$V_P=\frac{eN_Dh^2}{2\varepsilon_0\varepsilon_r},$$$ $$$I_p=\frac{e^2µ_nN_D^2Zh^3}{2L\varepsilon_0\varepsilon_r}.$$$

For a Schottky junction, the built-in voltage is,

$$$eV_{bi}=\phi_b-k_BTln\left(\frac{N_c}{N_D}\left(\frac{T}{300}\right)^\frac{3}{2}\right)$$$

Where $\phi_b$ is the Schottky barrier height. The equation above for the drian current is only valid if the MESFET is in the linear regime where $V_{D}\le V_p-V_{bi}+V_G$. For larger drain voltages, the drain current saturates to,

$$$I_{D,sat}=I_p\left[\frac{1}{3}-\frac{V_{bi}-V_G}{V_p}+\frac{2}{3}\left(\frac{V_{bi}-V_G}{V_p}\right)^\frac{3}{2}\right].$$$
 ID [mA] VD [V]
 $N_c=$ cm-3 @ 300 K $N_v=$ cm-3 @ 300 K $N_D=$ cm-3 $\phi_b=$ eV $\mu_n=$ cm2/Vs $h=$ μm $L=$ μm $Z=$ μm $\epsilon_r=$ $T=$ K $V_{D}$ (max)= V $V_g$ [1] = V $V_g$ [2] = V $V_g$ [3] = V $V_g$ [4] = V $V_g$ [5] = V $V_g$ [6] = V

$V_{bi}=$  V;  $I_p=$  mA;  $V_p=$  V.