PHT.301 Physics of Semiconductor Devices
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PHT.301 Physics of Semiconductor Devices | |
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Schottky diode IV characteristicsA Schottky contact is formed when a metal is deposited on a semiconductor. The current-voltage characteristic of a Schottky diode has the same form as that for a pn-diode, $$ I = I_S\left(\exp\left(\frac{eV}{\eta k_BT}\right) - 1\right)\hspace{0.5cm}\text{[A]}.$$Here $I$ is the current, $I_S$ is the saturation current, $e$ is the charge of an electron, $V$ is the voltage, $k_B$ is Boltzmann's constant, $T$ is the absolute temperature, and $\eta$ is the nonideality factor where typically $\eta=1$ for a Schottky diode. It is sometimes said that a Schottky diode turns on at a lower voltage than a pn-diode, but the equation for the two types of diodes is the same. The difference is that Schottky diodes typically have a much larger saturation current $I_S$ so the current of a Schottky diode is much larger for the same voltage. For a real diode there is always a resistance $R_S$ in series. This modifies the diode equation to, $$ I = I_S\left(\exp\left(\frac{e(V-IR_S)}{\eta k_BT}\right) - 1\right)\hspace{0.5cm}\text{[A]}.$$This complicates the calculation since $I$ now appears on both sides of the equation. However, such equations can be solved numerically, for instance by using a binary search. For a Schottky diode, the saturation current can be written as, $$I_S = \frac{Aem^*k_B^2}{2\pi^2\hbar^3}T^2\exp\left(-\frac{\phi_b}{k_BT}\right).$$Here $A$ is the area of the Schottky diode perpendicular to the current flow, $m^*$ is the effective mass, $\phi_b$ is the energy between the Fermi energy of the metal and the conduction band of the semiconductor at the interface called the Schottky barrier height and $T$ the temperature.
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