Part 2 : Nanostuctures Module 4 : Transport
Lecture 8 : Ohmic Contact
 
It is also possible to obtain an Ohmic contact between a metal and a semiconductor that would normally form a Schottky diode, such as a metal for which $ E_{Fm} < E_{Fsc}$. For such a contact, usually a heavy inhomogeneous doping (called graded doping) close to the interface is employed to achieve large barrier height having very narrow barrier width, as shown schematically in Fig. 4.20. In such a case, the main mechanism of carrier transport is tunneling through the narrow barrier (a topic to be dealt with later). The tunneling current is
$\displaystyle I \sim \exp\left[-\frac{2W}{\hbar}\sqrt{2m_e^*e(\phi_b-V)}\right],$
where $ W$ is the depletion layer width which can be approximated as
$\displaystyle W\approx \sqrt{\frac{2\varepsilon_{sc}}{eN_d}(\phi_b-V)},$
so that
$\displaystyle I \sim \exp\left[-\frac{\alpha}{\sqrt{N_d}}(\phi_b-V)\right],$
where $ \alpha= 4\sqrt{m_e^*\varepsilon_{sc}}/\hbar$.