Characterization of Semiconducting Materials Using the Van der Pauw Method

Semiconductors are currently an active topic of study due to the endless range of applications in electronic hardware and computer engineering. In this experiment, the material properties (i.e. resistivity $\rho$, Hall coefficient $R_{H}$, and mobility $\mu$) of a doped GaAs sheet is described by utilizing Hall Effect and the Van der Pauw method with varying temperature $T$ and magnetic field values $B$. It is determined that the sample is an $n$-type semiconductor using the sign of $R_H$, which is measured to be $R_H = -2.9 \times 10^{-12} \pm 0.1 \times 10^{-14} ~ \text{m}^{3} \text{C}^{-1}$, at $T = 303 ~\text{K}$ and $B = 3.3 ~\text{kGs}$. Furthermore, the rate of change for the slope $R_H$ and $T$ is increasing along $B$ at the rate of $\Delta k/ \Delta B = \left(3.6 \pm 0.5 \right) \times 10^{-16} ~\text{m}^3 (\text{CK} \cdot \text{kGs})^{-1}$, meaning the charge accumulation caused by the current and Lorentz force is quadratic in $B$. It is also discovered that $\mu$, and therefore the electron drift velocity is reduced proportionally at higher $T$-values. This method provides a potential analogue in quantum scales with the Quantum Hall Effect and characterisation of quantum dots.