C.3 Position Sensitive Detector (PSD)

A PSD is an optoelectronic device that provides an analog output current proportional to the displacement of the centroid of a light spot that hits the sensitive area of the device. Essentially, a PSD is a PIN diode that is sandwiched between two conductive layers connected to 4 electrodes, two by two (see Fig. C.3a). The top layer electrodes measure the position of the spot in the $ x$ direction and the other two ones measure the $ y$ direction. The diode usually operates in reverse biased mode: the P layer is kept at a negative voltage and the N layer, at a positive. When a photon hits the intrinsic (intermediate) layer of the diode, it produces a pair of hole-electron (see Fig. C.3b) that travel in opposite directions towards the conductive layers. Since there is a large amount of photons in a laser beam, a lot of pairs hole-electron are produced. The excess of charge in the conductors induce a current in the electrodes (see Fig. C.3c). The current of each electrode is proportional to the distance between the spot of light and the electrode. Therefore, the signals of the electrodes can be combined to infer the location of the light spot. If we consider a light beam that hits the sensitive area $ S$ of the PSD detector we can write the following relationships between the irradiance of the light ($ E(x,y)$) and the output signal of the PSD,

$\displaystyle I_\mathrm{left}-I_\mathrm{right}$ $\displaystyle \propto$ $\displaystyle \int_S x\,E(x,y)\cdot dS$  
$\displaystyle I_\mathrm{top}-I_\mathrm{bottom}$ $\displaystyle \propto$ $\displaystyle \int_S y\,E(x,y)\cdot dS$  
$\displaystyle I_\mathrm{left}+I_\mathrm{right}=I_\mathrm{top}+I_\mathrm{bottom}$ $\displaystyle \propto$ $\displaystyle \int_S E(x,y)\cdot dS$ (C.1)

where $ I_\mathrm{left},I_\mathrm{right},I_\mathrm{top},I_\mathrm{bottom}$ are the currents of the electrodes and $ dS$ is the differential of surface. The differences of current between the electrodes provide the averaged position of the light spot, while the addition of currents provide the total power of light. The addition and subtraction of currents and the application of a constant voltage to the electrodes is performed by using analog electronics in the Preamp board.

Figure C.3: Position Sensitive Detector. (a) Design of a PSD. (b) Side view of a PSD. Interaction with light, production of a pair hole-electron and traveling towards the electrodes. (c) Front view of a PSD. The currents produced in the electrodes depend on the position at which the light spot hits the detector.
\includegraphics[width=\textwidth]{figs/appendix2/psd.eps}

JM Huguet 2014-02-12