Electric Field Distribution in a Reverse-Biased p-n Junction

This problem is motivated by the use of crystals as detectors of energetic charged particles that pass completely through the crystal, leaving a trail of electron-ion pairs. Although the crystals are nominally insulators, the electrons so liberated are in the conduction band and can be separated from the ion by a DC electric field, resulting in a signal pulse on the electrodes plated onto opposite faces of the crystal. However, recombination of the drifting electrons at impurity sites is an issue, and it was eventually realized that the high purities of germanium and silicon required for successful transistors are also good for crystalline particle detectors. In addition, p-n diode junctions proved to be suitable for particle detectors [10]. A typical silicon p-n junction is illustrated below, in which a potential difference ΔV ≈ 0.8 V develops across the junction in the absence of an external bias voltage, due to the layers of (space) charge, a few μm thick. The p-side of the junction is doped with a bulk number density Np (or Na) of atoms (such as boron) with 3 valence electrons (compared to 4 for Si), called acceptors in that these atoms can accept electrons from neighboring atoms, the motion of which electrons in one direction corresponds to a current of (electrically positive) holes in the other. The n-side is doped with number density Nn (or Nd) of atoms with 5 valence electrons (such as phosphorus), called donors. A electron current can flow from the n-side to the p-side only if an external (forward) bias voltage Vp − Vn > ΔV is applied, and no (significant) electron current flows from the p-side to the n-side for any applied voltage less than this. The p-n junction acts as a diode/rectifier. Doped silicon has “free” charge carriers, predominantly holes in p-doping and predominantly electrons in n-doping. As such, the can be no electric field inside the doped silicon