Afsa Essay

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FORBIDDEN ENERGY GAP Aim: To determine the forbidden energy gap of germanium using four probe set up. Apparatus: Four probe set up, oven, thermometer, constant current source, etc Theory: In a single isolated atom discreet energy levels are present. In an aggregate of atoms, as in solid, the individual energy levels are so close together that they can be considered to be continuous, thus forming an energy band. The energy band containing all the valence electrons is called as the valence band while the energy band containing the conduction electrons is called as the conduction band. The energy gap between the conduction band and the valence band is called as the forbidden energy gap. In a semiconductor the conductivity and hence resistivity is a function of temperature. Resistivity / conductivity as a function of temperature can thus give an information about the forbidden energy gap of a semiconductor. One of the methods to determine the forbidden energy gap of a semiconductor is the four probe set up. Four probes are placed on a flat surface of the material whose resistivity is to be measured. Current is passed through the outer two electrodes and the potential is measured across the inner pair. For our sample, at T<363 K conduction is mainly due to the impurity carriers (extrinsic region), while for T>363 K conduction is due to electrons transferred to the conduction band (intrinsic region). In intrinsic region the slope of the resistivity as a function of inverse temperature is directly proportional to the band gap. Formulae: V ρ0 = --- 2 π s i Since the thickness of the crystal is small compared to the probe Distance, a correction factor for it has to be applied. Further bottom surface is non-conducting, hence the corrected resistivity is:

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