Sunday, June 6, 2010

Temperature dependence of the energy bandgap

The energy bandgap of semiconductors tends to decrease as the temperature is increased. This behavior can be understood if one considers that the interatomic spacing increases when the amplitude of the atomic vibrations increases due to the increased thermal energy. This effect is quantified by the linear expansion coefficient of a material. An increased interatomic spacing decreases the average potential seen by the electrons in the material, which in turn reduces the size of the energy bandgap. A direct modulation of the interatomic distance - such as by applying compressive (tensile) stress - also causes an increase (decrease) of the bandgap. The temperature dependence of the energy bandgap, Eg, has been experimentally determined yielding the following expression for Eg as a function of the temperature, T: where Eg(0), a and b are the fitting parameters. These fitting parameters are listed for germanium, silicon and gallium arsenide in Table below A plot of the resulting bandgap versus temperature is shown in Figure below for germanium, silicon and gallium arsenide.

Example 1 Calculate the energy bandgap of germanium, silicon and gallium arsenide at 300, 400, 500 and 600 K.
Solution The bandgap of silicon at 300 K equals: Similarly one finds the energy bandgap for germanium and gallium arsenide, as well as at different temperatures, yielding:


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