Measurement of the Conductivity Effective Mass in Semiconductors Using Infrared Reflection

There exist various approximate relationships between the conductivity effective mass of free carriers $m_c$ and the angular frequency ${\omega }_0$ of the reflectivity minimum in the infrared arising from the free-carrier dispersion. A detailed analysis of the reflectivity equation shows that it is possible to obtain a relationship between $m_c$ and ${\omega }_0$ when in addition one has a knowledge of the free-carrier concentration, the drift mobility, and the dielectric constant of the semiconductor at very high frequencies. This relationship is shown to yield a value of ${m_c}^{*}=0.145\mathrm{}$ for $n$-type germanium at room temperature using data presented in the literature. This value compares well with the value of ${m_c}^{*}=0.15\mathrm{}$ obtained using a combination of reflection and transmission measurements. The experimental work required to obtain accurate values for $m_c$ using this relationship is considerably less than that required by other techniques, such as cyclotron resonance, magnetoplasma, and combined infrared reflection and transmission measurements, which are presently used. Moreover, this procedure can be applied over very broad ranges of temperature and of free-carrier concentration.