During the absorption spectra measurement of an unknown...

During the absorption spectra measurement of an unknown semiconductor material, the peak of the spectra appears around $364 \mathrm{~nm}$. What is the band gap of the device and what material is this? If the majority carrier in that material will be able to move with $5 \times 105 \mathrm{~cm} / \mathrm{sec}$ velocity, what will be the carrier mass for that material?

Key Concepts

Effective Mass and Carrier Dynamics

The effective mass of a carrier in a semiconductor is a measure of its dynamical response to external forces, such as electric fields, taking into account the influence of the periodic lattice. This concept is often linked with the de Broglie relation, where momentum (p) can be expressed as h/? or ?k, and relates to the carrier’s velocity through p = m*v. Knowing the velocity of the charge carriers allows one to determine their effective mass, which is crucial for understanding carrier mobility and overall device performance.

Direct Band Gap Semiconductor Identification

Direct band gap semiconductors have the conduction band minimum and the valence band maximum occurring at the same point in momentum space (k-space), enabling efficient absorption and emission of light. Measuring an absorption peak around a specific wavelength (such as 364 nm, which corresponds to approximately 3.4 eV) can be used to match the experimental band gap with those of known materials. This method is important for identifying materials like Gallium Nitride (GaN), which is well-known for its ~3.4 eV band gap and wide use in optoelectronic applications.

Photon Energy and Band Gap Relationship

In semiconductor physics, the energy of a photon is related to its wavelength by the equation E = hc/?, where h is Planck’s constant and c is the speed of light. This relation is used to determine the band gap energy of a semiconductor by measuring the wavelength at which absorption occurs. The band gap is the minimum energy needed to excite an electron from the valence band to the conduction band, which is a critical parameter in determining the optical and electronic properties of the material.

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