Appealing analogies are proposed to elucidate two important fundamental topics related to semiconductor devices, namely the carrier scattering in a crystal and the derivation of the diffusion capacitance of a p-n junction. The motion of an electron in a semiconductor crystal, according to Schrodinger's wave equation, is likened to that of a photon in a dielectric medium, such as glass, as per Maxwell's electromagnetic wave equations. A circuit analogy is given to clarify and contrast quasistatic and rigorous techniques of deriving the diffusion capacitance of a p-n junction. The analogies capture all aspects of these topics, highlight the important fundamental issues that may escape an average student's notice, and remove any confusion that may exist in the student's mind because of different and partial treatments of the topics in existing textbooks. Exposure to these and other analogies also plays a role in developing analogical reasoning among students who may pursue research.