Double barrier resonant tunneling diode using annealing induced diffusion modified quantum well is proposed as a viable alternative to that using parabolic quantum well which requires complex techniques to fabricate it. The transmission coefficients are calculated using the hybrid incremental airy function plane wave approach. The room temperature current-voltage characteristics have been calculated using transmission coefficients. The current-voltage characteristics are found to be similar in both diodes.

Chemical potential and internal energy of a noninteracting Fermi gas at low temperature are evaluated using the Sommerfeld method in the fractional-dimensional space. When temperature increases, the chemical potential decreases below the Fermi energy for any dimension equal to 2 and above due to the small entropy, while it increases above the Fermi energy for dimensions below 2 as a result of high entropy. The ranges of validity of the truncated series expansions of these quantities are extended from low to intermediate temperature regime as well as from high to relatively low density regime by using the Pad ́e approximant technique.