Calculation of Electron Density in Nonparabolic Bands

It is shown that the integral $$\mathfrak{F}{\text{(ε,η)=2π}}^{\text{−1/2}}{\displaystyle {\int }_0^{\infty }}\frac{y^{\text{1/2}}{\text{(1+y/ε)}}^{\text{1/2}}\text{(1+2y/ε)dy}}{\exp \text{(y−η)+1}}$$ , which is useful for determining the electron density in a nonparabolic energy band of Kane type, may be evaluated in terms of a Bessel function in the Boltzmann limit and that in the narrow‐gap (small ε) limit, an approximation suggested by Bebb and Ratliff is quite accurate.