(Bug?) HP48 Equation Library

[Han]

Programming an equation library has lead me to learn about all sorts of stuff that I really never cared much about (and still do not -- but at least I am learning). Anyway, for those of you who have some background in materials science:

The following formulas are for carrier concentration of silicon (intrinsic density \( n_i \)) as a function of temperature \(T\):

\[ E_g = 1.17 - 4.73\times 10^{-4}\cdot \frac{T^2}{T+636} \]
\[ n_i = \sqrt{ N_c \cdot N_v} \cdot e^{-E_g/(2\cdot k\cdot T)} \]

The HP48 uses a value of \( 7.2756517951 \times 10^{15} \) for \( \sqrt{N_c \cdot N_v} \) -- the square root of the product of the effective density of states for the conductance and valence bands, respectively. However, I cannot seem to find any references where this is the case. The formulas I have found for the effective density states do not produce this value. Can anyone provide references to this value, or those of the appropriate \( N_c \) and \( N_v \) that form this value?