(adsbygoogle = window.adsbygoogle || []).push({}); Trouble replicating a calculation in "Silicon Nanoelectronics"

I'm reading the textbook "Silicon Nanoelectronics" and I've encountered an equation for the transmission probability, which you can see among the attachments.

In this equation, T is the transmission probability for a rectangular-shaped potential barrier with width d and height ϕ, where m* is the effective mass of silicon and q the elementary charge.

They go on to say that "From Equation (3.1), the barrier width

giving transmission probabilities of 1 × 10^-3 and 1 × 10^-6 at a barrier height of 100

mV can be estimated to be 10 and 5 nm, respectively."

I really, really want to replicate this estimation/calculation but I can't seem to do in. When I plug in the given numbers (ϕ = 100 mV, d = 5 or 10 nm, q = elementary charge, ħ = reduced Planck constant, and m* = effective mass silicon), I can't seem to get even remotely close to the listed probabilities. Perhaps the problem is the effective mass of silicon? I am not certain what value I should take, but I went with 0,2 times the mass of an electron (see: http://ecee.colorado.edu/~bart/book/effmass.htm)

Can anyone please show me how the writer approximately got 10nm and 5nm using the equation and the given probabilities? I know it's not a precise calculation, nor a precise equation, but I'd still like to see how he got this estimation.

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# Trouble replicating a calculation in Silicon Nanoelectronics

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