First off, please understand my background. I am doing a course in Digital Integrated Circuits and following the book CMOS Digital Integrated Circuits and Design by Kang (3rd Edition).
I barely have any requisite background in MOS structure and semiconductor devices as it is a course being taught along with this course. Therefore, please explain with the requisite background. Thank you 
There is a derivation regarding depletion layer width of a MOS structure with p substrate in depletion mode (i.e. the gate voltage is positive and small and the base of substrate is grounded).
To derive this, they have assumed that holes are thin horizontal layers parallel to the semiconductor-oxide surface. To move a layer of width $dx$,
$$
dQ = -q N_{a} dx
$$
My first question is, why is that sign negative? We’re trying to move a positive layer here, right?
Then, the derivation moves on to calculate the change of surface potential required to displace the charge sheet distance $x_{d}$ away i.e.
$$
dphi_{s} = -xfrac{dQ}{epsilon_{Si}} = frac{qN_{a}x}{epsilon_{Si}}dx
$$
which is supposedly derived from the Possion equation (which I haven’t been exactly taught well). Please explain how this part came to be.
Also, I am equally confused about the concept of surface potential, which according to the book is the fermi potential at the surface. I’m guessing the change in surface potential is imparted from the external bias applied. However, when they are integrating, they are integrating from $phi_{F}$, i.e. the bulk fermi potential to $phi_{S}$. So my question again is how is this change in surface potential when we are taking it from the bulk to the surface?
