= Solution
Take an abrupt equilibrium <p-n junction> with the p side at $x<0$ and the n side at $x>0$. In the quasi-neutral bulk, <electron holes> are the majority carriers on the p side and <Electrons> are the majority carriers on the n side. With ionized dopant densities $N_A,N_D$ and nondegenerate statistics,
$$
p_{p}\simeq N_A,\quad n_{p}\simeq n_i^2/N_A,\qquad
n_{n}\simeq N_D,\quad p_{n}\simeq n_i^2/N_D,
$$
where $n_i$ is the <intrinsic carrier concentration>. The <semiconductor mass-action law> $np=n_i^2$ applies at equilibrium. Both mobile populations are small in the <depletion region> compared with the dopant densities.
The <charge and carrier density of an abrupt p-n junction> must distinguish mobile populations from net charge. Diffusion leaves negatively charged ionized <acceptor impurities> on the p side and positively charged ionized <donor impurities> on the n side. Under the <depletion approximation>,
$$
\boxed{\rho(x)=\begin{cases}
-eN_A,&-x_p<x<0,\\
+eN_D,&0<x<x_n,\\
0,&x<-x_p\text{ or }x>x_n,
\end{cases}\qquad N_Ax_p=N_Dx_n.}
$$
The neutral bulks have large carrier densities but nearly zero net <charge density>. The <electric field> points from the positive donor region toward the negative acceptor region, balancing diffusion at equilibrium.
\Image[/past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2019/paper-2-a4-junction-densities.png]
{title=Illustrative equilibrium carrier densities and depletion-approximation net charge for a symmetric abrupt p-n junction}
The figure uses equal dopant densities only to show a simple symmetric sketch. Generally the more lightly doped side has the wider depleted interval. The carrier profiles are smooth, whereas the step-shaped net <charge density> is the ideal <depletion approximation>.
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