Question 4: Semiconductors and Logic Gates

Question

In a semiconductor $p$-n diode, the doping concentrations on $p$-side and $n$-side are $10^{15}$ atoms $/ \mathrm{cm}^3$ and $10^{18}$ atoms $/ \mathrm{cm}^3$, respectively. Which one of the following statements is true?

Accepted Answer

When a $\mathrm{p}-\mathrm{n}$ junction is formed, holes from the p -side and electrons from the n -side diffuse across the junction, leaving behind immobile ionized dopant atoms. The total negative charge on the p -side of the depletion region must exactly balance the total positive charge on the n -side:
$$ \left|Q_p\right|=\left|Q_n\right| $$
The charge in each region is the product of the electronic charge ( e ), the doping concentration and the volume of region (V).
$$ \mathrm{Q}=\mathrm{eNV} $$
The volume of region is the product of width of the depletion region ( w ) and the cross-sectional area (A),
$$ \mathrm{V}=\mathrm{Aw} $$
So, the charge in each region is $\mathrm{Q}=\mathrm{eNAw}$
On the p -side: $\mathrm{Q}_{\mathrm{p}}=\mathrm{e} \cdot \mathrm{A} \cdot \mathrm{N}_{\mathrm{a}} \cdot \mathrm{w}_{\mathrm{p}} \ldots$ (i)
On the n -side: $\mathrm{Q}_{\mathrm{n}}=\mathrm{q} \cdot \mathrm{A} \cdot \mathrm{N}_{\mathrm{d}} \cdot \mathrm{w}_{\mathrm{n}} \ldots$ (ii)
Where $w_p$ and $w_n$ are the widths of the depletion layer in the $p$ and $n$ regions, and $N_a$ and $N_d$ are the acceptor and donor concentrations.
Equating the two:
$$ e A N_a w_p=e A N_d w_n $$
$$\Rightarrow $$ $$ \frac{\mathrm{w}_{\mathrm{p}}}{\mathrm{w}_{\mathrm{n}}}=\frac{\mathrm{N}_{\mathrm{d}}}{\mathrm{~N}_{\mathrm{a}}} $$
The acceptor concentration in p -side is $\mathrm{N}_{\mathrm{a}}=10^{15}$ atoms $/ \mathrm{cm}^3$
The donor concentration in n -side is $\mathrm{N}_{\mathrm{d}}=10^{18}$ atoms $/ \mathrm{cm}^3$
Since $\mathrm{N}_{\mathrm{d}}>\mathrm{N}_{\mathrm{a}} \Rightarrow \mathrm{x}_{\mathrm{p}}>\mathrm{x}_{\mathrm{n}}$.
So, the depletion region penetrates deeper into the side that is more lightly doped.
Because the p -side has a much lower concentration ( $10^{15}$ ) than the n -side ( $10^{18}$ ), the depletion region width is more on the p-side.
Thus, the correct option is (B).

Answer

Widths of depletion region on either side of the interface are equal

Answer

The depletion region width is more on p -side compared to that in n -side

Answer

The depletion region width is more on $n$-side compared to that in $p$-side

Answer

No depletion region forms because of unequal doping concentrations on p and n -sides

Semiconductors and Logic Gates

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are 10^{15} atoms / \mathrm{cm}^3 and 10^{18} atoms / \mathrm{cm}^3, respectively. Which one of the following statements is true?

Choose the correct answer: