Foundations — Covalent bonding in silicon crystals

Before you can read the parent note you must be able to look at each symbol below and see a picture. We build them in order — each one uses only the ones before it.

1. The atom: a nucleus and shells

Look at the figure. Each ring is a shell. Electrons live on the rings, never between them — that "only certain rings allowed" rule is the first hint of energy levels we'll need later.

WHY do we care? Because chemistry — including bonding — is decided almost entirely by the outermost ring. The inner rings are full and stay out of the story.

2. Counting electrons: the number $Z$ and the configuration

The parent note writes silicon's arrangement as:

$1s^{2}2s^{2}2p^{6}3s^{2}3p^2$

This scary line is just a seating chart. Let's read every symbol:

So $3s^{2}3p^2$ means: on ring number 3, there are $2+2=4$ electrons.

3. Valence electrons — the only ones that matter

In the figure the inner rings are greyed out — they are "sealed away." Only the 4 outer electrons (highlighted) reach out to touch neighbours. This is why the parent note keeps saying "silicon has 4 valence electrons" — those 4 are the hands silicon shakes with.

4. The octet — why "8" is the magic number

WHY 8, not any number? The outer ring here ($s+p$ seats) has room for exactly $2+6=8$ electrons. A ring with every seat filled is low-energy and unreactive — like a full table where nobody needs to move.

Silicon has 4 and wants 8. It is exactly halfway:

5. Sharing a pair — the covalent bond, drawn

Follow the figure. The central silicon (blue) offers one electron to each of 4 neighbours; each neighbour offers one back. Count around the central atom:

$\underset{\text{its own}}{\underbrace{4}}+\underset{\text{one from each neighbour}}{\underbrace{4}}=8(\text{octet, complete!})$

6. Energy, and the unit "eV"

Everything about breaking bonds is measured in energy, so we need its unit.

The figure shows the idea as a ledge: bonded electrons sit on a low floor; a free electron sits on an upper floor; the height of the step is $E_g$. A small step (silicon) is easy to jump with a little heat; a tall step (diamond) is not. This picture becomes the Band theory of solids when we stack many atoms.

7. Heat, temperature $T$, and the "steep rise" symbols

To free an electron we heat the crystal. That brings in three more symbols.

WHY the exponential $e^{(\dots )}$ and not, say, a straight line? Because nature hands out "lucky big kicks" of thermal energy rarely, and the chance of a kick big enough to clear the step falls off multiplicatively as the step gets taller — that is exactly what $e^{-\text{(step)}/\text{(kick size)}}$ describes. A straight line can't capture "astronomically rare." This is why diamond ($E_g=5.5$) has vastly fewer free carriers than silicon ($E_g=1.12$), not just proportionally fewer.

8. How it all connects

Read top-left down: atoms → counting → 4 valence electrons → octet → covalent sharing → the crystal. Read the right branch: energy units → band gap → breaking bonds with heat → conduction. Both branches meet at $n_i$, the payoff quantity of the whole topic.

Equipment checklist

Cover the right side and test yourself — if you can answer each, you're ready for the parent note.

Connections

• Covalent bonding in silicon crystals — the parent topic these foundations feed
• Ionic vs covalent vs metallic bonding — the "share vs steal vs donate" comparison
• Diamond cubic crystal structure — where the tetrahedron and $109.5^{\circ }$ come from
• Band theory of solids — the band gap ledge, scaled to many atoms
• Intrinsic vs extrinsic semiconductors — meaning of $n_i$
• Electron-hole pair generation and recombination — the life of a hole