FinFET transistor structure: Foundations — Hardware deep dive

This page is the toolbox. Before you read FinFET transistor structure itself, every letter it throws at you should already feel like an old friend. We build them one at a time, each one earned before the next.

0. The stage: what a transistor physically is

Picture a garden hose. Water wants to flow from a tap (call it the source) to a bucket (the drain). Your hand squeezing the hose is the gate. Squeeze hard → no water (transistor OFF). Release → water flows (transistor ON). Everything in this topic is about how well your hand can squeeze as the hose gets thinner and shorter.

Source — where charge carriers come from.
Drain — where they flow to.
Gate — the controlling terminal; its voltage builds or removes the "squeeze."
Channel — the thin region of silicon between source and drain where current actually flows. This is the hose interior your hand pinches.

We need these four words because the whole topic is a fight for control of the channel between two rivals: the gate (which wants to switch it OFF) and the drain (which, at small sizes, sneaks in and keeps it ON — that is the leakage problem).

1. Voltage and electric field — the "push"

Why we need the field: the gate does not touch the channel — it acts through the insulator by projecting an electric field across it. When the parent note says "the drain's electric field starts to control the channel," it means the drain's voltage-slope reaches all the way to the channel and fights the gate. So a "field" is just "how far and how strongly a voltage's influence reaches."

2. Potential $ψ$ — voltage as a landscape

Picture a hilly terrain. The height at each spot is $ψ$ . A ball (a charge) rolls downhill. When the gate is OFF it raises a hill (a barrier) between source and drain, so no charge can roll across. Short-channel trouble is the drain lowering that hill from its side.

Why the topic needs $ψ (x, y)$ rather than one number: the whole game is where the potential is high or low across the device, not just its average. That is why it carries coordinates $x$ (vertical, into the fin) and $y$ (horizontal, source→drain).

3. The derivative $\frac{d ^{2} ψ}{d y ^{2}}$ — reading curvature

The parent's Poisson equation contains $\frac{d ^{2} ψ _{c} ( y )}{d y ^{2}}$ . Let us earn every piece.

Why the topic needs curvature: Poisson's equation (next section) says curvature of the potential is set by the charge present. Curvature is literally how bent the barrier-hill is — and a sharply bent hill is a strong barrier. So $\frac{d ^{2} ψ}{d y ^{2}}$ is the mathematical name for "how curved is the OFF-state hill along the channel."

Recall

What does a negative second derivative of $ψ$ look like as terrain? ::: A dome / hill that bends downward — the barrier the gate raises to block current.

4. Permittivity $ε$ and charge density $ρ$ — the two ingredients before Poisson

Before we can write Poisson's equation, we must earn its two remaining symbols: $ε$ and $ρ$ .

Two versions appear:

$ε_{0}$ — permittivity of empty space, a fixed constant of nature.
Relative permittivity $ε_{r}$ — a plain number telling how many times more than vacuum a material passes the field. Silicon: $ε_{s i} = 11.7 ε_{0}$ . Silicon-dioxide insulator: $ε_{o x} = 3.9 ε_{0}$ .

See Gate Oxide and High-k Dielectrics for why engineers hunt for oxides with a bigger $ε_{o x}$ .

5. Poisson's equation — charge bends the landscape

Now every symbol is defined, we can read the equation.

You do not need to solve it here — see Poisson's Equation in MOS Electrostatics. You only need the story: the presence of charge $ρ$ forces the potential-landscape to bend, and a "stiffer" material (bigger $ε$ ) bends less for the same charge. Where there is charge, the hill curves; the gate controls that curvature to build or flatten the barrier.

Why the topic needs it: it is the machine that produces the natural length $λ$ . The parent integrates Poisson's equation across the fin and out pops one number, $λ$ , that summarizes "how far the gate's grip reaches."

6. The geometry symbols — lengths and thicknesses

Now the easy but essential rulers. Each is a distance you could measure with a tiny ruler on the device cross-section.

Definition

$L_{g}$ — gate length: how long the gate is along the source→drain direction. This is "how short the channel is." Shrinking $L_{g}$ is the entire pressure of Moore's Law; it also causes Short-Channel Effects.
$t_{o x}$ — oxide thickness: how thin the insulator between gate and channel is. Thinner = gate sits closer = stronger grip.
$t_{s i}$ — silicon body thickness: the thickness of the conducting silicon body that the gate has to control, measured across the direction the gate squeezes.
$W_{f in}$ — fin width: the thickness of the vertical silicon wall. In a FinFET, the silicon body is the fin, so the body thickness and the fin width are the same distance: $t_{s i} = W_{f in}$ . (One is the general name, the other the FinFET-specific name for that same measurement.)
$H_{f in}$ — fin height: how tall the wall stands.

Why the topic needs all of them: they are the knobs. The natural length $λ$ is built from $t_{s i}$ and $t_{o x}$ ; the effective width is built from $H_{f in}$ and $W_{f in}$ . Control comes from the thin dimensions; current comes from the tall one.

7. The gate count $α$ — how many sides grip

8. Putting the rulers together: $λ$ and $W_{e f f}$

You now own every ingredient for the parent's two headline formulas.

Read them as sentences now, not symbols:

$λ$ : thin body, thin oxide, many gates → tight grip.
$W_{e f f}$ : tall fin → more current for free.

These lead directly to DIBL and Dennard Scaling once you see how $λ$ controls whether the OFF barrier survives.

Prerequisite map

Equipment checklist

Self-test: can you answer each without peeking?

What are the four regions of a transistor and their hose-analogy roles?

Source (tap, current from), Drain (bucket, current to), Gate (your squeezing hand, control), Channel (hose interior being pinched).

What is the formal relation between electric field

E

and voltage, and what does the minus sign mean?

E = - d V / d x

; the minus sign means the field points downhill, from high voltage to low voltage — the direction a positive charge is pushed.

What does the potential

ψ (x, y)

represent as a picture?

A terrain/landscape whose height is voltage at each point; charges roll downhill and the OFF-state gate raises a barrier hill.

What does the second derivative

\frac{d ^{2} ψ}{d y ^{2}}

measure?

Curvature — the slope of the slope; how sharply the barrier hill bends.

What is charge density

ρ

The amount of electric charge packed into each tiny volume of material (charge per unit volume).

Why does

ε_{0}

disappear from the

λ

formula?

Because

ε_{s i}

and

ε_{o x}

appear as a ratio, so the vacuum constant cancels, leaving relative permittivities

11.7

and

3.9

Are

t_{s i}

and

W_{f in}

the same or different?

Same distance, two names —

t_{s i}

is the general body-thickness symbol,

W_{f in}

is the FinFET-specific name for that identical edge.

What is

α

and why is it in the denominator of

λ

The number of gated surfaces (1 planar, ~3 FinFET); more gates = tighter grip = smaller

λ

= better control.

Which dimensions do you want thin, and which tall, and why?

Thin

t_{s i}, t_{o x}

(and thin fin) for control/small

λ

; tall

H_{f in}

for more current via large

W_{e f f}

State

λ

and

W_{e f f}

from memory.

λ = ε_{s i} t_{s i} t_{o x} / (α ε_{o x})

and

W_{e f f} = 2 H_{f in} + W_{f in}