Block 11 — Semiconductor Fundamentals and Diodes

Learning objectives

90-minute plan

• Warm-up (10 min):
  • Why does a diode conduct in one direction but not in the other?
  • Recall from EEE1: voltage, current direction, power, and resistors.
  • Recall from EEE2: transient overvoltages at inductive loads will later need diode protection.

• Core concepts (55 min):
  • Conductors, semiconductors, insulators, and the band gap.
  • Intrinsic conduction, electron conduction, hole conduction.
  • Doping: n-type and p-type material.
  • pn junction, depletion region, diffusion voltage.
  • Diode operation in forward and reverse direction.
  • Ideal and real diode characteristics.
  • Practical diode models for circuit calculations.

• Practice (20 min):
  • Determine diode polarity and conduction state.
  • Calculate current with a constant-voltage diode model.
  • Estimate differential resistance at a given operating point.
  • Compare ideal and real diode assumptions.

• Wrap-up (5 min):
  • Key messages: pn junction, forward/reverse bias, current limiting, diode models.
  • Preview: rectifiers, smoothing, protection circuits, LEDs, and Z-diode stabilizers in Block 12.

Conceptual overview

Core content

A short quantum view: why energy bands matter

Materials differ strongly in their specific resistance \(\rho\).

In a single atom, electrons can only have certain discrete energies (figure 2 1a and 1b). This is one result of quantum physics. A simple picture is the Bohr model: electrons are not allowed to move on arbitrary paths, but only on certain allowed energy levels.

In a solid, many atoms are very close together (figure 2 2a and 2b). Their individual energy levels interact and broaden into energy bands.

The two most important bands are:

• the valence band: the highest occupied band. Electrons here are still bound in the crystal.
• the conduction band: the next higher band. Electrons here can move through the crystal and contribute to current.

The energetic distance between them is the band gap \(E_{\rm g}\).

\[ \begin{align*} E_{\rm g} = W_{\rm conduction~band} - W_{\rm valence~band} \end{align*} \]

For semiconductors, the band gap is small enough that some electrons can be lifted from the valence band into the conduction band.

When an electron reaches the conduction band, it leaves behind a missing electron in the valence band. This missing electron behaves like a positive mobile charge carrier and is called a hole.

\[ \begin{align*} \text{energy input} \quad\Rightarrow\quad \text{electron-hole pair} \end{align*} \]

The opposite process is called recombination:

\[ \begin{align*} \text{electron}+\text{hole} \quad\Rightarrow\quad \text{released energy}. \end{align*} \]

Intrinsic conduction, electrons, and holes

In a pure semiconductor, some electrons can gain enough energy to leave their bonds. Then

1. The electron becomes mobile in the conduction band.
2. A 'missing electron' (technically: a defect electron or a hole) remains in the valence band.
3. This hole behaves like a positive mobile charge carrier.

At room temperature, only a very small fraction of thermal vibrations has enough energy to generate such electron-hole pairs in pure silicon. Nevertheless, this already creates measurable intrinsic conduction.

Doping: n-type and p-type semiconductors

Doping increases the number of mobile charge carriers much more effectively (see figure 3):

• n-doping adds donor atoms and therefore additional mobile electrons,
• p-doping adds acceptor atoms and therefore additional mobile holes.

Doping only works predictably when the semiconductor crystal is very pure.
The desired dopant atoms should dominate over unwanted impurities.

Doping means adding a very small amount of foreign atoms to the semiconductor crystal.

The pn junction

A diode is formed when p-doped and n-doped regions meet.

At the junction:

• electrons diffuse from the n-side into the p-side,
• holes diffuse from the p-side into the n-side,
• electrons and holes recombine,
• a region with almost no mobile charge carriers forms.

The depletion region behaves like an internal barrier.
Without an external voltage, it prevents a large current.

Forward and reverse operation

We define the diode voltage

\[ \begin{align*} u_{\rm AK}=u_{\rm A}-u_{\rm K}. \end{align*} \]

• \(u_{\rm AK}>0\): anode is more positive than cathode.
• \(u_{\rm AK}<0\): anode is more negative than cathode.

Ideal diode model

The simplest model is the ideal diode.

\[ \begin{align*} \text{forward direction: } u_{\rm AK}=0,\quad i_{\rm D}>0 \end{align*} \]

\[ \begin{align*} \text{reverse direction: } i_{\rm D}=0,\quad u_{\rm AK}<0 \end{align*} \]

Real diode characteristic

A real diode has an exponential current-voltage characteristic.

\[ \begin{align*} \boxed{ i_{\rm D} = {\color{red}{I_{\rm S}(T)}} \left( {\rm e}^{\frac{{\color{blue}{u_{\rm AK}}}}{{\color{green}{mU_{\rm T}}}}} -1 \right) } \end{align*} \]

with

\[ \begin{align*} U_{\rm T}=\frac{kT}{e}. \end{align*} \]

Often a turn-on voltage $U_{\rm TO}$ for typical currents (some $\rm mA$) at \(25^\circ{\rm C}\) are used.

Practical diode models for circuit calculation

For hand calculations we usually do not use the full exponential equation, because it is often too complex for a quick solution.
Instead the following is often used:

The differential forward resistance is

\[ \begin{align*} r_{\rm F} = \frac{\Delta U_{\rm F}}{\Delta I_{\rm F}}. \end{align*} \]

For large forward voltages compared with \(U_{\rm T}\), the diode equation leads approximately to

\[ \begin{align*} r_{\rm D} = \frac{{\rm d}u_{\rm D}}{{\rm d}i_{\rm D}} \approx \frac{mU_{\rm T}}{I_{\rm D}}. \end{align*} \]

Exercises

Common pitfalls

• Thinking a diode is just a resistor: A diode is nonlinear. The ratio \(U/I\) is not constant.
• Forgetting current limitation: A forward-biased diode needs a current-limiting component.
• Treating \(0.7~{\rm V}\) as exact: The forward voltage depends on current, temperature, and semiconductor material.
• Mixing anode and cathode: Current flows easily from anode to cathode when the diode is forward-biased.
• Ignoring reverse limits: Real diodes have maximum reverse voltage. LEDs often tolerate only small reverse voltages.
• Confusing hole movement with electron movement: Holes are missing electrons, but they behave like positive mobile charge carriers.
• Using the exponential diode equation without unit care: \(U_{\rm T}\) must be in volts and \(T\) in kelvin.

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