Block 11 — Semiconductor Fundamentals and Diodes

• 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.

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

In the band model, two energy ranges are especially important:

• the valence band, where electrons are bound,
• the conduction band, where electrons can move through the crystal.

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

<tabcaption tab_band_gap|Qualitative band model>

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

• the electron becomes mobile in the conduction band,
• a missing electron remains in the valence band,
• this missing electron behaves like a positive mobile charge carrier.

The missing electron is called a hole.

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

<tabcaption tab_doping|Doping of silicon>

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.

This region is called the depletion region or space-charge region.

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

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.

<tabcaption tab_diode_bias|Diode operation depending on \(u_{\rm AK}\)>

The simplest model is the ideal diode.

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

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

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

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

<tabcaption tab_diode_equation_symbols|Symbols in the diode equation>

At room temperature, \(U_{\rm T}\) is approximately

\[ \begin{align*} U_{\rm T}\approx 26~{\rm mV}. \end{align*} \]

Typical values at \(25^\circ{\rm C}\):

<tabcaption tab_typical_diode_values|Typical diode values>

For hand calculations we usually do not use the full exponential equation.

<tabcaption tab_diode_models|Diode models for circuit calculations>

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

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

A diode must usually be operated with a current-limiting element.

For the circuit

\[ \begin{align*} U_{\rm E} \rightarrow R \rightarrow D \end{align*} \]

the loop equation is

\[ \begin{align*} U_{\rm E} = U_R+U_{\rm D}. \end{align*} \]

With the constant-voltage model,

\[ \begin{align*} U_{\rm D}\approx U_{\rm TO}. \end{align*} \]

Therefore

\[ \begin{align*} I_{\rm D} \approx \frac{U_{\rm E}-U_{\rm TO}}{R}. \end{align*} \]

A Z-diode is operated in reverse breakdown. In its operating range, the diode voltage is approximately constant:

\[ \begin{align*} u_{\rm Z}\approx U_{\rm Z}. \end{align*} \]

The piecewise-linear model is

\[ \begin{align*} u_{\rm Z} \approx U_{\rm Z}+r_{\rm Z}i_{\rm Z}. \end{align*} \]

An LED is a diode that emits light in forward direction. The required forward voltage depends on the semiconductor material and therefore on the color.

<tabcaption tab_led_forward_voltage|Typical LED forward voltages>

• 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.