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| electrical_engineering_and_electronics_2:block11 [2026/05/18 03:07] – mexleadmin | electrical_engineering_and_electronics_2:block11 [2026/06/10 03:08] (current) – mexleadmin | ||
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| - | TBD | ||
| - | |||
| - | - Semiconductor components \\ (approx. 4 blocks, based on previous lectures on [[circuit_design: | ||
| - | - Fundamentals (conductors, | ||
| - | - Diodes (real characteristic curve, operating point, equivalent circuit) | ||
| - | - Zener diode | ||
| - | - LED | ||
| - | - Protective circuit with diodes | ||
| - | - Rectifier circuits (single-phase rectifier, center tap circuit, bridge rectifier, smoothing capacitor) | ||
| - | - Bipolar transistor (structure, designations, | ||
| - | - Transistor as a switch (circuit, switching times and behavior) | ||
| - | - MOSFET (structure, comparison with bipolar transistor) | ||
| - | - Optional: Transistor as an amplifier | ||
| - | |||
| - | |||
| ====== Block 11 — Semiconductor Fundamentals and Diodes ====== | ====== Block 11 — Semiconductor Fundamentals and Diodes ====== | ||
| Line 33: | Line 18: | ||
| \] | \] | ||
| at a qualitative level. | at a qualitative level. | ||
| - | * calculate simple diode operating points with a series resistor. | ||
| - | * identify basic diode types such as universal diodes, Z-diodes, and LEDs. | ||
| </ | </ | ||
| Line 94: | Line 77: | ||
| ===== Core content ===== | ===== Core content ===== | ||
| - | ==== Conductors, semiconductors, and insulators | + | < |
| + | |||
| + | === Introductory Example === | ||
| + | |||
| + | Microcontrollers often have many pins that evaluate signals between $0...5~\rm V$ as a digital signal. However, the input signal can be disturbed during transmission by small coupled pulses, e.g. from HF sources like mobile phones. This interference can cause the signal to leave the permitted voltage range of approx. $-0.5...5.5~\rm V$ and thus destroy the logical unit. | ||
| + | |||
| + | To prevent such destruction, | ||
| + | |||
| + | This chapter explains why a diode becomes conductive at a certain voltage, what has to be considered when using diodes, and which different types of diodes are available. | ||
| + | |||
| + | < | ||
| + | |||
| + | For the protection of digital interfaces that leave the device housing (e.g. USB), additional separate ICs are used that support this protection of the data processing chips. These protection diode ICs suppress the short-time voltages and are called __T__ransient __V__oltage __S__uppressor or TVS diodes. Typical TVS ICs are [[https:// | ||
| + | |||
| + | </ | ||
| + | |||
| + | <callout type=" | ||
| + | |||
| + | === Further reading === | ||
| + | |||
| + | * An introductory is available at [[https:// | ||
| + | |||
| + | </ | ||
| + | |||
| + | |||
| + | ==== A short quantum view: why energy bands matter | ||
| Materials differ strongly in their specific resistance \(\rho\). | Materials differ strongly in their specific resistance \(\rho\). | ||
| Line 100: | Line 108: | ||
| < | < | ||
| <panel type=" | <panel type=" | ||
| - | < | + | < |
| - | {{drawio> | + | {{drawio> |
| </ | </ | ||
| </ | </ | ||
| - | In the band model, | + | <panel type=" |
| + | The simple circuit view says: conductors conduct, insulators block, semiconductors | ||
| + | To understand **why** semiconductors can be controlled so well, we need a short look at the energy of electrons in a solid. | ||
| + | </ | ||
| - | * the **valence band**, where electrons | + | In a single atom, electrons |
| - | | + | This is one result of quantum physics. A simple picture is the Bohr model: |
| - | The energy | + | In a solid, many atoms are very close together (<imgref fig_bohr_to_band_model> |
| + | |||
| + | |||
| + | < | ||
| + | <panel type=" | ||
| + | < | ||
| + | {{drawio> | ||
| + | </ | ||
| + | </ | ||
| + | |||
| + | 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 | ||
| + | |||
| + | \[ | ||
| + | \begin{align*} | ||
| + | E_{\rm g} | ||
| + | = | ||
| + | W_{\rm conduction~band} | ||
| + | - | ||
| + | W_{\rm valence~band} | ||
| + | \end{align*} | ||
| + | \] | ||
| - | < | + | For semiconductors, |
| ^ Material type ^ Band model ^ Electrical behavior ^ | ^ Material type ^ Band model ^ Electrical behavior ^ | ||
| Line 119: | Line 155: | ||
| | insulator | large band gap | almost no mobile charge carriers | | | insulator | large band gap | almost no mobile charge carriers | | ||
| - | <panel type=" | + | <callout icon=" |
| - | A semiconductor can be imagined as a parking garage | + | An electron can become mobile if it receives enough energy to cross the band gap. |
| + | This energy can come, for example, from | ||
| + | |||
| + | * light, i.e. photons, | ||
| + | * lattice vibrations, i.e. thermal energy or phonons. | ||
| + | </ | ||
| + | |||
| + | 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**: | ||
| + | |||
| + | \[ | ||
| + | \begin{align*} | ||
| + | \text{electron}+\text{hole} | ||
| + | \quad\Rightarrow\quad | ||
| + | \text{released energy}. | ||
| + | \end{align*} | ||
| + | \] | ||
| + | |||
| + | <panel type=" | ||
| + | Imagine | ||
| + | |||
| + | * The **lower tribune** is close to the field and very popular. It is normally fully booked. This is the **valence band**. | ||
| + | * The **upper tribune** is farther away and less attractive. To get there, a person needs an extra “energy ticket”. This is the **conduction band**. | ||
| + | * The required energy ticket is the **band gap** \(E_{\rm g}\). | ||
| - | * The lower floor is almost full: the valence band. | + | If one person receives enough energy, they move from the full lower tribune to the upper tribune. |
| - | * The upper floor allows movement: the conduction band. | + | Now the person upstairs can move around more freely, like an electron |
| - | * The band gap is the energy needed to move an electron | + | |
| - | Doping adds useful “parking spots” or “missing spots” so that charge transport becomes much easier. | + | At the same time, an empty seat remains in the lower tribune. |
| + | When neighboring people move into that empty seat, the empty seat itself seems to move. | ||
| + | This moving empty seat is the analogy for a **hole**. | ||
| </ | </ | ||
| Line 133: | Line 203: | ||
| In a pure semiconductor, | In a pure semiconductor, | ||
| - | | + | |
| - | * a missing electron | + | |
| - | | + | |
| - | + | ||
| - | The missing electron is called a **hole**. | + | |
| < | < | ||
| Line 146: | Line 214: | ||
| </ | </ | ||
| - | <panel type=" | + | At room temperature, |
| - | Imagine a fully occupied row of seats. | + | Nevertheless, this already creates measurable **intrinsic conduction**. |
| - | If one student moves to the right into an empty seat, the empty seat appears to move to the left. | + | |
| - | + | ||
| - | The empty seat is not a real object, but it behaves as if it moves. | + | |
| - | A hole in a semiconductor is similar: it is a missing electron, but it behaves like a positive moving charge carrier. | + | |
| - | </ | + | |
| ==== Doping: n-type and p-type semiconductors ==== | ==== Doping: n-type and p-type semiconductors ==== | ||
| + | |||
| + | Doping increases the number of mobile charge carriers much more effectively (see <imgref fig_n_doping> | ||
| + | |||
| + | * 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. | Doping means adding a very small amount of foreign atoms to the semiconductor crystal. | ||
| - | < | + | < |
| - | <WRAP column half> | + | |
| <panel type=" | <panel type=" | ||
| - | < | + | < |
| - | {{: | + | {{drawio> |
| </ | </ | ||
| </ | </ | ||
| - | + | \\ | |
| - | <WRAP column half> | + | |
| - | <panel type=" | + | |
| - | < | + | |
| - | {{: | + | |
| - | </ | + | |
| - | </ | + | |
| - | </ | + | |
| < | < | ||
| Line 179: | Line 241: | ||
| | n-type | phosphorus, arsenic, antimony | electrons | donors | | | n-type | phosphorus, arsenic, antimony | electrons | donors | | ||
| | p-type | boron, aluminium, indium | holes | acceptors | | | p-type | boron, aluminium, indium | holes | acceptors | | ||
| + | |||
| + | </ | ||
| < | < | ||
| - | Doping does **not** mean that the semiconductor becomes strongly charged as a whole. | + | Doping does **not** mean that the semiconductor becomes strongly charged as a whole. |
| - | The crystal is still approximately electrically neutral. | + | The crystal is still approximately electrically neutral. |
| Doping mainly changes how many mobile charge carriers are available. | Doping mainly changes how many mobile charge carriers are available. | ||
| </ | </ | ||
| Line 193: | Line 257: | ||
| <panel type=" | <panel type=" | ||
| < | < | ||
| - | {{: | + | {{drawio>pnjunction.svg}} |
| </ | </ | ||
| </ | </ | ||
| Line 204: | Line 268: | ||
| * a region with almost no mobile charge carriers forms. | * a region with almost no mobile charge carriers forms. | ||
| - | This region is called the **depletion region** or **space-charge region**. | + | < |
| + | The region | ||
| + | This is called the **depletion region** or **space-charge region**. | ||
| + | </ | ||
| < | < | ||
| <panel type=" | <panel type=" | ||
| < | < | ||
| - | {{: | + | {{drawio>evolutionofpnjunction.svg}} |
| </ | </ | ||
| </ | </ | ||
| - | The depletion region behaves like an internal barrier. | + | The depletion region behaves like an internal barrier. |
| Without an external voltage, it prevents a large current. | Without an external voltage, it prevents a large current. | ||
| - | <panel type=" | + | <callout |
| - | The depletion region is like a spring-loaded door. | + | **Mnemonic: PANIC!** |
| - | | + | \[ |
| - | * In the other direction, the spring pushes the door more firmly closed. | + | \begin{align*} |
| + | \text{Positive Anode, Negative Is Cathode} | ||
| + | \end{align*} | ||
| + | \] | ||
| - | The diode behaves similarly: one polarity reduces the barrier, the other polarity increases it. | + | This helps to remember the forward direction of a diode. |
| - | </panel> | + | </callout> |
| ==== Forward and reverse operation ==== | ==== Forward and reverse operation ==== | ||
| Line 236: | Line 306: | ||
| * \(u_{\rm AK}>0\): anode is more positive than cathode. | * \(u_{\rm AK}>0\): anode is more positive than cathode. | ||
| - | * \(u_{\rm AK}<0\): anode is more negative than cathode. | + | * \(u_{\rm AK}<0\): anode is more negative than cathode. |
| + | \\ \\ | ||
| < | < | ||
| ^ Condition ^ Name ^ Effect on depletion region ^ Current ^ | ^ Condition ^ Name ^ Effect on depletion region ^ Current ^ | ||
| - | | \(u_{\rm AK}>0\) | forward bias | depletion region becomes smaller | large current possible | | + | | \(u_{\rm AK}>0\) | forward bias \\ forward voltage is $U_{\rm F} = u_{\rm AK}$ |
| - | | \(u_{\rm AK}<0\) | reverse bias | depletion region becomes larger | only small leakage current, until breakdown | | + | | \(u_{\rm AK}<0\) | reverse bias \\ reverse voltage is $U_{\rm R} = -u_{\rm AK}$ |
| + | </ | ||
| + | \\ | ||
| - | <callout | + | <WRAP> |
| - | **Mnemonic** | + | < |
| + | < | ||
| + | {{drawio> | ||
| + | </ | ||
| + | </ | ||
| - | \[ | ||
| - | \begin{align*} | ||
| - | \text{Positive Anode, Negative Is Cathode} | ||
| - | \end{align*} | ||
| - | \] | ||
| - | This helps to remember | + | <panel type=" |
| - | </callout> | + | Imagine two neighboring tribunes in a stadium (e.g. fan section and main tribune). |
| + | |||
| + | * On the **n-side**, there are many extra people. They represent mobile **electrons**. | ||
| + | * On the **p-side**, there are many empty seats. They represent mobile **holes**. | ||
| + | |||
| + | At first, people near the border can move into empty seats on the other side. \\ | ||
| + | After this happens, there are fewer mobile people and fewer mobile empty seats close to the border. | ||
| + | A locally empty border zone appears. This represents the **depletion region**. | ||
| + | |||
| + | The depletion region is therefore not an extra part inserted between the two sides. | ||
| + | It forms automatically because electrons and holes recombine near the pn junction. | ||
| + | |||
| + | In **forward | ||
| + | The empty border zone becomes narrower, and new people and empty seats are continuously supplied from the outside. A current can flow. | ||
| + | |||
| + | In **reverse bias**, the external voltage pulls people and empty seats away from the border. | ||
| + | The empty border zone becomes wider, so crossing becomes very unlikely. Only a tiny leakage current remains. | ||
| + | </panel> | ||
| ==== Ideal diode model ==== | ==== Ideal diode model ==== | ||
| Line 272: | Line 361: | ||
| \] | \] | ||
| - | < | + | < |
| - | <panel type=" | + | |
| - | < | + | |
| - | {{drawio>block11_ideal_diode_characteristic.svg}} | + | |
| - | </ | + | |
| - | </ | + | |
| <panel type=" | <panel type=" | ||
| Line 318: | Line 402: | ||
| ^ Symbol ^ Meaning ^ | ^ Symbol ^ Meaning ^ | ||
| - | | \(I_{\rm S}(T)\) | reverse saturation current, strongly temperature-dependent | | + | | \(I_{\rm S}(T)\) | reverse saturation current, strongly temperature-dependent |
| - | | \(m\) | emission coefficient, | + | | \(m\) | emission coefficient, |
| - | | \(U_{\rm T}\) | thermal voltage | | + | | \(U_{\rm T}\) | thermal voltage |
| - | | \(k\) | Boltzmann constant | | + | | \(k\) | Boltzmann constant |
| - | | \(e\) | elementary charge | | + | | \(e\) | elementary charge |
| - | | \(T\) | absolute temperature in \({\rm K}\) | | + | | \(T\) | absolute temperature in \({\rm K}\) | |
| - | + | </ | |
| - | At room temperature, | + | \\ |
| - | + | ||
| - | \[ | + | |
| - | \begin{align*} | + | |
| - | U_{\rm T}\approx 26~{\rm mV}. | + | |
| - | \end{align*} | + | |
| - | \] | + | |
| - | Typical values | + | Often a **turn-on voltage** $U_{\rm TO}$ for typical currents (some $\rm mA$) at \(25^\circ{\rm C}\) are used. |
| < | < | ||
| - | ^ Diode material ^ Approximate threshold voltage \(U_{\rm TO}\) ^ Reverse saturation current \(I_{\rm S}\) ^ | + | ^ Diode material |
| | silicon | \(\approx 0.7~{\rm V}\) | some \({\rm pA}\) | | | silicon | \(\approx 0.7~{\rm V}\) | some \({\rm pA}\) | | ||
| | germanium | \(\approx 0.3~{\rm V}\) | some \(\mu{\rm A}\) | | | germanium | \(\approx 0.3~{\rm V}\) | some \(\mu{\rm A}\) | | ||
| + | </ | ||
| + | |||
| <callout type=" | <callout type=" | ||
| - | The value \(0.7~{\rm V}\) for a silicon diode is not a physical constant. | + | * the turn-on voltage has also some alternative labeling: knee voltage, threshold voltage, diode voltage $U_{\rm D}$, forward voltage $U_{\rm F}$ |
| - | It is a useful approximation for typical currents in small signal and basic power circuits. | + | * The value \(U_{\rm TO} = 0.7~{\rm V}\) for a silicon diode is not a physical constant. |
| + | | ||
| </ | </ | ||
| + | |||
| + | < | ||
| + | {{url> | ||
| + | </ | ||
| ==== Practical diode models for circuit calculation ==== | ==== Practical diode models for circuit calculation ==== | ||
| - | For hand calculations we usually do not use the full exponential equation. | + | 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: | ||
| - | <WRAP> | + | <tabcaption tab_diode_models|Diode models |
| - | <panel type=" | + | |
| - | < | + | |
| - | {{drawio> | + | |
| - | </ | + | |
| - | </WRAP> | + | |
| - | < | + | ^ Model ^ Forward direction ^ Reverse direction ^ Use ^ Example ^ |
| + | | ideal diode | \(u_{\rm AK}=0\) | ||
| + | | constant-voltage model | \(u_{\rm AK}\approx U_{\rm TO}\) | ||
| + | | piecewise-linear model | \(u_{\rm AK}\approx U_{\rm TO}+r_{\rm F}\cdot i_{\rm D}\) | \(i_{\rm D}\approx 0\) | more accurate operating point | How does the diode voltage change when the current changes? | ||
| + | </tabcaption> | ||
| + | \\ | ||
| + | < | ||
| - | ^ Model ^ Forward direction ^ Reverse direction ^ Use ^ | ||
| - | | ideal diode | \(u_{\rm AK}=0\) | \(i_{\rm D}=0\) | switching logic, first estimate | | ||
| - | | constant-voltage model | \(u_{\rm AK}\approx U_{\rm TO}\) | \(i_{\rm D}\approx 0\) | quick current calculations | | ||
| - | | piecewise-linear model | \(u_{\rm AK}\approx U_{\rm TO}+r_{\rm F}i_{\rm D}\) | \(i_{\rm D}\approx 0\) | more accurate operating point | | ||
| The differential forward resistance is | The differential forward resistance is | ||
| Line 401: | Line 484: | ||
| \] | \] | ||
| </ | </ | ||
| - | |||
| - | ==== Operating point with a series resistor ==== | ||
| - | |||
| - | 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 | ||
| - | |||
| - | \[ | ||
| - | \begin{align*} | ||
| - | I_{\rm D} | ||
| - | \approx | ||
| - | \frac{U_{\rm E}-U_{\rm TO}}{R}. | ||
| - | \end{align*} | ||
| - | \] | ||
| - | |||
| - | <callout type=" | ||
| - | Never connect a normal diode or LED directly to an ideal voltage source in forward direction. | ||
| - | The diode current must be limited. | ||
| - | </ | ||
| - | |||
| - | ==== Z-diodes and LEDs as diode types ==== | ||
| - | |||
| - | 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 | ||
| - | |||
| - | \[ | ||
| - | \begin{align*} | ||
| - | u_{\rm Z} | ||
| - | \approx | ||
| - | U_{\rm Z}+r_{\rm Z}i_{\rm Z}. | ||
| - | \end{align*} | ||
| - | \] | ||
| - | |||
| - | <panel type=" | ||
| - | Z-diodes are useful for voltage limitation and voltage stabilization. | ||
| - | The practical circuits are treated in [[block12|Block 12]]. | ||
| - | </ | ||
| - | |||
| - | 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. | ||
| - | |||
| - | < | ||
| - | |||
| - | ^ LED color ^ Typical \(U_{\rm TO}\) ^ | ||
| - | | infrared | \(\approx 1.3~{\rm V}\) | | ||
| - | | red | \(\approx 1.6~{\rm V}\) | | ||
| - | | yellow | \(\approx 1.7~{\rm V}\) | | ||
| - | | green | \(\approx 1.8~{\rm V}\) | | ||
| - | | blue | \(\approx 3.2~{\rm V}\) | | ||
| - | |||
| - | <callout type=" | ||
| - | LEDs usually tolerate only small reverse voltages. | ||
| - | Do not operate an LED in reverse direction unless the datasheet explicitly allows it. | ||
| - | </ | ||
| - | |||
| - | ~~PAGEBREAK~~ ~~CLEARFIX~~ | ||
| ===== Exercises ===== | ===== Exercises ===== | ||
| Line 579: | Line 572: | ||
| \[ | \[ | ||
| \begin{align*} | \begin{align*} | ||
| - | U_{\rm | + | U_{\rm |
| \qquad | \qquad | ||
| R=1.0~{\rm k}\Omega. | R=1.0~{\rm k}\Omega. | ||
| Line 603: | Line 596: | ||
| U_R | U_R | ||
| = | = | ||
| - | U_{\rm | + | U_{\rm |
| = | = | ||
| 5.0~{\rm V}-0.7~{\rm V} | 5.0~{\rm V}-0.7~{\rm V} | ||
| Line 688: | Line 681: | ||
| \[ | \[ | ||
| \begin{align*} | \begin{align*} | ||
| - | U_{\rm | + | U_{\rm |
| \qquad | \qquad | ||
| R=560~\Omega. | R=560~\Omega. | ||
| Line 726: | Line 719: | ||
| \[ | \[ | ||
| \begin{align*} | \begin{align*} | ||
| - | U_{\rm | + | U_{\rm |
| = | = | ||
| RI_{\rm D} | RI_{\rm D} | ||
| Line 738: | Line 731: | ||
| \[ | \[ | ||
| \begin{align*} | \begin{align*} | ||
| - | U_{\rm | + | U_{\rm |
| = | = | ||
| RI_{\rm D} | RI_{\rm D} | ||
| Line 754: | Line 747: | ||
| I_{\rm D} | I_{\rm D} | ||
| = | = | ||
| - | \frac{U_{\rm | + | \frac{U_{\rm |
| \end{align*} | \end{align*} | ||
| \] | \] | ||
| Line 838: | Line 831: | ||
| ===== Embedded resources ===== | ===== Embedded resources ===== | ||
| - | |||
| - | <WRAP group> | ||
| - | <WRAP column half> | ||
| - | <panel type=" | ||
| - | Use this simulation to explore doping and the formation of a diode. | ||
| - | |||
| - | {{url> | ||
| - | </ | ||
| - | </ | ||
| - | |||
| - | <WRAP column half> | ||
| - | <panel type=" | ||
| - | Use this simulation to compare a resistor characteristic with the nonlinear diode characteristic. | ||
| - | |||
| - | {{url> | ||
| - | </ | ||
| - | </ | ||
| - | </ | ||
| ~~PAGEBREAK~~ ~~CLEARFIX~~ | ~~PAGEBREAK~~ ~~CLEARFIX~~ | ||