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-====== 2. Diodes and Transistors ======+====== 2 Diodes and Transistors ======
  
 <callout> A nice introduction to the bipolar transistor can be found in [[http://eng.libretexts.org/Bookshelves/Materials_Science/Supplemental_Modules_(Materials_Science)/Materials_and_Devices/Bipolar_Junction_Transistor|libretexts]]. Some of the following passages, videos and pictures are taken from this introduction. </callout> <callout> A nice introduction to the bipolar transistor can be found in [[http://eng.libretexts.org/Bookshelves/Materials_Science/Supplemental_Modules_(Materials_Science)/Materials_and_Devices/Bipolar_Junction_Transistor|libretexts]]. Some of the following passages, videos and pictures are taken from this introduction. </callout>
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   - Know how to distinguish electron mobility in metals, semiconductors, and insulators,   - Know how to distinguish electron mobility in metals, semiconductors, and insulators,
   - know what the intrinsic conductivity of a semiconductor is,   - know what the intrinsic conductivity of a semiconductor is,
-  - distinguish between electron and hole conduction and relate them to p- and n-doping,+  - distinguish between electron and hole conduction and relate them to P- and N-doping,
   - know what doping is and what it is used for   - know what doping is and what it is used for
   - know the difference between real and ideal diode,   - know the difference between real and ideal diode,
Zeile 56: Zeile 56:
 In metals, electrons are free to move. If an external voltage is applied, they follow the potential difference to the positive electrode: current flows. In insulators, on the other hand, the electrons are firmly bound to the atomic trunks. If a voltage is applied, they can at best be polarized. No current flows. In metals, electrons are free to move. If an external voltage is applied, they follow the potential difference to the positive electrode: current flows. In insulators, on the other hand, the electrons are firmly bound to the atomic trunks. If a voltage is applied, they can at best be polarized. No current flows.
  
-A semiconductor is a material whose conductivity lies between that of metals and that of insulators. The technologically most important example of a semiconductor is silicon. In the silicon crystal, the electrons are not freely movable as in metal, because they are bound to the atomic trunks. But a small supply of energy (e.g. thermal energy) is sufficient to release the electrons from the atoms. Then, when a voltage is applied, an electric current flows. This is called the **intrinsic conduction** (intrinsic conduction) of the semiconductor. When the electrons move around in the semiconductor, this is called **electron conduction**.+A semiconductor is a material whose conductivity lies between that of metals and that of insulators. The technologically most important example of a semiconductor is silicon. In the silicon crystal, the electrons are not freely movable as in metal, because they are bound to the atomic trunks. However, a small supply of energy (e.g. thermal energy) is sufficient to release the electrons from the atoms. Then, when a voltage is applied, an electric current flows. This is called the **intrinsic conduction** (intrinsic conduction) of the semiconductor. When the electrons move around in the semiconductor, this is called **electron conduction**.
  
 A hole with a positive electrical charge is created at the silicon atom from which the electron was removed. This is also called a defect electron. These holes can also move through the crystal lattice and thus generate an electric current. This is called **hole conduction**. Hole conduction can be thought of as a hole being filled by an electron from the neighboring atom. However, this creates a hole in the neighboring atom. Effectively, such a hole has migrated from one atom to another, carrying with it a positive electric charge. \\  A hole with a positive electrical charge is created at the silicon atom from which the electron was removed. This is also called a defect electron. These holes can also move through the crystal lattice and thus generate an electric current. This is called **hole conduction**. Hole conduction can be thought of as a hole being filled by an electron from the neighboring atom. However, this creates a hole in the neighboring atom. Effectively, such a hole has migrated from one atom to another, carrying with it a positive electric charge. \\ 
 <wrap> <wrap>
-<imgcaption pic1|n-doping></imgcaption>{{drawio>ndoping.svg}} +<imgcaption pic1|N-doping></imgcaption>{{drawio>ndoping.svg}} 
-<imgcaption pic2|p-doping></imgcaption>{{drawio>pdoping.svg}}+<imgcaption pic2|P-doping></imgcaption>{{drawio>pdoping.svg}}
 </wrap> </wrap>
  
 Most semiconductors are elements of the fourth main group, i.e. they have four electrons in the outer shell. This also applies to the element silicon. In the silicon lattice, each silicon atom is therefore connected to four neighboring atoms via a bond. If foreign atoms are added to this semiconductor material, the electrical conductivity can be modified. This is called **doping**. Most semiconductors are elements of the fourth main group, i.e. they have four electrons in the outer shell. This also applies to the element silicon. In the silicon lattice, each silicon atom is therefore connected to four neighboring atoms via a bond. If foreign atoms are added to this semiconductor material, the electrical conductivity can be modified. This is called **doping**.
  
-Atoms of the fifth main group (e.g. phosphorus) have five electrons in the outer shell. If these are added to the silicon crystal lattice, one electron is surplus at these points, as it is not needed for the four bonds in the crystal lattice. This electron is much more mobile than the electrons that contribute to the bond and therefore greatly increases conductivity by electron conduction. This addition of free negative charge carriers is called **n-doping**  (see <imgref pic1>).+Atoms of the fifth main group (e.g. phosphorus) have five electrons in the outer shell. If these are added to the silicon crystal lattice, one electron is surplus at these points, as it is not needed for the four bonds in the crystal lattice. This electron is much more mobile than the electrons that contribute to the bond and therefore greatly increases conductivity by electron conduction. This addition of free negative charge carriers is called **N-doping**  (see <imgref pic1>).
  
-On the other hand, by adding atoms of the third main group (e.g. aluminum), a so-called hole can be created at these points, as these atoms only have three electrons in the outer shell. This leads to an increase in conductivity by hole conduction. This addition of free positive charge carriers is called **p-doping**  (see <imgref pic2>).+On the other hand, by adding atoms of the third main group (e.g. aluminum), a so-called hole can be created at these points, as these atoms only have three electrons in the outer shell. This leads to an increase in conductivity by hole conduction. This addition of free positive charge carriers is called **P-doping**  (see <imgref pic2>).
  
 ++++ ++++
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 A hole with a positive electrical charge is created at the silicon atom from which the electron was removed. This is also called a defect electron. These holes can also move through the crystal lattice and thus generate an electric current. This is called **hole conduction**. Hole conduction can be thought of as a hole being filled by an electron from the neighboring atom. However, this creates a hole in the neighboring atom. Effectively, such a hole has migrated from one atom to another, carrying with it a positive electric charge. A hole with a positive electrical charge is created at the silicon atom from which the electron was removed. This is also called a defect electron. These holes can also move through the crystal lattice and thus generate an electric current. This is called **hole conduction**. Hole conduction can be thought of as a hole being filled by an electron from the neighboring atom. However, this creates a hole in the neighboring atom. Effectively, such a hole has migrated from one atom to another, carrying with it a positive electric charge.
  
-<wrap><imgcaption pic2|p-doping with aluminum></imgcaption> {{drawio>pdoping.svg}}</wrap> +<wrap><imgcaption pic2|P-doping with aluminum></imgcaption> {{drawio>pdoping.svg}}</wrap> 
-<wrap><imgcaption pic1|n-doping with phosphorus></imgcaption> {{drawio>ndoping.svg}}</wrap>+<wrap><imgcaption pic1|N-doping with phosphorus></imgcaption> {{drawio>ndoping.svg}}</wrap>
  
 Most semiconductors are elements of the fourth main group, i.e. they have four electrons in the outer shell. This also applies to the element silicon. In the silicon lattice, each silicon atom is therefore connected to four neighboring atoms via a bond. If foreign atoms are added to this semiconductor material, the electrical conductivity can be modified. This is called **doping**. Most semiconductors are elements of the fourth main group, i.e. they have four electrons in the outer shell. This also applies to the element silicon. In the silicon lattice, each silicon atom is therefore connected to four neighboring atoms via a bond. If foreign atoms are added to this semiconductor material, the electrical conductivity can be modified. This is called **doping**.
  
-Atoms of the fifth main group (e.g. phosphorus) have five electrons in the outer shell. If these are added to the silicon crystal lattice, one electron is surplus at these points, as it is not needed for the four bonds in the crystal lattice. This electron is much more mobile than the electrons that contribute to the bond and therefore greatly increases conductivity by electron conduction. This addition of free negative charge carriers is called **n-doping**  (see <imgref pic1>).+Atoms of the fifth main group (e.g. phosphorus) have five electrons in the outer shell. If these are added to the silicon crystal lattice, one electron is surplus at these points, as it is not needed for the four bonds in the crystal lattice. This electron is much more mobile than the electrons that contribute to the bond and therefore greatly increases conductivity by electron conduction. This addition of free negative charge carriers is called **N-doping**  (see <imgref pic1>).
  
-On the other hand, by adding atoms of the third main group (e.g. aluminum), a so-called hole can be created at these points, as these atoms only have three electrons in the outer shell. This leads to an increase in conductivity by hole conduction. This addition of free positive charge carriers is called **p-doping**  (see <imgref pic2>). </WRAP>+On the other hand, by adding atoms of the third main group (e.g. aluminum), a so-called hole can be created at these points, as these atoms only have three electrons in the outer shell. This leads to an increase in conductivity by hole conduction. This addition of free positive charge carriers is called **P-doping**  (see <imgref pic2>). </WRAP>
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
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 Since the crystal lattice already contains thermal energy at room temperature (the atomic trunks move), phonons are also present in the crystal. The phonons have a broad, energetic distribution. At room temperatures, the average energy of a phonon is $k_{\rm B}\cdot T = 26 ~\rm meV$ ($k_\rm B$ is the [[https://en.wikipedia.org/wiki/Boltzmann_constant|Boltzmann constant]]). In silicon, about $0.000 000 01~\%$ (about one in $10^{13}$) of phonons have sufficient energy to lift an electron from the valence band to the conduction band. However, this is sufficient to provide about 10 billion charge carriers ($10^{10}$) to pure silicon at room temperature and a volume of $1 ~\rm cm^3$ (about $5\cdot 10^{22}$ atoms). These charge carriers enable the intrinsic conduction described above. Since the crystal lattice already contains thermal energy at room temperature (the atomic trunks move), phonons are also present in the crystal. The phonons have a broad, energetic distribution. At room temperatures, the average energy of a phonon is $k_{\rm B}\cdot T = 26 ~\rm meV$ ($k_\rm B$ is the [[https://en.wikipedia.org/wiki/Boltzmann_constant|Boltzmann constant]]). In silicon, about $0.000 000 01~\%$ (about one in $10^{13}$) of phonons have sufficient energy to lift an electron from the valence band to the conduction band. However, this is sufficient to provide about 10 billion charge carriers ($10^{10}$) to pure silicon at room temperature and a volume of $1 ~\rm cm^3$ (about $5\cdot 10^{22}$ atoms). These charge carriers enable the intrinsic conduction described above.
  
-The previous subchapter also described another way of increasing the number of charge carriers: doping with impurity atoms. This requires that the semiconductor material used is very pure and crystalline. Impurities and crystalline impurities can also produce conductive charge carriers. The semiconductor material should have less than one defect per $10^{10}$ atoms (equivalent to about one person to humanity). In this case, intrinsic conduction would predominate in it. For doping, one impurity atom is added to $10^5...10^{10}$ semiconductor atoms. In the band model, n-doping results in additional electrons in the conduction band and additional positively charged fixed recombination centers due to the fixed positive atomic hulls, so-called (electron)** donors**  (<imgref pic0>: green circle for n-doping in 2.a, 2.b, 2.c). The additional electron is shown as a particle in 2.a and 2.b - in reality, it is more smeared out like the dark blue spot in 2.c, since the position is only fixed when measured. +The previous subchapter also described another way of increasing the number of charge carriers: doping with impurity atoms. This requires that the semiconductor material used is very pure and crystalline. Impurities and crystalline impurities can also produce conductive charge carriers. The semiconductor material should have less than one defect per $10^{10}$ atoms (equivalent to about one person to humanity). In this case, intrinsic conduction would predominate in it. For doping, one impurity atom is added to $10^5...10^{10}$ semiconductor atoms. In the band model, N-doping results in additional electrons in the conduction band and additional positively charged fixed recombination centers due to the fixed positive atomic hulls, so-called (electron)** donors**  (<imgref pic0>: green circle for N-doping in 2.a, 2.b, 2.c). The additional electron is shown as a particle in 2.a and 2.b - in reality, it is more smeared out like the dark blue spot in 2.c, since the position is only fixed when measured. 
-A p-doping creates additional holes in the valence band and fixed negatively charged recombination centers, so-called (electron) **acceptors** (red circles in 3.a, 3.b, 3.c). Similarly, the hole is shown as a particle in 3.a and 3.b, such as a smeared-out depletion area in 3.c+A P-doping creates additional holes in the valence band and fixed negatively charged recombination centers, so-called (electron) **acceptors** (red circles in 3.a, 3.b, 3.c). Similarly, the hole is shown as a particle in 3.a and 3.b, such as a smeared-out depletion area in 3.c
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
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-==== PN Junction ====+==== PN-Junction ====
  
-In a diode, two differently doped layers of silicon collide: p-doped silicon ("p-crystal") on one side and n-doped silicon ("n-crystal") on the other.+In a diode, two differently doped layers of silicon collide: P-doped silicon ("p-crystal") on one side and N-doped silicon ("N-crystal") on the other.
  
-The situation __without external voltage__ will be considered first (compare <imgref pic5>). On the n-doped side, many free-moving electrons will dissolve at room temperature, leaving acceptors stationary. The same can be seen on the p-doped side: the free-moving holes leave behind donors. in the middle, at the **pn-junction**, both moving charge carriers, electrons, and holes, meet. When they meet directly, the two charge carriers will cancel each other out, they **recombine**. This creates a photon (electromagnetic vibration) and/or a phonon (lattice vibration). The recombination forms a layer, the **depletion region**, which is largely free of free-moving charge carriers. The depletion region initially acts as an insulator.+The situation __without external voltage__ will be considered first (compare <imgref pic5>). On the N-doped side, many free-moving electrons will dissolve at room temperature, leaving acceptors stationary. The same can be seen on the P-doped side: the free-moving holes leave behind donors. in the middle, at the **PN-junction**, both moving charge carriers, electrons, and holes, meet. When they meet directly, the two charge carriers will cancel each other out, they **recombine**. This creates a photon (electromagnetic vibration) and/or a phonon (lattice vibration). The recombination forms a layer, the **depletion region**, which is largely free of free-moving charge carriers. The depletion region initially acts as an insulator.
  
 The <imgref pic5> shows this situation. Keep in mind, that the sharply drawn (red and green) circles represent the stationary charges and the bright and dark spots of the mobile electrons and holes. The <imgref pic5> shows this situation. Keep in mind, that the sharply drawn (red and green) circles represent the stationary charges and the bright and dark spots of the mobile electrons and holes.
  
-<WRAP><imgcaption pic5|Evolution of the p-n junction></imgcaption>{{drawio>evolutionofpnjunction.svg}}</WRAP>+<WRAP><imgcaption pic5|Evolution of the PN-junction></imgcaption>{{drawio>evolutionofpnjunction.svg}}</WRAP>
  
 __With external voltage $U_\rm D$__  on the diode, two cases are to be distinguished: __With external voltage $U_\rm D$__  on the diode, two cases are to be distinguished:
  
-  - Applying a positive voltage from the p-doped side to the n-doped side \\ (diode voltage = forward voltage $U_{\rm D} =  U_\rm F$, $U_\rm F>0$). +  - Applying a positive voltage from the P-doped side to the N-doped side \\ (diode voltage = forward voltage $U_{\rm D} =  U_\rm F$, $U_\rm F>0$). 
-  - Applying a negative voltage from the p-doped side to the n-doped side \\ (diode voltage = reverse voltage $U_{\rm D} = -U_\rm R$, $U_\rm R>0$).+  - Applying a negative voltage from the P-doped side to the N-doped side \\ (diode voltage = reverse voltage $U_{\rm D} = -U_\rm R$, $U_\rm R>0$).
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~  ~~PAGEBREAK~~ ~~CLEARFIX~~ 
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 ==== Applying a (positive) Forward Voltage $U_\rm F>0$ ==== ==== Applying a (positive) Forward Voltage $U_\rm F>0$ ====
  
-If a __positive potential is applied to the p-doped side__, the freely moving holes there are driven towards the pn-junction. The negative potential is then applied to the n-doped side, which also drives the freely moving electrons toward the pn-junction. At the pn-junction, holes, and electrons can neutralize each other. Thus, holes from the positive terminal and electrons from the negative terminal can continue to move in, and an electric current flows through the diode. The diode is connected in the **conducting direction**. In common Silicon diodes, about $0.7 ~\rm V$ is dropped in the forward direction. This means, of course, that the current does not pass the diode completely without resistance, but that the forward voltage $U_\rm S$ of about $0.7 ~\rm V$ must be applied from the outside.[(Note2>In the literature, the forward voltage can be found under other names: Forward voltage, Threshold voltage, Forward voltage, Buckling voltage, Forward voltage.)]. This voltage results from the energy difference of the band gap related to one electron, which is about $1.1~\rm eV$ for silicon but is reduced by thermal energy (phonons). +If a __positive potential is applied to the P-doped side__, the freely moving holes there are driven towards the PN-junction. The negative potential is then applied to the N-doped side, which also drives the freely moving electrons toward the PN-junction. At the PN-junction, holes, and electrons can neutralize each other. Thus, holes from the positive terminal and electrons from the negative terminal can continue to move in, and an electric current flows through the diode. The diode is connected in the **conducting direction**. In common Silicon diodes, about $0.7 ~\rm V$ is dropped in the forward direction. This means, of course, that the current does not pass the diode completely without resistance, but that the forward voltage $U_\rm S$ of about $0.7 ~\rm V$ must be applied from the outside.[(Note2>In the literature, the forward voltage can be found under other names: Forward voltage, Threshold voltage, Forward voltage, Buckling voltage, Forward voltage.)]. This voltage results from the energy difference of the band gap related to one electron, which is about $1.1~\rm eV$ for silicon but is reduced by thermal energy (phonons). 
  
 <WRAP><imgcaption pic6|Functionality of a semiconductor diode></imgcaption>{{drawio>voltagepnjunction.svg}}</WRAP> <WRAP><imgcaption pic6|Functionality of a semiconductor diode></imgcaption>{{drawio>voltagepnjunction.svg}}</WRAP>
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 ==== Appliying a Blocking Voltage $U_\rm R>0$ ==== ==== Appliying a Blocking Voltage $U_\rm R>0$ ====
  
-If the __diode is contacted in the opposite direction__, i.e. the positive pole on the n-doped side and the negative pole on the p-doped side, no current can flow. This is because the free electrons from the positive pole are sucked out of the n-doped side, and the free holes are removed from the p-doped side. In between, a so-called depletion zone without free charge carriers is created. No electric charge can be transported through this depletion zone and the diode cannot conduct "any current". The diode is connected in the **blocking direction**. In fact, the diode can still conduct a very small **blocking current**  $\boldsymbol{I_\rm S}$: Thermal energy keeps creating free electrons and free holes, which allow it to conduct. Thus it is also clear that the reverse current is temperature dependent. $I_{\rm S}(T)$ lies in the range $100~\rm nA...10~\rm µA$.+If the __diode is contacted in the opposite direction__, i.e. the positive pole on the N-doped side and the negative pole on the P-doped side, no current can flow. This is because the free electrons from the positive pole are sucked out of the N-doped side, and the free holes are removed from the P-doped side. In between, a so-called depletion zone without free charge carriers is created. No electric charge can be transported through this depletion zone and the diode cannot conduct "any current". The diode is connected in the **blocking direction**. In fact, the diode can still conduct a very small **blocking current**  $\boldsymbol{I_\rm S}$: Thermal energy keeps creating free electrons and free holes, which allow it to conduct. Thus it is also clear that the reverse current is temperature dependent. $I_{\rm S}(T)$ lies in the range $100~\rm nA...10~\rm µA$.
  
-<WRAP><imgcaption pic98|pn Junction for a Blocking voltage></imgcaption>{{drawio>negvoltagepnjunction.svg}}</WRAP>+<WRAP><imgcaption pic98|PN-Junction for a Blocking voltage></imgcaption>{{drawio>negvoltagepnjunction.svg}}</WRAP>
  
 If the reverse voltage is increased further, the free charge carriers are sucked out more and more. Above a certain negative voltage, the energy of the free charge carriers becomes so great that they knock out more charge carriers, which in turn knock out more charge carriers. This results in an avalanche of free-moving charge carriers and the diode becomes abruptly conductive. This situation is called **breakthrough**. The voltage is denoted $U_{\rm Z}$, after the discoverer [[https://de.wikipedia.org/wiki/Zener-Effekt|Clarence Zener]]. For an ordinary diode, the breakdown is problematic because it does not occur at a defined voltage. Without precise knowledge of this voltage, the rapid current rise will quickly destroy the diode. \\ If the reverse voltage is increased further, the free charge carriers are sucked out more and more. Above a certain negative voltage, the energy of the free charge carriers becomes so great that they knock out more charge carriers, which in turn knock out more charge carriers. This results in an avalanche of free-moving charge carriers and the diode becomes abruptly conductive. This situation is called **breakthrough**. The voltage is denoted $U_{\rm Z}$, after the discoverer [[https://de.wikipedia.org/wiki/Zener-Effekt|Clarence Zener]]. For an ordinary diode, the breakdown is problematic because it does not occur at a defined voltage. Without precise knowledge of this voltage, the rapid current rise will quickly destroy the diode. \\
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 ===== 2.3 Special diodes ===== ===== 2.3 Special diodes =====
  
-So far the silicon PN diode and the Z-diode were discussed. Additionally, other diodes are available for various applications. In the following, the most important ones will be briefly described.+So far the silicon PN diode and the Z-diode have been discussed. Additionally, other diodes are available for various applications. In the following, the most important ones will be briefly described.
  
-==== 2.3.1 Diodes for Electic Applications ====+==== 2.3.1 Diodes for Electric Applications ====
  
 ==== Germanium diode ==== ==== Germanium diode ====
Zeile 247: Zeile 247:
 ==== Schottky diode ==== ==== Schottky diode ====
  
-The Schottky diode also uses a different material. In the silicon Schottky diode, however, a metal is used instead of silicon only on the previously p-doped side. This eliminates the holes as charge carriers, which allows for "faster switching": available Schottky diodes have a forward voltage in the range of $U_{\rm S}=0.15...0.45~\rm V$. Although silicon Schottky diodes have similar advantages and disadvantages to the germanium diode, the disadvantages such as higher reverse current (compared to silicon PN diode) and lower slope are less pronounced. \\ +The Schottky diode also uses a different material. In the silicon Schottky diode, however, a metal is used instead of silicon only on the previously P-doped side. This eliminates the holes as charge carriers, which allows for "faster switching": available Schottky diodes have a forward voltage in the range of $U_{\rm S}=0.15...0.45~\rm V$. Although silicon Schottky diodes have similar advantages and disadvantages to the germanium diode, the disadvantages such as higher reverse current (compared to silicon PN diode) and lower slope are less pronounced. \\ 
 In most applications, the silicon Schottky diode is superior to the germanium diode. The circuit symbol (<imgref pic12>) stylizes an S for Schottky, which is especially visible with the non-normalized symbol. In most applications, the silicon Schottky diode is superior to the germanium diode. The circuit symbol (<imgref pic12>) stylizes an S for Schottky, which is especially visible with the non-normalized symbol.
  
Zeile 266: Zeile 266:
 ==== PIN diode ==== ==== PIN diode ====
  
-In the PIN diode, there is an undoped region (**i**ntrically non-conducting) between the **p**-doped and **n**-doped regions. The name is therefore derived from the existing layers of the diode. In all diodes, the carrier-free junction results in a capacitor. The capacitance of this capacitor is reciprocally proportional to the distance $d$ between the conducting regions: $C\sim \frac{1}{d}$. With the additional undoped region inserted, $d$ becomes larger and thus the capacitance becomes smaller. This capacitance is alternately charged and discharged in AC applications. A smaller capacitance improves the blocking performance at high frequencies. The broadened junction also increases the dielectric strength of the diode. The same circuit symbol is used for the PIN diode as for the classic PN diode.+In the PIN diode, there is an undoped region (**i**ntrically non-conducting) between the **P**-doped and **N**-doped regions. The name is therefore derived from the existing layers of the diode. In all diodes, the carrier-free junction results in a capacitor. The capacitance of this capacitor is reciprocally proportional to the distance $d$ between the conducting regions: $C\sim \frac{1}{d}$. With the additional undoped region inserted, $d$ becomes larger and thus the capacitance becomes smaller. This capacitance is alternately charged and discharged in AC applications. A smaller capacitance improves the blocking performance at high frequencies. The broadened junction also increases the dielectric strength of the diode. The same circuit symbol is used for the PIN diode as for the classic PN diode.
  
 <WRAP><imgcaption pic12|Absorption of photons in the intrinsic layer of a PIN-diode></imgcaption>{{drawio>pindiode.svg}}</WRAP> <WRAP><imgcaption pic12|Absorption of photons in the intrinsic layer of a PIN-diode></imgcaption>{{drawio>pindiode.svg}}</WRAP>
Zeile 275: Zeile 275:
 ==== Photodiode (solar cell) ==== ==== Photodiode (solar cell) ====
  
-A photodiode is a PIN diode that is constructed in such a way that the cross-section of the junction occupies a very large area. The structure of a photodiode is: an n-doped layer, an intrinsically conductive layer, and a p-doped layer. When a photon hits the diode, an electron-hole pair is generated, which is separated by the electric field in the PN junction: the electrons accumulate in the n-doped layer, and the holes in the p-doped layer (see <imgref pic12>). In a photodiode, the charge carriers are dissipated in a voltage-free manner. The number of charge carriers is proportional to the absorbed photons. The circuit symbol (<imgref pic11>) shows the incoming photons with arrows.+A photodiode is a PIN diode that is constructed in such a way that the cross-section of the junction occupies a very large area. The structure of a photodiode is: an N-doped layer, an intrinsically conductive layer, and a P-doped layer. When a photon hits the diode, an electron-hole pair is generated, which is separated by the electric field in the PN-junction: the electrons accumulate in the N-doped layer, and the holes in the P-doped layer (see <imgref pic12>). In a photodiode, the charge carriers are dissipated in a voltage-free manner. The number of charge carriers is proportional to the absorbed photons. The circuit symbol (<imgref pic11>) shows the incoming photons with arrows.
  
 <WRAP><imgcaption pic11|circuit symbol of a photodiode></imgcaption>{{drawio>photozdiode.svg}}</WRAP> <WRAP><imgcaption pic11|circuit symbol of a photodiode></imgcaption>{{drawio>photozdiode.svg}}</WRAP>
Zeile 336: Zeile 336:
 <panel type="info" title="Exercise 2.1.6 Circuit with multiple diodes"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Exercise 2.1.6 Circuit with multiple diodes"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
-The following simulation includes multiple diodes. The shown lambs light bright, when a voltage of $5~V$ or more drops over them. \\ +The following simulation includes multiple diodes. The shown lambs light bright, when a voltage of $5~\rm V$ or more drops over them. \\ 
 Which lambs will light up, when the switch is closed? Which lambs will light up, when the switch is closed?
  
Zeile 345: Zeile 345:
 <panel type="info" title="Exercise 2.1.7 Circuit with multiple diodes II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Exercise 2.1.7 Circuit with multiple diodes II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
-The following simulation includes multiple diodes. Assume a simple diode model (the forward voltage drop is $V_F=0.7~V$ and constant). The source voltage shall be $U0 = 4~V$.+The following simulation includes multiple diodes. Assume a simple diode model (the forward voltage drop is $V_F=0.6~\rm V$ and constant). The source voltage shall be $U0 = 4~\rm V$.
  
 Calculate the currents through $D1$, $R1$, and $R2$. Calculate the currents through $D1$, $R1$, and $R2$.
  
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
Zeile 356: Zeile 356:
 <panel type="info" title="Exercise 2.1.8 Circuit with multiple diodes III"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Exercise 2.1.8 Circuit with multiple diodes III"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
-The following simulation includes multiple diodes. Assume a simple diode model (the forward voltage drop is $V_F = 0.7~V$ and constant). The source voltage shall be $U0 = 5~V$.+The following simulation includes multiple diodes. Assume a simple diode model (the forward voltage drop is $V_{\rm F} = 0.7~\rm V$ and constant). The source voltage shall be $U0 = 5~\rm V$.
  
 Calculate the currents through $R1$, $D1$, and $D2$ depending on the switch state S. Calculate the currents through $R1$, $D1$, and $D2$ depending on the switch state S.
Zeile 366: Zeile 366:
 ====== Study Questions ======  ====== Study Questions ====== 
 === For self-study ===  === For self-study === 
-  * On a U-I diagram, draw the characteristic of an ideal diode and a real silicon diode and explain the differences. +  * On a U-I diagram, draw the characteristics of an ideal diode and a real silicon diode and explain the differences. 
-  * What is meant by n-doped and p-doped? +  * What is meant by N-doped and P-doped? 
   * How does a junction form inside the diode?    * How does a junction form inside the diode? 
   * What is meant by a threshold voltage?    * What is meant by a threshold voltage? 
Zeile 375: Zeile 375:
   * Draw the electric fields formed in the diode when no external field is applied.    * Draw the electric fields formed in the diode when no external field is applied. 
   * Explain how an external voltage can bring the diode into a conducting state.    * Explain how an external voltage can bring the diode into a conducting state. 
-  * Explain the working of a diode with the help of a sketch. Draw the following areas: p-doped part, n-doped part, and junction.  +  * Explain the working of a diode with the help of a sketch. Draw the following areas: P-doped part, N-doped part, and junction.  
-  * Given is a layered structure of a diode (n-doping and p-doping can be seen). How would the diode have to be connected to pass current? +  * Given is a layered structure of a diode (N-doping and P-doping can be seen). How would the diode have to be connected to pass current? 
   * Typical diode characteristic for silicon diodes.    * Typical diode characteristic for silicon diodes. 
   * Draw a characteristic curve for silicon diodes.    * Draw a characteristic curve for silicon diodes. 
Zeile 388: Zeile 388:
   * Rectifier circuits   * Rectifier circuits
     * Draw a half-wave rectifier. Draw a bridge rectifier.     * Draw a half-wave rectifier. Draw a bridge rectifier.
-    * Given a sinusoidal input voltage of 3V. Draw the waveform of the input voltage and the output voltage of the two rectifiers over 2 periods for 50 Hz in a graph.+    * Given a sinusoidal input voltage of $3~\rm V$. Draw the waveform of the input voltage and the output voltage of the two rectifiers over 2 periods for $50~\rm Hz$ in a graph.
     * How can the output voltage be smoothed? How can the output current be smoothed?     * How can the output voltage be smoothed? How can the output current be smoothed?
-    * Given a sinusoidal input voltage of 3V. What should be considered if very high frequencies are to be rectified? Draw a possible signal waveform of the input voltage and the output voltage of the two rectifiers over 2 periods for 50 GHz in a diagram.+    * Given a sinusoidal input voltage of $3~\rm V$. What should be considered if very high frequencies are to be rectified? Draw a possible signal waveform of the input voltage and the output voltage of the two rectifiers over 2 periods for $50 ~\rm GHz$ in a diagram.
     * Draw a circuit with which the __positive__  half-wave of a sinusoidal voltage can be cut off.     * Draw a circuit with which the __positive__  half-wave of a sinusoidal voltage can be cut off.
  
 === with answers ===  === with answers === 
  
-<quizlib id="quiz" rightanswers="[['a1'],['a0', 'a1', 'a2', 'a3'], ['a1', 'a3', 'a5'], ['a1', 'a2', 'a3'], ['a0', 'a1', 'a2', 'a3'], ['a0', 'a1']" submit="Check answers"> +<WRAP hide> <quizlib id="dummy" rightanswers="[[]]" submit="x"></quizlib> Only necessary to eliminate the score bar... </WRAP> 
-  + 
-<question title="Which of the following statement(s) is/are correct?" type="checkbox">  +<WRAP column half> 
-p-doping produces quasi-free electrons|  +<panel type="info" title="Exercise - Quiz"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 88%> 
-Conductivity in semiconductors happens via conduction and valence band| +<quizlib id="quiz1" rightanswers="[['a1']]" submit="check answers"> 
 +<question title="Which of the following statement(s) for real diodes is/are correct?" type="checkbox">  
 +P-doping produces quasi-free electrons|  
 +Conductivity in semiconductors happens via the conduction band and valence band| 
 The diode blocks at any negative voltage (reverse voltage).|   The diode blocks at any negative voltage (reverse voltage).|  
 The diode can be modeled as a voltage source and capacitor The diode can be modeled as a voltage source and capacitor
-</question> +</question></quizlib></WRAP></WRAP></panel> 
- + 
 +<panel type="info" title="Exercise - Quiz"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 88%> 
 +<quizlib id="quiz2" rightanswers="[['a0', 'a1', 'a2', 'a3']]" submit="check answers">
 <question title="On which physical properties does the forward voltage $U_S$ depend?" type="checkbox">  <question title="On which physical properties does the forward voltage $U_S$ depend?" type="checkbox"> 
 temperature|  temperature| 
Zeile 410: Zeile 415:
 LED color|  LED color| 
 breakdown voltage of the Z-diode  breakdown voltage of the Z-diode 
-</question> +</question></quizlib></WRAP></WRAP></panel> 
- + 
 +<panel type="info" title="Exercise - Quiz"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 88%> 
 +<quizlib id="quiz3" rightanswers="[['a1', 'a3', 'a5']]" submit="check answers">
 <question title="Which statement(s) about the junction is/are correct?" type="checkbox">  <question title="Which statement(s) about the junction is/are correct?" type="checkbox"> 
 There is no electric field in the junction|  There is no electric field in the junction| 
Zeile 419: Zeile 426:
 The junction is enlarged in the Schottky diode compared to the PN diode| The junction is enlarged in the Schottky diode compared to the PN diode|
 The junction forms a capacitor  The junction forms a capacitor 
-</question> +</question></quizlib></WRAP></WRAP></panel> 
- + 
 +</WRAP><WRAP column half> 
 +<panel type="info" title="Exercise - Quiz"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 88%> 
 +<quizlib id="quiz4" rightanswers="[['a1', 'a2', 'a3']]" submit="check answers"> 
 +<question title="The forward voltage ..." type="checkbox">  
 +... for silicon is fixed about 0.6 ... 0.7 V|  
 +... serves to allow electrons to cross the bandgap|  
 +... depends on the current range under consideration|  
 +... is smaller for germanium diodes than for silicon diodes.  
 +</question></quizlib></WRAP></WRAP></panel> 
 + 
 +<panel type="info" title="Exercise - Quiz"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 88%> 
 +<quizlib id="quiz5" rightanswers="[['a0', 'a1', 'a2', 'a3']]" submit="check answers">
 <question title="Statements about the conduction/valence band" type="checkbox">  <question title="Statements about the conduction/valence band" type="checkbox"> 
 Photon capture can move electrons from the conduction band to the valence band|  Photon capture can move electrons from the conduction band to the valence band| 
Zeile 426: Zeile 445:
 A donor creates one or more quasi-free electrons|  A donor creates one or more quasi-free electrons| 
 The band gap indicates the maximum energetic distance between the conduction and valence bands  The band gap indicates the maximum energetic distance between the conduction and valence bands 
-</question> +</question></quizlib></WRAP></WRAP></panel> 
-  + 
-<question title="The forward voltage ..." type="checkbox">  +<panel type="info" title="Exercise - Quiz"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 88%> 
-... for silicon is about 0.6 ... 0.7 V|  +<quizlib id="quiz6" rightanswers="[['a0', 'a1']]" submit="check answers">
-... serves to allow electrons to cross the bandgap|  +
-... depends on the current range under consideration|  +
-... is smaller for germanium diodes than for silicon diodes.  +
-</question> +
- +
 <question title="The forward current ..." type="checkbox">  <question title="The forward current ..." type="checkbox"> 
 ... Is dependent on the temperature|  ... Is dependent on the temperature| 
Zeile 440: Zeile 454:
 ... is logarithmic concerning the forward voltage|  ... is logarithmic concerning the forward voltage| 
 ... depends on the reverse voltage  ... depends on the reverse voltage 
-</question>  +</question></quizlib></WRAP></WRAP></panel> 
-</quizlib>+</WRAP>