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Chapter 1:  Semiconductor Diodes Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 1   Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Diodes Simplest Semiconductor Device It is a 2-terminal device
Slide 2 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Basic   operation Ideally it  conducts current in   only one direction and acts like an  open in the opposite direction
Slide 3 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Characteristics of an ideal diode: Conduction Region Look at the vertical line! In the conduction region, ideally •  the voltage across the diode is 0V,  •  the current is   , •  the forward resistance (R F ) is defined as R F  = V F /I F ,  • the diode acts like a short.
Slide 4 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Characteristics of an ideal diode: Non-Conduction Region Look at the horizontal line! In the non-conduction region, ideally  • all of the voltage is across the diode,  • the current is 0A, • the reverse resistance (R R ) is defined as R R  = V R /I R ,  • the diode acts like open.
Slide 5 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Semiconductor Materials Common materials used in the development of semiconductor devices: • Silicon (Si) • Germanium (Ge)
Slide 6 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Doping The electrical characteristics of Silicon and Germanium are improved by adding materials in a process called doping. The additional materials are in two types: • n-type • p-type
Slide 7 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. n-type  materials make the Silicon (or Germanium) atoms more negative. p-type  materials make  the Silicon (or Germanium) atoms more positive. Join n-type and p-type doped Silicon (or Germanium) to form a  p-n junction . n-type versus p-type
Slide 8 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. p-n junction When the materials are joined, the negatively charged atoms of the n-type doped side are attracted to the positively charged atoms of the p-type doped side. The electrons in the n-type material migrate across the junction to the p-type material (electron flow).  Or you could say the ‘holes’ in the p-type material migrate across the junction to the n-type material (conventional current flow). The result is the formation of a  depletion layer  around the junction. depletion  layer p n
Slide 9 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Operating Conditions •  No Bias •  Forward Bias •  Reverse Bias
Slide 10 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. No external voltage is applied: V D  = 0V and no current is flowing I D  = 0A. Only a modest depletion layer exists. No Bias Condition
Slide 11 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Reverse Bias Condition External voltage is applied across the p-n junction  in the opposite polarity of the p- and n-type materials. This causes the depletion layer to widen.  The electrons in the n-type material are attracted  towards the positive terminal and the ‘holes’ in  the p-type material are attracted towards the  negative terminal.
Slide 12 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Forward Bias Condition External voltage is applied across the p-n junction in the same polarity of the p- and n-type materials. The depletion layer is narrow. The electrons from the n-type material and ‘holes’ from the p-type material have sufficient energy to cross the junction.
Slide 13 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Actual Diode Characteristics Note the regions for No Bias, Reverse Bias, and Forward Bias conditions. Look closely at the scale for each of these conditions!
Slide 14 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. A diode, as any semiconductor device is not perfect!  There are two sets of currents: •  Majority Carriers The electrons in the n-type and ‘holes’ in the p-type material are the source of the majority of the current flow in a diode. •  Minority Carriers Electrons in the p-type and ‘holes’ in the n-type material are rebel currents. They produce a small amount of opposing current. Majority and Minority Carriers in Diode
Slide 15 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Another detail about the diode is the useful Zener region. The diode is in the reverse bias condition.  At some point the reverse bias voltage is so large the diode breaks down.  The reverse current increases dramatically.  This maximum voltage is called  avalanche breakdown voltage  and the current is called  avalanche current. Zener Region
Slide 16 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. The point at which the diode changes from No Bias condition to Forward Bias condition happens when the electron and ‘holes’ are given sufficient energy to cross the p-n junction. This energy comes from the external voltage applied across the diode. The Forward bias voltage required for a •  Silicon diode V T     0.7V •  Germanium diode V T     0.3V Forward Bias Voltage
Slide 17 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. As temperature increases it adds energy to the diode.  It reduces the required Forward bias voltage in Forward Bias condition. It increases the amount of Reverse current in Reverse Bias condition. It increases maximum Reverse Bias Avalanche Voltage. Germanium diodes are more sensitive to temperature variations than Silicon Diodes. Temperature Effects
Slide 18 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Semiconductors act differently to DC and AC currents. There are 3 types of resistances. •  DC or Static Resistance •  AC or Dynamic Resistance •  Average AC Resistance Resistance Levels
Slide 19 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. R D  = V D /I D [Formula 1.5] For a specific applied DC voltage V D ,  the diode will have a specific current I D , and a specific resistance R D . The amount of resistance R D , depends on the applied DC voltage.  DC or Static Resistance
Slide 20 Forward Bias region: •  The resistance depends on the amount of current (I D ) in the diode.  •  The voltage across the diode is fairly constant (26mV for 25  C).  •  rB ranges from a typical 0.1   for high power devices to 2   for low power, general purpose diodes. In some cases rB can be ignored. Reverse Bias region:  The resistance is essentially infinite. The diode acts like an open. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. AC or Dynamic Resistance [Formula 1.8]
Slide 21 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. AC resistance can be determined by picking 2 points on the characteristic curve developed for a particular circuit. [Formula 1.9] Average AC Resistance
Slide 22 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Data about a diode is presented uniformly for many different diodes. This makes cross-matching of diodes for replacement or design easier. 1. V F , forward voltage at a specific current and temperature 2. I F , maximum forward current at a specific temperature 3. I R , maximum reverse current at a specific temperature 4. PIV or PRV or V( BR ), maximum reverse voltage at a specific temperature 5. Power Dissipation, maximum power dissipated at a specific temperature 6. C, Capacitance levels in reverse bias 7. trr, reverse recovery time  8. Temperatures, operating and storage temperature ranges Diode Specification Sheets
Slide 23 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. In Reverse Bias the depletion layer is very large. The diode’s strong positive and negative polarities create capacitance, C T . The amount of capacitance depends on the reverse voltage applied. In Forward Bias storage capacitance or diffusion capacitance (C D ) exists as the diode voltage increases.  Capacitance
Slide 24 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. This is the amount of time it takes for the diode to stop conducting once the diode is switched from Forward Bias to Reverse Bias. Reverse Recovery Time (trr)
Slide 25 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Anode is abbreviated – A Cathode is abbreviated – K  (because the Cathode end of the diode symbol looks like a backwards K) Diode Symbol and Notation
Slide 26 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. A. Diode Checker B. Ohmmeter C. Curve Tracer Diode Testing
Slide 27 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. A. Diode Checker Many DMM’s have a diode checking function.  A normal diode will exhibit its Forward Bias voltage (V F ).  The diode should be tested out of circuit. Silicon diode    0.7V Germanium diode    0.3V
Slide 28 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. An ohmmeter set on a low ohms scale can be used to test a diode.  A normal diode will have the following readings.  The diode should be tested out of circuit. B. Ohmmeter
Slide 29 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. C. Curve Tracer A curve tracer is a specialized type of test equipment. It will display the characteristic curve of the diode in the test circuit. This curve can be compared to the specifications of the diode from a data sheet.
Slide 30 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Other Types of Diodes 1. Zener Diode 2. Light Emitting Diode 3. Diode Arrays
Slide 31 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. A Zener is a diode operated in reverse bias at the Peak Inverse Voltage (PIV) called the Zener Voltage (V Z ).  Symbol  Common Zener Voltages: 1.8V to 200V 1. Zener Diode
Slide 32 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 2. Light Emitting Diode (LED) This diode when forward biased emits photons. These can be in the visible spectrum. Symbol  The forward bias voltage is higher, usually around 2-3V.
Slide 33 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Multiple diodes can be packaged together in an integrated circuit (IC). A variety of combinations exist.  Example of an array: 3. Diode Arrays

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Ch01

  • 1. Chapter 1: Semiconductor Diodes Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
  • 2. Slide 1 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Diodes Simplest Semiconductor Device It is a 2-terminal device
  • 3. Slide 2 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Basic operation Ideally it conducts current in only one direction and acts like an open in the opposite direction
  • 4. Slide 3 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Characteristics of an ideal diode: Conduction Region Look at the vertical line! In the conduction region, ideally • the voltage across the diode is 0V, • the current is  , • the forward resistance (R F ) is defined as R F = V F /I F , • the diode acts like a short.
  • 5. Slide 4 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Characteristics of an ideal diode: Non-Conduction Region Look at the horizontal line! In the non-conduction region, ideally • all of the voltage is across the diode, • the current is 0A, • the reverse resistance (R R ) is defined as R R = V R /I R , • the diode acts like open.
  • 6. Slide 5 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Semiconductor Materials Common materials used in the development of semiconductor devices: • Silicon (Si) • Germanium (Ge)
  • 7. Slide 6 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Doping The electrical characteristics of Silicon and Germanium are improved by adding materials in a process called doping. The additional materials are in two types: • n-type • p-type
  • 8. Slide 7 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. n-type materials make the Silicon (or Germanium) atoms more negative. p-type materials make the Silicon (or Germanium) atoms more positive. Join n-type and p-type doped Silicon (or Germanium) to form a p-n junction . n-type versus p-type
  • 9. Slide 8 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. p-n junction When the materials are joined, the negatively charged atoms of the n-type doped side are attracted to the positively charged atoms of the p-type doped side. The electrons in the n-type material migrate across the junction to the p-type material (electron flow). Or you could say the ‘holes’ in the p-type material migrate across the junction to the n-type material (conventional current flow). The result is the formation of a depletion layer around the junction. depletion layer p n
  • 10. Slide 9 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Operating Conditions • No Bias • Forward Bias • Reverse Bias
  • 11. Slide 10 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. No external voltage is applied: V D = 0V and no current is flowing I D = 0A. Only a modest depletion layer exists. No Bias Condition
  • 12. Slide 11 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Reverse Bias Condition External voltage is applied across the p-n junction in the opposite polarity of the p- and n-type materials. This causes the depletion layer to widen. The electrons in the n-type material are attracted towards the positive terminal and the ‘holes’ in the p-type material are attracted towards the negative terminal.
  • 13. Slide 12 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Forward Bias Condition External voltage is applied across the p-n junction in the same polarity of the p- and n-type materials. The depletion layer is narrow. The electrons from the n-type material and ‘holes’ from the p-type material have sufficient energy to cross the junction.
  • 14. Slide 13 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Actual Diode Characteristics Note the regions for No Bias, Reverse Bias, and Forward Bias conditions. Look closely at the scale for each of these conditions!
  • 15. Slide 14 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. A diode, as any semiconductor device is not perfect! There are two sets of currents: • Majority Carriers The electrons in the n-type and ‘holes’ in the p-type material are the source of the majority of the current flow in a diode. • Minority Carriers Electrons in the p-type and ‘holes’ in the n-type material are rebel currents. They produce a small amount of opposing current. Majority and Minority Carriers in Diode
  • 16. Slide 15 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Another detail about the diode is the useful Zener region. The diode is in the reverse bias condition. At some point the reverse bias voltage is so large the diode breaks down. The reverse current increases dramatically. This maximum voltage is called avalanche breakdown voltage and the current is called avalanche current. Zener Region
  • 17. Slide 16 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. The point at which the diode changes from No Bias condition to Forward Bias condition happens when the electron and ‘holes’ are given sufficient energy to cross the p-n junction. This energy comes from the external voltage applied across the diode. The Forward bias voltage required for a • Silicon diode V T  0.7V • Germanium diode V T  0.3V Forward Bias Voltage
  • 18. Slide 17 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. As temperature increases it adds energy to the diode. It reduces the required Forward bias voltage in Forward Bias condition. It increases the amount of Reverse current in Reverse Bias condition. It increases maximum Reverse Bias Avalanche Voltage. Germanium diodes are more sensitive to temperature variations than Silicon Diodes. Temperature Effects
  • 19. Slide 18 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Semiconductors act differently to DC and AC currents. There are 3 types of resistances. • DC or Static Resistance • AC or Dynamic Resistance • Average AC Resistance Resistance Levels
  • 20. Slide 19 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. R D = V D /I D [Formula 1.5] For a specific applied DC voltage V D , the diode will have a specific current I D , and a specific resistance R D . The amount of resistance R D , depends on the applied DC voltage. DC or Static Resistance
  • 21. Slide 20 Forward Bias region: • The resistance depends on the amount of current (I D ) in the diode. • The voltage across the diode is fairly constant (26mV for 25  C). • rB ranges from a typical 0.1  for high power devices to 2  for low power, general purpose diodes. In some cases rB can be ignored. Reverse Bias region: The resistance is essentially infinite. The diode acts like an open. Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. AC or Dynamic Resistance [Formula 1.8]
  • 22. Slide 21 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. AC resistance can be determined by picking 2 points on the characteristic curve developed for a particular circuit. [Formula 1.9] Average AC Resistance
  • 23. Slide 22 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Data about a diode is presented uniformly for many different diodes. This makes cross-matching of diodes for replacement or design easier. 1. V F , forward voltage at a specific current and temperature 2. I F , maximum forward current at a specific temperature 3. I R , maximum reverse current at a specific temperature 4. PIV or PRV or V( BR ), maximum reverse voltage at a specific temperature 5. Power Dissipation, maximum power dissipated at a specific temperature 6. C, Capacitance levels in reverse bias 7. trr, reverse recovery time 8. Temperatures, operating and storage temperature ranges Diode Specification Sheets
  • 24. Slide 23 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. In Reverse Bias the depletion layer is very large. The diode’s strong positive and negative polarities create capacitance, C T . The amount of capacitance depends on the reverse voltage applied. In Forward Bias storage capacitance or diffusion capacitance (C D ) exists as the diode voltage increases. Capacitance
  • 25. Slide 24 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. This is the amount of time it takes for the diode to stop conducting once the diode is switched from Forward Bias to Reverse Bias. Reverse Recovery Time (trr)
  • 26. Slide 25 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Anode is abbreviated – A Cathode is abbreviated – K (because the Cathode end of the diode symbol looks like a backwards K) Diode Symbol and Notation
  • 27. Slide 26 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. A. Diode Checker B. Ohmmeter C. Curve Tracer Diode Testing
  • 28. Slide 27 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. A. Diode Checker Many DMM’s have a diode checking function. A normal diode will exhibit its Forward Bias voltage (V F ). The diode should be tested out of circuit. Silicon diode  0.7V Germanium diode  0.3V
  • 29. Slide 28 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. An ohmmeter set on a low ohms scale can be used to test a diode. A normal diode will have the following readings. The diode should be tested out of circuit. B. Ohmmeter
  • 30. Slide 29 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. C. Curve Tracer A curve tracer is a specialized type of test equipment. It will display the characteristic curve of the diode in the test circuit. This curve can be compared to the specifications of the diode from a data sheet.
  • 31. Slide 30 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Other Types of Diodes 1. Zener Diode 2. Light Emitting Diode 3. Diode Arrays
  • 32. Slide 31 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. A Zener is a diode operated in reverse bias at the Peak Inverse Voltage (PIV) called the Zener Voltage (V Z ). Symbol Common Zener Voltages: 1.8V to 200V 1. Zener Diode
  • 33. Slide 32 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. 2. Light Emitting Diode (LED) This diode when forward biased emits photons. These can be in the visible spectrum. Symbol The forward bias voltage is higher, usually around 2-3V.
  • 34. Slide 33 Robert Boylestad Digital Electronics Copyright ©2002 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Multiple diodes can be packaged together in an integrated circuit (IC). A variety of combinations exist. Example of an array: 3. Diode Arrays