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University Physics Volume 3

9.7 Semiconductor Devices

University Physics Volume 39.7 Semiconductor Devices
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  1. Preface
  2. Unit 1. Optics
    1. 1 The Nature of Light
      1. Introduction
      2. 1.1 The Propagation of Light
      3. 1.2 The Law of Reflection
      4. 1.3 Refraction
      5. 1.4 Total Internal Reflection
      6. 1.5 Dispersion
      7. 1.6 Huygens’s Principle
      8. 1.7 Polarization
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    2. 2 Geometric Optics and Image Formation
      1. Introduction
      2. 2.1 Images Formed by Plane Mirrors
      3. 2.2 Spherical Mirrors
      4. 2.3 Images Formed by Refraction
      5. 2.4 Thin Lenses
      6. 2.5 The Eye
      7. 2.6 The Camera
      8. 2.7 The Simple Magnifier
      9. 2.8 Microscopes and Telescopes
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    3. 3 Interference
      1. Introduction
      2. 3.1 Young's Double-Slit Interference
      3. 3.2 Mathematics of Interference
      4. 3.3 Multiple-Slit Interference
      5. 3.4 Interference in Thin Films
      6. 3.5 The Michelson Interferometer
      7. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 4 Diffraction
      1. Introduction
      2. 4.1 Single-Slit Diffraction
      3. 4.2 Intensity in Single-Slit Diffraction
      4. 4.3 Double-Slit Diffraction
      5. 4.4 Diffraction Gratings
      6. 4.5 Circular Apertures and Resolution
      7. 4.6 X-Ray Diffraction
      8. 4.7 Holography
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  3. Unit 2. Modern Physics
    1. 5 Relativity
      1. Introduction
      2. 5.1 Invariance of Physical Laws
      3. 5.2 Relativity of Simultaneity
      4. 5.3 Time Dilation
      5. 5.4 Length Contraction
      6. 5.5 The Lorentz Transformation
      7. 5.6 Relativistic Velocity Transformation
      8. 5.7 Doppler Effect for Light
      9. 5.8 Relativistic Momentum
      10. 5.9 Relativistic Energy
      11. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    2. 6 Photons and Matter Waves
      1. Introduction
      2. 6.1 Blackbody Radiation
      3. 6.2 Photoelectric Effect
      4. 6.3 The Compton Effect
      5. 6.4 Bohr’s Model of the Hydrogen Atom
      6. 6.5 De Broglie’s Matter Waves
      7. 6.6 Wave-Particle Duality
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    3. 7 Quantum Mechanics
      1. Introduction
      2. 7.1 Wave Functions
      3. 7.2 The Heisenberg Uncertainty Principle
      4. 7.3 The Schrӧdinger Equation
      5. 7.4 The Quantum Particle in a Box
      6. 7.5 The Quantum Harmonic Oscillator
      7. 7.6 The Quantum Tunneling of Particles through Potential Barriers
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    4. 8 Atomic Structure
      1. Introduction
      2. 8.1 The Hydrogen Atom
      3. 8.2 Orbital Magnetic Dipole Moment of the Electron
      4. 8.3 Electron Spin
      5. 8.4 The Exclusion Principle and the Periodic Table
      6. 8.5 Atomic Spectra and X-rays
      7. 8.6 Lasers
      8. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
    5. 9 Condensed Matter Physics
      1. Introduction
      2. 9.1 Types of Molecular Bonds
      3. 9.2 Molecular Spectra
      4. 9.3 Bonding in Crystalline Solids
      5. 9.4 Free Electron Model of Metals
      6. 9.5 Band Theory of Solids
      7. 9.6 Semiconductors and Doping
      8. 9.7 Semiconductor Devices
      9. 9.8 Superconductivity
      10. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    6. 10 Nuclear Physics
      1. Introduction
      2. 10.1 Properties of Nuclei
      3. 10.2 Nuclear Binding Energy
      4. 10.3 Radioactive Decay
      5. 10.4 Nuclear Reactions
      6. 10.5 Fission
      7. 10.6 Nuclear Fusion
      8. 10.7 Medical Applications and Biological Effects of Nuclear Radiation
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
    7. 11 Particle Physics and Cosmology
      1. Introduction
      2. 11.1 Introduction to Particle Physics
      3. 11.2 Particle Conservation Laws
      4. 11.3 Quarks
      5. 11.4 Particle Accelerators and Detectors
      6. 11.5 The Standard Model
      7. 11.6 The Big Bang
      8. 11.7 Evolution of the Early Universe
      9. Chapter Review
        1. Key Terms
        2. Key Equations
        3. Summary
        4. Conceptual Questions
        5. Problems
        6. Additional Problems
        7. Challenge Problems
  4. A | Units
  5. B | Conversion Factors
  6. C | Fundamental Constants
  7. D | Astronomical Data
  8. E | Mathematical Formulas
  9. F | Chemistry
  10. G | The Greek Alphabet
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  12. Index

Learning Objectives

By the end of this section, you will be able to:
  • Describe what occurs when n- and p-type materials are joined together using the concept of diffusion and drift current (zero applied voltage)
  • Explain the response of a p-n junction to a forward and reverse bias voltage
  • Describe the function of a transistor in an electric circuit
  • Use the concept of a p-n junction to explain its applications in audio amplifiers and computers

Semiconductors have many applications in modern electronics. We describe some basic semiconductor devices in this section. A great advantage of using semiconductors for circuit elements is the fact that many thousands or millions of semiconductor devices can be combined on the same tiny piece of silicon and connected by conducting paths. The resulting structure is called an integrated circuit (ic), and ic chips are the basis of many modern devices, from computers and smartphones to the internet and global communications networks.

Diodes

Perhaps the simplest device that can be created with a semiconductor is a diode. A diode is a circuit element that allows electric current to flow in only one direction, like a one-way valve (see Model of Conduction in Metals). A diode is created by joining a p-type semiconductor to an n-type semiconductor (Figure 9.23). The junction between these materials is called a p-n junction. A comparison of the energy bands of a silicon-based diode is shown in Figure 9.23(b). The positions of the valence and conduction bands are the same, but the impurity levels are quite different. When a p-n junction is formed, electrons from the conduction band of the n-type material diffuse to the p-side, where they combine with holes in the valence band. This migration of charge leaves positive ionized donor ions on the n-side and negative ionized acceptor ions on the p-side, producing a narrow double layer of charge at the p-n junction called the depletion layer. The electric field associated with the depletion layer prevents further diffusion. The potential energy for electrons across the p-n junction is given by Figure 9.24.

Figure a shows two blocks place side by side, in contact. The left one is labeled p and the right one is labeled n. Figure b shows a valence band at the bottom and a conduction band at the top. There are holes within the valance band on the left, labeled holes at the top of the valence band. There are electrons above the conduction line on the right, labeled electrons at the bottom of the conduction band. Impurity bands are shown above the holes and below the electrons.
Figure 9.23 (a) Representation of a p-n junction. (b) A comparison of the energy bands of p-type and n-type silicon prior to equilibrium.
Figure a shows two blocks place side by side, in contact. The left one is labeled p and the right one is labeled n. Minus signs are shown in the p block near the side in contact. Plus signs are shown in the n block near the side in contact. Figure b shows a valence band at the bottom and a conduction line at the top. The valence band is higher on the left side almost reaching the central line between the two bands. There are holes with the valence band at the top, on the left. The conduction line is lower on the right, almost reaching the central line between the two bands. There are electrons just above the line, on the right. The displacement of the bands is labeled eV subscript 0, potential difference prevents diffusion of electrons from n side to p side.
Figure 9.24 At equilibrium, (a) excess charge resides near the interface and the net current is zero, and (b) the potential energy difference for electrons (in light blue) prevents further diffusion of electrons into the p-side.

The behavior of a semiconductor diode can now be understood. If the positive side of the battery is connected to the n-type material, the depletion layer is widened, and the potential energy difference across the p-n junction is increased. Few or none of the electrons (holes) have enough energy to climb the potential barrier, and current is significantly reduced. This is called the reverse bias configuration. On the other hand, if the positive side of a battery is connected to the p-type material, the depletion layer is narrowed, the potential energy difference across the p-n junction is reduced, and electrons (holes) flow easily. This is called the forward bias configuration of the diode. In sum, the diode allows current to flow freely in one direction but prevents current flow in the opposite direction. In this sense, the semiconductor diode is a one-way valve.

We can estimate the mathematical relationship between the current and voltage for a diode using the electric potential concept. Consider N negatively charged majority carriers (electrons donated by impurity atoms) in the n-type material and a potential barrier V across the p-n junction. According to the Maxwell-Boltzmann distribution, the fraction of electrons that have enough energy to diffuse across the potential barrier is NeeV/kBTNeeV/kBT. However, if a battery of voltage VbVb is applied in the forward-bias configuration, this fraction improves to Nee(VVb)/kBTNee(VVb)/kBT. The electric current due to the majority carriers from the n-side to the p-side is therefore

I=NeeV/kBTeeVb/kBT=I0eeVb/kBT,I=NeeV/kBTeeVb/kBT=I0eeVb/kBT,
(9.35)

where I0I0 is the current with no applied voltage and T is the temperature. Current due to the minority carriers (thermal excitation of electrons from the valence band to the conduction band on the p-side and subsequent attraction to the n-side) is I0I0, independent of the bias voltage. The net current is therefore

Inet=I0(eeVb/kBT1).Inet=I0(eeVb/kBT1).
(9.36)

A sample graph of the current versus bias voltage is given in Figure 9.25. In the forward bias configuration, small changes in the bias voltage lead to large changes in the current. In the reverse bias configuration, the current is InetI0InetI0. For extreme values of reverse bias, the atoms in the material are ionized which triggers an avalanche of current. This case occurs at the breakdown voltage.

Graph of I subscript net versus V. An arrow pointing right from the y axis is labeled forward bias. An arrow pointing left from the y axis is labeled reverse bias. The curve goes up and right in the first quadrant and then becomes almost vertical at higher values of x and y. It crosses the positive x axis into the fourth quadrant  and then the negative y axis at minus I subscript 0. It travels left in a horizontal line till a point where it turns sharply down into what becomes an almost vertical line. The x value of the turning point is labeled breakdown voltage.
Figure 9.25 Current versus voltage across a p-n junction (diode). In the forward bias configuration, electric current flows easily. However, in the reverse bias configuration, electric current flow very little.

Example 9.6

Diode Current Attaching the positive end of a battery to the p-side and the negative end to the n-side of a semiconductor diode produces a current of 4.5×10−1A.4.5×10−1A. The reverse saturation current is 2.2×10−8A.2.2×10−8A. (The reverse saturation current is the current of a diode in a reverse bias configuration such as this.) The battery voltage is 0.12 V. What is the diode temperature?

Strategy The first arrangement is a forward bias configuration, and the second is the reverse bias configuration. In either case, Equation 9.2 gives the current.

Solution The current in the forward and reverse bias configurations is given by

Inet=I0(eeVb/kBT1).Inet=I0(eeVb/kBT1).

The current with no bias is related to the reverse saturation current by

I0Isat=2.2×10−8.I0Isat=2.2×10−8.

Therefore

InetI0=4.5×10−1A2.2×10−8A=2.0×108.InetI0=4.5×10−1A2.2×10−8A=2.0×108.

Equation 9.2 can be written as

InetI0+1=eeVb/kBT.InetI0+1=eeVb/kBT.

This ratio is much greater than one, so the second term on the left-hand side of the equation vanishes. Taking the natural log of both sides gives

eVbkBT=19.eVbkBT=19.

The temperature is therefore

T=eVbkB(119)=e(0.12V)8.617×10−5eV/K(119)=73K.T=eVbkB(119)=e(0.12V)8.617×10−5eV/K(119)=73K.

Significance The current moving through a diode in the forward and reverse bias configuration is sensitive to the temperature of the diode. If the potential energy supplied by the battery is large compared to the thermal energy of the diode’s surroundings, kBT,kBT, then the forward bias current is very large compared to the reverse saturation current.

Check Your Understanding 9.5

How does the magnitude of the forward bias current compare with the reverse bias current?

Interactive

Create a p-n junction and observe the behavior of a simple circuit for forward and reverse bias voltages. Visit this site to learn more about semiconductor diodes.

Junction Transistor

If diodes are one-way valves, transistors are one-way valves that can be carefully opened and closed to control current. A special kind of transistor is a junction transistor. A junction transistor has three parts, including an n-type semiconductor, also called the emitter; a thin p-type semiconductor, which is the base; and another n-type semiconductor, called the collector (Figure 9.26). When a positive terminal is connected to the p-type layer (the base), a small current of electrons, called the base current IB,IB, flows to the terminal. This causes a large collector current IcIc to flow through the collector. The base current can be adjusted to control the large collector current. The current gain is therefore

Ic=βIB.Ic=βIB.
(9.37)
Three blocks in contact are shown. From left to right they are labeled: emitter, n-type, base, p-type and collector, n-type. A voltage source is connected across the collector and emitter, with the collector being positive. Another voltage source is connected across the emitter and base, with the base being positive. A thick arrow starts from the emitter, goes through the other two blocks, comes out of the collector and travels along the first voltage loop. The arrow is labeled large electron flow, collector current. A thinner arrow from the base travels into the second voltage loop. This is labeled small electron flow, base current.
Figure 9.26 A junction transistor has three parts: emitter, base, and collector. Voltage applied to the base acts as a valve to control electric current from the emitter to the collector.

A junction transistor can be used to amplify the voltage from a microphone to drive a loudspeaker. In this application, sound waves cause a diaphragm inside the microphone to move in and out rapidly (Figure 9.27). When the diaphragm is in the “in” position, a tiny positive voltage is applied to the base of the transistor. This opens the transistor “valve” and allows a large electrical current flow to the loudspeaker. When the diaphragm is in the “out” position, a tiny negative voltage is applied to the base of the transistor, which shuts off the transistor valve so that no current flows to the loudspeaker. This shuts the transistor “valve” off so no current flows to the loudspeaker. In this way, current to the speaker is controlled by the sound waves, and the sound is amplified. Any electric device that amplifies a signal is called an amplifier.

Figure a shows three blocks in contact. From left to right they are labeled: emitter, n-type, base, p-type and collector, n-type. A loudspeaker is connected across the collector and emitter. A microphone is connected across the emitter and base. It is labeled diaphragm moves out. The voltage across the microphone is labeled base voltage. It is negative at the base. The figure is labeled little or no electron flow. Figure b shows a similar arrangement to figure a. A thick arrow starts from the emitter, goes through the other two blocks, comes out of the collector and travels along the loudspeaker loop. The arrow is labeled large electron flow, collector current. A thinner arrow from the base travels into the microphone loop. This is labeled small electron flow, base current. The polarity of the base voltage across the microphone is opposite from that in figure a. The microphone is labeled diaphragm moves in. The loudspeaker is shown to give out sound waves.
Figure 9.27 An audio amplifier based on a junction transistor. Voltage applied to the base by a microphone acts as a valve to control a larger electric current that passes through a loudspeaker.

In modern electronic devices, digital signals are used with diodes and transistors to perform tasks such as data manipulation. Electric circuits carry two types of electrical signals: analog and digital (Figure 9.28). An analog signal varies continuously, whereas a digital signal switches between two fixed voltage values, such as plus 1 volt and zero volts. In digital circuits like those found in computers, a transistor behaves like an on-off switch. The transistor is either on, meaning the valve is completely open, or it is off, meaning the valve is completely closed. Integrated circuits contain vast collections of transistors on a single piece of silicon. They are designed to handle digital signals that represent ones and zeroes, which is also known as binary code. The invention of the ic helped to launch the modern computer revolution.

Two graphs of V versus t are shown. The first, labeled analog signal has an irregular sinusoidal wave. The second, labeled digital signal has a square wave.
Figure 9.28 Real-world data are often analog, meaning data can vary continuously. Intensity values of sound or visual images are usually analog. These data are converted into digital signals for electronic processing in recording devices or computers. The digital signal is generated from the analog signal by requiring certain voltage cut-off value.
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