Introduction to Semiconductors !

Introduction to Semiconductors !
Introduction to Semiconductors !
Introduction to Semiconductors !
Introduction to Semiconductors !
Introduction to Semiconductors !
 Introduction to Semiconductors !
 Introduction to Semiconductors !
 Introduction to Semiconductors !
 Introduction to Semiconductors !
 Introduction to Semiconductors !
 Introduction to Semiconductors !
 Introduction to Semiconductors !
 Introduction to Semiconductors !
 Introduction to Semiconductors !
 Introduction to Semiconductors !
 Introduction to Semiconductors !

Electrical Resistivity of Semiconductors:

 

The conductivity of a material thus depends on the number of free charge carriers (electrons and holes). The reciprocal of the conductivity of a material is referred to as its resistivity. The electrical resistivity of semiconductors lies between that of metallic conductors and non-conductors (insulators). The following table provides an overview of the classification of materials as conductors, semiconductors and insulators. A few examples of materials that are frequently employed in electrical engineering and electronics are given.

Designation

 

 Resistivity

Ρ(Ωcm)

 Conductivity

Κ(1/(Ωcm))

Material

 

 Insulators 1020 10-20 Amber
  1018 10-18 Paraffin wax
  1016 10-16 Polystyrene
  1014 10-14 Carbon
  1012 10-12 Hard porcelain
  1010 10-10 PVC
  108 10-8 Marble, glass
 Semiconductors 106 10-6  Selenium
  104 10-4 Silicon, pure
  100 100 Germanium, pure
  10-2 102

 Indium arsenide, gallium arsenide

 Conductors 10-6  106 Copper
  10-8  108 Silver

Although the semiconductor materials selenium and germanium are still occasionally encountered today, silicon is the most widely used material. In addition, "modern" compound semiconductors and organic semiconductors, such as gallium arsenide, zinc sulphide and pentacene, are increasingly gaining in importance. These are primarily employed in optoelectronics.

Pure semiconductor materials have a purity grade of 1010, which means that there is one impurity atom for every 1010 semiconductor atoms.

Doping:

 

The electrical behaviour of a semiconductor can be influenced by intentionally contaminating it with impurity atoms. In this instance, contamination means that an impurity atom of a higher (more valence electrons) or lower (fewer valence electrons) valency is introduced in place of one of the original atoms of the semiconductor. This results in the generation of a surplus of either negative charge carriers (electrons) or positive change carriers (holes). In both cases, this causes the number of free charge carriers to increase.

The charge carrier density of a semiconductor can be raised by intentionally introducing impurity atoms. This allows the resistivity to be varied over wide ranges, depending on the quantity of impurity atoms added.

The intentional contamination of a semiconductor with impurity atoms is called doping. A distinction is made between n-doping (electrons) and p-doping (holes). This is illustrated in the following two diagrams.

Introduction to Semiconductors !

N-doping with a phosphorous atom (with a valency of 5) 

Introduction to Semiconductors !

P-doping with a boron atom (with a valency of 3)

Silicon Crystal Structure:

 

The structure of the crystal lattice of a semiconductor may be explained using an element that is a semiconductor, silicon, as an example.

Silicon is the 14th element in the periodic table. A silicon atom therefore contains 14 protons, 14 neutrons and 14 electrons. According to the Bohr model of the atom, the two inner shells are completely occupied with electrons (2 + 8). This means that the silicon atom has four electrons, the valence electrons, in its outer shell. These are responsible for conductivity. The electrons in the inner shells are not shown in the following diagram.  

 Introduction to Semiconductors !

Atoms have a tendency to change the number of electrons in their outer shell so that it is fully occupied. Silicon atoms can either donate their four valence electrons or else accept four electrons from neighbouring atoms. The high degree of purity of the crystal means that they do not have any opportunity to form bonds with neighbouring impurity atoms. They therefore form atomic bonds with one another in which valence electrons circulate back and forth between neighbouring atoms, so that the outer shells of some atoms are temporarily fully occupied . This process is called covalent bonding.

 Introduction to Semiconductors !

Conductivity and Temperature Dependence:

 

The influence of energy causes individual electrons to break free of their bonds every now and again. These electrons leave behind an atom with a missing negative charge - an electron hole. This hole, also known as a defect electron, constitutes a positive charge. The free electron wanders aimlessly about within the crystal until is encounters a hole again, whereupon it jumps back into a permanent atomic union. A recombination has taken place. 

 Introduction to Semiconductors !

This process produces some proportion of the intrinsic conductivity. Another contribution comes from electrons from atoms at the edge of the crystal lattice, which are responsible for a certain degree of intrinsic conduction because they have not entered into covalent bonds. Residual impurity atoms may constitute a third factor.

The intrinsic conductivity is specified by what is termed the intrinsic charge carrier density, which gives the number of electrons that are available for conduction relative to a particular volume of a material.

Temperature dependence:

Increasing the temperature, i.e. feeding energy into the system, causes the crystal structure to vibrate more and more and the number of broken bonds to rise. This leads to an increasing number of free electrons in the crystal, i.e. the intrinsic charge carrier density of a semiconductor is temperature dependent. As the temperature rises, so also does the number of free charge carriers, hence the conductivity rises and the resistance falls too. If the temperature sinks, fewer and fewer free electrons are available, so the conductivity falls and the resistance climbs. The charge carrier density of a semiconductor is therefore always specified for a particular temperature. This is also the reason why the performance data for semiconductor components are always given with reference to a particular ambient temperature (usually 25° C). The following table shows the charge carrier density of some semiconductors at 300° Kelvin (about 27° Celsius):

 Material  Intrinsic charge carrier density ni
 Metals

 2 * 1022 cm-3

 Germanium

 2.33 * 1013 cm-3

 Silicon

 1.02 * 1010 cm-3

 Gallium arsenide

 2.0 * 106 cm-3

A pure semiconductor exhibits no intrinsic conduction through pair formation at 0° Kelvin (absolute zero). Because of this behaviour, semiconductors have a negative temperature coefficient.

The reference temperature of 300° Kelvin is the value typically used for characterising semiconductor materials. In data sheets for components, an ambient temperature of 25° Celsius is normally assumed. 

P-N Junction:

 

Semiconductor components are fabricated from both p-doped and n-doped material. The transition zone between the doped regions is of critical importance for the function of the semiconductor component. At the junctions, a region develops in which the free charge carriers diffuse out across the boundary surface. Hence electrons cross into the p-region and holes cross into the n-region. This leads to recombination, as a result of which almost all the free charge carriers become bound. A depletion layer arises in which no free charge carriers are present.

 Introduction to Semiconductors !

The directional distribution of the charge carriers creates a space charge zone which acts to prevent any further enlargement. This zone is therefore only a few µm thick.

The zone that arises as a result of the depletion layer that has been stripped of charge carriers acts like the dielectric of a capacitor. Although its capacitance is very small, it has a very noticeable effect at higher frequencies.

Forward Biasing:

 

If the negative terminal of a voltage source is attached to the n-material and the positive terminal to the p-material, an electric field again arises. This field causes additional free electrons from the negative terminal to be pushed into the n-material and electrons in the p-material to be drawn out  by the positive terminal, so that the holes travel to the positive terminal. The depletion layer narrows.

 Introduction to Semiconductors !If the voltage is increased, the depletion layer disappears completely and current flows. The level of the applied voltage at which a current flows is dependent on the semiconductor material and is called the forward voltage UF.

The forward voltage is typically about 0.3 V for a germanium diode and 0.7 V for a silicon diode.

Reverse Biasing:

 

If the positive terminal of a voltage source is attached to the n-material and the negative terminal to the p-material, an electric field arises. This field causes the free electrons in the n-material to travel to the positive terminal and the holes in the p-material to become filled with electrons from the negative terminal. The depletion layer widens.

  Introduction to Semiconductors !

If the voltage is increased, the depletion layer widens accordingly. Once the depletion layer has expanded to fill the entire width of the crystal, any further increase in the voltage would result in a sudden strong current flow, which would destroy the p-n junction. The voltage at which the depletion layer has expanded to fill the entire crystal is called the maximum reverse voltage.

Circuit Symbol Diode:

A component with one p-n junction is called a diode. The diode has two terminals, which are termed the cathode and the anode. The cathode is usually marked with a ring on an actual component. The circuit symbol for a diode looks like this:

Introduction to Semiconductors !

The following diagram illustrates once again the arrangement of the n-region and p-region as well as the anode and cathode in comparison with a real diode.

 Introduction to Semiconductors !

Diode Characteristics:

 

The forward and reverse bias behaviour of the diode can be clearly illustrated as a characteristic describing the relationship between the diode current and the diode voltage.

Introduction to Semiconductors !

A distinction is made between the forward direction and the reverse direction.

In the following experiment, we shall determine the characteristic of a silicon diode. We begin by connecting a DC voltage across a series resistor R1 and the diode D1. This voltage is increased in steps while measuring the forward voltage (UF) and current (IF) at each step; these are recorded in a table of values before being displayed as a graph. The same experiment is then performed again after switching the polarity of the applied voltage. This allows us to measure the reverse voltage (UR) and current (IR).

Zener Diode Fundamentals:

 

Zener diodes, or Z-diodes for short, were named after the physicist C.M. Zener. In electronics, Zener diodes have achieved great importance as voltage limiting elements.

Introduction to Semiconductors !

Circuit symbol for a Zener diode

Function description:
Zener diodes, too, act like a valve for electric current. They allow the current to pass in the forward direction from anode to cathode, and behave like normal silicon diodes in this region. In the reverse direction they block the current, but only up to a defined voltage, which is called the Zener voltage. On reaching this voltage, the Zener diode becomes conducting. 
The Zener voltage is specified during the manufacturing process. There are a wide variety of types, beginning from small voltages such as 2.7 V and ranging up to over 100 V. Zener diodes are operated in the reverse direction.

Real diodes:
A component type designation is printed on the real components. The cathode is marked with a ring. The breakdown voltage or Zener voltage is also printed on the diode.

 Introduction to Semiconductors !

The properties of the real diode diverge slightly from those of the ideal diode. It possesses neither ideal conducting nor ideal blocking properties. These properties are particularly apparent when viewing the Zener diode characteristic.

 Introduction to Semiconductors !

  • Forward biasing:
    Zener diodes have a low forward voltage of approximately 0.7 V. The forward bias region is not of interest for typical applications. 
  • Reverse bias properties:
    Beginning at the Zener voltage according to which the diodes are defined and which is specified for a current IZ = 5 mA, Zener diodes are able to conduct. They then possess a small resistance whose value can be determined from the gradient of the reverse bias characteristic.
    Zener diodes are subject to limits such as, for example, maximum temperature or maximum power dissipation, which must not be exceeded.

Voltage Stabilisation:

 

The typical Zener diode application circuit is introduced in this section.

 Introduction to Semiconductors !

Zener diodes are employed for stabilising DC voltages which may also have a ripple component. The basic circuit is also often used in combination with power transistors and / or operational amplifiers.

The purpose of the circuit is to maintain as constant a voltage as possible across a load resistance while the input voltage fluctuates or the load resistance changes. The series resistor R1 has the task of limiting the current. The voltage difference between the supplied voltage and the Zener voltage of the diode that constitutes the output voltage is dropped across it.

The stabilising effect of the Zener diode circuit relies on the fact that, in the region of the characteristic above the breakdown voltage, a large change in the current produces only a small change in the voltage. This can be seen very easily in the following example, which is taken from the data sheet for diodes of type ZPD.

 Introduction to Semiconductors !

 

This effect can, however, be maintained only within a narrow working range. If the input voltage falls too low or the load resistance becomes too small, the voltage at the load resistance sinks below the Zener voltage and the stabilising effect is lost. If the input voltage rises too high, the currents I and IZ also increase sharply; this results in high power dissipation in the series resistor and the Zener diode, which can cause the destruction of the components if they have been wrongly dimensioned.

 

For the circuit shown in the diagram, values can be calculated as follows:

The voltage at R1 can be calculated directly:

UR1 = 7 V - 4.7 V = 2.3 V
This means that the current I through R1 is:I = UR1 / R1 = 2.3 V / 180 ohms = 12.8 mA
The current IO through R5 can then be calculated:IO = 4.7 V / 680 ohms = 6.9 mA
This allows the diode current IZ to be calculated too:IZ = I - IO = 5.9 mA

If the manufacturer of the Zener diode specifies a maximum power dissipation of 0.5 W in the data sheet, the maximum current for the given Zener voltage works out to be

IZMAX = 0.5 W / 4.7 V = 106 mA

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