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Understanding Semiconductors: Covalent Bonding & Impurities in Si, Ge, & GaAs, Lecture notes of Engineering

The concept of semiconductors, focusing on covalent bonding, intrinsic carriers, and impurities in silicon, germanium, and gallium arsenide. It covers the structure of the lattice, valence electrons, trivalent and pentavalent atoms, and the impact of impurities on conductivity.

What you will learn

  • What are intrinsic carriers in semiconductors?
  • What are donor and acceptor impurities in semiconductors?
  • What is covalent bonding in semiconductors?
  • How does the doping process affect the conductivity of semiconductor materials?
  • How does the number of free electrons in a semiconductor material change with temperature?

Typology: Lecture notes

2020/2021

Uploaded on 07/19/2021

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Semiconductors: elements having conductivity between a good conductor and insulator
2 Classes of Semiconductor
1.Single crystal: have repetitive crystal structure (ex: Ge and Si)
2.Compound: constructed of two or more semiconductor materials of different atomic structures. (ex:
GaAs, CdS, GaN, GaAsP)
Ge, Si and GaAs most frequently used in the construction of electronic devices
1939 discovery of diodes
1947 discovery of transistor
Germanium was used almost exclusively because:
o Relatively easy to find
o Available in large quantities
o Relatively easy to refine to obtain very high levels of purity which is an important
aspect in the fabrication process
But diodes and transistors constructed using Ge suffered from low levels of reliability due to its
sensitivity to change in temperature
1954 first silicon transistor was introduced
Silicon:
o have improved temperature sensitivity
o One of the most abundant materials on earth
o Has the benefit of years of development
o Is the leading semiconductor materials for electronic components and ICs
1970’s first GaAs transistor was developed
GaAs Transistor: had a speed of operation up to 5 times that of Silicon
GaAs:
o was more difficult to manufacture at high levels of purity
o was more expensive
o Had little design support
o Often used as the base material for new high-speed, very large scale integrated
(VLSI) circuit designs
To fully appreciate why Si, Ge, and GaAs are the semiconductors of choice for the electronics
industry requires some understanding of the atomic structure of each and how the atoms are bound
together to form a crystalline structure.
The fundamental components of an atom are:
electron
proton
neutron
In the lattice structure, neutrons and protons form the nucleus and electrons appear in fixed orbits
around the nucleus. The Bohr model for the three materials is provided in the following figure.
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pf9
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pfd
pfe
pff
pf12
pf13
pf14
pf15
pf16
pf17
pf18
pf19
pf1a
pf1b
pf1c
pf1d
pf1e
pf1f
pf20

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Semiconductors: elements having conductivity between a good conductor and insulator

  • 2 Classes of Semiconductor
  1. Single crystal: have repetitive crystal structure (ex: Ge and Si)
  2. Compound: constructed of two or more semiconductor materials of different atomic structures. (ex: GaAs, CdS, GaN, GaAsP)
  • Ge, Si and GaAs – most frequently used in the construction of electronic devices
  • 1939 – discovery of diodes
  • 1947 – discovery of transistor Germanium was used almost exclusively because:

o Relatively easy to find o Available in large quantities o Relatively easy to refine to obtain very high levels of purity which is an important aspect in the fabrication process But diodes and transistors constructed using Ge suffered from low levels of reliability due to its sensitivity to change in temperature

  • 1954 – first silicon transistor was introduced Silicon:

o have improved temperature sensitivity o One of the most abundant materials on earth o Has the benefit of years of development o Is the leading semiconductor materials for electronic components and ICs

  • 1970’s – first GaAs transistor was developed
  • GaAs Transistor : had a speed of operation up to 5 times that of Silicon GaAs:

o was more difficult to manufacture at high levels of purity o was more expensive o Had little design support o Often used as the base material for new high-speed, very large scale integrated (VLSI) circuit designs To fully appreciate why Si, Ge, and GaAs are the semiconductors of choice for the electronics industry requires some understanding of the atomic structure of each and how the atoms are bound together to form a crystalline structure.

The fundamental components of an atom are:

  • electron
  • proton
  • neutron In the lattice structure, neutrons and protons form the nucleus and electrons appear in fixed orbits around the nucleus. The Bohr model for the three materials is provided in the following figure.

From the given figure:

  • Silicon (Si): 14 electrons (2,8,4)
  • Germanium (Ge): 32 electrons (2,8,18,4)
  • Gallium (Ga): 31 electrons (2,8,18,3)
  • Arsenide (As): 33 electrons (2,8,18,5) Valence electron: Electrons at the outermost shell
  • The term valence is used to indicate that the potential (ionization potential) required to remove any one of these electrons from the atomic structure is significantly lower than that required for any other electron in the structure. Tetravalent: atoms that have four valence electrons (Si and Ge) Trivalent: atoms that have three valence electrons (Ga) Pentavalent : atoms that have five valence electrons (As) Covalent Bonding: Bonding of atoms strengthened by the sharing of electrons In a pure silicon or germanium crystal the four valence electrons of one atom form a bonding arrangement with four adjoining atoms, as shown: This bonding of atoms, strengthened by the sharing of electrons, is called covalent bonding. Because GaAs is a compound semiconductor, there is sharing between the two different atoms, as shown:
  • Have positive temperature coefficient
  • Resistance increases with an increase in heat
  • No. of carriers do not increase with temperature but their vibration pattern about a relatively fixed location makes it difficult for a sustained flow of carriers through the material. Semiconductors:
  • Have negative temperature coefficient
  • Resistance decreases with an increase in heat
  • Increasing numbers of valence electrons absorb sufficient thermal energy to break the covalent bond and to contribute to the number of free carriers.

Bohr’s Atomic Model

According to Danish Physicist Neils Bohr in 1913:

  • An atom consists of a positively charged nucleus around which negatively charged electrons revolve in different circular orbits
  • The electrons can revolve around the nucleus only in certain permitted orbits i.e. orbits of certain radii are allowed
  • The electrons in each permitted orbit have a certain fixed amount of energy. The larger the orbit (i.e. larger radius), the greater is the energy of electrons
  • If an electron is given additional energy (e.g. heat, light etc.), it is lifted to the higher orbit. The atom is said to be in a state of excitation. As it falls back to the original higher orbit, it gives back the acquired energy in the form of heat, light, or other radiations Silicon Atomic Structure (showing orbits and radii):

Energy Levels

Energy Level Diagram (showing energy levels of a single isolated atom of silicon):

  • Each orbit of an atom has a single energy
  • The larger the orbit of an electron, the greater is its energy and higher is the energy level
  • when the atom is in a solid, the electron in any orbit can have a range of energies
  • The range of energies possessed by an electron in a solid is known as energy band.

Important Energy Bands in Solids:

  • Valence band: The range of energies (i.e. band) possessed by valence electrons
  • Conduction Band: The range of energies (i.e. band) possessed by conduction band electrons o Conduction Electrons : ▪ free electrons which are responsible for the conduction of current in a conductor ▪ valence electrons that are loosely attached to the nucleus and get detached due to some external source
  • Forbidden energy gap. The separation between the conduction band and valence band on the energy level diagram

Classification of Solids and Energy Bands

  • Insulator : valence band is full while the conduction band is empty
  • Semiconductors : the valence band is almost filled and the conduction band is almost empty
  • Conductors : valence and conduction bands overlap each other
  • Since the inserted impurity atom has donated a relatively “free” electron to the structure: The diffused impurities with five valence electrons are called donor atoms
  • n-type material, even with a large number of “free” carriers is still electrically neutral since ideally the number of positively charged protons in the nuclei is still equal to the number of “free” and orbiting negatively charged electrons in the structure
  • effect of doping process on the relative conductivity: o discrete energy level (called the donor level) appears in the forbidden band with an Eg significantly less than that of the intrinsic material o Impact: at room temperature, there are a large number of carriers (electrons) in the conduction level and the conductivity of the material increases significantly P-type materials :
  • Created by adding trivalent impurities (boron, gallium, and indium) to intrinsic material
  • There is an insufficient number of electrons to complete the covalent bonds of the newly formed lattice.
  • The resulting vacancy is called a hole and is represented by a small circle or positive sign due to the absence of a negative charge.
  • Since the resulting vacancy will readily accept a “free” electron: The diffused impurities with three valence electrons are called acceptor atoms Electron versus Hole Flow If a valence electron acquires sufficient kinetic energy to break its covalent bond and fills the void created by a hole, then a vacancy, or hole, will be created in the covalent bond that released the electron. There is, therefore, a transfer of holes to the left and electrons to the right Majority and Minority Carriers
  • In an n-type material the electron is called the majority carrier and the hole the minority carrier
  • In a p-type material the hole is the majority carrier and the electron is the minority carrier

Semiconductor Diode deals with the following topics:

  • Semiconductor Diode and the PN junction
  • Diode Biasing (Forward and Reverse)
  • VI Characteristic of a Diode
  • Diode Shockley’s Equation
  • Diode Structure and Symbol
  • Ideal Diode vs Practical Diode
  • Resistance Levels
  • Diode Equivalent Circuits or Diode Models
  • Diode Specification Sheet
  • Diode Testing
  • Zener Diodes
  • Light Emitting Diode (LED)

The students are expected to learn the following:

  • Recall also that there are as many electrons as protons in the n - type material before the formation of the PN junction, making the material neutral in terms of net charge, which is also true for the p - type material.
  • Upon the formation of the PN junction, the n region loses free electrons as they diffuse across the junction, creating a layer of positive charges (pentavalent ions) near the junction
  • The p region then loses holes as the electrons (that already crossed the junction from the n region) and holes combine, creating a layer of negative charges (trivalent ions) near the junction.
  • The two layers of positive and negative charges form the depletion region as shown in b of the above figure. depletion – refers to the fact that the region near the PN junction is depleted of charge carriers (electrons and holes) due to diffusion across the junction
  • The depletion region is formed very quickly and is very thin compared to the n region and p region.
  • At the end of the initial surge of free electrons across the PN junction, the depletion region has expanded to a point where equilibrium is established and no further diffusion of electrons will occur across the junction.
  • As electrons continue to diffuse across the junction, more and more positive and negative charges are created near the junction as the depletion region is formed.
  • There will come to a point where the total negative charge in the depletion region repels any further diffusion of electrons (negatively charged particles) into the p region.
  • The depletion region acts as a barrier to the further movement of electrons across the junction.
  • As defined by Coulomb’s law, there is a force acting on charges when there is a positive and a negative charge near each other.
  • The depletion region has many positive charges and many negative charges on the opposite sides of the PN junction.
  • Forces between opposite charges form a “field of forces” known as an electric field illustrated in b of the above figure by the red arrows between positive charges negative charges.
  • The said field is a barrier to free electrons in the n region.
  • To move an electron through the electric field in the depletion region, external energy must be applied.
  • The amount of voltage required to move electrons through the electric field is the potential difference of the electric field across the depletion region known as the barrier potential expressed in volts.
  • Moreover, a certain amount of voltage equal to the barrier potential and with proper polarity must be applied across a PN junction before electrons will begin to flow across the junction.
  • The barrier potential of a PN junction depends on several factors, including the type of semiconductive material, the amount of doping, and temperature.
  • The typical barrier potential is 0.7 V for silicon and 0.3 V for germanium at 25°C.

PN Junction and Depletion Region Energy Diagrams

  • Due to the differences in the atomic characteristics of the pentavalent and trivalent impurity atoms, the valence and conduction bands in an n - type material are at slightly lower energy levels than the valence and conduction bands in a p - type material. Energy diagram for a PN junction at the instant of formation:
  • Note in the figure that the valence and conduction bands in the n region are at lower energy levels than those in the p region (but with a significant amount of overlapping).
  • The free electrons in the n region that can occupy the upper part of the conduction band in terms of their energy can easily diffuse across the junction, even without an additional energy, and temporarily become free electrons in the lower part of the p - region conduction band.
  • After crossing the junction, the electrons quickly lose energy and fall into holes in the p - region valence band.
  • As the diffusion continues, the depletion region begins to form and the energy level of the n - region conduction band decreases.
  • The decrease in the energy level of the conduction band in the n region is due to the loss of higher-energy electrons that have diffused across the junction to the p region.
  • It will come to a point that there are no electrons left in the n - region conduction band with enough energy to get across the junction to the p - region conduction band, where there is the alignment of the top of the n - region conduction band and the bottom of the p - region conduction band.
  • The junction then is said to be at equilibrium and the depletion region is complete because diffusion has ceased. Energy diagram for a PN junction at equilibrium:
  • The bias-voltage source imparts sufficient energy to the free electrons for them to overcome the barrier potential of the depletion region and move on through into the p region.
  • Upon reaching the p region, the said conduction electrons have lost enough energy to immediately combine with holes in the valence band.
  • The electrons then are in the valence band in the p region since they have lost too much energy overcoming the barrier potential to remain in the conduction band.
  • On the other hand, the positive side of the bias-voltage source attracts the valence electrons toward the left end of the p region
  • The holes in the p region provide the medium or “pathway” for these valence electrons to move through the p region.
  • The electrons move from one hole to the next toward the left.
  • The holes in the p region effectively (not actually) move to the right toward the junction.
  • This effective flow of holes is called the hole current.
  • Hole current can also be viewed as being created by the flow of valence electrons through the p region.
  • Holes provide the only means for these valence electrons to flow.
  • As the electrons flow out of the p region through the external connection (conductor) and to the positive side of the bias-voltage source, they leave holes behind in the p region.
  • These electrons become conduction electrons in the metal conductor (recall that the conduction band in a conductor overlaps the valence band so that it takes much less energy for an electron to be a free electron in a conductor than in a semiconductor).
  • Then, there is continuous availability of holes effectively moving toward the PN junction to combine with the continuous stream of electrons as they come across the junction into the p region.
  • As more electrons flow into the depletion region, the number of positive ions is reduced.
  • As more holes effectively flow into the depletion region on the other side of the PN junction, the number of negative ions is reduced.
  • The reduction in positive and negative ions during forward bias causes the depletion region to narrow. The diode at equilibrium (no bias): Forward-biased diode:
  • Forward bias narrows the depletion region and produces a voltage drop across the PN junction equal to the barrier potential.
  • Recall that the electric field between the positive and negative ions in the depletion region on either side of the junction creates an “energy hill” that prevents free electrons from diffusing across the junction at equilibrium.
  • This “energy hill” via the presence of the electric field is known as the barrier potential.
  • When a forward bias is applied, the free electrons are provided with enough energy from the bias voltage source to overcome the barrier potential and effectively “climb the energy hill” and cross the depletion region.
  • The energy that the electrons require in order to pass through the depletion region is equal to the barrier potential.
  • That is, the electrons give up an amount of energy equivalent to the barrier potential when they cross the depletion region.
  • This energy loss causes a voltage drop across the PN junction equal to the barrier potential (0.7 V for silicon).
  • An additional small voltage drop occurs across the p and n regions due to the internal resistance of the material.
  • This resistance (for a doped semiconductive material), known as the dynamic resistance , is very small and can usually be neglected.

Reverse Bias

Reverse bias is the condition that essentially prevents current through the diode

  • The limiting resistor is not important in reverse bias since there is essentially no current.
  • Based on the reverse-bias connection, the positive side of the bias-voltage source “pulls” the free electrons (majority carriers in the n region) away from the PN junction.
  • As the electrons flow toward the positive side of the voltage source, additional positive ions are created, resulting in a widening of the depletion region and depletion of majority carriers.
  • In the p region, electrons from the negative side of the voltage source enter as valence electrons and move from hole to hole toward the depletion region where they create additional negative ions.
  • Again, this results in a widening of the depletion region and depletion of majority carriers.
  • The flow of valence electrons can be viewed as holes being “pulled” toward the positive side.
  • The initial flow of charge carriers is transitional and lasts for only a very short time after the reverse-bias voltage is applied.
  • The availability of majority carriers decreases as the depletion region widens.
  • As more of the n and p regions become depleted of majority carriers, the electric field between the positive and negative ions increases in strength until the potential across the depletion region equals the bias voltage.
  • Afterward, the transition current essentially ceases except for a very small reverse current that can usually be neglected.
  • The extremely small current that exists in reverse bias after the transition current dies out is caused by the minority carriers (produced by thermally generated electron-hole pairs) in the n and p regions.
  • The small number of free minority electrons in the p region is “pushed” toward the PN junction by the negative bias voltage.
  • When these minority carriers (electrons) reach the wide depletion region, they “fall down the energy hill” and combine with the minority holes in the n region as valence electrons and flow toward the positive bias voltage, creating a small hole current.
  • Since the conduction band in the p region is at a higher energy level than the conduction band in the n region, the minority electrons easily pass through the depletion region because there is no requirement for additional energy. The figure below shows the presence of the extremely small reverse current in a reverse-biased diode due to the minority carriers from thermally generated electron-hole pairs.
  • Normal operation for a forward-biased diode is above the knee of the curve.
  • From the figure, point A corresponds to a zero-bias condition, point B signifies the forward voltage less than the barrier potential of 0.7 V, and point C depicts the forward voltage approximately equal to the barrier potential.
  • The forward voltage will increase slightly above 0.7 V as the external bias voltage and forward current continue to increase above the knee.
  • In practical application, the forward voltage can be as much as approximately 0.9 V (depending on the forward current). This figure is an expanded view of the V - I characteristic curve, illustrating the dynamic resistance:
  • In contrast to the linear resistance, the resistance of the forward-biased diode is not constant over the entire curve.
  • Because the resistance changes as the curve progress, it is called dynamic or ac resistance.
  • The resistance is greatest below the knee of the curve because the current increases very little for a given change in voltage.
  • The resistance starts to decrease in the region of the knee of the curve and goes smallest above the knee where there is a large change in current for a given change in voltage.
  • As the reverse-bias voltage is gradually increased, there is a very small reverse current, and the voltage across the diode increases.
  • When the applied bias voltage is increased to a value where the reverse voltage across the diode ( V R) reaches the breakdown value ( V BR), the reverse current begins to increase rapidly
  • As the reverse-bias voltage is increased continuously, the current continues to increase very rapidly, but the voltage across the diode increases very little above V BR.
  • For most PN junction devices, the breakdown is not a normal mode of operation. This figure shows the V - I characteristic curve for a reverse-biased diode:
  • The diode has very little reverse current until the reverse voltage across the diode reaches approximately V BR at the knee of the curve.
  • Beyond the knee, the reverse voltage remains at approximately V BR, but I R increases very rapidly, resulting in overheating and possible damage.
  • The breakdown voltage for a typical silicon diode can vary, but a minimum value of 50 V is not unusual. This figure illustrates the complete voltage-current characteristic for a diode:
  • In the forward-bias condition, the forward current increases for a given value of forward voltage as the temperature is increased; the barrier potential consequently decreases.
  • In the reverse-bias condition, the reverse current increases as the temperature are increased; the breakdown voltage consequently decreases.

Temperature Effects

where:

  • IS is the reverse saturation current
  • VD is the applied bias voltage across the diode
  • n is an ideality factor, a function of the operating conditions and physical construction, ranging between 1 (for higher levels of diode current) and 2 (for lower levels of diode current)
  • VT is the thermal voltage defined by: o where: ▪ k is Boltzmann’s constant (1.38 x 10-^23 J/K) ▪ T is the absolute temperature in K ▪ q is the magnitude of electronic charge = 1.6 x 10-^19 C
  • A diode is a single PN junction device with conductive contacts and wire leads connected to each region.
  • One part of the diode is an n - type semiconductor, the other a p - type semiconductor.
  • The figure below shows the schematic symbol for a general-purpose or rectifier diode.
  • The n region is called the cathode and the p region is called the anode.
  • The “arrow” in the symbol points in the direction of the conventional current (opposite to electron flow).

Bias Connection Using Diode Schematic Symbol

Forward-Bias Connection:

  • The positive terminal of the source is connected to the anode through a current limiting resistor
  • The negative terminal of the source is connected to the cathode
  • The forward current (IF) is from anode to cathode
  • The forward voltage drop (VF) due to the barrier potential is from positive at the anode to negative at the cathode

Reverse-Bias Connection:

  • the negative terminal of the source is connected to the anode side of the diode
  • the positive terminal of the source is connected to the cathode side of the diode
  • the reverse current is extremely small and can be considered to be zero
  • the entire bias voltage (VBIAS) appears across the diode The behavior of a semiconductor diode is analogous to the behavior of a mechanical switch.
  • In the forward-bias region, the diode acts like a closed switch, permitting a generous flow of charge in the forward-bias direction (in accordance with the diode symbol). o This is generally accepted when the supply exceeds the barrier potential
  • In the reverse-bias region (before the diode enters the avalanche region), the level of current is so small in most cases that it can be approximated as 0 A. o The diode may then be represented by an open switch.
  • Generally, the semiconductor diode behaves in a manner similar to a mechanical switch; it can control whether current will flow between its two terminals.
  • However, the semiconductor diode is different from a mechanical switch; the diode will only permit current to flow in one direction.
  • An ideal diode is one whose barrier potential is 0 V. o This supports the fact that at any current level (in the forward-bias region, of course), the voltage across the ideal diode is 0 V and the resistance is 0 Ω. (short circuit equivalent)
  • An ideal diode has no current when reverse-biased. o Therefore, the resistance in the reverse-bias region is ∞ Ω. (open circuit equivalent)
  • Commercially, there is a resistance associated with a diode that is greater than 0 Ω.
  • If the associated resistance is small enough compared to other resistors of the network in series with the diode, it is often a good approximation that the effect of associated resistance may be neglected.