BASIC KNOWLEDGE A detailed study of intrinsic vs extrinsic semiconductors

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Intrinsic and extrinsic semiconductor devices have always been a subject of discussion due to their band structures, and exceptional electrical properties. But do you know that recent technological advancements allow the light dopant addition of only one part in 100 million atoms? Let us understand the two main semiconductors in detail and list their differences.

An overview of semiconductors

The term “Semi” is enough to provide an idea about its conductivity. A semiconductor is a device that has electric conductivity between conductors and insulators. It is neither a perfect conductor nor an insulator. The purpose of a semiconductor device is to control the current flow depending on various factors such as input voltage, temperature, and the addition of impurities. When electric voltage is applied across a semiconductor, it allows the current to flow against some resistance.

In conductors, the current carriers are strictly electrons. But in the case of semiconductor devices, the charge carriers can either be electrons, holes, or both. However, some semiconductors allow either the electrons or holes to enable current flow inside. These devices are still semiconductors due to the values of conductivity, resistivity, and behavior with respect to temperature, time, and input voltage.

Semiconductors

Understanding the difference between n- and p-type semiconductors

Classification of semiconductors

Semiconductors categorize into two types depending on their atomic structure.

• Single-element semiconductor: The elemental semiconductor is made from a group of similar atoms to form a crystal. Examples include Silicon, Germanium, Tin, Selenium, and Tellurium. Similar atoms group together to form a crystal lattice structure.

• Compound semiconductors: The compound semiconductor is made from a group of two or more atoms to form a crystal. Examples include Gallium Arsenide (GaAs), Lead Telluride (PbTe), Cadmium Sulphide (CdS), Indium Phosphide (InP), etc. Two of the most popular compound semiconductors are Silicon Carbide (SiC) and Gallium Nitride (GaN) due to their applications in high power devices and automotive industry.

The second classification of semiconductors is based on their purity level.

• Intrinsic semiconductor: The intrinsic semiconductor is the purest form of semiconductor that conducts electricity and offers resistance in the ideal optimal range. However, intrinsic semiconductors are poor conductors in practice.

• Extrinsic semiconductor: The extrinsic semiconductor is an impure semiconductor designed to conduct and offer resistance in the desired range. When pure, this type of semiconductor conducts poorly. Impurities are introduced in pure semiconductors to modify their electrical properties. Extrinsic semiconductors behave optimally within the specified range upon the addition of impurities.

Let us understand intrinsic and extrinsic semiconductors in detail and compare them to find their similarities and differences.

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Semiconductors: A Comprehensive Guide

A complete guide to intrinsic semiconductors

An intrinsic semiconductor device is the purest form of semiconductor that conducts electricity against minimal resistance. The other names of the intrinsic semiconductor are undoped semiconductors and i-type semiconductors. Silicon and Germanium are two of the purest Semiconductor substances that were studied in detail throughout the twentieth century.

The orbital energy in an atom increases in the order of increasing inter-nuclear distance. The orbit closest to the atomic nucleus has the lowest energy due to its stability and inability to participate in a bond. High ionization energy is required to extract these locked electrons from the inner shells near the atomic nucleus. The outer shells away from the atomic nucleus are higher in energy and capable of forming ionic and covalent bonds. It is because lesser energy is required to excite the outer shell electrons.

There are five electron shells around the atomic nucleus named K, L, M, N, and O. These shells contain subshells s, p, d, f, and g. The principal quantum number (n) is associated with each shell and an azimuthal quantum number (l) is related to the subshells.

These values of n and l are fixed:

N = 1 (K), 2 (L), 3 (M), 4 (N), 5(O).

l= 0 (s), 1 (p), 2 (d), 3 (f), 4 (g).

According to the electronic configuration and Afbau’s principle, each subshell has discrete “N” states.

• s subshell has 2N possible states.

• p subshell has 6N possible states.

• d subshell has 10N possible states.

• f subshell has 14N possible states.

• g subshell has 18N possible states.

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Let us look at the following table to understand energy level calculations in Silicon and Germanium atoms:

The table clearly shows that subshells at a greater interatomic distance are at higher energy levels than compared to stable, and locked inner subshells. There are some exceptions in the list where (n+1)s subshell fills before (n)d or (n)f subshells. But these subshells are not stable because of the high interatomic distance.

Silicon and Germanium semiconductors exist in the form of crystals. Large groups of atoms are held in the crystal together to form a periodically repeating lattice structure.

Silicon Si (Z=14) is 1s², 2s², 2p⁶, 3s², 3p²

Let us consider an isolated Silicon atom:

• The first shell K (subshell 1s²) has an energy level lower than the second shell L (subshells 2s², 2p⁶). The third shell M (subshells 3s², 3p²) has the highest energy level compared to the lower shells K and L.

• The first energy level K (subshell 1s²) is filled with two electrons and bound tightly to the atomic nucleus.

• The L shell ( subshells 2s², 2p⁶) has 8 electrons. It is the second energy level full of electrons and bound to the previous shell through a strong inter-atomic force.

• Four electrons are in the third energy level M shell (subshells 3s², 3p²). The 3s subshell is filled with two electrons but the 3p subshell is partially filled. There are only two electrons in the 6N possible states of subshell 3p with four empty states.

• In Silicon, the subshells 1s², 2s², and 2p⁶ are filled with electrons and closely bound to the nucleus with a strong inter-atomic attractive force. The higher subshells 3s², and 3p² are partially filled with 4 electrons out of 8N possible states.

Germanium Ge (Z=32): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p²

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Let us consider an isolated Germanium atom:

• There are two electrons in the first energy level K shell (subshell 1s²), eight electrons in the second energy level L shell ( subshells 2s², 2p⁶), and eighteen electrons in the third energy level M-shell (subshells 3s², 3p⁶, 3d¹⁰).

• The 4s² subshell gets filled before the 3d¹⁰ because it has a lower energy state. However, the 4s² subshell is above the 3d¹⁰ subshell. The interatomic force is stronger in 3d¹⁰ compared to 4s². It makes the electrons in the 4s² subshell capable of forming a bond.

• Four electrons are in the fourth energy level N shell (subshells 4s², 4p²). The fourth energy level is partially filled with electrons. The 4s subshell is full of electrons but the 4p subshell is partially filled. There are only two electrons in the 6N possible states with 4 empty states in the 4p subshell.

• In Germanium, subshells 1s², 2s², 2p⁶, 3s², 3p⁶, and 3d¹⁰ similarly filled with electrons. The higher subshells 4s², and 4p² are partially filled with 4 empty levels out of 8N possible states.

When multiple Silicon or Germanium atoms are bound together in a crystal, the higher energy level of each atom interacts with the others. All Silicon and Germanium atoms are closely packed in their respective crystals separated by the least atomic spacing “r”. The atoms start to form four covalent bonds with neighboring atoms. The higher subshells 3s², and 3p² of all the Silicon atoms and 4s², and 4p² of the Germanium atoms in their crystals form energy bands. These four electrons are shared with the 4 neighboring atoms to form covalent bonds that hold the crystal tightly. The Covalent bonds in a semiconductor are often referred to as Valence bonds.

The low energy level band full of electrons is called Valence Band (E_V) and the higher empty energy band is known as Conduction Band (E_C). The distance or gap between the conduction band and the valence band is known as Forbidden Energy Gap, denoted by E_g. The Fermi Level is an energy level at 0 K below which all electrons are locked in the energy band and above which all the subshells are empty.

For intrinsic semiconductors, the forbidden energy gap is less than 3 eV. The forbidden energy gap is 0 eV for conductors and 6 eV for Insulators. The Fermi Level lies in between the Valence band and Conduction Band.

Forbidden Band Gap for some intrinsic semiconductors:

The temperature-dependent behavior

The electrons must gain enough kinetic energy to break the valence bond and cross the forbidden energy gap to enter the conduction band. As electrons move from the low energy state to the higher energy state, current flows through the semiconductor.

Case 1: Temperature 0 K
At absolute zero, the valence electrons are locked in the valence band of a semiconductor. The electrons do not have sufficient kinetic energy to jump from the low-level valence band to the higher energy conduction band. There is no flow of current in the semiconductor at 0K. Hence, the semiconductor acts as a poor conductor at low temperatures.

Case 2: Temperature 300 K
As the temperature increases beyond 0 K and reaches room temperature at 300K, the electrons get thermally excited. The electrons jump from the lower energy valence band to the conduction band, crossing the forbidden energy gap. The semiconductor starts conducting against a certain resistance.

Explaining the current flow

It is difficult to excite the electrons near the nucleus of Silicon in subshells 1s², 2s², and 2p⁶ and subshells 1s², 2s², 2p⁶, 3s², 3p⁶, and 3d¹⁰ in Germanium because interatomic force is the strongest. The ionization potential decreases with the increase in atomic radii. The four valence electrons in the outermost subshells (3s², and 3p² in Silicon and 4s², and 4p² in Germanium) have a lower ionization potential compared to the inner electrons.

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The valence electrons in the valence band get excited when the temperature increases from 0 K to 300 K (room temperature). Another reason for excitation could be photons from a nearby light source. Whenever these valence electrons attain a free state from the valence bond, they gain kinetic energy to leave the valence band and cross the forbidden energy gap. The valence electrons jump from the low-energy valence band to the higher-energy conduction band and break the valence bond. The variation in input voltage can control the motion of these free electrons in the semiconductor. These free electrons moving through the crystal are the intrinsic carriers.

When a valence bond breaks, an electron gains kinetic energy to attain a “free state”. The absence of electrons creates a vacancy inside the valence bond called a hole, denoted by a +e. Similar to electrons, holes move inside the semiconductor and are responsible for current flow. But holes are positively charged particles carrying the same charge as an electron. Hence, an intrinsic semiconductor allows bipolar current flow against the resistance. The electrons are the majority charge carriers while the holes are the minority charge carriers of intrinsic semiconductors.

Mathematically, the number of holes created in a semiconductor should be equal to the number of electrons exiting a valence bond. It is because the electrons leave a positively charged gap to neutralize the net charge. Another electron may enter the valence bond and occupy the positively charged gap hole. Even before combining with a hole, the same electron would create another hole in its original valence bond. The neutralization of electrons and holes in a semiconductor is termed electron-hole recombination.

The number density of intrinsic carrier concentration is the equivalence of the number density of electrons to the number density of holes. The intrinsic carrier concentration in a semiconductor increases with the rise in temperature. The rate of creation of electron-hole pairs is equal to electron-hole recombination.

This implies that Germanium has more free charge carriers and a lesser forbidden energy gap compared to Silicon. It makes Germanium a better conductor of electricity at higher temperatures.

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Understanding extrinsic semiconductors in detail

In practical life, intrinsic semiconductors behave as poor conductors at room temperatures. The electrons may not gain enough thermal or photonic energy to break the valence bond, cross the forbidden energy gap and enter the high-energy conduction band. Impurities called dopants are added in predetermined quantities in the intrinsic semiconductors to modify their conductivity characteristics, band structure, ionization efficiency, and other electrical properties up to a desired level. An extrinsic semiconductor is obtained after adding a significant amount of impurities. However, the number of dopants must be 1 part to a million of the parent atoms in a semiconductor.

Doping in extrinsic semiconductors

Doping is the process of adding impure atoms in a semiconductor to alter its band structure and improve its conductivity. The process of doping is achievable through three main methods:

• 1. Injecting a diffusion layer of impure atoms may either occupy spaces of holes in the valence band or move in between the crystal lattice structure.

• 2. Heating a semiconductor device with impure atoms in a crystal container to attain desired ionization efficiency.

• 3. Bombarding semiconductor atoms with impure atoms to form a new production layer.

Types of Dopants

There are mainly two types of impurities: Pentavalent and Trivalent dopants.

Pentavalent Dopants: n-type extrinsic semiconductors
Phosphorus P (Z=15): 1s², 2s², 2p⁶, 3s², 3p³
Arsenic Ar (Z=33): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p³
Antimony Kr (Z=51): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰, 5p³

There are three energy levels formed in the n-type semiconductor

• 1. Lowest energy level valence band.

• 2. Higher mid-energy donor level.

• 3. Highest energy level conduction band.

The Fermi level in the n-type semiconductor lies in the forbidden energy gap slightly below the Conduction band. The donor level in a Pentavalent impurity lies at 0.05 eV for Silicon and 0.01 eV for Germanium.

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Trivalent Dopants: p-type extrinsic semiconductors
Boron (Z=5): 1s², 2s², 2p¹
Aluminium Al (Z=13): 1s², 2s², 2p⁶, 3s², 3p¹
Gallium Ga (Z=31): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p¹
Indium In (Z=49): 1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰, 5p¹

The Trivalent impurities are added to the semiconductors because of the number of electrons in the valence band. The Trivalent dopants have three valence electrons in their high-energy outermost subshells. The extrinsic semiconductor obtained upon the addition of a Trivalent acceptor impurity is termed a p-type extrinsic semiconductor.

The Trivalent dopant is added to pure Silicon or Germanium crystal through diffusion. As Silicon and Germanium have four valence electrons in their outer subshells, the Trivalent impurity with its three electrons forms a covalent bond with their atoms. The three electrons of the Trivalent impurity are shared with the semiconductor crystal while one place is left unoccupied in the covalent bond. The unoccupied bond creates a positively charged hole in the semiconductor crystal. When the temperature reaches 300 K, the hole attracts another valence electron quickly to neutralize the charge. The same electron forms another hole in its bond. In this way, more holes are generated in the semiconductor crystal. The positively charged holes are the majority charge carriers and electrons are the minority charge carriers in an extrinsic p-type semiconductor.

The holes in the p-type extrinsic semiconductor occupy a discrete energy level, known as the Acceptor level in the semiconductor crystal. The acceptor level lies slightly above the valence band. The thermally excited electrons on the valence band quickly reach the conduction band to generate a large number of positively charged holes in the valence band.

There are three energy levels formed in the n-type semiconductor

• 1. Lowest energy level valence band.

• 2. Lower mid-energy acceptor level.

• 3. Highest energy level conduction band.

The Fermi level in the p-type semiconductor lies in the forbidden energy gap slightly above the Valence band. The acceptor level in a Trivalent impurity lies at 0.05 eV for Silicon and 0.01 eV for Germanium.

Mass-action law of charge carriers

In extrinsic semiconductors, the number density of majority, and minority charge carriers are not the same.

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Difference between intrinsic and extrinsic semiconductors

Intrinsic semiconductors are the purest form of semiconductors but are poor conductors of electricity at room temperatures. But the intrinsic semiconductors are made into extrinsic semiconductors by adding impurities. These dopants increase the electrical conductivity, modify band structure and decrease resistivity in an extrinsic semiconductor at a desired level.

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