Semiconductors

Semiconductor materials are fundamental for the production of many devices; without them we would not have technologies such as cellphones, computers, solar plates and, in general, most of electronic devices. But how can we understand what semiconductors really are?

In respect to the electrical conduction, materials can be labeled as conductors, insulators or semiconductors; the main difference is in the efficiency of which each material regarding the electrical conduction. Conductors are the most efficient, insulators are the least efficient and semiconductors are found "in between" these two ends (thus the prefix "semi"). Those previously mentioned materials are formed by atoms, like everything else. Semiconductors are made up with atoms which possess some "special features" (semiconductor properties); germanium and silicon are examples, those being the most used atoms, with semiconductor properties, in the industry.

Now we will describe what is the science behind semiconductors. However, for that, we will need to get familiar to some key concepts.

What is a crystal? A crystal is a structure which, in the atomic-molecular scale, displays a periodic structure, that is, the atoms are arranged in such a way that they make up an uniform pattern that repeats along the crystal, as shown in photo 1 for a diamond.

What is a unit cell? A unit cell is the smallest "portion" the crystalline structure can be "fragmented". Multiple unit cells make up the crystal, as shown in photos 2 and 3.

What is a "pure crystal"? It is a crystal made up of one element only.

What is a crystal with "impurities"? I t is a crystal that have a few distinct atoms besides its base-element. Photo 4 displays a network of silicon atoms (base-element) with the presence of a few antimony atoms (impurities).

What is "doping"? Doping is a controlled process of introducing a few impurity atoms in a crystal network in a way to benefit the electrical conduction. The introduction of impurities is very subtle; thus, the periodicity of the crystalline structure is not changed significantly.

The atoms in a crystal are bonded via covalent bonds, chemical bounds in which the electrons in the outermost atoms' shell (valence shell) are shared in order for the atoms to achieve stability, as shown in photo 5.

Despite the electrons in the valence shells forming covalent bondings, which are typically strong, it is possible to some of them end up absorbing energy from external-natural sources, those being in the form of thermal or luminous energy. If they absorb the "right amount" (quantum) necessary, the electrons will break their related covalent bonds, freeing themselves from the atom. In that sense we now have an ionized atom (because it just lost and electron) and a free particle with electric charge (electron). Electric charged particles that are free to move are capable of conducting electricity and, since we have now free electrons, the system can conduct electricity.

It is notable that, at room temperature, the thermal energy provided by the environment to the semiconductor material is enough to free some electrons from the atoms, thus allowing it to conduct electricity. For a semiconductor material, as we increase the environment's temperature, more electrons are freed, increasing the efficiency of electrical conduction. This characteristic of semiconductors differs from the behavior of conductors. As we increase the environment's temperature, conductor materials tend to have their electrical resistivity increased and, by consequence, their electrical conductivity decreased, since these amounts are inversely according to ρ=1/σ, where ρ is the material's resistivity and σ is the material's conductivity.

In the studies of semiconductors, certain "tools", such as diagrams, are extremely useful for the comprehension of certain phenomena. For now, we will look at energy diagrams. Let us consider an isolated hydrogen atom. The hydrogen has a single electron, which ends up being the "valence electron" (electron in the valence shell). In case that electron absorbs a certain amount of energy, it will "jump" to a higher energy level (higher shell) and, after some time, it will return to its initial energy level, emitting a photon in the process, as shown by Bohr's atomic model in photo 6.

It is common to associate an energy diagram that represents the energy levels that an electron can "transit" between, as shown in photo 7.

The energy levels are quantized, that is, the electrons can only assume specific energy values in the atomic system. The "gaps" in between the energy levels mark energy settings the electron cannot assume. Furthermore, note in photo 7 that the hydrogen's ionization energy for the ground state (that is, for n=1) is 13.6 eV. This means 13.6 eV are required to "detach" the electron sitting at n=1 from the rest of the atom, Similarly, valence electrons from the atoms composing the crystal network are also associated to energy diagrams which, in the context, are called "band structures".

Semiconductors, conductors and insulators all have band structures diagrams, which associate the valence electrons in the atoms present in the material. The "gaps" in those diagrams are called "forbidden gaps" because the electrons are not allowed to assume the energy configurations delimited by these gaps because the energy levels are quantized, as mentioned in the previous paragraph. There are also the "valence band" (energy levels the valence electrons in the atom can assume) and the "conduction band"(energy levels the free electrons can assume). The band structures diagrams for insulators, semiconductors and conductors are shown in photos 8 to 11, with additional details included. Note in photo 11 how the semiconductor's band structure diagram is found in between the insulator's (which has a huge forbidden gap, thus limiting the number of electrons in the conduction band) and the conductor's (in which the bands "overlap", favoring the number of electrons in the conduction band).

At a temperature close to T=0 K, almost no atom in the semiconductor material will be ionized because there is no (thermal) energy to detach the valence electrons. At this temperature the semiconductor material behaves like an insulator (since it won't conduct electricity). As mentioned, as we give in more energy to the semiconductor material (such as by heating up the environment), valence electrons are freed and the material starts to conduct current (resembling, in that regard, a conductor material).

A very interesting feature semiconductors possess is the possibility of decreasing the energy gaps artificially, increasing the number of electrons in the conduction band and, consequently, favoring the conduction of electrical current. In order to do that, the doping process is required. A controlled inception of distinct elements (which also have semiconductor properties) is made. Even though these new "impurities" added are not expressive in quantity (at a ratio of 1 impurity atom to 10 million crystal network atoms)*, the addition is enough to substantially populate the conduction band. When we analyze semiconductor materials, we have to consider the two types: P-type and N-type.

(at a ratio of 1 impurity atom to 10 million crystal network atoms)*: this ratio varies.

N-type semiconductor materials: are those in which the added impurity atoms have 5 electrons in each of their valence shells. Due to the fact that each base-element of the crystal network has 4 valence electrons (like silicon and germanium, for example), the base-atoms will only make up 4 covalent bonds with each impurity atom. We can note that the impurity atoms will have a valence electron not forming any bond. That electron will then be only lightly bounded to his respective atom; thus, it won't take much to make it free (that is, the transition from the valence band to the conduction band will be easier if compared to a pure crystal). Photo 5 shows a crystal network composed by silicon and antimony impurities (constituting an n-type material).

The addition of these impurity atoms also results in the appearance of new "habitable energy levels" on the forbidden gap (the electrons can now occupy certain levels in the previously inaccessible zone). An electron in these new energy levels will go to the conduction band more easily, since the transition energy required, E_g, is lower. See photo 12 for a better understanding of the doping effect in a crystal.

P-type semiconductor materials: are those in which the added impurity atoms have 3 electrons in each of their valence shells. In this case, each impurity atom forms up 3 covalent bonds with the crystal's base atoms, resulting in an "empty space". It is important to highlight the fact that, regardless the representation, the positive sign does not indicate a positive electrical charge, but rather the empty space due to the absence of the fourth covalent bond. The empty spaces are called "holes", and are easily filled by free electrons. Photo 14 shows a crystal network with silicon as the base-element and boron as the impurity, constituting a P-type material.

We highlight that N-type materials also have holes, which arise when valence electrons become free electrons (leaving the said hole in the atom). However, in a N-type material, there is a predominance of (free) electrons over holes. In a P-type material there is a predominance of holes over (free) electrons. A material composed by both N-type and P-type semiconductors constitutes a fundamentally important material, called diode (which will be discussed in later articles).

The presence of holes creates a "dynamic" in the crystal network. Consider photo 13. It is possible that, in case a valence electron absorbs energy and becomes free, it can be eventually "captured" by the impurity's atom hole, covering it. However, the atom that just lost its electron has a hole now. We can understand this process as if there was an "electron-hole flux" (although in the "physical sense", the hole itself was not transferred; a hole was "filled" in a given place and another hole "appeared" somewhere else).

To assure the central point was captured, photo 15 shows, briefly, in a more "physical sense", the process of transition between the valence and conduction bands.

The band structure graphs were shown in photos 8, 9, 10 and 11. It is worth noting that those graphs repeat themselves for each change in the k values by ±π/a due to the periodicity of the crystal. Furthermore, photo 16 shows a unidimensional analysis; tridimensional analysis possesses a greater complexity, as shown in photo 17.

(Photo 17)

The concepts involved in the understanding of semiconductors are also used in the studies of thermoluminescence, in which a given material emits radiation via transition of electrons between the bands, including the "unlocked" energy levels in the "forbidden region".

But what are the advantages provided by semiconductors?

Semiconductor devices:

-> are extremely compact

-> do not require heating (they function as soon as the circuit is turned on)

->have a practically endless lifespan

-> are shockproof

-> require a relatively low voltage to function

With these (and many others) benefits, semiconductors are fundamental to the composition of many of the modern technologies, such as solar plates (which will be discussed in later articles), transistors, diodes along a multitude of other devices that are the basis of modern electronics.

Special thanks to professor David A.B. Miller for the excellent quantum mechanics (and its applications) course.

Reference material:

Quantum Mechanics for Scientists and Engineers (David A.B. Miller)

Electronic Devices and Circuit Theory (Robert Boylestad e Louis Nashelsky)

Physics for scientists and engineers volume III (Paul Tipler e Gene Mosca)