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7.4.2: Semiconductors and Doped Semiconductors

  • Page ID
    85122
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    There are many different semiconductor materials. But most semiconductor devices used today are based on silicon, and almost all PV solar panels in the world are made of silicon1. Therefore, we will focus our attention on silicon only.

    Silicon (Si) is the fourteenth element in the Periodic Table, which means that its nucleus contains 14 protons. So, to stay neutral, an Si atom also contains 14 electrons. Four of them are the valence electrons, i.e., those that form the outermost electron shell of the atoms. The valence electrons are used by atoms to make chemical bonds with other atoms (of different elements, or with atoms of the same element). There are several types of chemical bonding. One of the is the so-called covalent bonding, in which pairs of electrons are shared by two atoms. In silicon crystals, each Si atom has four other Si atoms as its nearest-neighbors. It’s coupled to each nearest- neighbor by a covalent bond, to which each of the two contributes one valence electron. A simplified scheme of the arrangement of atoms and the valence electrons in a Si crystal is shown in the Fig. \(\PageIndex{1}\). The scheme in the figure is largely simplified, because in a Si crystal an atom and its four nearest neighbors do not lie in the same plane: an atom is positioned in the center of a tetrahedron formed by it’s four nearest neighbors. Yet, there is no way of graphically presenting a 3-dimensional (3-D) arrangement of atoms on a 2-D piece of paper, or a computer screen – so, out of necessity, in the figure the 3-D actual arrangement is replaced by a 2-D square lattice, in which there is the same number of nearest neighbors as in the real 3-D crystal.

    Left tetrahedral unit cell of silicon, similar to that in diamond of carbon, right showing four valence electrons around Si atoms in an array
    Figure \(\PageIndex{1}\): Left image: In solid silicon the atoms are arranged into a so-called “three-dimmensional tetrahedral lattice”, in which each atom is coupled with four nearest neighbors that form the vertices of a tetrahedron. The atoms are coupled by covalent bonds – i.e., every pair of nearest neighbors shares a pair of electrons. If one attempted to present such a situation graphically by adding electrons to the left-side image, it would become really messy – therefore, it’s better to use an approximation and plot instead a two-dimensional square array to show a square array as this in the right-side image: here the green spheres represent the “cores”, i.e., atoms “stripped” from their four outer electrons the four outer electrons – which are shown as small red spheres marked with a minus sign. The pairs of electrons in between Si atoms represent symbolically the covalent bonds (sources: left image – Wikimedia Commons, the right one plotted by the author).

    By the way, the spatial arrangement of atoms in a Si crystal is identical as the arrangement of carbon (C) atoms in a diamond crystal – therefore one can often find the following statement in literature: silicon crystallizes in the diamond structure.

    In a pure Si crystals the electrons forming the covalent bonds are “firmly anchored” to their “parent atoms” and are very reluctant to move. Therefore, pure Si is a very poor conductor of electric current. The same is true for other semiconductors. They are not insulators, but their electric conductivity is orders of magnitude lower that the conductivity of metals. In logarithmic scale the conductivity of semiconductors is located more or less half way between the conductivity of insulators and of metals – it’s where their name comes from, semi- meaning “half” in Latin.

    However, there are ways of greatly enhancing the conductivity of silicon (and other semiconductors, too) by an artificial method known as doping. There are methods of substituting a small number of Si atoms in a crystals by other elements, then called dopants, or doping agents. A doping agent often used in silicon is phosphorus (P), the 15th element in the Periodic Table. It has then a total of 15 electrons, of which five are valence electrons. If a P atoms is placed in between four Si neighbors, four of its electrons are paired with the neighbor electrons to form covalent bonds – and the fifth phosphorus electron has no electron to get paired with, so it remains only weakly coupled with its “parent” P atom. Because of the thermal vibrations of atoms in the crystal, such electron gets easily “de-coupled” from its “parent” and can migrate away, becoming an mobile electron. And it’s mobile electrons which are needed in a material to conduct electric current through it. So, silicon doped with phosphorus becomes a conductor – not as good a conductor as a typical metal (e.g., Cu, or Al), but much-much better than a pure silicon.

    4 by 5 arrays of Si atoms with 1 P atom. With time the extra electron from the P atom can migrate throughout the array
    Figure \(\PageIndex{2}\): A model of n-type silicon, i.e., one in which a small number of silicon atoms are replaced by atoms of an element with five external electrons (e.g., by atoms of Phosphorus, P, shown as the magenta- color sphere). Of the five, one electron (indicated by the small blue arrow in image A) cannot participate in covalent bonding. It’s only weakly coupled with its “parent” atom and may gradually migrate away from it, as shown in the images marked as B, C and D (source: aop).

    The phosphorus atoms in silicon are called donors, because they donate extra electrons to the crystal. Silicon doped with phosphorus is referred to as n- type – because it contains extra negative current-carrying particles (mobile electrons, it means). However, let’s keep in mind that the crystal as a whole remains neutral, because the charge of those “extra electrons” is balanced by the extra positive charge of the “parent” P atoms.

    Same as previous figure but doped with Boron showing migration of the hole
    Figure \(\PageIndex{3}\): A model of p-type Si, in which a small number of silicon atoms are replaced by atoms of an element with only three outer electrons (e.g., by Boron, B, shown as the cyan-colored sphere). Then, in one covalent bond there is only a single electron – where the other should be, there is a “hole”. It is not easy to draw emptiness, something that does exist and at the same time does not exist – therefore, we used a small ghost as a symbol of such hole (ghosts do not exist, by they also do exist, right?). Like an extra electron in n-type Si, a hole may also migrate from it’s “parent atom”. Thus, it can act as a positive current carrier (source: aop)

    Interestingly, this is not the only way of making Si conducting. One can dope the Si crystal with atoms which have not 5, but 3 valence electrons. For instance, with boron (B), the fifth element in Periodic Table. It has a total of five electrons, and three of them are valence electrons. So, when a B atom sits in between four Si neighbor atoms, only three covalent bonds can be fully formed – in the fourth, one electron is missing. Such an incomplete bond is called a hole. But such hole is not firmly “anchored” to the B atom– it may start migrating from its “parent”: it may exchange places with an electron from a nearby covalent bond, then with an electron form another bond, and so on – as is illustrated in Fig. \(\PageIndex{3}\). The effect is such as if a positive charge were wandering around the crystal lattice. As electrons in an n-type crystal, such holes can also carry electric current across the crystal. Because the current carriers are positive, such crystals are referred to as p- type ones. And because the B atoms effectively “capture” electrons, they are called acceptors.

    Again, as in the case of n-type silicon, it should be stressed that the crystal as a whole remains neutral, even though it contains positive holes – because their positive charge is neutralized by the negative charge of the electrons “trapped” by the boron acceptors.

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    1.with the exception, e.g., of the PV panels supplying power to spacecrafts like the Skylab – in order to achieve the highest possible efficiency, they are made of combinations of several semiconducting materials; but they are only a small fraction of all PV panels manufactured globally


    7.4.2: Semiconductors and Doped Semiconductors is shared under a CC BY 1.3 license and was authored, remixed, and/or curated by Tom Giebultowicz.

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