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Title: MURA105T3 Author: ffb3dm Created Date: 2/3/2006 4:43:41 PM. When a doped semiconductor contains mostly free holes it is called 'p-type', and when it contains mostly free electrons it is known as 'n-type'. The semiconductor materials used in electronic devices are doped under precise conditions to control the concentration and regions of p- and n-type dopants.

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Welcome to the first edition of Semiconductor Devices, an open educational resource (OER). The goal of this text, as its name implies, is to allow the reader to become proficient in the analysis and design of circuits utilizing discrete semiconductor devices. It progresses from basic diodes through bipolar and field effect transistors. Student Project: Physics of Semiconductor Devices Exam Question: Eﬀective mass - Exam October 2011 Q: In a semiconductor where the bottom of the conduction band is at k =0, an electron moves with a wave-number k = 109m−1. If the eﬀective mass of electrons in the conduction band is 0.5m e, what is the energy of this electron measured from the bottom of the conduction band?

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Semiconductor, any of a class of crystalline solids intermediate in electrical conductivity between a conductor and an insulator. Semiconductors are employed in the manufacture of various kinds of electronic devices, including diodes, transistors, and integrated circuits. Such devices have found wide application because of their compactness, reliability, power efficiency, and low cost. As discrete components, they have found use in power devices, optical sensors, and light emitters, including solid-state lasers. They have a wide range of current- and voltage-handling capabilities and, more important, lend themselves to integration into complex but readily manufacturable microelectronic circuits. They are, and will be in the foreseeable future, the key elements for the majority of electronic systems, serving communications, signal processing, computing, and control applications in both the consumer and industrial markets.

Semiconductor materials

Solid-state materials are commonly grouped into three classes: insulators, semiconductors, and conductors. (At low temperatures some conductors, semiconductors, and insulators may become superconductors.) The figure shows the conductivities σ (and the corresponding resistivities ρ = 1/σ) that are associated with some important materials in each of the three classes. Insulators, such as fused quartz and glass, have very low conductivities, on the order of 10⁻¹⁸ to 10⁻¹⁰siemens per centimetre; and conductors, such as aluminum, have high conductivities, typically from 10⁴ to 10⁶ siemens per centimetre. The conductivities of semiconductors are between these extremes and are generally sensitive to temperature, illumination, magnetic fields, and minute amounts of impurity atoms. For example, the addition of about 10 atoms of boron (known as a dopant) per million atoms of silicon can increase its electrical conductivity a thousandfold (partially accounting for the wide variability shown in the preceding figure).

The study of semiconductor materials began in the early 19th century. The elemental semiconductors are those composed of single species of atoms, such as silicon (Si), germanium (Ge), and tin (Sn) in column IV and selenium (Se) and tellurium (Te) in column VI of the periodic table. There are, however, numerous compound semiconductors, which are composed of two or more elements. Gallium arsenide (GaAs), for example, is a binary III-V compound, which is a combination of gallium (Ga) from column III and arsenic (As) from column V. Ternary compounds can be formed by elements from three different columns—for instance, mercury indium telluride (HgIn₂Te₄), a II-III-VI compound. They also can be formed by elements from two columns, such as aluminum gallium arsenide (Al_xGa_{1 − x}As), which is a ternary III-V compound, where both Al and Ga are from column III and the subscript x is related to the composition of the two elements from 100 percent Al (x = 1) to 100 percent Ga (x = 0). Pure silicon is the most important material for integrated circuit applications, and III-V binary and ternary compounds are most significant for light emission.

Prior to the invention of the bipolar transistor in 1947, semiconductors were used only as two-terminal devices, such as rectifiers and photodiodes. During the early 1950s germanium was the major semiconductor material. However, it proved unsuitable for many applications, because devices made of the material exhibited high leakage currents at only moderately elevated temperatures. Since the early 1960s silicon has become by far the most widely used semiconductor, virtually supplanting germanium as a material for device fabrication. The main reasons for this are twofold: (1) silicon devices exhibit much lower leakage currents, and (2) silicon dioxide (SiO₂), which is a high-quality insulator, is easy to incorporate as part of a silicon-based device. Thus, silicon technology has become very advanced and pervasive, with silicon devices constituting more than 95 percent of all semiconductor products sold worldwide.

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Many of the compound semiconductors have some specific electrical and optical properties that are superior to their counterparts in silicon. These semiconductors, especially gallium arsenide, are used mainly for optoelectronic and certain radio frequency (RF) applications.

Electronic properties

The semiconductor materials described here are single crystals; i.e., the atoms are arranged in a three-dimensional periodic fashion. Part A of the figure shows a simplified two-dimensional representation of an intrinsic (pure) silicon crystal that contains negligible impurities. Each silicon atom in the crystal is surrounded by four of its nearest neighbours. Each atom has four electrons in its outer orbit and shares these electrons with its four neighbours. Each shared electron pair constitutes a covalent bond. The force of attraction between the electrons and both nuclei holds the two atoms together. For isolated atoms (e.g., in a gas rather than a crystal), the electrons can have only discrete energy levels. However, when a large number of atoms are brought together to form a crystal, the interaction between the atoms causes the discrete energy levels to spread out into energy bands. When there is no thermal vibration (i.e., at low temperature), the electrons in an insulator or semiconductor crystal will completely fill a number of energy bands, leaving the rest of the energy bands empty. The highest filled band is called the valence band. The next band is the conduction band, which is separated from the valence band by an energy gap (much larger gaps in crystalline insulators than in semiconductors). This energy gap, also called a bandgap, is a region that designates energies that the electrons in the crystal cannot possess. Most of the important semiconductors have bandgaps in the range 0.25 to 2.5 electron volts (eV). The bandgap of silicon, for example, is 1.12 eV, and that of gallium arsenide is 1.42 eV. In contrast, the bandgap of diamond, a good crystalline insulator, is 5.5 eV.

At low temperatures the electrons in a semiconductor are bound in their respective bands in the crystal; consequently, they are not available for electrical conduction. At higher temperatures thermal vibration may break some of the covalent bonds to yield free electrons that can participate in current conduction. Once an electron moves away from a covalent bond, there is an electron vacancy associated with that bond. This vacancy may be filled by a neighbouring electron, which results in a shift of the vacancy location from one crystal site to another. This vacancy may be regarded as a fictitious particle, dubbed a “hole,” that carries a positive charge and moves in a direction opposite to that of an electron. When an electric field is applied to the semiconductor, both the free electrons (now residing in the conduction band) and the holes (left behind in the valence band) move through the crystal, producing an electric current. The electrical conductivity of a material depends on the number of free electrons and holes (charge carriers) per unit volume and on the rate at which these carriers move under the influence of an electric field. In an intrinsic semiconductor there exists an equal number of free electrons and holes. The electrons and holes, however, have different mobilities; that is, they move with different velocities in an electric field. For example, for intrinsic silicon at room temperature, the electron mobility is 1,500 square centimetres per volt-second (cm²/V·s)—i.e., an electron will move at a velocity of 1,500 centimetres per second under an electric field of one volt per centimetre—while the hole mobility is 500 cm²/V·s. The electron and hole mobilities in a particular semiconductor generally decrease with increasing temperature.

Electrical conduction in intrinsic semiconductors is quite poor at room temperature. To produce higher conduction, one can intentionally introduce impurities (typically to a concentration of one part per million host atoms). This is called doping, a process that increases conductivity despite some loss of mobility. For example, if a silicon atom is replaced by an atom with five outer electrons, such as arsenic (see part B of the figure), four of the electrons form covalent bonds with the four neighbouring silicon atoms. The fifth electron becomes a conduction electron that is donated to the conduction band. The silicon becomes an n-type semiconductor because of the addition of the electron. The arsenic atom is the donor. Similarly, part C of the figure shows that, if an atom with three outer electrons, such as boron, is substituted for a silicon atom, an additional electron is accepted to form four covalent bonds around the boron atom, and a positively charged hole is created in the valence band. This creates a p-type semiconductor, with the boron constituting an acceptor.

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Semiconductors :- Most of the solids can be placed in one of the two classes: Metals and insulators. Metals are those through which electric charge can easily flow, while insulators are those through which electric charge is difficult to flow. This distinction between the metals and the insulators can be explained on the basis of the number of free electrons in them. Metals have a large number of free electrons which act as charge carriers, while insulators have practically no free electrons.

There are however, certain solids whose electrical conductivity is intermediate between metals and insulators. They are called ‘Semiconductors’. Carbon, silicon and germanium are examples of semi-conductors. In semiconductors the outer most electrons are neither so rigidly bound with the atom as in an insulator, nor so loosely bound as in metal. At absolute zero a semiconductor becomes an ideal insulator.

Semiconductors are the materials whose electrical conductivity lies in between metals and insulator. The energy band structure of the semiconductors is similar to the insulators but in their case, the size of the forbidden energy gap is much smaller than that of the insulator. In this class of crystals, the forbidden gap is of the order of about 1ev, and the two energy bands are distinctly separate with no overlapping. At absolute o0, no electron has any energy even to jump the forbidden gap and reach the conduction band. Therefore the substance is an insulator. But when we heat the crystal and thus provide some energy to the atoms and their electrons, it becomes an easy matter for some electrons to jump the small (» 1 ev) energy gap and go to conduction band. Thus at higher temperatures, the crystal becomes a conductors. This is the specific property of the crystal which is known as a semiconductor.

Effect of temperature on conductivity of Semiconductor

At 0K, all semiconductors are insulators. The valence band at absolute zero is completely filled and there are no free electrons in conduction band. At room temperature the electrons jump to the conduction band due to the thermal energy. When the temperature increases, a large number of electrons cross over the forbidden gap and jump from valence to conduction band. Hence conductivity of semiconductor increases with temperature.

INTRINSIC SEMICONDUCTORS

Pure semiconductors are called intrinsic semi-conductors.In a pure semiconductor, each atom behaves as if there are 8 electrons in its valence shell and therefore the entire material behaves as an insulator at low temperatures.

A semiconductor atom needs energy of the order of 1.1ev to shake off the valence electron. This energy becomes available to it even at room temperature. Due to thermal agitation of crystal structure, electrons from a few covalent bonds come out. The bond from which electron is freed, a vacancy is created there. The vacancy in the covalent bond is called a hole.

This hole can be filled by some other electron in a covalent bond. As an electron from covalent bond moves to fill the hole, the hole is created in the covalent bond from which the electron has moved. Since the direction of movement of the hole is opposite to that of the negative electron, a hole behaves as a positive charge carrier. Thus, at room temperature, a pure semiconductor will have electrons and holes wandering in random directions. These electrons and holes are called intrinsic carriers.

As the crystal is neutral, the number of free electrons will be equal to the number of holes. In an intrinsic semiconductor, if ne denotes the electron number density in conduction band, nh the hole number density in valence band and ni the number density or concentration of charge carriers, then

n_e = n_h = n_i

extrinsic semiconductors

As the conductivity of intrinsic semi-conductors is poor, so intrinsic semi-conductors are of little practical importance. The conductivity of pure semi-conductor can, however be enormously increased by addition of some pentavalent or a trivalent impurity in a very small amount (about 1 to 106 parts of the semi-conductor). The process of adding an impurity to a pure semiconductor so as to improve its conductivity is called doping. Such semi-conductors are called extrinsic semi-conductors. Extrinsic semiconductors are of two types :

i) n-type semiconductor

ii) p-type semiconductor

n-type semiconductor

When an impurity atom belonging to group V of the periodic table like Arsenic is added to the pure semi-conductor, then four of the five impurity electrons form covalent bonds by sharing one electron with each of the four nearest silicon atoms, and fifth electron from each impurity atom is almost free to conduct electricity. As the pentavalent impurity increases the number of free electrons, it is called donor impurity. The electrons so set free in the silicon crystal are called extrinsic carriers and the n-type Si-crystal is called n-type extrinsic semiconductor. Therefore n-type Si-crystal will have a large number of free electrons (majority carriers) and have a small number of holes (minority carriers).

In terms of valence and conduction band one can think that all such electrons create a donor energy level just below the conduction band as shown in figure. As the energy gap between donor energy level and the conduction band is very small, the electrons can easily raise themselves to conduction band even at room temperature. Hence, the conductivity of n-type extrinsic semiconductor is markedly increased.

In a doped or extrinsic semiconductor, the number density of the conduction band (ne) and the number density of holes in the valence band (nh) differ from that in a pure semiconductor. If ni is the number density of electrons is conduction band, then it is proved that

n_e n_h = n_i2

p-type semiconductor

If a trivalent impurity like indium is added in pure semi-conductor, the impurity atom can provide only three valence electrons for covalent bond formation. Thus a gap is left in one of the covalent bonds. The gap acts as a hole that tends to accept electrons. As the trivalent impurity atoms accept electrons from the silicon crystal, it is called acceptor impurity. The holes so created are extrinsic carriers and the p-type Si-crystal so obtained is called p-type extrinsic semiconductor. Again, as the pure Si-crystal also possesses a few electrons and holes, therefore, the p-type si-crystal will have a large number of holes (majority carriers) and a small number of electrons (minority carriers).

It terms of valence and conduction band one can think that all such holes create an accepter energy level just above the top of the valance band as shown in figure. The electrons from valence band can raise themselves to the accepter energy level by absorbing thermal energy at room temperature and in turn create holes in the valence band.

Number density of valence band holes (nh) in p-type semiconductor is approximately equal to that of the acceptor atoms (Na) and is very large as compared to the number density of conduction band electrons (ne). Thus,

n_h» N_a > > n_e

electrical resistivity of semiconductors

Consider a block of semiconductor of length l1 area of cross-section A and having number density of electrons and holes as ne and nh respectively. Suppose that on applying a potential difference, say V, a current I flows through it as shown in figure. The electron current (Ic) and the hole current (Ih) constitute the current I flowing through the semi conductor i.e.

I = Ie + Ih (i)

It ne is the number density of conduction band electrons in the semiconductor and ve, the drift velocity of electrons then

Ie = eneAve

Similarly, the hole current, Ih = enhAvh

From (i) I = eneAve + enhAvh

I = eA(neve + nhvh) (ii)

If r is the resistivity of the material of the semiconductor, then the resistance offered by the semiconductor to the flow of current is given by :

R = r l/A (iii)

Since V = RI, from equation (ii) and (iii) we have

V = RI = r l/A eA (neve + nh vh)

V = r le(neve + nhvh) (iv)

If E is the electric field set up across the semiconductor, then:

E = V/l (v)

from equation (iv) and (v), we have

E = re (neve + nhvh)

1/r = e (ne ve/E + nh vh/E)

On applying electric field, the drift velocity acquired by the electrons (or holes) per unit strength of electric field is called mobility of electrons (or holes). Therefore,