Semiconductor Devices and materials

Semiconductor devices

1. Semiconductor devices are electronic components that exploit the electronic properties of semiconductor materials, principally silicon, germanium, and gallium arsenide, as well as organic semiconductors.
2. 

Semiconductor materials are useful because their behavior can be easily manipulated by the addition of impurities, known as doping. Semiconductor conductivity can be controlled by introduction of an electric or magnetic field, by exposure to light or heat, or by mechanical deformation of a doped monocrystalline grid; thus, semiconductors can make excellent sensors. Current conduction in a semiconductor occurs via mobile or "free" electrons and holes, collectively known as charge carriers. Doping a semiconductor such as silicon with a small amount of impurity atoms, such as phosphorus or boron, greatly increases the number of free electrons or holes within the semiconductor. When a doped semiconductor contains excess holes it is called "p-type", and when it contains excess free electrons it is known as "n-type", where p (positive for holes) or n (negative forelectrons) is the sign of the charge of the majority mobile charge carriers. The semiconductor material used in devices is doped under highly controlled conditions in a fabrication facility, or fab, to control precisely the location and concentration of p- and n-type dopants. The junctions which form where n-type and p-type semiconductors join together are called p–n junctions.

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.) Figure 1 shows theconductivities 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.

The conductivity of a semiconductor is generally sensitive to temperature, illumination, magnetic fields, and minute amounts of impurity atoms. For example, the addition of less than 0.01 percent of a particular type of impurity can increase the electrical conductivity of a semiconductor by four or more orders of magnitude (i.e., 10,000 times). The ranges of semiconductor conductivity due to impurity atoms for five common semiconductors are given in Figure 1.

The study of semiconductor materials began in the early 19th century. Over the years, many semiconductors have been investigated. The table shows a portion of the periodic table related to semiconductors. The elemental semiconductors are those composed of single species of atoms, such as silicon (Si), germanium (Ge), and gray tin (Sn) in column IV and selenium (Se) and tellurium (Te) in column VI. There are, however, numerous compound semiconductors that 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.

Portion of the periodic table of elements related to semiconductors

	column
period	II	III	IV	V	VI
2		boron B	carbon C	nitrogen N
3	magnesium Mg	aluminum Al	silicon Si	phosphorus P	sulfur S
4	zinc Zn	gallium Ga	germanium Ge	arsenic As	selenium Se
5	cadmium Cd	indium In	tin Sn	antimony Sb	tellurium Te
6	mercury Hg		lead Pb

Ternary compounds can be formed by elements from three different columns, as, 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 (AlxGa1 − xAs), 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 application, 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 a practical substitute, virtually supplanting germanium as a material for semiconductor fabrication. The main reasons for this are twofold: (1) silicon devices exhibit much lower leakage currents, and (2) high-quality silicon dioxide (SiO2), which is an insulator, is easy to produce. Silicon technology is now by far the most advanced among all semiconductor technologies, and silicon-based devices constitute more than 95 percent of all semiconductor hardware sold worldwide.

Many of the compound semiconductors have electrical and optical properties that are absent in silicon. These semiconductors, especially gallium arsenide, are used mainly for high-speed and optoelectronic applications.

Statistical Thermodynamics

Thermodynamics describes the behavior of systems containing a large number of particles. These systems are characterized by their temperature, volume, number and the type of particles. The state of the system is then further described by its total energy and a variety of other parameters including the entropy. Such a characterization of a system is much simpler than trying to keep track of each particle individually, hence its usefulness. In addition, such a characterization is general in nature so that it can be applied to mechanical, electrical and chemical systems.

The term thermodynamics is somewhat misleading as one deals primarily with systems in thermal equilibrium. These systems have constant temperature, volume and number of particles and their macroscopic parameters do not change over time, so that the dynamics are limited to the microscopic dynamics of the particles within the system.

Statistical thermodynamics is based on the fundamental assumption that all possible configurations of a given system, which satisfy the given boundary conditions such as temperature, volume and number of particles, are equally likely to occur. The overall system will therefore be in the statistically most probable configuration. The entropy of a system is defined as the logarithm of the number of possible configurations multiplied with Boltzmann’s constant. While such definition does not immediately provide insight into the meaning of entropy, it does provide a straightforward analysis since the number of configurations can be calculated for any given system. Laws of thermodynamics Three laws must be postulated. These cannot be proven in any way and have been developed though the observation of a large number of systems. Heat is a form of energy. The second law can be stated either (a) in its classical form or (b) in its statistical form Heat can only flow from a higher temperature to a lower temperature. The entropy of a closed system (i.e. a system of particles which does not exchange heat, work or particles with its surroundings) tends to remain constant or increases monotonically over time. Both forms of the second law could not seem more different. A more rigorous treatment is required to prove the equivalence of both. The entropy of a system approaches a constant as the temperature approaches zero Kelvin. The first law is common knowledge to most people and the classical form of the second law is clearly consistent with everyday observation. The third law can be further explained (but not proven) based on the definition provided above. As the temperature approaches zero Kelvin, the thermal energy approaches zero as well. As particles have less thermal energy, they will be more likely to occupy the lowest possible energy states of a given system. This reduces the number of possible configurations since fewer and fewer states can be occupied. As the temperature approaches zero Kelvin, the number of configurations and hence the entropy becomes constant. Electronic properties The semiconductor materials treated here are single crystals—i.e., the atoms are arranged in a three-dimensional periodic fashion. Figure 2A shows a simplified two-dimensional representation of an intrinsic silicon crystal that is very pure and contains a negligibly small amount of 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 electronpair constitutes a covalent bond. The force of attraction for the electrons by both nuclei holds the two atoms together. At low temperatures the electrons are bound in their respective positions in the crystal; consequently, they are not available for electrical conduction. At higher temperatures thermal vibration may break some of the covalent bonds. The breaking of a bond yields a free electron that can participate in current conduction. Once an electron moves away from a covalent bond, there is an electron deficiency in that bond. This deficiency may be filled by one of the neighbouring electrons, which results in a shift of the deficiency location from one site to another. This deficiency may thus be regarded as a particle similar to an electron. This fictitious particle, dubbed a hole, carries a positive charge and moves, under the influence of an applied electric field, in a direction opposite to that of an electron. p-n Junctions Electrostatic analysis of a p-n diode The electrostatic analysis of a p-n diode is of interest since it provides knowledge about the charge density and the electric field in the depletion region. It is also required to obtain the capacitance-voltage characteristics of the diode. The analysis is very similar to that of a metal-semiconductor junction  General discussion - Poisson's equation The general analysis starts by setting up Poisson's equation: (4.3.1) where the charge density, r, is written as a function of the electron density, the hole density and the donor and acceptor densities. To solve the equation, we have to express the electron and hole density, n and p, as a function of the potential, f, yielding: (4.3.2) with (4.3.3) where the potential is chosen to be zero in the n-type region, far away from the p-n interface. This second-order non-linear differential equation (4.3.2) cannot be solved analytically. Instead we will make the simplifying assumption that the depletion region is fully depleted and that the adjacent neutral regions contain no charge. This full depletion approximation is the topic of the next section. Junction capacitance Any variation of the charge within a p-n diode with an applied voltage variation yields a capacitance, which must be added to the circuit model of a p-n diode. This capacitance related to the depletion layer charge in a p-n diode is called the junction capacitance. The capacitance versus applied voltage is by definition the change in charge for a change in applied voltage, or: (4.3.20) The absolute value sign is added in the definition so that either the positive or the negative charge can be used in the calculation, as they are equal in magnitude. Using equation (4.3.7) and (4.3.18) one obtains: (4.3.21) A comparison with equation (4.3.17), which provides the depletion layer width, xd, as a function of voltage, reveals that the expression for the junction capacitance, Cj, seems to be identical to that of a parallel plate capacitor, namely: (4.3.22) The difference, however, is that the depletion layer width and hence the capacitance is voltage dependent. The parallel plate expression still applies since charge is only added at the edge of the depletion regions. The distance between the added negative and positive charge equals the depletion layer width, xd. The capacitance of a p-n diode is frequently expressed as a function of the zero bias capacitance, Cj0: (4.3.23) Where (4.3.24) A capacitance versus voltage measurement can be used to obtain the built-in voltage and the doping density of a one-sided p-n diode. When plotting the inverse of the capacitance squared, one expects a linear dependence as expressed by: (4.3.25) The capacitance-voltage characteristic and the corresponding 1/C2 curve are shown in Figure 4.3.2. Figure 4.3.2 : Capacitance and 1/C2 versus voltage of a p-n diode with Na = 1016 cm-3, Nd = 1017 cm-3 and an area of 10-4 cm2. The built-in voltage is obtained at the intersection of the 1/C2 curve and the horizontal axis, while the doping density is obtained from the slope of the curve. (4.3.26) Example 4.3 Consider an abrupt p-n diode with Na = 1018 cm-3 and Nd = 1016 cm-3. Calculate the junction capacitance at zero bias. The diode area equals 10-4 cm2. Repeat the problem while treating the diode as a one-sided diode and calculate the relative error. Solution The built in potential of the diode equals: The depletion layer width at zero bias equals: And the junction capacitance at zero bias equals: Repeating the analysis while treating the diode as a one-sided diode, one only has to consider the region with the lower doping density so that And the junction capacitance at zero bias equals The relative error equals 0.5 %, which justifies the use of the one-sided approximation. A capacitance-voltage measurement also provides the doping density profile of one-sided p-n diodes. For a p+,/sup>-n diode, one obtains the doping density from: (4.3.27) while the depth equals the depletion layer width, obtained from xd = esA/Cj. Both the doping density and the corresponding depth can be obtained at each voltage, yielding a doping density profile. Note that the capacitance in equations (4.3.21), (4.3.22), (4.3.25), and (4.3.27) is a capacitance per unit area. As an example, we consider the measured capacitance-voltage data obtained on a 6H-SiC p-n diode. The diode consists of a highly doped p-type region on a lightly doped n-type region on top of a highly doped n-type substrate. The measured capacitance as well as 1/C2is plotted as a function of the applied voltage. The dotted line forms a reasonable fit at voltages close to zero from which one can conclude that the doping density is almost constant close to the p-n interface. The capacitance becomes almost constant at large negative voltages, which corresponds according to equation (4.3.27) to a high doping density. Figure 4.3.3 : Capacitance and 1/C2 versus voltage of a 6H-SiC p-n diode. The doping profile calculated from the date presented in Figure 4.3.3 is shown in Figure 4.3.4. The figure confirms the presence of the highly doped substrate and yields the thickness of the n-type layer. No information is obtained at the interface (x = 0) as is typical for doping profiles obtained from C-V measurements. This is because the capacitance measurement is limited to small forward bias voltages since the forward bias current and the diffusion capacitance affect the accuracy of the capacitance measurement. Figure 4.3.4 : Doping profile corresponding to the measured data, shown in Figure 4.3.3. 4.3.5. The linearly graded p-n junction   A linearly graded junction has a doping profile, which depends linearly on the distance from the interface. (4.3.28) To analyze such junction we again use the full depletion approximation, namely we assume a depletion region with width xn in the n-type region and xp in the p-type region. Because of the symmetry, we can immediately conclude that both depletion regions must be the same. The potential across the junction is obtained by integrating the charge density between x = - xp and x = xn = xp twice resulting in: (4.3.29) Where the built-in potential is linked to the doping density at the edge of the depletion region such that: (4.3.30) The depletion layer with is then obtained by solving for the following equation: (4.3.31) Since the depletion layer width depends on the built-in potential, which in turn depends on the depletion layer width, this transcendental equation cannot be solved analytically. Instead it is solved numerically through iteration. One starts with an initial value for the built-in potential and then solves for the depletion layer width. A possible initial value for the built-in potential is the bandgap energy divided by the electronic charge, or 1.12 V in the case of silicon. From the depletion layer width, one calculates a more accurate value for the built-in potential and repeats the calculation of the depletion layer width. As one repeats this process, one finds that the values for the built-in potential and depletion layer width converge. The capacitance of a linearly graded junction is calculated like before as: (4.3.32) Where the charge per unit area must be recalculated for the linear junction, namely: (4.3.33) The capacitance then becomes: (4.3.34) The capacitance of a linearly graded junction can also be expressed as a function of the zero-bias capacitance or: (4.3.35) Where Cj0 is the capacitance at zero bias, which is given by: (4.3.36) 4.3.6. The abrupt p-i-n junction   A p-i-n junction is similar to a p-n junction, but contains in addition an intrinsic or un-intentionally doped region with thickness, d, between the n-type and p-type layer. Such structure is typically used if one wants to increase the width of the depletion region, for instance to increase the optical absorption in the depletion region. Photodiodes and solar cells are therefore likely to be p-i-n junctions. The analysis is also similar to that of a p-n diode, although the potential across the undoped region, fu, must be included in the analysis. Equation (4.3.16) then becomes: (4.3.37) (4.3.38) while the charge in the n-type region still equals that in the p-type region, so that (4.3.12) still holds: (4.3.39) Equations (4.3.37) through (4.3.39) can be solved for xn yielding: (4.3.40) From xn and xp, all other parameters of the p-i-n junction can be obtained. The total depletion layer width, xd, is obtained from: (4.3.41) The potential throughout the structure is given by: (4.3.42) (4.3.43) (4.3.44) where the potential at x = -xn was assumed to be zero. 4.3.6.1. Capacitance of the p-i-n junction The capacitance of a p-i-n diode equals the series connection of the capacitances of each region, simply by adding both depletion layer widths and the width of the undoped region: (4.3.45) 4.3.7. Solution to Poisson’s equation for an abrupt p-n junction   Applying Gauss's law one finds that the total charge in the n-type depletion region equals minus the charge in the p-type depletion region: (4.3.46) Poisson's equation can be solved separately in the n-type and p-type region as was done in section 3.3.7yielding an expression for (x = 0) which is almost identical to equation (3.3.22): (4.3.47) where fn and fp are assumed negative if the semiconductor is depleted. Their relation to the applied voltage is given by: (4.3.48) One obtains fn and fp as a function of the applied voltage by solving the transcendental equations. For the special case of a symmetric doping profile, or Nd = Na, these equations can easily be solved yielding: (4.3.49) The depletion layer widths also equal each other and are given by: (4.3.50) Using the above expression for the electric field at the origin, we find: (4.3.51) where  is the extrinsic Debye length. The relative error of the depletion layer width as obtained using the full depletion approximation equals: (4.3.52) So that for  = 1, 2, 5, 10, 20 and 40, one finds the relative error to be 45, 23, 10, 5.1, 2.5 and 1.26 % Two-terminal junction devices A p-n junction diode is a solid-state device that has two terminals. Depending on impurity distribution, device geometry, and biasing condition, a junction diode can perform various functions. There are more than 50,000 types of diodes with voltage ratings from less than 1 volt to more than 2,000 volts and current ratings from less than 1 milliampere to more than 5,000 amperes. A p-n junction also can generate and detect light and convert optical radiation into electrical energy. Rectifier This type of p-n junction diode is specifically designed to rectify an alternating current—i.e., to give a low resistance to current flow in one direction and a very high resistance in the other direction. Such diodes are generally designed for use as power-rectifying devices that operate at frequencies from 50 hertz to 50 kilohertz. The majority of rectifiers have power-dissipation capabilities from 0.1 to 10 watts and a reverse breakdown voltage from 50 to more than 5,000 volts. (A high-voltage rectifier is made from two or more p-n junctions connected in series.) Zener diode This voltage regulator is a p-n junction diode that has a precisely tailored impurity distribution to provide a well-defined breakdown voltage. It can be designed to have a breakdown voltage over a wide range from 0.1 volt to thousands of volts. The Zener diode is operated in the reverse direction to serve as a constant voltage source, as a reference voltage for a regulated power supply, and as a protective device against voltage and current transients. Varactor diode The varactor (variable reactor) is a device whose reactance can be varied in a controlled manner with a bias voltage. It is a p-n junction with a special impurity profile, and its capacitance variation is very sensitive to reverse-biased voltage. Varactors are widely used in parametric amplification, harmonic generation, mixing, detection, and voltage-variable tuning applications. Tunnel diode A tunnel diode consists of a single p-n junction in which both the p and n sides are heavily doped with impurities. The depletion layer is very narrow (about 100 angstroms). Under forward biases, the electrons can tunnel or pass directly through the junction, producing a negative resistance effect (i.e., the current decreases with increasing voltage). Because of its short tunneling time across the junction and its inherent low noise (random fluctuations either of current passing through a device or of voltage developed across it), the tunnel diode is used in special low-power microwave applications, such as a local oscillator and a frequency-locking circuit. Schottky diode Such a diode is one that has a metal-semiconductor contact (e.g., an aluminum layer in intimate contact with an n-type silicon substrate). It is named for the German physicist Walter H. Schottky, who in 1938 explained the rectifying behaviour of this kind of contact. The Schottky diode is electrically similar to a p-n junction, though the current flow in the diode is due primarily to majority carriers having an inherently fast response. It is used extensively for high-frequency, low-noise mixer and switching circuits. Metal-semiconductor contacts can also be nonrectifying; i.e.,the contact has a negligible resistance regardless of the polarity of the applied voltage. Such a contact is called an ohmic contact. All semiconductor devices as well as integrated circuits need ohmic contacts to make connections to other devices in an electronic system. Thyristors Thyristor, any of several types of transistors having four semiconducting layers and therefore three p-njunctions; the thyristor is a solid-state analogue of the thyratron vacuum tube, and its name derives from the combination of the two words thyratron and transistor. A common form of thyristor is the silicon-controlled rectifier (SCR), used to convert alternating current (AC) to direct current (DC) and widely used as a component of devices that control motor speeds, liquid levels, temperatures, and pressures. Thyristors constitute a family of semiconductor devices that exhibit bistable characteristics and can be switched between a high-resistance, low-current “off” state and a low-resistance, high-current “on” state. The operation of thyristors is intimately related to the bipolar transistor, in which both electrons and holes are involved in the conduction process (see semiconductor: Electronic properties). Because of their two stable states (on and off) and low power dissipations in these states, thyristors are used in applications ranging from speed control in home appliances to switching and power conversion in high-voltage transmission lines. More than 40,000 types of thyristors are available, with current ratings from a few milliamperes to more than 5,000 amperes and voltage ratings extending to 900,000 volts. Metal-semiconductor field-effect transistors The metal-semiconductor field-effect transistor (MESFET) is a unipolar device, because its conduction process involves predominantly only one kind of carrier. The MESFET offers many attractive features for applications in both analog and digital circuits. It is particularly useful for microwave amplifications and high-speed integrated circuits, since it can be made from semiconductors with high electron mobilities (e.g., gallium arsenide, whose mobility is five times that of silicon). Because the MESFET is a unipolar device, it does not suffer from minority-carrier effects and so has higher switching speeds and higher operating frequencies than do bipolar transistors. A perspective view of a MESFET is given in Figure 7A. It consists of a conductivechannel with two ohmic contacts, one acting as the source and the other as thedrain. The conductive channel is formed in a thin n-type layer supported by a high-resistivity semi-insulating (nonconducting) substrate. When a positive voltage is applied to the drain with respect to the source, electrons flow from the source to the drain. Hence, the source serves as the origin of the carriers, and the drain serves as the sink. The third electrode, the gate, forms a rectifying metal-semiconductor contact with the channel. The shaded area underneath the gate electrode is thedepletion region of the metal-semiconductor contact. An increase or decrease of the gate voltage with respect to the source causes the depletion region to expand or shrink; this in turn changes the cross-sectional area available for current flow from source to drain. The MESFET thus can be considered a voltage-controlled resistor. A typical current-voltage characteristic of a MESFET is shown in Figure 7B, where thedrain current ID is plotted against the drain voltage VD for various gate voltages. For a given gate voltage (e.g., VG = 0), the drain current initially increases linearly with drain voltage, indicating that the conductive channel acts as a constant resistor. As the drain voltage increases, however, the cross-sectional area of the conductive channel is reduced, causing an increase in the channel resistance. As a result, the current increases at a slower rate and eventually saturates. At a given drain voltage the current can be varied by varying the gate voltage. For example, for VD = 5 V, one can increase the current from 0.6 to 0.9 mA by forward-biasing the gate to 0.5 V, as shown in Figure 7B, or one can reduce the current from 0.6 to 0.2 mA by reverse-biasing the gate to −1.0 V. A device related to the MESFET is the junction field-effect transistor (JFET). The JFET, however, has a p-n junction instead of a metal-semiconductor contact for the gate electrode. The operation of a JFET is identical to that of a MESFET. There are basically four different types of MESFET (or JFET), depending on the type of conductive channel. If, at zero gate bias, a conductive n channel exists and a negative voltage has to be applied to the gate to reduce the channel conductance, as shown in Figure 7B, then the device is an n-channel “normally on” MESFET. If the channel conductance is very low at zero gate bias and a positive voltage must be applied to the gate to form an n channel, then the device is an n-channel “normally off” MESFET. Similarly, p-channel normally on and p-channel normally off MESFETs are available. To improve the performance of the MESFET, various heterojunction field-effect transistors (FETs) have been developed. A heterojunction is a junction formed between two dissimilar semiconductors, such as the binary compound GaAs and the ternary compound AlxGa1 − xAs. Such junctions have many unique features that are not readily available in the conventional p-n junctions discussed previously. Figure 8 shows a cross section of a heterojunction FET. The heterojunction is formed between a high-bandgap semiconductor (e.g., Al0.4Ga0.6As, with a bandgap of 1.9 eV) and one of a lower bandgap (e.g., GaAs, with a bandgap of 1.42 eV). By proper control of the bandgaps and the impurity concentrations of these two materials, a conductive channel can be formed at the interface of the two semiconductors. Because of the high conductivity in the conductive channel, a large current can flow through it from source to drain. When a gate voltage is applied, the conductivity of the channel will be changed by the gate bias, which results in a change of drain current. The current-voltage characteristics are similar to those of the MESFET shown in Figure 7B. If the lower-bandgap semiconductor is a high-purity material, the mobility in the conductive channel will be high. This in turn can give rise to higher operating speed.