Electronics has undergone important and rapid developments over the last 60 years, which have generated a large range of theoretical and practical notions.
This book presents a comprehensive treatise of the evolution of electronics for the reader to grasp both fundamental concepts and the associated practical applications through examples and exercises.
This first volume of the Fundamentals of Electronics series comprises four chapters devoted to elementary devices, i.e. diodes, bipolar junction transistors and related devices, field effect transistors and amplifiers, their electrical models and the basic functions they can achieve.
Volumes to come will deal with systems in the continuous time regime, the various aspects of sampling signals and systems using analog (A) and digital (D) treatments, quantized level systems, as well as DA and AD converter principles and realizations.
Pierre Muret, Universite?Grenobles-Alpes, France.
1. Diodes and Applications.
2. Bipolar Junction Transistors and Applications.
3. Field Effect Transistors and Applications.
4. Amplifiers, Comparators and Other Analog Circuits.
Diodes and Applications
1.1. Semiconductor physics and current transport in pn diodes
1.1.1. Energy and concentration of mobile Charge carriers (electrons and holes)
Studies of electrons' physical properties indicate that they appear either as particles with a movement quantity (or impulse) of p and mass m, or as waves of wavelength ? and wave vector k. Between these values, De Broglie's wave mechanics establishes the following relation: , where h = 6.62 ×10-34 J·s and h = h/2 p.
Figure 1.1. Silicon crystal lattice (Ångstrom distances, equal to 0.1 nm)
Here, kinetic energy is , while potential energy corresponds to the work of the attractive force between 1 electron and 1 proton until they are approximately separated by the atomic radius, that is a0 ~ 0.2 nm; therefore, (with e = 1.6×10-19 Coulomb and e ~10-10 Farad/m in a semiconductor such as Si) to the order of 10-19 J, or a little less than 1 eV.
In an isolated atom, quantum mechanics makes a connection between energy and the wave frequency associated with each electron, so that the energy of each can only take certain values known as energy levels. When the atoms are in a solid such as silicon, which can hold a crystal shape where atoms are arranged in a regular and periodic manner in space (Figure 1.1), the potential in terms of the electrons is that determined by the atoms' nuclei as well as other electrons, also becoming regular and periodic in space.
A consequence of this is the transformation of energy levels into allowed energy bands separated by a forbidden bandgap (Figure 1.2). These allowed bands are made up of as many energy levels as there are electrons in the solid, also known as energy states or quantum states, spread over an energy range of several electron volts.
Figure 1.2. Energy bands of a solid (full and empty quantum states in dark and hatched color, respectively)
Only a single electron can be placed in the allowed bands per quantum state, both for isolated atoms and in solids.
Conduction is only possible if electrons can change quantum state, as this allows them to acquire kinetic energy and movement. This change can occur in the case of metals, as the allowed band with the highest energy levels, known as the conduction band, is only ever partially filled; conversely, this can only occur when the temperature increases above absolute zero in semiconductors, since the forbidden band separates a full valence band from an empty conduction band at absolute zero. This is because thermal excitation induces the transfer of some electrons from the valence band into the conduction band. In the case of semiconductors, statistics show that the product of electron concentration n in the conduction band and of holes p (that is the absence of electrons that may be considered as positively charged particles with a positive mass) in the valence band is equal to the square of the intrinsic concentration ni:
where Eg = width of the forbidden bandgap, k = Boltzmann constant = 1.38×10-23 J/K and Nc, Nv = density of effective state in the conduction and valence bands (m-3) so that NcNv = B T3 (T in °K and B to the order of 5×1043 m-6 K-3 for silicon).
Solids with semiconductor characteristics are chiefly those whose atoms have 4 electrons on their peripheral layer, that is those in column IV of the periodic table (2s2 2p2 configuration for diamond, 3 s2 3p2 for silicon, 4s2 4p2 for germanium, or mixed for SiC) or also those made up of atoms from columns III and V (called III-V, such as GaAs, GaP, InP, InAs, GaN, AlN and InN) or columns II and VI (called II-VI, such as ZnO, ZnSe, CdTe, CdS and ZnTe).
Accordingly, we can only consider the peripheral electrons, of which there are on average 4 per atom, whose charge is balanced by four nucleus protons (either 3 and 5, or 2 and 6 for materials III-V and II-VI, respectively).
Figure 1.3. Periodic table of elements
In intrinsic semiconductors, that is ideally without any impurities, there are as many holes as electrons, such that n = p = ni the density of intrinsic carriers, since an excited electron in the conduction band automatically leaves a hole in the valence band (Figure 1.4).
This situation is modified by doping, which corresponds to the introduction of foreign atoms, also known as impurities. Doped semiconductors are far more useful, since we can favor either conduction by electrons or conduction by holes. The relation still applies, however:
- - for n doping of semiconductors IV-IV: n = ND >> p by introducing atoms located in a column further to the right, which then become a concentration of ND donors;
- - for p doping of semiconductors IV-IV: p = NA >> n by introducing atoms located in a column further to the left, which then become a concentration of NA acceptors. For III-V and II-VI, doping occurs along the same lines, that is by increasing or decreasing the number of nucleus protons by one unit with the impurity relative to the atom that is being replaced.
By means of doped semiconductors (Figure 1.5), we can obtain zones with localized charges (ionized donors or acceptors) if the mobile carriers (electrons or holes) have been carried into another zone of the component by an electric field.
The combination of several such zones, known as space-charge zones or more commonly, depleted zones, also allows us to obtain this electric field and create components. Moreover, a p type zone in contact with an n type zone forms a pn diode. The asymmetry of fixed charges in both zones leads to asymmetry of electrical characteristics and the rectification effect.
Figure 1.4. Flattened structure of a doped intrinsic covalent semiconductor (electrons represented by a full black circle, holes by a hollow black circle)
The fixed charges that remain in a depletion zone after the departure of electrons are positive due to the surplus positive charge (5+ on the proton and 4- for the peripheral electrons) on the nucleus of ionized donors. On the other hand, the fixed charges that remain in a type p depletion zone after the departure of holes are negative due to the electron that has taken the place of the hole when it leaves the ionized acceptor (3+ on the proton and 4- for the peripheral electrons), which is a surplus negative charge (Figure 1.5). In an n-type semiconductor, the electrons are majority carriers while the holes are minority carriers, and the opposite is true for a p-type semiconductor.
Figure 1.5. Flattened structure of a doped covalent semiconductor (electrons represented by a full black circle, holes by a hollow black circle)
1.1.2. Conduction mechanisms
In neutral semiconductors and depletion zones, we see two types current density (in A/m2 or A/cm2) in steady state:
- - a conduction current density enµn E for electrons and epµp E for holes, or in total Jc = e(nµn + pµn) E, where µn and µp is the mobility of electrons and holes, respectively, and E is the electric field vector, which gives rise to the Ohm law in conductors.
- - a diffusion current density: eD1 grad(n) = µnkT grad(n) for electrons, - eDpgrad(p) = - µpkT grad(p) for holes, with Dn and Dp representing the diffusion coefficients according to the Einstein relation Dn = µnkT/e and Dp = µpkT/e, that is, in total Jd = µnkT grad(n) - µpkT grad(p).
However, the spatial shape of potential in the depletion zones will determine these currents, since it is here that we find the strongest electric fields and charge carrier concentration gradients. We can discern the two p and n zones of the pn diode, each of which is divided to one neutral zone in contact with the external electrodes and one depletion zone charged by ionized impurities, positive on the n side and negative on the p side. These zones contain concentrations of the carriers represented in Figure 1.6.
The difference in carrier concentrations is very significant in the neutral zones and in most parts of the depletion zones. In addition, in the absence of any voltage applied to the diode (so at a total current of zero), the total current in terms of conduction and diffusion for each type of carrier must be cancelled out, since the electrons and holes are independent in an ideal diode. As we will see in section 1.4.1, one consequence of this is that current Id in the diode depends exponentially on the external applied potential Vd. There exists a charge of minority carriers injected into each neutral zone that is proportional to Id in forward bias (Vd > 0), when the number of majority charges is increased, with a diffusion current that is predominant:
where Vd = voltage applied at the p terminal relative to the n terminal. We write the...