EE301 Electronics I , Fall

Transcription

1 EE301 Electronics I , Fall

2 1. Introduction to Microelectronics (1 Week/3 Hrs.) Introduction, Historical Background, Basic Consepts 2. Rewiev of Semiconductors (1 Week/3 Hrs.) Semiconductor materials and their properties, Covalent Bond Model, Drift currents and Mobility, Impurities in Semiconductors, Electron and Hole Concentrations In Doped Semiconductor, Mobility and Resistivity in Doped Semiconductors, Diffusion Currents, Energy Band Model 3. Diodes & Applications of Diodes (2 Weeks/6 Hrs.) The Ideal Diode, pn junction as a Diode, Large-Signal and Small-Signal Operation, the i v Characteristics of the Diode, Applications of Diodes: Half-wave And Full- Wave Rectifier Circuits, Voltage Regulation, Limiting Circuits, Voltage Doublers, Diodes as Level Shifters. 4. Bipolar Junction Transistors (BJTs) & BJT Amplifiers (3 Weeks/9 Hrs.) Physical Structure of The BJTs, Operation of BJTs in Active Mode, BJT Models and Characteristics, Large-Signal Model, the i v Characteristics, Concept of Transconductance, Small-Signal Model, Early Effect, Operation of BJTs in Saturation Mode, NPN and PNP Transistors. General Considerations for BJT Amplifiers, Biasing. 5. MOSs & CMOS Amplifiers (3 Weeks/9 Hrs.) Structure of MOSFET, Operation of MOSFET, Qualitative Analysis, Derivation of I-V Characteristics, Channel-Length Modulation, Large-Signal Model, Small-Signal Model 6. Operational Amplifiers (Op-Amps) (2 Weeks/6 Hrs.) General Considerations, Op-Amp-Based Circuits, Noninverting Amplifier, Inverting Amplifier, Integrator and Differentiator, Voltage Adder, Nonlinear Functions, Precision Rectifier. 7. Cascaded Stages & Current Mirrors (2 Weeks/6 Hrs.) Cascaded Stages, Cascade as a Current Source, Cascade as an Amplifier, Current Mirrors, Initial Thoughts, Bipolar Current Mirror, MOS Current Mirror.

3 Electronic materials generally can be divided into three categories: insulators, conductors, and semiconductors. The primary parameter used to distinguish among these materials is the resistivity (ρ), with units of cm Diamond, one of the highest quality insulators, has a very large resistivity, ρ = cm. On the other hand, pure copper, a good conductor, has a resistivity of only ρ = 3x10 6. cm Semiconductors occupy the full range of resistivities between the insulator and conductor boundaries; moreover, the resistivity can be controlled by adding various impurity atoms to the semiconductor crystal.

4 Elemental semiconductors are formed from a single type of atom (column IV of the periodic table of elements; see Table 2.2), whereas compound semiconductors can be formed from combinations of elements from columns III and V or columns II and VI. These later materials are often referred to as III V (3 5) or II VI (2 6) compound semiconductors. Historically, germanium was one of the first semiconductors to be used. However, it was rapidly supplanted by silicon, which today is the most important semiconductor material. The compound semiconductor materials gallium arsenide (GaAs) and indium phosphide (InP) are the most important material for optoelectronic applications, including light-emitting diodes (LEDs), lasers, and photodetectors.

5 Atoms can bond together in amorphous, polycrystalline, or single-crystal forms. Amorphous materials have a disordered structure, whereas polycrystalline material consists of a large number of small crystallites. Most of the useful properties of semiconductors, however, occur in high-purity, single-crystal material. Silicon column IV in the periodic table has four electrons in the outer shell. Single-crystal material is formed by the covalent bonding of each silicon atom with its four nearest neighbors in a highly regular threedimensional array of atoms, as shown in Figure below.

6 Much of the behavior we discuss can be visualized using the simplified twodimensional covalent bond model of Fig At temperatures approaching absolute zero, all the electrons reside in the covalent bonds shared between the atoms in the array, with no electrons free for conduction. The outer shells of the silicon atoms are full, and the material behaves as an insulator. As the temperature increases, thermal energy is added to the crystal and some bonds break, freeing a small number of electrons for conduction, as in Fig. 2.3.

7 The density of these free electrons is equal to the intrinsic carrier density n i, cm 3, which is determined by material properties and temperature: Ex: Calculate the value of n i in silicon at room temperature (300 K).

8 Band gap energy E G is the minimum energy needed to break a covalent bond in the semiconductor crystal, thus freeing electrons for conduction. The density of conduction (or free) electrons is represented by the symbol n (electrons/cm 3 ), and for intrinsic material n = n i. The term intrinsic refers to the generic properties of pure material. Although n i is an intrinsic property of each semiconductor, it is extremely temperaturedependent for all materials. Figure (in previous slide) has examples of the strong variation of intrinsic carrier density with temperature for germanium, silicon, and gallium arsenide.

9 A second charge carrier is actually formed when the covalent bond in Fig. 2.3 is broken. As an electron, which has charge q equal to 1.602x10 19 C, moves away from the covalent bond, it leaves behind a vacancy in the bond structure in the vicinity of its parent silicon atom. The vacancy is left with an effective charge of +q. An electron from an adjacent bond can fill this vacancy, creating a new vacancy in another position. This process allows the vacancy to move through the crystal. The moving vacancy behaves just as a particle with charge +q and is called a hole. Hole density is represented by the symbol p (holes/cm 3 ).

10 As already described, two charged particles are created for each bond that is broken: one electron and one hole. For intrinsic silicon, n = n i = p, and the product of the electron and hole concentrations is pn = n i 2 The pn product is given by above Eq. whenever a semiconductor is in thermal equilibrium. In thermal equilibrium, material properties are dependent only on the temperature T, with no other form of stimulus applied. This eq. does not apply to semiconductors operating in the presence of an external stimulus such as an applied voltage or current or an optical excitation.

11 DRIFT CURRENTS Electrical resistivity ρ and its reciprocal, conductivity σ, characterize current flow in a material when an electric field is applied. Charged particles move or drift in response to the electric field, and the resulting current is called drift current. The drift current density j is defined as;

12 MOBILITY We know from electromagnetics that charged particles move in response to an applied electric field. This movement is termed drift, and the resulting current flow is known as drift current. Positive charges drift in the same direction as the electric field, whereas negative charges drift in a direction opposed to the electric field. At low fields carrier drift velocity v (cm/s) is proportional to the electric field E (V/cm); the constant of proportionality is called the mobility (μ): Conceptually, holes are localized to move through the covalent bond structure, but electrons are free to move about the crystal. Thus, one might expect hole mobility to be less than electron mobility.

13 The real advantages of semiconductors emerge when impurities are added to the material in minute but well-controlled amounts. This process is called impurity doping, or just doping, and the material that results is termed a doped semiconductor. Impurity doping enables us to change the resistivity over a very wide range and to determine whether the electron or hole population controls the resistivity of the material. The following discussion focuses on silicon, although the concepts of impurity doping apply equally well to other materials. The impurities that we use with silicon are from columns III and V of the periodic table. DONOR IMPURITIES IN SILICON ACCEPTOR IMPURITIES IN SILICON

14 Donor impurities in silicon are from column V, having five valence electrons in the outer shell. The most commonly used elements are phosphorus, arsenic, and antimony. When a donor atom replaces a silicon atom in the crystal lattice, as shown in Fig. 2.6, four of the five outer shell electrons fill the covalent bond structure; it then takes very little thermal energy to free the extra electron for conduction. At room temperature, essentially every donor atom contributes (donates) an electron for conduction. Each donor atom that becomes ionized by giving up an electron will have a net charge of +q and represents an immobile fixed charge in the crystal lattice. Donor Atom

15 Acceptor impurities in silicon are from column III and have one less electron than silicon in the outer shell. The primary acceptor impurity is boron, which is shown in place of a silicon atom in the lattice in Fig Because boron has only three electrons in its outer shell, a vacancy exists in the bond structure, and it is easy for a nearby electron to move into this vacancy, creating another vacancy in the bond structure. This mobile vacancy represents a hole that can move through the lattice, as illustrated in Fig. 2.7(a) and (b), and the hole may simply be visualized as a particle with a charge of +q. Each impurity atom that becomes ionized by accepting an electron has a net charge of q and is immobile in the lattice, as in Fig. 2.7(a).

16 We now discover how to calculate the electron and hole concentrations in a semiconductor containing donor and acceptor impurities. In doped material, the electron and hole concentrations are no longer equal. If n > p, the material is called n- type, and if p > n, the material is referred to as p-type. The carrier with the larger population is called the majority carrier, and the carrier with the smaller population is termed the minority carrier. Two additional pieces of information are needed. First, the semiconductor material must remain charge neutral, which requires that the sum of the total positive charge and negative charge be zero. Ionized donors and holes represent positive charge, whereas ionized acceptors and electrons carry negative charge. Thus charge neutrality requires; It can be shown theoretically that pn = n i 2 even for doped semiconductors in thermal equilibrium, and this is valid for a very wide range of doping concentrations.

17 n-type MATERIAL N D > N A Solving pn = n i 2 for p and substituting into previous eq. yields a quadratic equation for n: In practical situations N D N A 2n i, and n is given approximately by n N D N A. The formulas above should be used for N D > N A. p-type MATERIAL N A > N D Solving pn = n i 2 for n and substituting into previous eq. yields a quadratic equation for p: In practical situations N A N D 2n i, and p is given approximately by p N A N D. The formulas above should be used for N A > N D.

18 The introduction of impurities into a semiconductor such as silicon actually degrades the mobility of the carriers in the material. Impurity atoms have slightly different sizes than the silicon atoms that they replace and hence disrupt the periodicity of the lattice. In addition, the impurity atoms are ionized and represent regions of localized charge that were not present in the original crystal. Both these effects cause the electrons and holes to scatter as they move through the semiconductor and reduce the mobility of the carriers in the crystal. Figure 2.8 shows the dependence of mobility on the total impurity doping density N T = N A + N D in silicon. μ n n μ p p Remember that impurity doping also determines whether the material is n- or p-type, and simplified expressions can be used to calculate the conductivity of most extrinsic material.

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20 Example : Calculate the resistivity of silicon doped with a donor density N D = 2x10 15 /cm 3. What is the material type? Classify the sample as an insulator, semiconductor, or conductor.

21 As already described, the electron and hole populations in a semiconductor are controlled by the impurity doping concentrations N A and N D. Up to this point we have tacitly assumed that the doping is uniform in the semiconductor, but this need not be the case. Changes in doping are encountered often in semiconductors, and there will be gradients in the electron and hole concentrations. Gradients in these free carrier densities give rise to a second current flow mechanism, called diffusion. The free carriers tend to move (diffuse) from regions of high concentration to regions of low concentration in much the same way as a puff of smoke in one corner of a room rapidly spreads throughout the entire room. The diffusion current densities are proportional to the negative of the carrier gradient:

22 The diffusion current densities are proportional to the negative of the carrier gradient: The proportionality constants D p and D n are the hole and electron diffusivities, with units cm 2 s. Diffusivity and mobility are related by Einstein s relationship: The quantity kt q = V T is called the thermal voltage V T, and its value is approximately V at room temperature. Typical values of the diffusivities (also referred to as the diffusion coefficients) in silicon are in the range 2 to 35 cm 2 s for electrons and 1 to 15 cm 2 s for holes at room temperature.

23 Generally, currents in a semiconductor have both drift and diffusion components. The total electron and hole current densities j T n and j T p can be found by adding the corresponding drift and diffusion components; Using Einstein s relationship, gives us a powerful mathematics approach for analyzing the behavior of semiconductors and forms the basis for many of the results.

24 The energy band model for a semiconductor is a useful alternative view of the electron hole creation process and the control of carrier concentrations by impurities. Quantum mechanics predicts that the highly regular crystalline structure of a semiconductor produces periodic quantized ranges of allowed and disallowed energy states for the electrons surrounding the atoms in the crystal. Figure 2.10 is a conceptual picture of this band structure in the semiconductor, in which the regions labeled conduction band and valence band represent allowed energy states for electrons. Energy E V corresponds to the top edge of the valence band and represents the highest permissible energy for a valence electron. Energy E C corresponds to the bottom edge of the conduction band and represents the lowest available energy level in the conduction band. Although these bands are shown as continuums in Fig. 2.10, they actually consist of a very large number of closely spaced, discrete energy levels.

25 Electrons are not permitted to assume values of energy lying between E C and E V. The difference between E C and E V is called the bandgap energy E G : In silicon at very low temperatures ( 0 K), the valence band states are completely filled with electrons, and the conduction band states are completely empty, as shown in Fig The semiconductor in this situation does not conduct current when an electric field is applied. There are no free electrons in the conduction band, and no holes exist in the completely filled valence band to support current flow. The band model of Fig corresponds directly to the completely filled bond model of Fig. 2.2.

26 As temperature rises above 0 K, thermal energy is added to the crystal. A few electrons gain the energy required to surmount the energy bandgap and jump from the valence band into the conduction band, as shown in Fig Each electron that jumps the bandgap creates an electron hole pair.

27 Figures 2.13 to 2.15 present the band model for extrinsic material containing donor and/or acceptor atoms. In Fig. 2.13, a concentration NDof donor atoms has been added to the semiconductor. The donor atoms introduce new localized energy levels within the bandgap at a donor energy level E D near the conduction band edge. The value of E C E D for phosphorus is approximately ev, so it takes very little thermal energy to promote the extra electrons from the donor sites into the conduction band. The density of conduction-band states is so high that the probability of finding an electron in a donor state is practically zero, except for heavily doped material (large N D ) or at very low temperature. Thus at room temperature, essentially all the available donor electrons are free for conduction.

28 In Fig. 2.14, a concentration N A of acceptor atoms has been added to the semiconductor. The acceptor atoms introduce energy levels within the bandgap at the acceptor energy level E A near the valence band edge. The value of E A E V for boron is approximately ev, and it takes very little thermal energy to promote electrons from the valence band into the acceptor energy levels. At room temperature, essentially all the available acceptor sites are filled, and each promoted electron creates a hole that is free for conduction.

29 The situation for a compensated semiconductor, one containing both acceptor and donor impurities, is depicted in Fig for the case in which there are more donor atoms than acceptor atoms. Electrons seek the lowest energy states available, and they fall from donor sites, filling all the available acceptor sites. The remaining free electron population is given by n = N D N A. The energy band model just discussed represents a conceptual model that is complementary to the covalent bond model of Sec Together they help us visualize the processes involved in creating holes and electrons in doped semiconductors.

30 END OF CHAPTER 2 Dr. Yılmaz KALKAN