ECE221 Semiconductor Diodes: PDF Overview

# Semiconductor Diodes ## Chapter objectives * Become aware of the general characteristics of three important semiconductor materials: Si, Ge, GaAs. * Understand conduction using electron and hole theory. * Be able to describe the difference between n- and p-type materials. * Develop a clea...

# Semiconductor Diodes ## Chapter objectives * Become aware of the general characteristics of three important semiconductor materials: Si, Ge, GaAs. * Understand conduction using electron and hole theory. * Be able to describe the difference between n- and p-type materials. * Develop a clear understanding of the basic operation and characteristics of a diode in the no-bias, forward-bias, and reverse-bias regions. * Be able to calculate the DC, AC, and average AC resistance of a diode from the characteristics. * Understand the impact of an equivalent circuit whether it is ideal or practical. * Become familiar with the operation and characteristics of a Zener diode and light-emitting diode. ## 1.1 Introduction One of the noteworthy things about this field, as in many other areas of technology, is how little the fundamental principles change over time. Systems are incredibly smaller, current speeds of operation are truly remarkable, and new gadgets surface every day, leaving us to wonder where technology is taking us. However, if we take a moment to consider that the majority of all the devices in use were invented decades ago and that design techniques appearing in texts as far back as the 1930s are still in use, we realize that most of what we see is primarily a steady improvement in construction techniques, general characteristics, and application techniques rather than the development of new elements and fundamentally new designs. The result is that most of the devices discussed in this text have been around for some time, and that texts on the subject written a decade ago are still good references with content that has not changed very much. The major changes have been in the understanding of how these devices work and their full range of capabilities, and in improved methods of teaching the fundamentals associated with them. The benefit of all this to the new student of the subject is that the material in this text will, we hope, have reached a level where it is relatively easy to grasp and the information will have application for years to come. The miniaturization that has occurred in recent years leaves us to wonder about its limits. Complete systems now appear on wafers thousands of times smaller than the single element of earlier networks. The first integrated circuit (IC) was developed by Jack Kilby while working at Texas Instruments in 1958 (Fig. 1.1). Today, the Intel® CoreTM i7 Extreme Edition Processor of Fig. 1.2 has 731 million transistors in a package that is only slightly larger than a 1.67 sq. inches. In 1965, Dr. Gordon E. Moore presented a paper predicting that the transistor count in a single IC chip would double every two years. Now, more than 45 years, later we find that his prediction is amazingly accurate and expected to continue for the next few decades. We have obviously reached a point where the primary purpose of the container is simply to provide some means for handling the device or system and to provide a mechanism for attachment to the remainder of the network. Further miniaturization appears to be limited by four factors: the quality of the semiconductor material, the network design technique, the limits of the manufacturing and processing equipment, and the strength of the innovative spirit in the semiconductor industry. The first device to be introduced here is the simplest of all electronic devices, yet has a range of applications that seems endless. We devote two chapters to the device to introduce the materials commonly used in solid-state devices and review some fundamental laws of electric circuits. ## 1.2 Semiconductor Materials: Ge, Si, AND GaAs The construction of every discrete (individual) solid-state (hard crystal structure) electronic device or integrated circuit begins with a semiconductor material of the highest quality. Semiconductors are a special class of elements having a conductivity between that of a good conductor and that of an insulator. In general, semiconductor materials fall into one of two classes: single-crystal and compound. Single-crystal semiconductors such as germanium (Ge) and silicon (Si) have a repetitive crystal structure, whereas compound semiconductors such as gallium arsenide (GaAs), cadmium sulfide (CdS), gallium nitride (GaN), and gallium arsenide phosphide (GaAsP) are constructed of two or more semiconductor materials of different atomic structures. The three semiconductors used most frequently in the construction of electronic devices are Ge, Si, and GaAs. In the first few decades following the discovery of the diode in 1939 and the transistor in 1947 germanium was used almost exclusively because it was relatively easy to find and was available in fairly large quantities. It was also relatively easy to refine to obtain very high levels of purity, an important aspect in the fabrication process. However, it was discovered in the early years that diodes and transistors constructed using germanium as the base material suffered from low levels of reliability due primarily to its sensitivity to changes in temperature. At the time, scientists were aware that another material, silicon, had improved temperature sensitivities, but the refining process for manufacturing silicon of very high levels of purity was still in the development stages. Finally, however, in 1954 the first silicon transistor was introduced, and silicon quickly became the semiconductor material of choice. Not only is silicon less temperature sensitive, but it is one of the most abundant materials on earth, removing any concerns about availability. The flood gates now opened to this new material, and the manufacturing and design technology improved steadily through the following years to the current high level of sophistication. As time moved on, however, the field of electronics became increasingly sensitive to issues of speed. Computers were operating at higher and higher speeds, and communication systems were operating at higher levels of performance. A semiconductor material capable of meeting these new needs had to be found. The result was the development of the first GaAs transistor in the early 1970s. This new transistor had speeds of operation up to five times that of Si. The problem, however, was that because of the years of intense design efforts and manufacturing improvements using Si, Si transistor networks for most applications were cheaper to manufacture and had the advantage of highly efficient design strategies. GaAs was more difficult to manufacture at high levels of purity, was more expensive, and had little design support in the early years of development. However, in time the demand for increased speed resulted in more funding for GaAs research, to the point that today it is often used as the base material for new high-speed, very large scale integrated (VLSI) circuit designs. This brief review of the history of semiconductor materials is not meant to imply that GaAs will soon be the only material appropriate for solid-state construction. Germanium devices are still being manufactured, although for a limited range of applications. Even though it is a temperature-sensitive semiconductor, it does have characteristics that find application in a limited number of areas. Given its availability and low manufacturing costs, it will continue to find its place in product catalogs. As noted earlier, Si has the benefit of years of development, and is the leading semiconductor material for electronic components and ICs. In fact, Si is still the fundamental building block for Intel's new line of processors. ## 1.3 Covalent Bonding and Intrinsic Materials To fully appreciate why Si, Ge, and GaAs are the semiconductors of choice for the electronics industry requires some understanding of the atomic structure of each and how the atoms are bound together to form a crystalline structure. The fundamental components of an atom are the electron, proton, and neutron. In the lattice structure, neutrons and protons form the nucleus and electrons appear in fixed orbits around the nucleus. The Bohr model for the three materials is provided in Fig. 1.3. As indicated in Fig. 1.3, silicon has 14 orbiting electrons, germanium has 32 electrons, gallium has 31 electrons, and arsenic has 33 orbiting electrons (the same arsenic that is a very poisonous chemical agent). For germanium and silicon there are four electrons in the outermost shell, which are referred to as valence electrons. Gallium has three valence electrons and arsenic has five valence electrons. Atoms that have four valence electrons are called tetravalent, those with three are called trivalent, and those with five are called pentavalent. The term valence is used to indicate that the potential (ionization potential) required to remove any one of these electrons from the atomic structure is significantly lower than that required for any other electron in the structure. In a pure silicon or germanium crystal the four valence electrons of one atom form a bonding arrangement with four adjoining atoms, as shown in Fig. 1.4. This bonding of atoms, strengthened by the sharing of electrons, is called covalent bonding. Because GaAs is a compound semiconductor, there is sharing between the two different atoms, as shown in Fig. 1.5. Each atom, gallium or arsenic, is surrounded by atoms of the complementary type. There is still a sharing of electrons similar in structure to that of Ge and Si, but now five electrons are provided by the As atom and three by the Ga atom. Although the covalent bond will result in a stronger bond between the valence electrons and their parent atom, it is still possible for the valence electrons to absorb sufficient kinetic energy from external natural causes to break the covalent bond and assume the "free" state. The term free is applied to any electron that has separated from the fixed lattice structure and is very sensitive to any applied electric fields such as established by voltage sources or any difference in potential. The external causes include effects such as light energy in the form of photons and thermal energy (heat) from the surrounding medium. At room temperature there are approximately $1.5 × 10^{10}$free carriers in 1 $cm^3$ of intrinsic silicon material, that is, 15,000,000,000 (15 billion) electrons in a space smaller than a small sugar cube-an enormous number. The term intrinsic is applied to any semiconductor material that has been carefully refined to reduce the number of impurities to a very low level-essentially as pure as can be made available through modern technology. The free electrons in a material due only to external causes are referred to as intrinsic carriers. Table 1.1 compares the number of intrinsic carriers per cubic centimeter (abbreviated n₁) for Ge, Si, and GaAs. It is interesting to note that Ge has the highest number and GaAs the lowest. In fact, Ge has more than twice the number as GaAs. The number of carriers in the intrinsic form is important, but other characteristics of the material are more significant in determining its use in the field. One such factor is the relative mobility (μη) of the free carriers in the material, that is, the ability of the free carriers to move throughout the material. Table 1.2 clearly reveals that the free carriers in GaAs have more than five times the mobility of free carriers in Si, a factor that results in response times using GaAs electronic devices that can be up to five times those of the same devices made from Si. Note also that free carriers in Ge have more than twice the mobility of electrons in Si, a factor that results in the continued use of Ge in high-speed radio frequency applications. | Semiconductor | Intrinsic Carriers ni | Intrinsic Carriers (per cubic centimeter) | | :-----------: | :----------------: | :---------------------------------------: | | GaAs | 1 | $1.7 × 10^6$ | | Si | 5 | $1.5 × 10^{10}$ | | Ge | 2 | $2.5 × 10^{13}$ | | Semiconductor | µn (cm²/V.s | | :-----------: | :-----------: | | Si | 16 | | Ge | 3900 | | GaAs | 8500 | One of the most important technological advances of recent decades has been the ability to produce semiconductor materials of very high purity. Recall that this was one of the problems encountered in the early use of silicon-it was easier to produce germanium of the required purity levels. Impurity levels of 1 part in 10 billion are common today, with higher levels attainable for large-scale integrated circuits. One might ask whether these extremely high levels of purity are necessary. They certainly are if one considers that the addition of one part of impurity (of the proper type) per million in a wafer of silicon material can change that material from a relatively poor conductor to a good conductor of electricity. We obviously have to deal with a whole new level of comparison when we deal with the semiconductor medium. The ability to change the characteristics of a material through this process is called doping, something that germanium, silicon, and gallium arsenide readily and easily accept. The doping process is discussed in detail in Sections 1.5 and 1.6. One important and interesting difference between semiconductors and conductors is their reaction to the application of heat. For conductors, the resistance increases with an increase in heat. This is because the numbers of carriers in a conductor do not increase significantly with temperature, but their vibration pattern about a relatively fixed location makes it increasingly difficult for a sustained flow of carriers through the material. Materials that react in this manner are said to have a positive temperature coefficient. Semiconductor materials, however, exhibit an increased level of conductivity with the application of heat. As the temperature rises, an increasing number of valence electrons absorb sufficient thermal energy to break the covalent bond and to contribute to the number of free carriers. Therefore: Semiconductor materials have a negative temperature coefficient. ## 1.4 Energy Levels Within the atomic structure of each and every isolated atom there are specific energy levels associated with each shell and orbiting electron, as shown in Fig. 1.6. The energy levels associated with each shell will be different for every element. However, in general: The farther an electron is from the nucleus, the higher is the energy state, and any electron that has left its parent atom has a higher energy state than any electron in the atomic structure. Note in Fig. 1.6a that only specific energy levels can exist for the electrons in the atomic structure of an isolated atom. The result is a series of gaps between allowed energy levels where carriers are not permitted. However, as the atoms of a material are brought closer together to form the crystal lattice structure, there is an interaction between atoms, which will result in the electrons of a particular shell of an atom having slightly different energy levels from electrons in the same orbit of an adjoining atom. The result is an expansion of the fixed, discrete energy levels of the valence electrons of Fig. 1.6a to bands as shown in Fig. 1.6b. In other words, the valence electrons in a silicon material can have varying energy levels as long as they fall within the band of Fig. 1.6b. Figure 1.6b clearly reveals that there is a minimum energy level associated with electrons in the conduction band and a maximum energy level of electrons bound to the valence shell of the atom. Between the two is an energy gap that the electron in the valence band must overcome to become a free carrier. That energy gap is different for Ge, Si, and GaAs; Ge has the smallest gap and GaAs the largest gap. In total, this simply means that: An electron in the valence band of silicon must absorb more energy than one in the valence band of germanium to become a free carrier. Similarly, an electron in the valence band of gallium arsenide must gain more energy than one in silicon or germanium to enter the conduction band. This difference in energy gap requirements reveals the sensitivity of each type of semiconductor to changes in temperature. For instance, as the temperature of a Ge sample increases, the number of electrons that can pick up thermal energy and enter the conduction band will increase quite rapidly because the energy gap is quite small. However, the number of electrons entering the conduction band for Si or GaAs would be a great deal less. This sensitivity to changes in energy level can have positive and negative effects. The design of photodetectors sensitive to light and security systems sensitive to heat would appear to be an excellent area of application for Ge devices. However, for transistor networks, where stability is a high priority, this sensitivity to temperature or light can be a detrimental factor. The energy gap also reveals which elements are useful in the construction of light-emitting devices such as light-emitting diodes (LEDs), which will be introduced shortly. The wider the energy gap, the greater is the possibility of energy being released in the form of visible or invisible (infrared) light waves. For conductors, the overlapping of valence and conduction bands essentially results in all the additional energy picked up by the electrons being dissipated in the form of heat. Similarly, for Ge and Si, because the energy gap is so small, most of the electrons that pick up sufficient energy to leave the valence band end up in the conduction band, and the energy is dissipated in the form of heat. However, for GaAs the gap is sufficiently large to result in significant light radiation. For LEDs (Section 1.9) the level of doping and the materials chosen determine the resulting color. Before we leave this subject, it is important to underscore the importance of understanding the units used for a quantity. In Fig. 1.6 the units of measurement are electron volts (eV). The unit of measure is appropriate because $W (energy) = QV$ (as derived from the defining equation for voltage: $V = W/Q$). Substituting the charge of one electron and a potential difference of 1 V results in an energy level referred to as one electron volt. That is, $W = QV \\ = (1.6 × 10^{-19} C)(1 V) \\ = 1.6 × 10^{-19} J$ and $1 eV = 1.6 × 10^{-19} J$ $(1.1)$ ## 1.5 n-TYPE AND p-TYPE MATERIALS Because Si is the material used most frequently as the base (substrate) material in the construction of solid-state electronic devices, the discussion to follow in this and the next few sections deals solely with Si semiconductors. Because Ge, Si, and GaAs share a similar covalent bonding, the discussion can easily be extended to include the use of the other materials in the manufacturing process. As indicated earlier, the characteristics of a semiconductor material can be altered significantly by the addition of specific impurity atoms to the relatively pure semiconductor material. These impurities, although only added at 1 part in 10 million, can alter the band structure sufficiently to totally change the electrical properties of the material. A semiconductor material that has been subjected to the doping process is called an extrinsic material. There are two extrinsic materials of immeasureable importance to semiconductor device fabrication: n-type and p-type materials. Each is described in some detail in the following subsections. ### n-Type Material Both n-type and p-type materials are formed by adding a predetermined number of impurity atoms to a silicon base. An n-type material is created by introducing impurity elements that have five valence electrons (pentavalent), such as antimony, arsenic, and phosphorus. Each is a member of a subset group of elements in the Periodic Table of Elements referred to as Group V because each has five valence electrons. The effect of such impurity elements is indicated in Fig. 1.7 (using antimony as the impurity in a silicon base). Note that the four covalent bonds are still present. There is, however, an additional fifth electron due to the impurity atom, which is unassociated with any particular covalent bond. This remaining electron, loosely bound to its parent (antimony) atom, is relatively free to move within the newly formed n-type material. Since the inserted impurity atom has donated a relatively "free" electron to the structure: Diffused impurities with five valence electrons are called donor atoms. It is important to realize that even though a large number of free carriers have been established in the n-type material, it is still electrically neutral since ideally the number of positively charged protons in the nuclei is still equal to the number of free and orbiting negatively charged electrons in the structure. The effect of this doping process on the relative conductivity can best be described through the use of the energy-band diagram of Fig. 1.8. Note that a discrete energy level (called the donor level) appears in the forbidden band with an $E_{g}$ significantly less than that of the intrinsic material. Those free electrons due to the added impurity sit at this energy level and have less difficulty absorbing a sufficient measure of thermal energy to move into the conduction band at room temperature. The result is that at room temperature, there are a large number of carriers (electrons) in the conduction level, and the conductivity of the material increases significantly. At room temperature in an intrinsic Si material there is about one free electron for every $10^{12}$ atoms. If the dosage level is 1 in 10 million ($10^7$), the ratio $10^{12} / 10^{7} = 10^5$ indicates that the carrier concentration has increased by a ratio of 100,000:1. ### p-Type Material The p-type material is formed by doping a pure germanium or silicon crystal with impurity atoms having three valence electrons. The elements most frequently used for this purpose are boron, gallium, and indium. Each is a member of a subset group of elements in the Periodic Table of Elements referred to as Group III because each has three valence electrons. The effect of one of these elements, boron, on a base of silicon is indicated in Fig. 1.9. Note that there is now an insufficient number of electrons to complete the covalent bonds of the newly formed lattice. The resulting vacancy is called a hole and is represented by a small circle or a plus sign, indicating the absence of a negative charge. Since the resulting vacancy will readily accept a free electron: The diffused impurities with three valence electrons are called acceptor atoms. The resulting p-type material is electrically neutral, for the same reasons described for the n-type material. The effect of the hole on conduction is shown in Fig. 1.10. If a valence electron acquires sufficient kinetic energy to break its covalent bond and fills the void created by a hole, then a vacancy, or hole, will be created in the covalent bond that released the electron. There is, therefore, a transfer of holes to the left and electrons to the right, as shown in Fig. 1.10. The direction to be used in this text is that of conventional flow, which is indicated by the direction of hole flow. In the intrinsic state, the number of free electrons in Ge or Si is due only to those few electrons in the valence band that have acquired sufficient energy from thermal or light sources to break the covalent bond or to the few impurities that could not be removed. The vacan- cies left behind in the covalent bonding structure represent our very limited supply of holes. In an n-type material, the number of holes has not changed significantly from this intrinsic level. The net result, therefore, is that the number of electrons far outweighs the number of holes. For this reason: In an n-type material (Fig. 1.11a) the electron is called the majority carrier and the hole the minority carrier. For the p-type material the number of holes far outweighs the number of electrons, as shown in Fig. 1.11b. Therefore: In a p-type material the hole is the majority carrier and the electron is the minority carrier. When the fifth electrode of a donor atoms leaves the parent atome, the atom remaining acquires a not positive charge, hence the plus sign in e donor-ion representation for similar reasons, the minus sign appears in the acceptor ion. ## 1.6 Semiconductor Diode Now that both n- and p-type materials are available, we can construct our first solid-state electronic device: The semiconductor diode, with applications too numerous to mention, is created by simply joining an n-type and a p-type material together, nothing more, just the joining of one material with a majority carrier of electrons to one with a majority carrier of holes. The basic simplicity of its construction simply reinforces the importance of the development of this solid-state era. At the instant the two materials are "joined" the electrons and the holes in the region of the junction will combine, resulting in a lack of free carriers in the region near the junction, as shown in Fig. 1.12a. Note in Fig. 1.12a that the only particles displayed in this region are the positive and the negative ions remaining once the free carriers have been absorbed. This region of uncovered positive and negative ions is called the depletion region due to the "depletion" of free carriers in the region. If leads are connected to the ends of each material, a two-terminal device results, as shown in Figs. 1.12a and 1.12b. Three options then become available: no bias, forward bias, and reverse bias. The term bias refers to the application of an external voltage across the two terminals of the device to extract a response. The condition shown in Figs. 1.12a and 1.12b is the no-bias situation because there is no external voltage applied. It is simply a diode with two leads sitting isolated on a laboratory bench. In Fig. 1.12b the symbol for a semiconductor diode is provided to show its correspondence with the p-n junction. In each figure it is clear that the applied voltage is 0 V (no bias) and the resulting current is 0 A, much like an isolated resistor. The absence of a voltage across a resistor results in zero current through it. Even at this early point in the discussion it is important to note the polarity of the voltage across the diode in Fig. 1.12b and the direction given to the current. Those polarities will be recognized as the defined polarities for the semiconductor diode. If a voltage applied across the diode has the same polarity across the diode as in Fig. 1.12b, it will be considered a positive voltage. If the reverse, it is a negative voltage. The same standards can be applied to the defined direction of current in Fig. 1.12b. Under no-bias conditions, any minority carriers (holes) in the n-type material that find themselves within the depletion region for any reason whatsoever will pass quickly into the p-type material. The closer the minority carrier is to the junction, the greater is the attraction for the layer of negative ions and the less is the opposition offered by the positive ions in the depletion region of the n-type material. We will conclude, therefore, for future discussions, that any minority carriers of the n-type material that find themselves in the depletion region will pass directly into the p-type material. This carrier flow is indicated at the top of Fig. 1.12c for the minority carriers of each material. The majority carriers (electrons) of the n-type material must overcome the attractive forces of the layer of positive ions in the n-type material and the shield of negative ions in the p-type material to migrate into the area beyond the depletion region of the p-type material. However, the number of majority carriers is so large in the n-type material that there will invariably be a small number of majority carriers with sufficient kinetic energy to pass through the depletion region into the p-type material. Again, the same type of discussion can be applied to the majority carriers (holes) of the p-type material. The resulting flow due to the majority carriers is shown at the bottom of Fig. 1.12c. A close examination of Fig. 1.12c will reveal that the relative magnitudes of the flow vectors are such that the net flow in either direction is zero. This cancellation of vectors for each type of carrier flow is indicated by the crossed lines. The length of the vector representing hole flow is drawn longer than that of electron flow to demonstrate that the two magnitudes need not be the same for cancellation and that the doping levels for each material may result in an unequal carrier flow of holes and electrons. In summary, therefore: In the absence of an applied bias across a semiconductor diode, the net flow of charge in one direction is zero. In other words, the current under no-bias conditions is zero, as shown in Figs. 1.12a and 1.12b. ### Reverse-Bias Condition (VD < 0 V) If an external potential of V volts is applied across the p-n junction such that the positive terminal is connected to the n-type material and the negative terminal is connected to the p-type material as shown in Fig. 1.13, the number of uncovered positive ions in the depletion region of the n-type material will increase due to the large number of free electrons drawn to the positive potential of the applied voltage. For similar reasons, the number of uncovered negative ions will increase in the p-type material. The net effect, therefore, is a widening of the depletion region. This widening of the depletion region will establish too great a barrier for the majority carriers to overcome, effectively reducing the majority carrier flow to zero, as shown in Fig. 1.13a. The number of minority carriers, however, entering the depletion region will not change, resulting in minority-carrier flow vectors of the same magnitude indicated in Fig. 1.12c with no applied voltage. The current that exists under reverse-bias conditions is calledThe reverse saturation current and is represented by Is. The reverse saturation current is seldom more than a few microamperes and typically in nA, except for high-power devices. The term saturation comes from the fact that it reaches its maximum level quickly and does not change significantly with increases in the reverse-bias potential, as shown on the diode characteristics of Fig. 1.15 for VD 0 V. The reverse-biased If the characteristics or specification sheet for a diode is not available the resistance rav can be approximated by the ac resistance ra ### Simplified Equivalent Circuit For most applications, the resistance rav is sufficiently small to be ignored in comparison to the other elements of the network. Removing rav from the equivalent circuit is the same as implying that the characteristics of the diode appear as shown in Fig. 1.31. Indeed, this approximation is frequently employed in semiconductor circuit analysis as demonstrated in Chapter 2. The reduced equivalent circuit appears in the same figure. It states that a forward- biased silicon diode in an electronic system under de conditions has a drop of 0.7 V across it in the conduction state at any level of diode current (within rated values, of course). ### Ideal Equivalent Circuit Now that rav has been removed from the equivalent circuit, let us take the analysis a step further and establish that a 0.7-V level can often be ignored in comparison to the applied voltage level. In this case the equivalent circuit will be reduced to that of an ideal diode as shown in Fig. 1.32 with its characteristics. In Chapter 2 we will see that this approximation is often made without a serious loss in accuracy. In industry a popular substitution for the phrase "diode equivalent circuit" is diode modela model by definition being a representation of an existing device, object, system, and so on. In fact, this substitute terminology will be used almost exclusively in the chapters to follow. For clarity, the diode models employed for the range of circuit parameters and applications are provided in Table 1.7 with their piecewise-linear characteristics. Each will be investigated in greater detail in Chapter 2. There are always exceptions to the general rule, but itis fairly safe to say that the simplified equivalent model will be employed most frequently in the analysis of electronic systems, whereas the ideal diode is frequently applied in the analysis of power supply systems where larger voltages are encountered. | Type | Conditions | Model | Characteristics | | :----------------------- | :--------------------------------------------------------------------------- | :------------------------------------------------------------------------------------------- | --------: | | Piecewise-linear model | | Illustration of a battery, an ideal diode and a resistor in series | Picture 1 | | Simplified model | $R_{network} >> r_{av}$ | Illustration of a battery and an ideal diode connected in series by a wire | Picture 2 | | Ideal device | $R_{network} >> r_{av}$ $E_{Network} >> V_{K}$ | Symbol of a diode | Picture 3 | ### Summary The characteristics have been superimposed to compare the ideal Si diode to a real-world Si diode. First impressions might suggest that the commercial unit is a poor impression of the ideal switch. However, when one considers that the only major difference is that the commercial diode rises at a level of 0.7 V rather than 0 V, there are a number of similarities between the two plots. When a switch is closed the resistance between the contacts is assumed to be 0 Ω. At the plot point chosen on the vertical axis the diode current is 5 mA and the voltage across the diode is 0 V. Substituting into Ohm's law results in: $Rp = \frac{V_{D}}{I_{D}} = \frac{0V}{5 mA} = 0 {\Omega}$ In fact: At any current level on the vertical line, the voltage across the ideal diode is $\pm 0 V$ and the resistance is $\pm 0 {\Omega}$. For the horizontal section, if we again apply Ohm's law, we find: $R_{R} = \frac{V_{D}}{I_{D}} = \frac{20 V}{0 mA} = \infty {\Omega}$ Again: Because the current is OmA anywhere on the horizontal line, the resistance is considered to be infinite ohms(an open-circuit) of any point on the axis. Due to the shape and the location of the curve for the commercial unit in the forward-bias region there will be a resistance associated with the diode that is greater than 0 Ω However, if that resistance is small enough compared to other resistors of the network in series with the diode, it is often a good approximation to simply assume the résistance of the commercial unit is 0 Ω In the reverse-bias region, if we assume the reverse saturation current is so small it can be approximated as 0 mA we have the same open-circuit equivalence provided by the open switch. The result therefore, is that there are sufficient similarities between the ideal switch and the semiconductor diode to make it an effective electronic device. In the next section the various resistance levels of importance is determined for use in the next chapter, wherethe response of diodes in an actual network is examined ## 1.10 TRANSIENT DIFFUSION CAPACITOR It is important to realize that: Every electronic or electrical device is frequency sensitive. That is, the terminal characteristics of any device will change with frequency. Even the resistance of a basic resistor, as of any construction, will be sensitive to the applied frequency. At low to mid-frequencies most resistors can be considered fixed in value. However, as we approach high frequencies, stray capacitive and inductive effects start to play a role and will affect the total impedance level of the element For the diode it is the stray capacitance levels that have the greatest effect At low frequen- cies and relatively small levels of capacitance the reactance of a capacitor, determined by Xc = 1/2πfC, is usually so high it can be considered innite in magnitude, represented by an open circuit, and ignored. At high frequencies, however, the level of Xc can drop to the point where it will introduce a low-reactance "shorting" path. If this shorting path is across the diode, it can essentially keep the diode from affecting the response of the network In the p-n semiconductor diode, there are two capacitive effects to be considered. Both types of capacitance are present in the forward- and reverse-bias regions, but one so out- weighs the other in each region that we consider the effects of only one in each region Recall that the basic equation for the capacitance of a parallel-plate capacitor is defined by C = E A / d, where is the permittivity of the dielectric (insulator) between the plates of area A separated by a distance d In a diode the depletion region (free of carriers) behaves essentially like an insulator between the layers of opposite charge. Since the depletion width (d )will in- crease with increased reverse-bias potential, the resulting transition capacitance will decrease as shown in Fig. 133. The fact that the capacitance is dependent on the applied reverse-bias potential has application in a number of electronic systems. In fact, in Chapter 16 the varactor diode will be introduced whose operation is wholly dependent on this phenomenon. This capacitance, called the transition (Cr), barriers, or depletion region capacitance, is determined by ## 1.12 Specification Sheets Data on specific semiconductor devices are normally provided by the manufacturer in one of two times, most frequently they give a very brIef description limited to perhaps one page. At other times, they give a thorough examining characteristics using graphs, artwork, tables, and so on. In either case, there are specific pieces of data would be included for proper use of the device. they include: 1. The forward voltage at specified current at specified temperature 2. The maximum forward current at a specified temperature 3. The reverse saturation current are at A specified voltage and temperature 4. The reverse voltage rating private or power level or be our where BR becomes from the term "Breakdown"(at a specific temperature) 5. The Mexican power distribution level at particular temperature 6. Capacitance levels 7. Reverse recoverytime TRR 8. operating temperature range Type Equation Table1.6. Resistance Level Special Graphics Determination VD DC or static ROD = Special graphics AD Defined as a tangent line.AVD 1.7 1 1.9 Dioda Eguivalent And as illustrated a few paragraphs ago, and finally we have their temperature coefficient, also note that it can be positive in both can be negative for less than 5 V devices and and it is interesting to note that in that case, it is for diodes were the centre-forward but by increasing temperature so as the temperature increases at all at the operating region we will assume that we never get into the reverse by his vision so that whatever change and whatever the curve is not we can forget it ## 1.7 Ideal Versus Practical In the previous section we find that a 𝑝 – 𝑛 junction will permit a generous flow of charge when forward-biased and a