Diodes And Transistors

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Department of EECSSpring 2007EE100/42-43Rev. 1Diodes and Transistors1. IntroductionSo far in EE100 you have seen analog circuits. You started with simple resistive circuits,then dynamical systems (circuits with capacitors and inductors) and then op-amps. Thenyou learned how circuit elements do not operate the same at all frequencies.Now you will learn about two very important circuit elements – diodes1 and transistors.These elements make the world of digital electronics “tick”. Digital electronics hasrevolutionized industry over the last 40 years. In the second half of this course, you willlearn some of the fundamental concepts (Boolean algebra, microcontrollers, processorI/O and digital systems interfacing) behind this revolution. However, before you do so,you should understand the two devices – diodes and transistors – that were responsiblefor this revolution.2. Organization of this documentIn this document, we will talk about diodes and transistors. First we will discuss verybasic semiconductor physics. We won’t discuss the details because the point of thiscourse is electronic circuits, not semiconductor physics. A detailed understanding ofsemiconductor physics is important only when you deal with microelectronic circuits. Weare just building breadboard circuits in this class, thus it is enough if you have an intuitiveunderstanding of the semiconductor physics. If you want to learn the detailed physicsbehind these devices, you should consider taking EECS 130 at the University ofCalifornia, Berkeley.Next we will talk about diodes, followed by the bipolar junction transistor. In the case ofboth devices, we will talk about the nonlinear models, load line analysis and applications.We will conclude this chapter by looking at how transistors can be used as logic devices.This will lead naturally to our discussion of digital systems.Please note that I have chosen to discuss the bipolar junction transistor instead of the fieldeffect transistor. The reason: bipolar transistors are the mainstay of interface elements tomicrocontrollers. Thus you will be seeing a lot of BJTs when you work with sensorinterfaces.3. Basic Semiconductor Physics [4] [2] [6]A semiconductor is a solid whose electrical conductivity is in between that of a metaland that of an insulator, and can be controlled over a wide range, either permanently ordynamically.Semiconductors are tremendously important technologically and1Diodes are really not used in digital circuits anymore. However they are fundamental in circuits likepower electronics. Moreover, they are simpler to understand than transistors. So we start our discussion ofnonlinear electronics with diodes.

Department of EECSSpring 2007EE100/42-43Rev. 1economically. Silicon is used to create the most semiconductors commercially but dozensof other materials are used as well.Semiconductor devices, electronic components made of semiconductor materials, areessential in modern electrical devices, from computers to cellular phones to digital audioplayers.Elemental or intrinsic semiconductors are materials consisting of elements from groupIV of the periodic table. Figure 1 below depicts the lattice arrangement for silicon (Si),one of the more common semiconductors. At sufficiently high temperatures, thermalenergy causes the atoms in the lattice to vibrate; when sufficient kinetic energy is present,some of the valence electrons break their bonds with the lattice structure and becomeavailable as conduction electrons. These free electrons enable current flow in asemiconductor.Figure 1. Lattice structure of siliconHowever, if you have to heat up a semiconductor for electron flow, then how can it beused at room temperature? The answer to this is: doping. Doping consists of addingimpurities to the crystalline structure of the semiconductor. For example, if we addphosphorous atoms to silicon, then we will have an extra electron floating around in thelattice because phosphorous has five valence electrons. Thus phosphorous atoms are alsocalled donors, refer to figure 2. A doped semiconductor is also called as an extrinsicsemiconductor. Silicon doped with donors is also called n-type semiconductor becauseof the abundance of electrons.

Department of EECSSpring 2007EE100/42-43Rev. 1Figure 2. Silicon doped with phosporousThere is another kind of conduction that can take place in semiconductors. Suppose wedope silicon with elements from group III of the periodic table, say boron. This is shownin figure 3. Now we have some missing orbitals or places where electrons can go. Thusthe electrons are moving to the left. The vacancy caused by the departure of a freeelectron is called a hole. Note that whenever a hole is present, we have, in effect apositive charge. The positive charges also contribute to the conduction process, in thesense that if an electron “jumps” to fill a neighboring hole, thereby neutralizing a positivecharge, it correspondingly creates a new hole at a neighboring location. Becauseelements from group III of the periodic table “accept electrons”, they are also calledacceptors. Silicon doped with acceptors is also called a p-type semiconductor becauseof the abundance of holes.Figure 3. Silicon doped with boron. The movement of an electron to the left is equivalent to a holemoving to the right.It is important to point out here that mobility – that is, the ease with which chargecarriers move across the lattice differs greatly for electrons and holes. In the case ofsilicon doped with phosphorous, we have free electrons in the lattice that can moveeasily. In contrast, when silicon is doped with boron, holes move only if a neighboringelectron jumps to fill the empty bond.

Department of EECSSpring 2007EE100/42-43Rev. 1Now that we have learned about p-type and n-type semiconductors, we come to thecentral concept in semiconductor devices: the pn junction. When a p-type and n-typematerial are brought in contact, a number of interesting properties arise. Figure 4 showsthe pn junction.Figure 4. The pn junctionIn the interface layer between the p-type and n-type material, a nonconducting layercalled the depletion region occurs. This is because the electrical charge carriers in dopedn-type silicon (electrons) and p-type silicon (holes) attract and eliminate each other in aprocess called recombination. By manipulating this nonconductive layer, p-n junctionsare commonly used as diodes: electrical switches that allow a flow of electricity in onedirection but not in the other (opposite) direction. This property is explained in terms ofthe forward-bias and reverse-bias effects, where the term bias refers to an application ofelectric voltage to the p-n junction. This leads to our discussion of diodes, in the nextsection.4. Diodes [2]In simple terms, a diode is a device that restricts the direction of flow of charge carriers(electrons in this class) [1]. Essentially, it allows an electric current to flow in onedirection, but blocks it in the opposite direction. Thus, the diode can be thought of as anelectronic version of a check valve. Circuits that require current flow in only onedirection typically include one or more diodes in the circuit design. Today the mostcommon diodes are made from semiconductor materials such as silicon or germanium.There are a variety of diodes; A few important ones are described below.Normal (p-n) diodesThe operation of these diodes is the subject of this document. Usually made ofdoped silicon or, more rarely, germanium. Before the development of modernsilicon power rectifier diodes, cuprous oxide and later selenium was used; its lowefficiency gave it a much higher forward voltage drop (typically 1.4–1.7 V per"cell," with multiple cells stacked to increase the peak inverse voltage rating inhigh voltage rectifiers), and required a large heat sink (often an extension of thediode's metal substrate), much larger than a silicon diode of the same currentratings would require. The vast majority of all diodes are the p-n diodes found inCMOS integrated circuits, which include 2 diodes per pin and many other internaldiodes.Switching diodesSwitching diodes, sometimes also called small signal diodes, are single diodes ina discrete package. A switching diode provides essentially the same function as aswitch. Below the specified applied voltage it has high resistance similar to an

Department of EECSSpring 2007EE100/42-43Rev. 1open switch, while above that voltage it suddenly changes to the low resistance ofa closed switch.Schottky diodesSchottky diodes are constructed from a metal to semiconductor contact. Theyhave a lower forward voltage drop than a standard diode. Their forward voltagedrop at forward currents of about 1 mA is in the range 0.15 V to 0.45 V, whichmakes them useful in voltage clamping applications and prevention of transistorsaturation.Varicap or varactor diodesThese are used as voltage-controlled capacitors. These are important in PLL(phase-locked loop) and FLL (frequency-locked loop) circuits, allowing tuningcircuits, such as those in television receivers, to lock quickly, replacing olderdesigns that took a long time to warm up and lock.Zener diodesDiodes that can be made to conduct backwards. This effect, called Zenerbreakdown, occurs at a precisely defined voltage, allowing the diode to be used asa precision voltage reference.Light-emitting diodes (LEDs)In a diode formed from a direct band-gap semiconductor, such as galliumarsenide, carriers that cross the junction emit photons when they recombine withthe majority carrier on the other side. Depending on the material, wavelengths (orcolors) from the infrared to the near ultraviolet may be produced. The forwardpotential of these diodes depends on the wavelength of the emitted photons: 1.2 Vcorresponds to red, 2.4 to violet. The first LEDs were red and yellow, and higherfrequency diodes have been developed over time. All LEDs are monochromatic;'white' LEDs are actually combinations of three LEDs of a different colorEsaki or tunnel diodesThese have a region of operation showing negative resistance caused by quantumtunneling, thus allowing amplification of signals and very simple bistable circuits.These diodes are also the type most resistant to nuclear radiation.Gunn diodesThese are similar to tunnel diodes in that they are made of materials such as GaAsor InP that exhibit a region of negative differential resistance. With appropriatebiasing, dipole domains form and travel across the diode, allowing high frequencymicrowave oscillators to be built.Peltier diodesThese are used as sensors and heat engines for thermoelectric cooling.

Department of EECSSpring 2007EE100/42-43Rev. 1a. Introduction – the nonlinear diode modelThe circuit schematic symbol of a diode is shown in figure 5. Hence comparing theschematic symbol to the pn junction in figure 4, we see the anode is the p-typesemiconductor and the cathode is the n-type semiconductor.Figure 5. Diode schematic symbol and actual picture of a common 1N914 diode (the black stripe in thepicture is the cathode). Conventional current can flow from the anode to the cathode, but not the other wayaround. Notice that in EE, the Anode is the positive terminal and the cathode is the negative terminal.A diode’s I-V characteristic is shown in figure 6 below.Figure 6. Diode IV characteristics. PIV is the Peak-Inverse-Voltage of the diodeForward bias occurs when the p-type block is connected to the positive terminal of thebattery and the n-type is connected to the negative terminal of the battery, as shownbelow.

Department of EECSSpring 2007EE100/42-43Rev. 1Figure 7. Forward biasing a diodeWith this set-up, the holes in the p-type region and the electrons in the n-type region arepushed towards the junction. This reduces the width of the depletion zone and eventuallyonce enough potential is applied to overcome the depletion potential, the diode startsconducting. This depletion potential (or diode turn-on voltage) is shown in figure 6 as0.65 V for silicon and 0.2 V for germanium diodes. Reverse-bias is analogous toforward bias except, the battery terminals are reversed and this leads to an increase indepletion potential. Therefore, the diode does not conduct. Too much reverse-bias leadsto breakdown in diode functionality.Notice the nonlinear nature of the diode I-V characteristic. An approximate2 equationdescribing the I-V graph above is given below.I I S (eVnVT 1)Here:I is the current through the diode,IS is a scale factor called the saturation current,V is the voltage across the diode,VT is the thermal voltage,and n is the emission coefficient.The emission coefficient n varies from about 1 to 2 depending on the fabrication processand semiconductor material. In many cases, it is approximately equal to 1 and thusomitted. The thermal voltage VT is approximately 25 mV at room temperature (25 C or298K). Is is typically 10-12 A.As you can see, the diode equation is nonlinear and complex. Using this equation tomodel the diode in a circuit results in complex transcendental equations. For example,consider very simple circuit shown in figure 8.2The Shockley ideal diode equation does not account for the breakdown region of the diode.

Department of EECSSpring 2007EE100/42-43Rev. 1Figure 8. Simple diode circuitUsing KVL:12 VD1 VR1 VD1 i (1000) VD1 ( I S (eVD 1nVT 1))(1000)You can solve the last equation above using a tool like Mathematica:Mathematica gives a value of approximately 0.58 V for the voltage and 11.42 mA for thecurrent. However the point of this exercise is that you cannot solve the equation abovewithout a calculator. Therefore we will now introduce a very important graphical methodto solve circuits – load lines.b. Load line AnalysisConsider the circuit in figure 8 again. We know the diode I-V is given by:I D (10 12)(eVD10.025 1)(1)Using KVL and Ohm’s law:12 VD1 iR1 VD1 I D R1Note the current going through the diode, resistor and voltage source is the same. This isthe key to load lines. It enables us to impose another restriction on the (VD1,ID) pair:

Department of EECSSpring 2007EE100/42-43Rev. 1ID 12 VD1R1(2)Graphically, we can plot (1) and (2) on the same set of axis. This is done in figure 9below.Figure 9. Load line as plotted using MATLAB. Point of intersection is the solution to the system.The commands to do this in MATLAB are: n 1; Vt 0.025; Is 10 -12; VD1 [-5:0.01:0.6]; ID Is*(exp(VD1/(n*Vt)) - 1); plot(VD1,ID); hold; VD2 [-5:0.01:12]; ID2 (12-VD2)/R1; plot(VD2,ID2);The point of intersection is also called as the Quiescent-point (Q-point) or DC operatingpoint of the system. Thus load lines are a graphical way to solve circuits. Notice thatload lines are very useful when a circuit has a single nonlinear element. Although youcould use the method when the circuit has multiple nonlinear elements, it becomes tricky.

Department of EECSSpring 2007EE100/42-43Rev. 1Therefore, we need to derive a simpler model for the diode. There are two kinds ofmodels that we will study – the large signal model and the small signal model [2].c. Large Signal Diode ModelsA large signal model of the diode describes the overall behavior of the diode in thepresence of large voltages and currents.i. Ideal Diode ModelOur first large-signal model treats the diode as a simple on/off device. This is the modelused most (90%) of the time in electronics. Figure 10 illustrates how, on a large scale,the I-V characteristic of a typical diode may be approximated by an open circuit when V 0 and by a short circuit when I 0.Figure 10. Ideal diode modelFrom here on, this diode model will be known as the ideal diode model. In spite of itssimplicity, the ideal diode model can be very useful in analyzing diode circuits. Let usanalyze the circuit shown in figure 8 using the ideal diode model. We will develop atechnique to determine if the diode is conducting or not with the aid of the ideal diodemodel.

Department of EECSSpring 2007EE100/42-43Rev. 1Assume first the diode is conducting (or equivalently, that I 03). This enables us tosubstitute the short circuit model in place of the diode as shown in figure 11.Figure 11. Short circuit model replacement for the diodeNotice that I have drawn the orientation of the diode above the short circuit model. Thisis an important technique I urge you to follow. This will help you remember theorientation of the diode. Now, the current flowing through the circuit is given by:12 12 mA1kLet us now compare the answers we obtained from the Mathematica, load-line and theideal diode model. Refer to table 1.I I from Mathematica11.42 mAI from load-line11.44 mAI from ideal diode model12 mATable 1. Comparison of different current values. Notice the excellent agreement between the values.Now, suppose we had guessed the operating state of the diode incorrectly: let us assumethe diode in figure 8 is off. Hence, we will replace the diode with an open circuit modelas shown in figure 12.Figure 12. Guessing an incorrect diode operating state3Note that I 0, V 0 on the graph is an interesting point: both the open-circuit model and the shortcircuit model satisfy this condition. Hence the only way to find out if the diode is operating in this state isempirically. But we will not be dealing with such circuits in this course.

Department of EECSSpring 2007EE100/42-43Rev. 1Now, the voltage developed across the open circuit is V 12 V. But as you know, if thediode is off, then the voltage developed across the diode has to be negative. Hence ourassumption is incorrect: the diode has to be on.An important note about this technique: when you have multiple diodes in a circuit youshould make educated guesses about the diode states. This is because the number ofpossible states grows exponentially as the number of diodes. For example, if you had 4diodes in a circuit, each diode has two possible states: on or off. Therefore, you willhave 16 total possibilities of states. Making an educated guess of the diode state willgreatly simplify the problem. You will have a change to do this in the practice problemssection of this chapter.ii. Offset Diode ModelExamining figure 6 closely, it becomes that apparent a diode needs an “on” voltagebefore it starts functioning. The offset diode model consists of an ideal diode in serieswith a battery of strength equal to this “on” (or offset) voltage. From figure 6, you cansee the offset voltage to be 0.65 volts for silicon diodes and 0.2 volts for germaniumdiodes. We will use a value of 0.6 volts unless otherwise stated. Figure 13 shows theoffset diode model.Figure 13. Offset diode model

Department of EECSSpring 2007EE100/42-43Rev. 1d. Diode Exercises41. Determine the operating point of the diode in figure 14 below and compute the poweroutput of the 12 V battery. The I-V graph of the 1N914 diode is given in figure 15.Hint: Find the Thevenin equivalent seen by the diode and use a load line to find the Qpoint. Once you find the diode current and voltage, you can solve for the current throughthe battery to find the power output.Figure 14. Simple circuit with one diodeFigure 15. 1N914 I-V characteristic4These examples are from other textbooks and online sources. Due to a lack of time, we (me and the TAs)are not posting solutions to the problems. If you can email the answers (and complete solutions) to me, Iwill post it on the website (with proper credits).

Department of EECSSpring 2007EE100/42-43Rev. 12. Determine the voltage across and current through the diode in figure 16. Assume thediode is ideal.Figure 16. Circuit for problem 23. [Diode Logic] This problem shows you can build logic gates out of diodes. You willlearn about logic gates when we talk about digital systems. For the circuit below, fill inthe table for the value Vx given the different combinations of values for V1 and V2.Assume the diodes are ideal.Figure 17. Diode logic gateV1 (volts)0055V2 (volts)0505Vx (volts)Table 2. Diod

direction typically include one or more diodes in the circuit design. Today the most common diodes are made from semiconductor materials such as silicon or germanium. There are a variety of diodes; A few important ones are described below. Normal (p-n) diodes The operation of these diodes is the subject of this document. Usually made of

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