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Chapter 3 Solid-State Diodes and Diode Circuits
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Chapter 3 Solid-State Diodes and Diode Circuits

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  1. Chapter 3Solid-State Diodes and Diode Circuits Microelectronic Circuit Design Richard C. JaegerTravis N. Blalock Microelectronic Circuit Design McGraw-Hill Chap 3 -1

  2. Chapter Goals • Understand diode structure and basic layout • Develop electrostatics of the pn junction • Explore various diode models including the mathematical model, the ideal diode model, and the constant voltage drop model • Understand the SPICE representation and model parameters for the diode • Define regions of operation of the diode (forward, reverse bias, and reverse breakdown) • Apply the various types of models in circuit analysis • Explore different types of diodes Discuss the dynamic switching behavior of the pn junction diode • Explore diode applications • Practice simulating diode circuits using SPICE Microelectronic Circuit Design McGraw-Hill Chap 3 -2

  3. Diode Introduction • A diode is formed by interfacing an n-type semiconductor with a p-type semiconductor. • A pn junction is the interface between n and p regions. Diode symbol Microelectronic Circuit Design McGraw-Hill Chap 3 -3

  4. PN Junction Animation • Formation of PN Junction – applet • PN Junction space charge profile and electric field – applet • Biased PN Junction - applet Microelectronic Circuit Design McGraw-Hill

  5. pn Junction Electrostatics Donor and acceptor concentration on either side of the junction. Concentration gradients give rise to diffusion currents. Microelectronic Circuit Design McGraw-Hill Chap 3 -5

  6. Drift Currents • Diffusion currents lead to localized charge density variations near the pn junction. • Gauss’ law predicts an electric field due to the charge distribution: • Assuming constant permittivity, • Resulting electric field gives rise to a drift current. With no external circuit connections, drift and diffusion currents cancel. There is no actual current, since this would imply power dissipation, rather the electric field cancels the diffusion current ‘tendency.’ Microelectronic Circuit Design McGraw-Hill Chap 3 -6

  7. Space Charge Region Formation at the pn Junction Microelectronic Circuit Design McGraw-Hill Chap 3 -7

  8. Potential across the Junction Charge Density Electric Field Potential Microelectronic Circuit Design McGraw-Hill Chap 3 -8

  9. Width of Depletion Region Combining the previous expressions, we can form an expression for the width of the space-charge region, or depletion region. It is called the depletion region since the excess holes and electrons are depleted from the dopant atoms on either side of the junction. Microelectronic Circuit Design McGraw-Hill Chap 3 -9

  10. Width of Depletion Region (Example) Problem: Find built-in potential and depletion-region width for given diode Given data:On p-type side: NA=1017/cm3 on n-type side: ND=1020/cm3 Assumptions: Room-temperature operation with VT=0.025 V Analysis: Microelectronic Circuit Design McGraw-Hill Chap 3 -10

  11. Diode Electric Field (Example) • Problem: Find electric field and size of individual depletion layers on either side of pn junction for given diode • Given data:On p-type side: NA=1017/cm3 on n-type side: ND=1020/cm3 from earlier example, • Assumptions: Room-temperature operation • Analysis: Microelectronic Circuit Design McGraw-Hill Chap 3 -11

  12. Internal Diode Currents Mathematically, for a diode with no external connections, the total current expressions developed in chapter 2 are equal to zero. The equations only dictate that the total currents are zero. However, as mentioned earlier, since there is no power dissipation, we must assume that the field and diffusion current tendencies cancel and the actual currents are zero. When external bias voltage is applied to the diode, the above equations are no longer equated to zero. Microelectronic Circuit Design McGraw-Hill Chap 3 -12

  13. Diode Junction Potential for Different Applied Voltages Microelectronic Circuit Design McGraw-Hill Chap 3 -13

  14. Diode i-v Characteristics Turn-on voltage marks point of significant current flow. Is is called the reverse saturation current. Microelectronic Circuit Design McGraw-Hill Chap 3 -14

  15. Diode Equation where IS = reverse saturation current (A) vD = voltage applied to diode (V)q = electronic charge (1.60 x 10-19 C)k = Boltzmann’s constant (1.38 x 10-23 J/K)T = absolute temperaturen = nonideality factor (dimensionless)VT = kT/q = thermal voltage (V) (25 mV at room temp.) IS is typically between 10-18 and 10-9 A, and is strongly temperature dependent due to its dependence on ni2. The nonideality factor is typically close to 1, but approaches 2 for devices with high current densities. It is assumed to be 1 in this text. Microelectronic Circuit Design McGraw-Hill Chap 3 -15

  16. Diode Voltage and Current Calculations (Example) Problem: Find diode voltage for diode with given specifications Given data: IS=0.1 fA ID= 300 mA Assumptions: Room-temperature dc operation with VT=0.025 V Analysis: WithIS=0.1 fA With IS=10 fA With ID= 1 mA, IS=0.1 fA Microelectronic Circuit Design McGraw-Hill Chap 3 -16

  17. Diode Current for Reverse, Zero, and Forward Bias • Reverse bias: • Zero bias: • Forward bias: Microelectronic Circuit Design McGraw-Hill Chap 3 -17

  18. Semi-log Plot of Diode Current and Current for Three Different Values of IS Microelectronic Circuit Design McGraw-Hill Chap 3 -18

  19. Diode Temperature Coefficient Diode voltage under forward bias: Taking the derivative with respect to temperature yields Assuming iD >> IS, IS ni2, and VGO is the silicon bandgap energy at 0K. For a typical silicon diode Microelectronic Circuit Design McGraw-Hill Chap 3 -19

  20. PTAT Voltage and Electronic Thermometry • The well-defined temperature dependence of the diode voltage is used as the basis for most digital themometers. • PTAT Voltage(Voltage proportional to absolute temperature) VPTAT = VD1-VD2 = VTln(ID1/IS) -VTln(ID2/IS) =VTln(ID1/ID2) = KT/qln(ID1/ID2) • By using two diode, the temperature dependence of Is has been eliminated from the equation. Microelectronic Circuit Design McGraw-Hill

  21. PTAT Thermometer Microelectronic Circuit Design McGraw-Hill

  22. Reverse Bias External reverse bias adds to the built-in potential of the pn junction. The shaded regions below illustrate the increase in the characteristics of the space charge region due to an externally applied reverse bias, vD. Microelectronic Circuit Design McGraw-Hill Chap 3 -22

  23. Reverse Bias (cont.) External reverse bias also increases the width of the depletion region since the larger electric field must be supported by additional charge. Microelectronic Circuit Design McGraw-Hill Chap 3 -23

  24. Reverse Bias Saturation Current We earlier assumed that reverse saturation current was constant. Since it results from thermal generation of electron-hole pairs in the depletion region, it is dependent on the volume of the space charge region. It can be shown that the reverse saturation gradually increases with increased reverse bias. IS is approximately constant at IS0 under forward bias. Microelectronic Circuit Design McGraw-Hill Chap 3 -24

  25. Reverse Breakdown Increased reverse bias eventually results in the diode entering the breakdown region, resulting in a sharp increase in the diode current. The voltage at which this occurs is the breakdown voltage, VZ. 2 V < VZ< 2000 V Microelectronic Circuit Design McGraw-Hill Chap 3 -25

  26. Reverse Breakdown Mechanisms • Avalanche BreakdownSi diodes with VZ greater than about 5.6 volts breakdown according to an avalanche mechanism. As the electric field increases, accelerated carriers begin to collide with fixed atoms. As the reverse bias increases, the energy of the accelerated carriers increases, eventually leading to ionization of the impacted ions. The new carriers also accelerate and ionize other atoms. This process feeds on itself and leads to avalanche breakdown. Microelectronic Circuit Design McGraw-Hill Chap 3 -26

  27. Reverse Breakdown Mechanisms (cont.) • Zener BreakdownZener breakdown occurs in heavily doped diodes. The heavy doping results in a very narrow depletion region at the diode junction. Reverse bias leads to carriers with sufficient energy to tunnel directly between conduction and valence bands moving across the junction. Once the tunneling threshold is reached, additional reverse bias leads to a rapidly increasing reverse current. • Breakdown Voltage Temperature CoefficientTemperature coefficient is a quick way to distinguish breakdown mechanisms. Avalanche breakdown voltage increases with temperature, zener breakdown decreases with temperature. For silicon diodes, zero temperature coefficient is achieved at approximately 5.6 V. Microelectronic Circuit Design McGraw-Hill Chap 3 -27

  28. Breakdown Region Diode Model In breakdown, the diode is modeled with a voltage source, VZ, and a series resistance, RZ. RZ models the slope of the i-v characteristic. Diodes designed to operate in reverse breakdown are called Zener diodes and use the indicated symbol. Microelectronic Circuit Design McGraw-Hill Chap 3 -28

  29. PN Junction Capacitance • The capacitance is important under dynamic signal conditions because it prevents the voltage across the diode from changing instantaneously. Microelectronic Circuit Design McGraw-Hill

  30. Reverse Bias Capacitance Changes in voltage lead to changes in depletion width and charge. This leads to a capacitance that we can calculate from the charge voltage dependence. Cj0 is the zero bias junction capacitance per unit area. Microelectronic Circuit Design McGraw-Hill Chap 3 -30

  31. Reverse Bias Capacitance (cont.) Diodes can be designed with hyper-abrupt doping profiles that optimize the reverse-biased diode as a voltage controlled capacitor. Circuit symbol for the variable capacitance diode (varactor) Microelectronic Circuit Design McGraw-Hill Chap 3 -31

  32. Forward Bias Capacitance In forward bias operation, additional charge is stored in neutral region near edges of space charge region. tTis called diode transit time and depends on size and type of diode. Additional diffusion capacitance, associated with forward region of operation is proportional to current and becomes quite large at high currents. Microelectronic Circuit Design McGraw-Hill Chap 3 -32

  33. Schottky Barrier Diode One semiconductor region of the pn junction diode is replaced by a non-ohmic rectifying metal contact.A Schottky contact is easily added to n-type silicon,metal region becomes anode. n+ region is added to ensure that cathode contact is ohmic. Schottky diode turns on at lower voltage than pn junction diode, has significantly reduced internal charge storage under forward bias. Microelectronic Circuit Design McGraw-Hill Chap 3 -33

  34. Schottky Diode • Key uniqueness: fast switching from ON to OFF and back. • Widely used: • in analog circuits: in track and hold circuits in A/D converters,pin drivers of IC test equipment • in communications and radar applications: as detectors and mixers,also as varactors Microelectronic Circuit Design McGraw-Hill

  35. Fermi Level & Fermi Function • The Fermi function f(E) gives the probability that a given available electron energy state will be occupied at a given temperature. • Fermi level is the top of the collection of electron energy levels at absolute zero temperature. At higher temperatures, f(E) = 0.5 at Fermi level. Microelectronic Circuit Design McGraw-Hill

  36. Density of Energy States Microelectronic Circuit Design McGraw-Hill

  37. Population of Conduction Band for a Semiconductor Microelectronic Circuit Design McGraw-Hill

  38. Energy Band View of Diode Operation • For a p-n junction at equilibrium, the fermi levels match on the two sides of the junctions. Electrons and holes reach an equilibrium at the junction and form a depletion region. Microelectronic Circuit Design McGraw-Hill

  39. Reverse Bias • To reverse-bias the p-n junction, the p side is made more negative, making it "uphill" for electrons moving across the junction. The conduction direction for electrons in the diagram is right to left, and the upward direction represents increasing electron energy. Microelectronic Circuit Design McGraw-Hill

  40. Forward Bias Microelectronic Circuit Design McGraw-Hill

  41. Schottky Diode Energy Band Diagram • Electrons flow into the metal until equilibrium is reached between the diffusion of electrons from the semiconductor into the metal and the drift of electrons caused by the field created by the ionized impurity atoms. This equilibrium is characterized by a constant Fermi energy throughout the structure. Microelectronic Circuit Design McGraw-Hill

  42. Ohmic Contact • a contact between a metal and a semiconductor is typically a Schottky barrier contact.  • However, if the semiconductor is very highly doped, the Schottky barrier depletion region becomes very thin.  At very high doping levels, a thin depletion layer becomes quite transparent for electron tunneling.  • a practical way to make a good ohmic contact is to make a very highly doped semiconductor region between the contact metal and the semiconductor. Microelectronic Circuit Design McGraw-Hill

  43. Diode Spice Model Rs is inevitable series resistance of a real device structure. Current controlled current source represents ideal exponential behavior of diode. Capacitor specification includes depletion-layer capacitance for reverse-bias region as well as diffusion capacitance associated with junction under forward bias. Typical default values: Saturation current= 10 fA, Rs = 0W, Transit time= 0 second Microelectronic Circuit Design McGraw-Hill Chap 3 -43

  44. Diode Layout Microelectronic Circuit Design McGraw-Hill Chap 3 -44

  45. Diode Circuit Analysis: Basics • Loop equation for given circuit is: • This is also called the load line for the diode. Solution to this equation can be found by: • Graphical analysis using load-line method. • Analysis with diode’s mathematical model. • Simplified analysis with ideal diode model. • Simplified analysis using constant voltage drop model. V and R may represent Thevenin equivalent of a more complex 2-terminal network.Objective of diode circuit analysis is to find quiescent operating point for diode, consisting of dc current and voltage that define diode’s i-v characteristic. Microelectronic Circuit Design McGraw-Hill Chap 3 -45

  46. Load-Line Analysis (Example) Problem: Find Q-point Given data:V=10 V, R=10kW. Analysis: To define the load line we use, VD= 0 VD= 5 V, ID =0.5 mA These points and the resulting load line are plotted.Q-point is given by intersection of load line and diode characteristic: Q-point = (0.95 mA, 0.6 V) Microelectronic Circuit Design McGraw-Hill Chap 3 -46

  47. Analysis using Mathematical Model for Diode Problem: Find Q-point for given diode characteristic. Given data: IS =10-13 A, n=1, VT =0.0025 V Analysis: is load line, given by a transcendental equation. A numerical answer can be found by using Newton’s iterative method. • Make initial guess VD0. • Evaluate f and its derivative f’ for this value of VD. • Calculate new guess for VD using • Repeat steps 2 and 3 till convergence. • Using a spreadsheet we get : • Q-point = ( 0.9426 mA, 0.5742 V) • Since, usually we don’t have accurate saturation current and significant tolerances for sources and passive components, we need answers precise up to only 2or 3 significant digits. Microelectronic Circuit Design McGraw-Hill Chap 3 -47

  48. Analysis using Ideal Model for Diode • If diode is forward-biased, voltage across diode is zero. If diode is reverse-biased, current through diode is zero. • vD =0 for iD >0 and iD =0 for vD < 0 • Thus diode is assumed to be either on or off. Analysis is conducted in following steps: • Select diode model. • Identify anode and cathode of diode and label vD and iD. • Guess diode’s region of operation from circuit. • Analyze circuit using diode model appropriate for assumed operation region. • Check results to check consistency with assumptions. Microelectronic Circuit Design McGraw-Hill Chap 3 -48

  49. Analysis using Ideal Model for Diode: Example Since source is forcing positive current through diode assume diode is on. Q-point is(1 mA, 0V) Since source is forcing current backward through diode assume diode is off. Hence ID =0 . Loop equation is: Q-point is (0, -10 V) our assumption is right. our assumption is right. Microelectronic Circuit Design McGraw-Hill Chap 3 -49

  50. Analysis using Constant Voltage Drop Model for Diode Analysis: Since 10V source is forcing positive current through diode assume diode is on. vD = Von for iD >0 and iD = 0 for vD < Von. Microelectronic Circuit Design McGraw-Hill Chap 3 -50