1. Chapter 3 Solid-State Diodes and Diode Circuits
Microelectronic Circuit Design
Richard C. Jaeger Travis N. Blalock
Modified by Ming Ouhyoung
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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 bias, 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
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Diode Introduction
A diode is formed by joining an n-type semiconductor with a p-type semiconductor.
A pn junction is the interface between n and p regions.
Diode symbol
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4. metallurgical junction
plane in the p-n junction at which concentration of acceptors is the same as concentration of donors.
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5. pn Junction Electrostatics
Donor and acceptor concentration on either side of the junction. Concentration gradients give rise to diffusion currents.
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Diffusion
Diffusion from a microscopic and macroscopic point of view. Initially, there are solute molecules on the left side of a barrier (purple line) and none on the right. The barrier is removed, and the solute diffuses to fill the whole container. Top: A single molecule moves around randomly.
Middle: With more molecules, there is a clear trend where the solute fills the container more and more uniformly. Bottom: With an enormous number of solute molecules, all apparent randomness is gone: The solute appears to move smoothly and systematically from high-concentration areas to low-concentration areas following Fick’s laws.
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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.’
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9. Space-Charge Region Formation at the pn Junction
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10. Potential Across the Junction
Charge Density
Electric Field
Potential
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11. 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 = V
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εs = 11.7 εo, where εo = 8.85*10-14 F/cm q = 1.60*10-19 C
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13. 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 equal to zero.
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14. 3.2 The i-v characteristics of the diode
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15. Diode Junction Potential for Different Applied Voltages
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16. Diode i-v Characteristics
The turn-on voltage marks the point of significant current flow.
Is is called the reverse saturation current.
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3.3 The Diode Equation
where IS = reverse saturation current (A) vD = voltage applied to diode (V) q = electronic charge (1.60 x C) k = Boltzmann’s constant (1.38 x J/K) T = absolute temperature n = nonideality factor (dimensionless) VT = kT/q = thermal voltage (V) (25 mV at room temp.)
IS is typically between 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.
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IS, the reverse bias saturation current for an ideal p-n diode is given by, (Schubert 2006, 61)
where
IS is the reverse bias saturation current,
e is elementary charge
A is the cross-sectional area
Dp,n are the diffusion coefficients of holes and electrons, respectively,
ND,A are the donor and acceptor concentrations at the n side and p side, respectively,
ni is the intrinsic carrier concentration in the semiconductor material,
τp,n are the carrier lifetimes of holes and electrons, respectively.
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19. 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 = V
Analysis:
With IS = 0.1 fA
With IS = 10 fA
With ID = 1 mA, IS = 0.1 fA
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20. 3.4 Diode characteristics under Reverse, Zero, and Forward bias
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21. Diode Current for Reverse, Zero, and Forward Bias
Reverse bias:
Zero bias:
Forward bias:
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Semi-log Plot of Forward Diode Current and Current for Three Different Values of IS
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26. 3.5 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
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The Nobel Prize in Chemistry 2011 is awarded to Dan Shechtman for the discovery of quasicrystals.
The achievement of Dan Shechtman is clearly not only the discovery of quasicrystals, but the realization of the importance of this result and the determination to communicate it to a skeptical scientific community.
盡信書，不如無書
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To make the discovery even more astounding, Shechtman found that by rotating the sample he could identify additional 5-fold axes as well as 3-fold and 2-fold. It became clear that the symmetry of his sample was not merely 5-fold but icosahedral (figure 4).
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Figure 4. Original electron diffraction images taken by Dan Shechtman. The angular relationship between the various zones examined by Shechtman shows that the sample exhibits icosahedral symmetry6.
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Figure 7. Pentagonal Penrose tiling.
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An important discovery that helped pave the way for the understanding of the discovery of quasicrystals was the construction and analysis by Penrose of his famous pentagonal tiling. The pentagonal Penrose tiling (figure 7) is a self-similar pattern with 5-fold symmetry, long-range order and no translational periodicity. de Bruijn applied the higher dimensional approach to Penrose tiles, and Mackay subjected an image of the vertices of a Penrose tiling to optical diffraction and was able to show that it has a discrete diffraction diagram. These early results were certainly instrumental in allowing Levine and Steinhardt to accomplish their remarkable early analysis (and resulting paper) on quasicrystals, and helped establish the credibility of the discovery.
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35. Properties of quasicrystals
Intermetallic quasicrystals are typically hard and brittle materials with unusual transport properties and very low surface energies. Thermal and electronic transport in solid materials is normally enhanced by phonons and Bloch waves that develop as a consequence of the periodic
nature of crystals.
The low surface energy of quasicrystals make them corrosion- and adhesion-resistant and imparts them with low friction coefficients.
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Surface energy
Surface energy quantifies the disruption of intermolecular bonds that occur when a surface is created. In the physics of solids, surfaces must be intrinsically less energetically favorable than the bulk of a material, otherwise there would be a driving force for surfaces to be created, removing the bulk of the material.
The surface energy may therefore be defined as the excess energy at the surface of a material compared to the bulk.
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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.
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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.
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39. Reverse Bias Saturation Current
We earlier assumed that the 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.
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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
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41. Reverse Breakdown Mechanisms
Avalanche Breakdown Si 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.
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42. Reverse Breakdown Mechanisms (cont.)
Zener Breakdown Zener 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 Coefficient Temperature coefficient is a quick way to distinguish breakdown mechanisms. Avalanche breakdown voltage increases with temperature, whereas Zener breakdown decreases with temperature. For silicon diodes, zero temperature coefficient is achieved at approximately 5.6 V.
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43. 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.
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44. 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.
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45. 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)
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46. Forward Bias Capacitance
In forward bias operation, additional charge is stored in neutral region near edges of space charge region.
tT is called diode transit time and ranges from to more than 10-6 s depending 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.
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47. 3.8 Schottky Barrier Diode
One semiconductor region of the pn junction diode can be replaced by a non-ohmic rectifying metal contact. A Schottky contact is easily formed on n-type silicon. The metal region becomes the anode. An n+ region is added to ensure that the cathode contact is ohmic.
Schottky diodes turn on at a lower voltage than pn junction diodes and have significantly reduced internal charge storage under forward bias.
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3.9 Diode Spice Model
Rs represents the inevitable series resistance of a real device structure. The current controlled current source models the ideal exponential behavior of the diode. Capacitor C includes depletion-layer capacitance for the reverse-bias region as well as diffusion capacitance associated with the junction under forward bias.
Typical default values: Saturation current IS = 10 fA, Rs = 0 W, transit time TT = 0 seconds, N = 1
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Diode Layout
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51. 3.10 Diode Circuit Analysis: Basics
The loop equation for the diode circuit is:
This is also called the load line for the diode. The solution to this equation can be found by:
Graphical analysis using the load-line method.
Analysis with the diode’s mathematical model.
Simplified analysis with the ideal diode model.
Simplified analysis using the constant voltage drop (CVD) model.
V and R may represent the Thévenin equivalent of a more complex 2-terminal network. The objective of diode circuit analysis is to find the quiescent operating point for the diode.
Q-Point = (ID, VD)
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52. Load-Line Analysis (Example)
Problem: Find diode Q-point
Given data: V = 10 V, R = 10kW.
Analysis:
To define the load line we use,
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)
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53. Analysis using Mathematical Model for Diode
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 = ( mA, V)
Since, usually we don’t have accurate saturation current values and significant tolerances exist for sources and passive components, we need answers precise to only 2or 3 significant digits.
Problem: Find the Q-point for a given diode characteristic.
Given data: IS =10-13 A, n=1, VT = V
Analysis:
The solution is given by a transcendental equation. A numerical answer can be found by using Newton’s iterative method.
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Newton’s method
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55. Analysis using Ideal Model for Diode
If an ideal diode is forward-biased, the voltage across the diode is zero. If an ideal diode is reverse-biased, the current through the diode is zero.
vD = 0 for iD > 0 and iD = 0 for vD < 0
Thus, the diode is assumed to be either on or off. Analysis is conducted in following steps:
Select a diode model.
Identify anode and cathode of the diode and label vD and iD.
Guess diode’s region of operation from circuit.
Analyze circuit using diode model appropriate for assumed region of operation.
Check results to check consistency with assumptions.
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56. Analysis using Ideal Model for Diode: Example
Since source is forcing current backward through diode assume diode is off. Hence ID = 0 . Loop equation is:
Our assumption is correct and the Q-Point = (0, -10 V)
Since source appears to force positive current through diode, assume diode is on.
Our assumption is correct, and the Q-Point = (1 mA, 0V)
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57. Analysis using Constant Voltage Drop Model for Diode
Since the 10-V source appears to force positive current through the diode, assume diode is on.
vD = Von for iD > 0 and vD = 0 for vD < Von.
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58. Two-Diode Circuit Analysis
Analysis: The ideal diode model is chosen. Since the 15-V source appears to force positive current through D1 and D2, and the -10-V source is forcing positive current through D2, assume both diodes are on.
Since the voltage at node D is zero due to the short circuit of ideal diode D1,
The Q-points are (-0.5 mA, 0 V) and (2.0 mA, 0 V)
But, ID1 < 0 is not allowed by the diode, so try again.
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59. Two-Diode Circuit Analysis (contd.)
Since the current in D1 is zero, ID2 = I1,
Q-Points are D1 : (0 mA, V):off
D2 : (1.67 mA, 0 V) :on
Now, the results are consistent with the assumptions.
Analysis: Since current in D2 is valid, but that in D1 is not, the second guess is D1 off and D2 on.
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60. 3.12 Analysis of Diodes in Reverse Breakdown Operation
Choose 2 points (0V, -4 mA) and (-5 V, -3 mA) to draw the load line. It intersects the i-v characteristic at the Q-point: (-2.9 mA, -5.2 V).
Using the piecewise linear model:
Using load-line analysis:
Since IZ > 0 (ID < 0), the solution is consistent with Zener breakdown.
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61. Voltage Regulator Using the Zener Diode
For proper regulation, Zener current must be positive. If the Zener current < 0, the Zener diode no longer controls the voltage across the load resistor and the voltage regulator is said to have “dropped out of regulation”.
The Zener diode keeps the voltage across load resistor RL constant. For Zener breakdown operation, IZ > 0.
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Voltage Regulator Using a Zener Diode: Example Including Zener Resistance
Problem: Find the output voltage and Zener diode current for a Zener diode regulator.
Given data: VS = 20 V, R = 5 kW, RZ = 0.1 kW, VZ = 5 V
Analysis: The output voltage is a function of the current through the Zener diode.
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63. Line and Load Regulation
Line regulation characterizes how sensitive the output voltage is to input voltage changes. (Circuit on previous page, Figure 3.41)
Load regulation characterizes how sensitive the output voltage is to changes in load current withdrawn from regulator.
Load regulation is the Thévenin equivalent resistance looking back into the regulator from the load terminals.
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Rectifier Circuits
A basic rectifier converts an ac voltage to a pulsating dc voltage.
A filter then eliminates ac components of the waveform to produce a nearly constant dc voltage output.
Rectifier circuits are used in virtually all electronic devices to convert the 120-V 60-Hz ac power line source to the dc voltages required for operation of electronic devices.
In rectifier circuits, the diode state changes with time and a given piecewise linear model is valid only for a certain time interval.
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65. Half-Wave Rectifier Circuit with Resistive Load
For the positive half-cycle of the input, the source forces positive current through the diode, the diode is on, and vO = vS.
During the negative half cycle, negative current can’t exist in the diode. The diode is off, current in resistor is zero, and vO = 0 .
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66. Half-Wave Rectifier Circuit with Resistive Load (cont.)
Using the constant voltage drop CVD model, during the on-state of the diode vO = (VP sinwt)- Von. The output voltage is zero when the diode is off.
Often a step-up or step-down transformer is used to convert the 120-V, 60-Hz voltage available from the power line to the desired ac voltage level as shown.
Time-varying components in the rectifier output are removed using a filter capacitor.
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Peak Detector Circuit
As the input voltage rises, the diode is on, and the capacitor (initially discharged) charges up to the input voltage minus the diode voltage drop.
At the peak of the input voltage, diode current tries to reverse, and the diode cuts off. The capacitor has no discharge path and retains a constant voltage providing a constant output voltage:
Vdc = VP - Von
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68. Half-Wave Rectifier Circuit with RC Load
As the input voltage rises during the first quarter cycle, the diode is on and the capacitor (initially discharged) charges up to the peak value of the input voltage.
At the peak of the input, the diode current tries to reverse, the diode cuts off, and the capacitor discharges exponentially through R. Discharge continues till the input voltage exceeds the output voltage which occurs near the peak of next cycle. This process then repeats once every cycle.
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Peak Diode Current
In rectifiers, nonzero current exists in the diode for only a very small fraction of period T, yet an almost constant dc current flows out of the filter capacitor to load.
The total charge lost from the filter capacitor in each cycle is replenished by the diode during a short conduction interval causing high peak diode currents.
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70. Peak Inverse Voltage Rating
The peak inverse voltage (PIV) rating of the rectifier diode is the diode breakdown voltage.
When the diode is off, the reverse-bias across the diode is Vdc - vS. When vS reaches negative peak,
The PIV value corresponds to the minimum value of Zener breakdown voltage required for the rectifier diode.
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AM demodulation
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AM Demodulation
The waveform for a 100% amplitude modulated (AM) signal is shown in the figure below and described mathematically by vAM = 2(1+sin ωMt) sin ωCt V in which ωC is the carrier frequency (fC = 50 kHz) and ωM is the modulating frequency (fM = 5 kHz).
The envelope of the AM signal contains the information being transmitted, and the envelope can be recovered from the signal using a simple half-wave rectifier.
The R2C1 time constant is set to filter out the carrier frequency but follow the signal’s envelope.
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77. First-order Linear Circuits
ReqiC + vC = vOC (t)
Q = C * v
i = dQ/dt
iC = C dv/dt
vC(t) = vOC (1 – e(-t/ReqC) )
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78. Full-Wave Rectifiers (10/12)
Full-wave rectifiers cut capacitor discharge time in half and require half the filter capacitance to achieve a given ripple voltage. All specifications are the same as for half-wave rectifiers.
Reversing polarity of the diodes gives a full-wave rectifier with negative output voltage.
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79. Full-Wave Bridge Rectification
The requirement for a center-tapped transformer in the full-wave rectifier is eliminated through use of 2 extra diodes. All other specifications are the same as for a half-wave rectifier except PIV = VP.
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80. Rectifier Topology Comparison
Filter capacitors are a major factor in determining cost, size and weight in design of rectifiers.
For a given ripple voltage, a full-wave rectifier requires half the filter capacitance as that in a half-wave rectifier. Reduced peak current can reduce heat dissipation in diodes. Benefits of full-wave rectification outweigh increased expenses and circuit complexity (an extra diode and center-tapped transformer).
The bridge rectifier eliminates the center-tapped transformer, and the PIV rating of the diodes is reduced. Cost of extra diodes is negligible.
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81. Rectifier Topology Comparison and Design Tradeoffs
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82. Dynamic Switching Behavior of Diodes
The non-linear depletion-layer capacitance of the diode prevents the diode voltage from changing instantaneously and determines turn-on and recovery times. Both forward and reverse current overshoot the final values when the diode switches on and off as shown. Storage time is given by:
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83. Photo Diodes and Photodetectors
If the depletion region of a pn junction diode is illuminated with light with sufficiently high frequency, photons can provide enough energy to cause electrons to jump the semiconductor bandgap to generate electron-hole pairs:
h =Planck’s constant = x J-s
 = frequency of optical illumination
l = wavelength of optical illumination
c = velocity of light = 3 x 108 m/s
Photon-generated current can be used in photodetector circuits to generate an output voltage
The diode is reverse-biased to enhance depletion-region width and electric field.
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84. Solar Cells and Light-Emitting Diodes
In solar cell applications, optical illumination is constant, and dc current IPH is generated. The goal is to extract power from the cell, and the i-v characteristics are plotted in terms of cell current and cell voltage. For a solar cell to supply power to an external circuit, the ICVC product must be positive, and the cell should be operated near the point of maximum output power Pmax.
Light-Emitting Diodes (LEDs) use recombination processes in the forward-biased pn junction diode to produce light. When a hole and electron recombine, an energy equal to the bandgap of the semiconductor is released as a photon.
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End of Chapter 3
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