1. Microelectronic Circuits Zhou Lingling
Chapter 3 Diodes
Functionality and Physical Operation
2018/11/14
J. Chen

2. Content
3.1 The Ideal Diode 3.2 Terminal Characteristics of Junction Diodes 3.3 Modeling the Diode Forward Characteristic 3.4 Operation in the Reverse Breakdown Region—Zener Diodes 3.5 Rectifier Circuits （整流电路） 3.6 Limiting and Clamping Circuits （限幅与钳位电路） 3.7 Physical Operation of Diodes 3.8 Special Diode Types 3.9 The SPICE Diode Model and Simulation Examples
J. Chen
2018/11/14

3. 3.1 Linear and Nonlinear Devices
So far, almost all the devices we have learnt are linear
Many signal-processing functions, however, are implemented by nonlinear devices
Nonlinear amplifier
Linear amplifier
J. Chen
2018/11/14

4. 3.1 Symbol and characteristic
Diode (二极管) is the simplest and most fundamental nonlinear circuit element i i
(d) Equivalent circuit
in the forward direction
i > 0  v =0 v
(a) Diode circuit symbol v i
Anode
Cathode
---Reverse bias---
---Forward bias---
(c) Equivalent circuit
in the reverse direction
v < 0  i=0 i v v
(b) i–v characteristic of the ideal diode
Note: measures should be taken to limit the forward current and the reverse voltage!
J. Chen
2018/11/14

5. 3.2 Junction Diodes and its Characteristics
The most important region is the boundary between n-type and p-type semiconductor, which is called pn junction(pn结)
(v)
The diode i–v relationship
(mA)
pn junction
J. Chen
2018/11/14

6. 3.2 Junction Diodes and its Characteristics
(mA)
(nA)
The diode i–v relationship
(Note the scale expansion / compression)
cut-in voltage
J. Chen
2018/11/14

7. 3.3 The Diode Models Mathematic Model： Forward biased Reverse biased
where 𝑰 𝒔 saturation current
𝒗 𝑻 = 𝒌𝑻 𝒒 thermal voltage(~25 mv at room temperature)
𝒏=𝟏𝟐 (In general, n = 1)
J. Chen
2018/11/14

8. 3.3 Temperature dependence
Voltage mV/C
Temperature dependence of the diode forward characteristic
J. Chen
2018/11/14

9. 3.3 The Diode Models
Circuit Model : usually derived by approximating the curve into piecewise-line
According to practical applications, there are different models, such as
Simplified diode model
The constant-voltage-drop model
Small-signal model
High-frequency model
Zener Diode Model
J. Chen
2018/11/14

10. Forward bias  short circuit Reverse bias  open circuit
3.3 Ideal Diode Model
Forward bias  short circuit
Reverse bias  open circuit
J. Chen
2018/11/14

11. 3.3 Simplified Diode Model
Piecewise-linear model of the diode forward characteristic
Equivalent circuit representation.
J. Chen
2018/11/14

12. 3.3 Constant-Voltage-Drop Model
The constant-voltage-drop model of the diode forward characteristics and its equivalent-circuit representation.
J. Chen
2018/11/14

13. 3.3 Small-Signal* Model rd (n = 2)
Incremental resistance rd
*The signal amplitude is sufficiently small such that the excursion at Q along the i-v curve is limited to a short, almost linear segment.
J. Chen
2018/11/14

14. 3.3 High-Frequency Model
Related to the bias
J. Chen
2018/11/14

15. 3.4 Zener Diode Model
The diode i–v characteristic with the breakdown region shown in some detail
J. Chen
2018/11/14

16. 3.5 The Application of Diode Circuits
Rectifier circuits
Half-wave rectifier
Full-wave rectifier
The peak rectifier
Voltage regulator (稳压器)
Limiter (限幅器)
Logic Circuits
J. Chen
2018/11/14

17. 3.5 Half-Wave Rectifier (a) Half-wave rectifier (b) Equivalent circuit
(d) Input and output waveforms
(c) Transfer characteristic
J. Chen
2018/11/14

18. 3.5 Parameter determination
In selecting diodes for rectifier design, two important parameters must be specified:
The current-handling capability
The peak inverse voltage (PIV)
It is usually prudent, however, to select a diode that has a reverse breakdown voltage at least 50% greater than the expected PIV.
J. Chen
2018/11/14

19. 3.5 Full-Wave Rectifier Transfer characteristic
Transformer with a center-tapped （中心抽头） secondary winding +
Transfer characteristic +
Input and output waveforms
J. Chen
2018/11/14

20. 3.5 The Bridge Rectifier Circuit Input and output waveforms J. Chen
2018/11/14

21. 3.5 Peak Rectifier
The pulsating nature of the output voltage produced by the rectifier circuits makes it unsuitable as a dc supply for electronic circuits.
A simple way to reduce the variation of the output voltage is to place a capacitor across the load resistor.
The filter capacitor serves to reduce substantially the variations in the rectifier output
J. Chen
2018/11/14

22. 3.5 Peak Rectifier
Voltage and current waveforms in the peak rectifier circuit with
𝑅𝐶≫𝑇,
where T is the period.
J. Chen
2018/11/14

23. 3.5 Peak Rectifier Block diagram of a dc power supply J. Chen
2018/11/14

24. 3.7 Physical Operation of the diode
How can a diode present totally different behavior in forward and backward bias?
To answer the question, we need to know:
Material, structure and the related features (crystal and semiconductor in particular)
New particles to carry charge in addition to electrons
New mechanism(s) of conduction in addition to what we have known
Techniques to manufacture the devices
J. Chen
2018/11/14

25. 3.7 Basic semiconductor concepts
Intrinsic Semiconductor (本征半导体)
Doped Semiconductor (掺杂半导体)
Carriers (载流子)
Diffusion (扩散运动)
Drift (漂移运动)
J. Chen
2018/11/14

26. 3.7 Elements and material
Periodic table
J. Chen
2018/11/14

27. 3.7 Material and structure
Structure is another important factor to determine the physical and chemical characteristics of the material！
allotrope(同素异形体), e.g.
diamond
graphite
J. Chen
2018/11/14

28. 3.7 Crystal and noncrystal
Regular shape, fixed freezing temperature, fixed boiling point, etc.
Why? Regular lattice structure！
Atoms can not tell from each other: they behave uniquely
In noncrystal, however, the atoms of the same element usually play different roles, e.g. Polymer
aromatic hydrogen bonds
(芳香氢键)
J. Chen
2018/11/14

29. 3.7 Silicon（硅/矽） IV element
Each atom is bound with four neighbors via Covalent Bond
Its atomic structure is tetrahedron(四面体，与金刚石相同)
Monocrystalline silicon
polycrystalline silicon
单晶硅
多晶硅
Tetrahedron
(四面体)
J. Chen
2018/11/14

30. 3.7 2-D representation of the silicon crystal+4 +4 +4 +4 +4 +4 +4 +4
Silicon
atoms
Covalent bond
Valence electrons
J. Chen
2018/11/14

31. Energy bands resulted in from energy level splitting
3.7 Transition
The movement of electrons between the energy bands is call transition (跃迁).
Transition is always accompanied with energy change (absorption or emission of photons and/or phonons, temperature change, etc.)
Energy bands resulted in from energy level splitting
J. Chen
2018/11/14

32. 3.7 Intrinsic semiconductor
Microelectronic Circuits Zhou Lingling
3.7 Intrinsic semiconductor
Pure semiconductor
At 0 K, all bonds are intact and no free electrons are available for current conduction
Ev(价带)
Ec(导带)
Eg = Ec - Ev @
The energy bands and the states of electrons
in Si/Ge at T= 0 K
J. Chen
2018/11/14

33. 3.7 Thermal ionization
At room temperature, some of the covalent bonds are broken by thermal ionization
Each broken bond gives rise to a free electron and a hole, both of which become available for current conduction
Carriers（载流子）
Free electron ---produced by thermal ionization. It can move freely in the lattice structure so as to form current
Hole---empty position in broken covalent bond. It can also “move” freely to form current
J. Chen
2018/11/14

34. 3.7 Recombination & thermal equilibrium
The free electron is a negative charge and the hole is a positive charge. Both of them can move in the crystal structure, so as to form electric current.
Recombination
A free electron may fill into a hole, resulting in the disappearance of a pair of carriers ( a free electron and a hole).
Thermal equilibrium
At a steady temperature, the recombination rate is equal to the ionization rate  thermal equilibrium (热平衡)
The concentration of the carriers at thermal equilibrium does not change and can be calculated.
J. Chen
2018/11/14

35. 3.7 Carrier concentration
Carrier concentration in thermal equilibrium
where
(k : Boltzmann constant)
At room temperature (T=300K) for Si,
J. Chen
2018/11/14

36. 3.7 Important notes
𝒏 𝒊 strongly depends on temperature. The high the temperature is, the dramatically great the carrier concentration is
At room temperature only one of every billion atoms is ionized
Silicon’s conductivity is between that of conductors and insulators. Actually the characteristic of intrinsic silicon approaches to insulators
J. Chen
2018/11/14

37. 3.7 Doped semiconductor
Conductivity of the semiconductor can be significantly changed by doping.
There are two types of doped semiconductors: n type and p type.
They are used to form pn junction.
J. Chen
2018/11/14

38. 3.7 n type semiconductor P
Bound charge
J. Chen
2018/11/14

39. 3.7 n type semiconductor
Donor--- pentavalent impurity provides free electrons (usually entirely ionized at room temperature)
Positive bound charge---impurity atom donating electron gives rise to positive bound charge
Majority carriers---free electrons (mostly generated by ionized donor and a very tiny portion by thermal ionization) .
Minority carriers---holes (only generated by thermal ionization) .
J. Chen
2018/11/14

40. 3.7 Carrier concentration for n type
Thermal equilibrium equation
Electric neutral equation
where ND is the donor concentration
J. Chen
2018/11/14

41. 3.7 Carrier concentration for n type
In a n type Si, the following relationships hold (at room temperature):
and
J. Chen
2018/11/14

42. 3.7 p type semiconductor
Acceptor--- trivalent impurity provides holes (usually entirely ionized)
Negative bound charge --- impurity atom accepting hole give rise to negative bound charge
Majority carriers---holes (mostly generated by ionized acceptor and a tiny small portion by thermal ionization)
Minority carriers--- free electrons (only generated by thermal ionization) Al
J. Chen
2018/11/14

43. 3.7 Carrier concentration for p type
Thermal equilibrium equation
Electric neutral equation
where NA is the acceptor concentration
J. Chen
2018/11/14

44. 3.7 Carrier concentration for p type
In a p type Si, the following relationships hold (at room temperature):
and
J. Chen
2018/11/14

45. 3.7 Conclusion on the doped semiconductor
Majority carrier is only determined by the impurity. It is independent of temperature.
Minority carrier is strongly affected by temperature.
If the temperature is high enough, the characteristic of doped semiconductor will decline to that of intrinsic semiconductor
J. Chen
2018/11/14

46. 3.7 Doping compensation
On p type semiconductor (substrate), n type semiconductor can be formed by injecting donors with 𝑁 𝐷 ≫ 𝑁 𝐴 into the specific area.
or reversely. NA ND +
J. Chen
2018/11/14

47. The boundary between n and p type semiconductor is the pn junction.
3.7 Doping compensation
The boundary between n and p type semiconductor is the pn junction.
This is the basic step for VLSI fabrication technology.
J. Chen
2018/11/14

48. 3.7 Semiconductor materials
IV:
Si---today’s IC technology is based entirely on silicon
Ge---early used for diode and transistor, and presently used mostly for opto-electronic devices
III-V:
Gallium arsenide (GaAs)---used for microwave circuits
InP---used for optoelectronics
II-VI: used for luminescence, IF, etc.
J. Chen
2018/11/14

49. 3.7 Carriers movement
There are two mechanisms for holes and free electrons to move in the silicon crystal.
Drift
The carrier motion is generated by the electrical field across a piece of silicon. This motion will produce drift current (漂移电流).
Diffusion
The carrier motion is generated by the carrier concentration gradient. The motion of carriers from high concentration area to low one will give rise to diffusion current(扩散电流)
J. Chen
2018/11/14

50. 3.7 Drift and drift current
Drift velocities
Drift current densities
where are the constants called mobility of holes and electrons, respectively
J. Chen
2018/11/14

51. 3.7 Drift and drift current
Total drift current density
Resistivity
J. Chen
2018/11/14

52. 3.7 Resistivity for intrinsic semiconductor
Resistivity is inversely proportional to the carrier concentration of intrinsic semiconductor
Temperature coefficient (TC) for resistivity of intrinsic semiconductor is negative due to positive TC of ni
J. Chen
2018/11/14

53. 3.7 Resistivities for doped semiconductor
Resistivities are inversely proportional to the concentration of doped impurities.
Temperature coefficient for resistivity of doped semiconductor is positive due to negative TC of mobility
For n type
For p type
J. Chen
2018/11/14

54. 3.7 Diffusion and diffusion current
A bar of intrinsic silicon (a) in which the hole concentration profile shown in (b) has been created along the x-axis by some unspecified mechanism.
J. Chen
2018/11/14

55. 3.7 Diffusion and diffusion current
where are the diffusion constants or diffusivities for hole and electron, respectively
The diffusion current density is proportional to the slope of the concentration curve, or the concentration gradient.
J. Chen
2018/11/14

56. 3.7 Einstein relationship
Einstein relationship exists between the carrier diffusivity and mobility:
where VT is thermal voltage(温度电压当量), At room temperature， =
J. Chen
2018/11/14

57. Usually the pn junction is asymmetric, p+n or pn+
The superscript “+” denotes the region of more heavily doped in comparison with the other region
J. Chen
2018/11/14

58. 3.7 The carriers movement in a pn junction
Recall of semiconductor characteristics:
p-type: majority carriers (holes)+ very few amount of minority carriers (free electrons) + negative bound charges
n-type: majority carriers (free electrons)+ very few amount of minority carriers (holes) + positive bound charges
Carriee movement in pn junction
J. Chen
2018/11/14

59. 3.7 pn junction under open-circuit condition
Procedure of
forming pn junction
Diffusion
Space charge
(a) the pn junction
Drift
Equilibrium
(b) the potential distribution
J. Chen
2018/11/14

60. 3.7 Junction built-in voltage
The junction built-in voltage(内建电场)
It depends on doping concentration and temperature
Its TC is negative.
J. Chen
2018/11/14

61. 3.7 Width of the depletion region
Depletion region exists almost entirely on the slightly doped side.
Width depends on the voltage across the junction.
J. Chen
2018/11/14

62. 3.7 i-v Characteristics
The diode i–v relationship with some scales expanded
and others compressed in order to reveal details
J. Chen
2018/11/14

63. 3.7 The pn junction under forward-bias
The pn junction excited by a constant-current source supplying a current I in the forward direction.
The depletion layer narrows and the barrier voltage decreases by V volts, which appears as an external voltage in the forward direction.
动画演示
J. Chen
2018/11/14

64. 3.7 Carrier distribution under forward-bias
Minority-carrier distribution in a forward-biased pn junction.
J. Chen
2018/11/14

65. 3.7 Excess minority carrier concentration
where
diffusion length
excess-minority-carrier lifetime
Exponential relationship
Small voltage incremental gives rise to great incremental of excess minority carrier concentration
J. Chen
2018/11/14

66. 3.7 Total current under forward-bias
where
Is---saturation current
A---junction cross-sectional area
J. Chen
2018/11/14

67. 3.7 Turn-on voltage
A conduction diode has approximately a constant voltage drop across it. It’s called turn-on voltage.
For silicon, 𝑉 𝐷(𝑜𝑛) =0.7 (𝑣).
Diodes with different current rating will exhibit the turn-on voltage at different currents.
Negative TC,
J. Chen
2018/11/14

68. 3.7 The pn junction under reverse-bias
The pn junction excited by a constant-current source I in the reverse direction.
To avoid breakdown, I is kept smaller than IS.
Note that the depletion layer widens and the barrier voltage increases by VR volts, which appears between the terminals as a reverse voltage.
动画演示
J. Chen
2018/11/14

69. 3.7 Carrier distribution under reverse-biasUR
p-type area
n-type area
pn0
nn0
pp0
np0 x
J. Chen
2018/11/14

70. 3.7 i-v characteristic equation
Independent of voltage
where Is is the saturation current. It is proportional to ni2, which is a strong function of temperature.
J. Chen
2018/11/14

71. 3.7 The pn junction in the breakdown region
The pn junction excited by a reverse-current source I, where I > IS
The junction breaks down, and a voltage VZ , with the polarity indicated, develops across the junction.
J. Chen
2018/11/14

72. 3.7 Breakdown mechanisms Zener effect Avalanche effect
Occurs in heavily doping semiconductor
Breakdown voltage is less than 5v.
Carriers generated by electric field---field ionization.
TC is negative.
Avalanche effect
Occurs in slightly doping semiconductor
Breakdown voltage is more than 7v.
Carriers generated by collision.
TC is positive.
Remember:
pn junction breakdown is not a destructive process, provided that the maximum specified power dissipation is not exceeded.
J. Chen
2018/11/14

73. 3.7 Junction Capacitance Diffusion Capacitance
Charge stored in bulk region changes with the change of voltage across pn junction gives rise to capacitive effect
Small-signal diffusion capacitance
扩散电容 Cd, 由多数载流子在扩散过程中的积累引起，正向偏置时起主要作用
J. Chen
2018/11/14

74. 3.7 Junction Capacitance Depletion capacitance
Charge stored in depletion layer changes with the change of voltage across pn junction, which gives rise to capacitive effect.
Small-signal depletion capacitance UR
UR+ΔU
势垒电容 Cb
由PN结的空间电荷区形成，又称结电容。反向偏置时起主要作用
J. Chen
2018/11/14

75. 3.7 Diffusion Capacitance
According to the definition:
The charge stored in bulk region is obtained from the following equations:
J. Chen
2018/11/14

76. 3.7 Diffusion Capacitance
The expression for diffusion capacitance:
Forward-bias, linear relationship
Reverse-bias, almost inexistence
J. Chen
2018/11/14

77. 3.7 Depletion Capacitance
According to the definition:
Actually this capacitance is similar to parallel plate capacitance.
J. Chen
2018/11/14

78. 3.7 Depletion Capacitance
A more general formula for depletion capacitance is :
where m is called grading coefficient.
If the concentration changes sharply,
J. Chen
2018/11/14

79. 3.7 Junction Capacitance Remember:
Diffusion and depletion capacitances are incremental capacitances, only are applied under the small-signal circuit condition.
They are not constants, they have relationship with the voltage across the pn junction.
J. Chen
2018/11/14

80. SUMMARY
The silicon junction diode is basically a pn junction. Such a junction is formed in a single silicon crystal.
A silicon diode conducts a negligible current until the forward voltage is at least 0.5 V. Then the current increases a decade per 60 mV or 120 mV (depending on the value of n).
In the reverse direction, a silicon diode conducts a current on the order of 10-9A. This current is much greater than Is and increases with the magnitude of reverse voltage.
J. Chen
2018/11/14

81. SUMMARY
Beyond a certain value of reverse voltage breakdown occurs, and current increases rapidly with a small corresponding increase in voltage.
A hierarchy of diode models exists. The selection of an appropriate model depends on the application.
There are other semiconductors. However Si is dominant for electronic devices because:
better thermal stability due to large bandgap
abundant (27 % in the Earth) and cheap
J. Chen
2018/11/14

82. “When you find yourself competing with silicon, don’t.”
SUMMARY
“When you find yourself competing with silicon, don’t.”
Arno Penzias, joined Bell Lab in 1961
best known for his work in radio astronomy, winning a Nobel Prize in 1978 for research that enabled a better understanding of the origins of the universe.
Tingye Li, joined Bell Lab in 1957
a world-renowned scientist in the fields of microwaves, lasers and optical communications. His innovational work on lightwave communications has had a far-reaching impact on information technology for decades
J. Chen
2018/11/14

83. Homework Feb. 29 March 7 3.5；3.20；3.30； 3.52；3.63 ；3.106；3.114 J. Chen
2018/11/14