1. CP 208 Digital Electronics Class Lecture 4 February 18, 2009

2. In This Class We Will Discuss Following Topics: Chap 3 Diodes
3.1 The Ideal Diode
3.7 Physical Operation of Diodes
3.9 The SPICE Diode Model
Chap 5 Bipolar Junction Diodes (BJTs)
5.10 The Basic BJT Digital Logic Inverter

3. 4/16/2017
Diodes 3

4. Diode The Simplest and Most Fundamental Non-Linear Ckt Element
Like Resistor, Diode has Two Terminals
Unlike Resistor Diode has Non-Linear I-V Characteristics
To Understand Diode Function We Start with a FICTITUOS Element – Ideal Diode
Then Physical Operation which will be Foundation for Understanding FETs BJTs

5. 3.1 The Ideal Diode Two Terminal Device with The Symbol
Positive Terminal Anode and Negative Cathode
And I-V Characteristics as:

6. 4/16/2017
When Negative Voltage is Applied (Reverse Biased), No Current Flows and Diode behaves as Open Circuit and Said to be Cut Off or OFF
When Positive Voltage is Applied (Forward Biased), Zero Votage Drop Appears and Diode behaves as Short Circuit Circuit and Said to be Turned On or ON
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7. 4/16/2017
External Circuit Must be Designed to Limit Forward Current and Reverse Voltage to Predetermined Safe Value
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8. The I-V of Ideal Diode is Highly non-linear, but it contains two Straight-Line Segments 90° to one Another – Piecewise Linear.
Application in Which Signal on Device Terminal Swing only Along non-linear portion then Device is Linear for that Application

9. 4/16/2017
3.1.2 Diode Logic Gates
Diodes together with Resistors can be used to implement Digital Logic
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OR Gate, Y=A+B+C
AND Gate, Y=A.B.C

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Example 3.2
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11. 3.7 Physical Operation of Diode
A semiconductor diode is basically a pn junction – p-type semiconductor material brought into close contact with n-type material (practically n and p regions in Si)
Terminals -- wire connections are made through metal (Al) contacts to n and p regions
Besides being Diode, pn junction is the basic element of BJTs and plays an important role in the operation of FETs

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Intrinsic Silicon
Two-dimensional Silicon Crystal, Circles represent the silicon atoms, with +4 positive charge neutralized by the charge of the four valence electrons. Covalent bonds are formed by sharing of the valence electrons. At 0 K, all bonds are intact and no free electrons are available for current conduction.
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13. At room temperature some bonds are broken by thermal ionization and some electrons are free.
Bond breaks, Electron leaves parent atom leaving behind +ve charge (hole). Electron from neighboring atom moves to fill hole creating another hole.
Essentially, by repetition of the process, positive charge (hole) is moving thru crystal and available for conduction.
Intrinsic Silicon

14. Intrinsic Silicon
Equal number of Electrons and Holes Result by Thermal Ionization (Generation of Electron/Hole Pair EHP)
While moving randomly these pairs recombine and disappear as well (Recombination)
Recombination Rate is Proportional to number of free Electrons and Holes, which in turn is determined by Ionization Rate
Generation is Strong Function of Temperature
In Thermal Equilibrium Recombination is equal to Generation and Concentration of e/h can be calculated: n = p = ni and ni is free electrons or holes concentration in Intrinsic Silicon at a given T

15. Intrinsic Silicon At an absolute temp T (in Kelvin) the
Where B = 5.4x1031 (for Si), k is Boltzmann’s constant and EG Band gap energy (1.12 eV for Si) is minimum energy required to break a bond for EHP generation
At 300 K (RT) the Eq. gives ni = 1.5x1010 carriers/cm3 for Intrinsic Si
Note that Si has about 5x1022 atoms/cm3, So at room temp only One of every Billion atom is ionized !!

16. Diffusion and Drift
Diffusion and Drift – Two mechanisms by which Holes and Electrons move thru Si
Diffusion of carriers takes place if Concentration Gradient is present and Gives rise to Net Flow of Charge (Current)
Hole Diffusion Current in x-direction: Magnitude is Proportional to Slope of Concentration Gradient

17. Diffusion and Drift Similarly Electron Diffusion Current
In Semiconductors, Carrier also move through another mechanism – Drift
Carrier Drift Occurs when Electric Field is Applied Across a Piece of Si
Carriers are Accelerated by the E Field and Acquire Drift Velocity (Holes drift in E direction and Electrons opposite)

18. Diffusion and Drift
Hole Drift Current through a Si with hole density p as a result of E Field applied is:
Similarly, Electron Drift Current is:
Total Drift Current will be sum of both:
Note that this is a form of Ohm’s law, resistively in ohm-cm is given by:

19. Diffusion and Drift
Finally, a simple relationship between diffusivity and mobility exist, know as Einstein Relationship:
VT is known as Thermal Voltage = 25 mV at RT

20. Doped Semiconductors
In Intrinsic Si the Holes and Electrons have equal Concentration and strongly dependent on temperature
While in Doped Semiconductors Carriers of one kind (either hole or electron) are predominant
Doped silicon in which majority of charge carriers are negatively charged electrons is called n-type
With majority of +ve holes is p-type

21. Doped Semiconductors
Doping of Si to make it n or p type is achieved by introducing small number of impurity atoms
Introducing impurity atoms of pentavalent element such as P results in n-type Si
Each P atom replacing Si atom is donating a free electron to Si Crystal
Note that for free electron no hole is generated, hence majority of charge carriers in P doped silicon are electrons

22. Silicon Crystal Doped By a Pentavalent Element
Silicon Crystal Doped By a Pentavalent Element. Each Dopant Atom Donates a Free Electron and is Thus Called a Donor. The Doped Semiconductor Becomes n Type.
4/16/2017
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23. Doped Semiconductors
If the Donor Atom (P) concentration is ND in thermal equilibrium the free electron concentration in n-type Si is nno will be:
In Thermal equilibrium the product of electron and hole concentration remains constant, that is,
nn0pn0 = ni2
Concentration of holes would be,
Minority holes are function of Temp while Majority Electrons are independent of Temp.

24. Doped Semiconductors
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Similarly When Silicon Crystal Doped with a Trivalent Impurity Boron, Each dopant atom gives rise to a hole, and the Semiconductor becomes p type.
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25. Doped Semiconductors
Introducing impurity atoms of Trivalent element such as B results in p-type Si
Each B atom replacing Si atom is accepting a free electron from Si Crystal to form a covalent bond, thus each B atom gives rise to Hole
Note that for Hole no electron is generated, hence majority of charge carriers in B doped silicon are Holes

26. Doped Semiconductors
If the Donor Atom (B) concentration is NA in thermal equilibrium the free Hole concentration in p-type Si is pp0 will be:
In Thermal equilibrium the product of electron and hole concentration remains constant, that is,
np0pp0 = ni2
Concentration of Electrons would be,
Minority Electrons are function of Temp while Majority Holes are independent of Temp.

27. 3.7.2 pn Junction Under Open Circuit Conditions
The pn junction with no applied voltage (open-circuited terminals)
+ denote majority holes in p-type
- denote majority electron in n-type
Minority carriers in both sides are not shown

28. Diffusion Current ID:
Because Hole concentration is high in p region and low in n region, holes diffuse to n region, likewise, electrons diffuse to p region, giving rise to Diffusion Current ID from p to n side

29. Depletion Region:
The Electrons that diffuse from n region to p region leave behind + charged donor atoms in n region near junction.
In p region electron recombine with holes and create – charge on Acceptor Atoms in p region near junction.
Thus the area near junction becomes depleted of free electrons and holes on both sides and a net bound charges are established.

30. The Carrier Depletion Region or Depletion Region is also called Space Charge Region
Charge on both sides cause an Electric Field to be established and hence a potential difference results across depletion region as shown
Thus the Electric Field opposes any further diffusion of carriers, in fact, voltage drop V0 across depletion region acts as barrier for carriers. Larger the barrier smaller number of carrier will be able to diffuse. ID strongly depends on V0.

31. Drift Current Is and Equilibrium
A current component due to minority-carrier drift also exist across the junction.
Some thermally generated holes in n region diffuse to the edge of depletion region where they experience E Field and are swept across junction to p region. Same for electrons in p region.
These two add together to form drift current Is from n to p side
Is is independent of V0 and strongly dependent on Temp

32. Under open-circuit no external current exists, thus, two opposite currents across junction should be equal, ID = IS.
This Equilibrium condition is maintained by V0
If ID exceeds IS it will result creating more bound charges on both sides, widening the depletion region, and increase V0. This in turn will cause ID to decrease until equilibrium is reached

33. The Junction Built-In Voltage
The V0 across pn junction is given by:
Typically for Si at RT, V0 is in the range of 0.6 V to 0.8 V
The voltage measured between pn junction terminals is zero, this is because the contact voltages existing at the metal-semiconductor junctions at diode terminals exactly balance the barrier voltage.

34. Width of Depletion Region
Usually the doping levels on both sides are not equal hence the depletion region is not same on both sides
In order to cover same amount of charge the deletion region will extend deeper in lightly doped material
If xp is width of depletion region in p side and xn is in n side for equal charges on both sides, qxpANA = qxnAND Or

35. 3.7.3 Reverse-Bias Conditions
Excite pn junction with constant
current source I in reverse direction
I < IS. I in ckt will be carried by
Electrons Flowing from n to p
Free Electrons leave n and Holes leave p region
Results in more – and + charges to build at junction – increase width of depletion region and voltage across it, causing ID to reduce, IS constant
In Steady state (equilibrium) IS – ID = I
The increase in Voltage above V0 will appear at diode terminals as Reverse Voltage VR

36. Depletion Layer Capacitance
Just like Capacitor when V
changes the Charge changes
Charge on either side of junction
Is equal, so using n side:
qJ = qn = qNDxnA
In terms of depletion-layer width, Wdep
And Wdep is given by
Combing both eqs gives for non-linear qJ-VR and is plotted above

37. Depletion Layer Capacitance
This is not a linear capacitor
Using Small Signal Approx.
Depletion-capacitance is
Slope at bias point Q:
Alternatively, we can treat depletion layer as parallel plate capacitor, Cj = εA / Wdep

38. The pn Junction in Reverse Breakdown Region
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The pn Junction in Reverse Breakdown Region
The pn junction excited by a reverse-current source I > IS. The junction breaks down, and a voltage VZ , with the polarity indicated, develops across the junction.
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39. 3.7.5 Forward Bias Condition
Excite pn junction with constant
current source I in forward
direction
Supply Free Electrons to n and
Holes to p region. Results:
Neutralize – and + charges at junction – decrease width of depletion region and voltage across it, causing ID to increase, IS constant
In Steady state (equilibrium) ID – IS = I
The Voltage V0 decrease by Forward Voltage V
This cause Holes injection in n and Electrons Injection in p regions

40. Minority-carrier distribution in a forward-biased pn junction (NA > ND). In Steady state excess minority carrier profile remains constant. This distribution gives rise to increase of Diffusion current ID above IS as these carriers diffuse and disappear by recombination and equal number is replenished by external circuit
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41. Current-Voltage Relationship
Consider the current component caused by holes injected in n region.
Concentration of minority carriers at the edge of Depletion Region is:
Hole distribution in n region is:
Where
The hole diffusion current in n region at xn is:

43. Current-Voltage Relationship
Similarly the Electron diffusion current in p region at - xp is:
Since both Jp and Jn are in same direction they can be added and multiplied by A to get total current;

44. Diffusion Capacitance
FB junction in steady state has certain amount of excess-carrier charge stored in each p and n bulk region
If terminal voltage changes this charge has to change before new steady state is achieved
This gives rise to another capacitive effect
The charge stored due to excess minority-carrier holes in n region:

46. Diffusion Capacitance
Similarly for electron charge stored in p region
Total charge
Where τT is Mean Transit Time of diode
For small changes around bias point small signal diffusion capacitance Cd is

47. The Cd is directly proportional to I and is negligibly small when diode is reverse biased
To keep Cd Small τT must be small an important requirement for diodes intended for high speed and high frequency operation

48. The SPICE Diode Model
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The Static Behavior is modeled by exponential i-v
Dynamic Behavior by the non-linear CD which is sum of the Diffusion cap Cd and junction cap Cj
Series RS represent total R of n and p regions. It is ideally zero but is few ohms for small-signal diodes
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49. The SPICE Diode Model
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For small Signal SPICE Uses incremental resistance rd and incremental values of Cd and Cj
Table 3.3 provide partial parameters list used by SPICE
For discrete diodes parameter values can be determined from diode data sheets. PSPICE includes param. in lib.
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50. 4/16/2017
Bipolar Junction
Transistors (BJTs) 50

51. Bipolar Junction Transistors (BJTs)
Mode EBJ CBJ
Cutoff Reverse Reverse
Active Forward Reverse
Saturation Forward Forward

52. BJT as Amplifier and Switch

53. The Basic BJT Digital Logic Inverter
We learned in Chap 1 that Logic Inverter is Most Fundamental Component of Digital System
We will use this BJT Ckt to realize Logic inverter
Makes use of Cutoff and Saturation modes of BJT to work as Logic Inverter
In these modes the power dissipation is low

54. For
RB=10 kΩ, RC=1k Ω, β = 50, and VCC=5V
In the ckt the VTC is Shown

55. Saturated vs Nonsaturated BJT Digital Ckts
Inverter we just discussed belongs to saturated variety of BJT Digital ckts – TTL
Some TTL versions are in use, Generally saturated bipolar digital ckts are no more technology of choice in Digital System Design
The reason being the speed of operation
Long time delay to turn off a saturated BJT

56. Minority carrier distribution in base region of saturated BJT: Blue triangle gradient gives the diffusion current across base
Grey rectangle causes transistor to be driven deeper into saturation
To achieve high speeds the BJT should not saturate – Current Mode Logic or ECL (Chap 11)

57. Home Work No. 3
Problem 3. 6
Problem 3.10
Problem 5.168
Problem 5.171

58. In Next Class We Will Discuss: Chap 4 MOS Field-Effect Transistors
4.1 Device Structure and Physical Operation
4.2 Current-Voltage Characteristics