1. Solid State Electronics II (물리전자 II)
Fall Semester, 2012
Instructor:
Prof. Jong-Chul Lee 1

2. Course Information  Text Book:
- Ben G. Streetman, Solid State Electronic Devices,
6th ed., Prentice Hall, 2006.
- Lecture Notes
Contents : - Basic principles of S/C devices
(p-n junction, BJT, MESFET, MOSFET)
- HEMT, HBT
- Si/SiGe, BiCMOS, etc. 2

3. Course Information  Class Schedule : - Sept. 01 ~ Dec. 15 Grading :
- 10:30 ~ 11:45 AM (Tuesday)
9:00 ~ 10:15 PM (Thursday)
- Office Hours : 1:30 ~ 3:00 PM (Monday & Tuesday)
Grading :
- Attendance : 10 % HW, Quiz, Term paper : 20 %
- Mid Term : 30 % Final Exam : 40 %
- Presentation (optional) 3

4. Donald A. Neamen, Semiconductor Physics And Devices, Third Edition,
Course Information
 References
Donald A. Neamen, Semiconductor Physics And Devices, Third Edition,
MacGraw-Hill, 2002.
Robert F. Pierret, Semiconductor Device Fundamentals, Addison-Wesley,
1996. 4

5. Chap. 5. Junctions 5.1. Fabrication of p-n Junctions
Grown Junctions
▶ Crystal Growth ---> abrupt change in p-type and
n-type doping (epitaxial growth)
Alloyed Junctions      
        ▶ Convenient technique for making p-n junctions
        ▶ An example : n-type Ge substrate + In pellet 5

6. 6

7. 7

8. 5.1.2. Alloyed Junctions Fig. 5-1. Alloying Process (a) In Pellet
(b) @160°lower temp., increase of solubility (Ge --> In)
(c) As temp. goes down, Ge gets out of In. 8

9. Diffusion
▶ Impurity concentration profile for diffusion (Fig. 5. 2) 9

10. 10

11. Fig. 5-10. Fabrication steps of p-n junction11

12. Fabrication steps (cont.)12

13. 5.1.4. Ion Implantation ( keV or  MeV) ; Gaussian Formula
: Direct implantation of energetic ions into the semiconductor
( keV or  MeV)
; Gaussian Formula
 : implanted dose [ions/cm2]
     Rp : projected range ; average penetration depth
     △Rp : straggle (half-width of the e-1/2 of the peak) 13

14. 5.1.4. Ion Implantation (Cont.)
Fig Gaussian distributions
of implanted impurities 14

15. 5.2. Equilibrium Conditions
5.2.1 The Contact Potential 15

16. Fig. 5-7. Characteristic of p-n junction at equilibrium
The Contact Potential (Cont.)
Particle flow
current
electron diff.
hole diff.
electron drift
hole drift
W:   transition region
       space charge region
       depletion region
V0:  contact potential
       built-in potential
       diffusion potential
Fig Characteristic of p-n junction at equilibrium 16

17. 5.2.1. The Contact Potential (Cont.)
At equilibrium, net currents (diff. & drift ) must be zero. (check Fig. 5-7(c) )
                Jp(drift) + Jp(diff.) = 0                                   (5-2a)
                Jn(drift) + Jn(diff.) = 0                                   (5-2b)
◎ Relationship between V0 and n( or p)
From eqn.(4-23b) ,
(5-3)
  (5-4) 17

18. 5.2.1. The Contact Potential (Cont.)
Using eqn.(4-25),  (Electric field takes place in the direction of decreasing potential)
& from Einstein relation,   Eq. (5-4) becomes
                                       
(5-5)  18

19. 5.2.1. The Contact Potential (Cont.)
With Vn-Vp= V0 & boundary conds : Pp & both sides of W .
                 
(5-6)
               (5-7)
                        (5-8)    19

20. 5.2.1. The Contact Potential (Cont.)
Eqn. (5-7) →
                 
                                     (5-9)
       
@ equilibrium ,
          →                                            (5-10) 20

21. Example 5.1
Ex.5-1) Si p-n junction : Na=1018cm-3 (p-side), Nd=5×1015 cm-3 (n-side)
              (a) Fermi Level 300 K
Assume Pp=Na and Nn=Nd
         
p side ;                  (3-25b)
        
similarly , 21

22. Example 5.1(Cont.)
       (b) Equilibrium band diagram
                                 22

23. Example 5.1 (Cont.)
(c) Eqn.( 5-8 ) ; 23

24. 5.2.2. Equilibrium Fermi Levels
Eqn. ( 5-9 ) & Eqn.(3-19) ;
      
                          (5-11a)           
(5-11b)   
(5-12) 24

25. 5.2.3. Space Charge at a Junction
Fig Space charge and electric field distribution within the transition
region of a p-n junction with Nd >Na 25

26. Poisson’s Equation
: relates the gradient of the electric field to the local space charge
at any point x.
(5-16)
Assuming (p-n) can be neglected within the transition region and complete
Ionization of the impurities ( ) 26

27. Poisson’s Equation (Electric field)
Integration of eqn.  (5-15) ;
(5-16)
(5-17); the max. value of
the electric field 27

28. 5.2.3. Space Charge at a Junction (Cont.)
(5-18)
(5-19)
(xnoNd = xp0Na),     W = xno + xp0 28

29. 5.2.3. Space Charge at a Junction (Cont.)
(5-20)
(5-21)
Using eqn. (5.8) ,
(5-22) 29

30. 5.2.3. Space Charge at a Junction (Cont.)
(5-23b) 30

31. Example 5.2
Ex.5.2) From Ex. 5-1,
Si p-n junction : Na=1018cm-3 (p-side), Nd=5×1015 cm-3 (n-side)
      A(circular cross section)=π(5×10-4)2 cm2
Calculate V0 , xn0, xp0 , Q+ , and E0  
     Sketch  E(x) and charge density
From Eq. (5-8)
= V 31

32. Example 5.2 (Cont.)
Eqn.(5-21) →
Eqn.(5-23) →
→   W xn0 32

33. Example 5.2 (Cont.)
(5-13)  →
(5-17)  → 33

34. Example 5.2 (Cont.) 34

35. 5.3. Forward- and Reverse-biased Junctions; Steady State Conditions
Qualitative Description
of Current Flow
at a Junction 35

36. Fig. 5-13. Effects of a bias at a p-n junction36

37. Fig. 5-14. V-I relationship in p-n junction37

38. ⅰ). I= I(diff.) - ｜I(gen.)｜ = 0 for V=0 (5-24)
ⅱ).  For V = Vf  (forward bias)
      → diffusion current increases by ｜I(gen.)｜eqV/kT
ⅲ).  For V = -Vr (reverse bias)
    →   diffusion current is the equilibrium value
       = ｜I(gen.)｜= I0
▶ Total current ; 38

39. 5.3.2.  Carrier Injection
 Hole concentration ratio at the equilibrium :
(5-26)
with bias ,
(5-27)
Since variation of majority carrier can be neglected at low level injection,
[ pp ≈ p(-xp0)] 39

40. 5.3.2 Carrier Injection (Cont.)
(5-26)÷(5-27);
(5-28)
 With applying V, the hole concentration at xn0 increases with eqV/kT compared to
the one at equilibrium.
Excess hole concentration at xn0;
(5-29)
Similarly, Excess electron concentration at -xP0,
(5-30) 40

41. 5.3.2 Carrier Injection (Cont.)
※ Recall : p.121, section 4.4.4  ;  41

42. 5.3.2 Carrier Injection (Cont.)
If p-n region is larger than the diffusion length Ln, Lp,
(5-31a)
(5-31b)
; Distribution of Excess Carriers 42

43. 5.3.2. Carrier Injection (Cont.)
 Hole diffusion current at n-type and arbitrary point, xn can be
written as follows from Eq. (4-40);
    (5-32)
( IP = Jp • A) 43

44. 5.3.2. Carrier Injection (Cont.)
▶  Hole diffusion current at arbitrary point, xn is proportional to the
excess hole concentration at that point  !!!
▶ Therefore, hole current injected in the n-type,
For electron current; 44

45. 5.3.2. Carrier Injection (Cont.)
∴ Total current (neglecting recombination in transition region) ;
hole current – electron current (because of opposite direction) 
                   
(5-35)
(5-36)
  → Diode Equation
For reverse bias : V= -Vr   (Vr 》 kT/q)
                  → I ≈ -I0 45

46. ※ Depending on Majority carrier injection
※ p+-n junction
※ Depending on Majority
carrier injection 46

47. 5.3.3. Minority and Majority Carrier Currents
1) For forward bias 47

48. 2) For reverse bias 48

49. 5.4. Reverse-Bias Breakdown49

50. 5.4.1.  Zener Breakdown 50

51. ※ Summary for Zener Breakdown  Heavily doped material (∴ W: small )
 At low bias voltage, n-type conduction band (empty states)
  → opposite side of p-type valence band (filled states)
 Tunneling of electrons ( → large reverse currents)  ; Zener Effect 51

52. 5.4.2.  Avalanche Breakdown
(a) A single ionizing collision by        (b) Impact ionization process
   an incoming electron 52

53. (c) Multiplication Process (d) Breakdown Voltage
where 3≤m≤6 → 53

54. ※ Summary for Avalanche Breakdown  Lightly doped material   
 Lightly doped material
 Large electric field ( Large drift carrier velocity )
 Impact ionization of host atoms by energetic carriers.
 Generally, VBR increases with Eg of the material
     (∵ Eg ↑ → energy for ionizing collision ↑)
 Emax in W increases with doping in lightly doped side.
      → VBR decreases as doping increases. (See next page) 54

55. For p+-n junction ; See Fig. 5-22 (page 190)! Vbr (V) vs. Nd (cm-3)
for a p+-n juction
For p-n+  junction ; 55

56. 56

57. 5.5. Transient and A-C Conditions
Time Variation of Stored Charge
From eqn.(4-31), Continuity Equation,
(5-45)
Current density at time t can be obtained by integrating both sides,
(5-46) 57

58. 5.5.1. Time Variation of Stored Charge
Since the current at p+-n junction becomes the hole current at xn=0 ( Jp(xn=∞) = 0),
Total injected current can be given by
(5-47)
where 58

59. 5.5.1. Time Variation of Stored Charge (Cont.)
 Meaning : → The hole current (≈total current) injected into p+-n junction
is determined by the following two charge storage effects.
① The usual recombination term, Qp/τp, in which the excess carrier distribution
is replaced every τp seconds
② a charge build-up (or depletion) term, dQp/dt, which allows for the fact that the
distribution of excess carriers can be increasing or decreasing in a time-
dependent situation.
 Note state ;  dQp/dt = 0 (the variation with regarding time = 0) 59

60. 5.5.1. Time Variation of Stored Charge (Cont.)
* For the case of the Step Turn-off Transient (Fig. 5-27) , 60

61. Fig. 5-27. Step Turn-off Transient Effects in a p+-n diode
(a) Current shape through the diode
(b) Decay of stored charge in the n region
(c) Excess hole distribution in the n-region as a function of time during
the transient
i(t > 0) = 0 (i(t  0) = I )   
Qp (t=0) = Iτp 61

62. Laplace transform → eqn.(5-47) ;
(5-48) 62

63.  Excess carrier concentration at xn=0 is given from eqn.(5-29),
(5-49)
 If we can find the correct value of pn(t), the junction voltage, v(t) can be
given. However, it is not easy to find out the exact value of pn(t), related to
Qp(t) from Eq. (5-48) and therefore v(t) 63

64. Quasi-Steady State Approximation
p(xn,t) shows the distribution form which is different from exponential function as shown in Fig. 5-20(c) with proceeding the transient condition. If Quasi-steady state approximation is assumed,
That is,   
(Assuming as exponential function)                (5-50)
                             
(5-51)
   
→                                                   (5-52) 64

65. ; Junction Voltage (Turn-off Transient)
Using Eqn. (5-49),
← eqn. (5-48)
(5-53)
; Junction Voltage (Turn-off Transient) 65

66.  p-n junction voltage can not be changed instantaneously just as
 Meaning:
 p-n junction voltage can not be changed instantaneously just as
current can be changed to turn-off (zero).
 Instead, the junction voltage responds to the change of current
for a limited time 66

67. 5.5.2. Reverse Recovery Transient
□ p+-n junction
□ Bias : +E ↔ -E
           
i) e(t) = +E (forward bias)
  i(t) = If ≈ E/R
(∵Junction voltage is small)
ii) e(t) = -E (t > 0)   (reverse bias)
   i(t) = Ir ≈ -E/R
Junction voltage and stored charge can not be changed instantaneously
(need some time)  Characteristics just as Fig (b) and (c) 67

68. tsd : Storage Delay Time68

69. Example 5.5
From eqn.(5-47) ;
Using Laplace transforms, 69

70. Example 5.5 (Cont.) Assuming that Qp(t)=qALppn (Eq. 5-52)
Since pn(t) = 0 when t = tsd, 70

71. 5.5.4. Capacitance of p-n Junctions
(1) the junction capacitance (due to dipole in transition region)
      ; Dominant under reverse bias
(2) the charge storage capacitance (due to slow change in voltage responding
to the change of current ← charge storage effect) ; Dominant under forward bias
Fig. Equivalent circuit of a diode
         Cs : charge storage capacitance
         Cj : junction capacitance 71

72. 5.5.4. Capacitance of p-n Junctions (Cont.)
The relationship between the charge Q and voltage, V within transition
region :
(5-56)
(5-57)
Charge at one side of the junction,
(5-58) 72

73. 5.5.4. Capacitance of p-n Junctions (Cont.)
From Eq. (5-23),
(5-59)
Eq. (5-59) → Eq. (5-58) ;
(5-60)
→   73

74. ▶ ; Voltage Variable Capacitance (→ Varactor)
Since charge Q is nonlinear to (V0 - V), junction capacitance, when the reverse bias is applied, becomes
(5-61)
(5-62)
▶ ; Voltage Variable Capacitance (→ Varactor) 74

75. For p+-n junction ( Na >> Nd ),
(5-63)
▶ From the Junction Capacitance, the impurity concentration in the area
of lightly doped can be obtained. 75

76. For the case of Forward-bias,
(5-64)
(For V >> V)
(5-65) 76

77. a-c component of current ;
a-c conductance ;
(5-66)
a-c component of current ;
where
▶         →  Serious limiting factor for high speed devices!! 77

78. 5.6. Deviations from the Simple Theory
Effects of Contact Potential on Carrier Injection
Diode equation in p-n junction :
At p+-n junction,
(5-68)
※ Recall: (Eq. 3-19);   78

79. If n region is highly doped,
If the forward-bias is , the current due to the injected hole into n-type becomes nearly zero. Since the Fermi-level is near the valence band on the p-side (Evp), the energy difference at thermal equilibrium will be
If n region is highly doped, 79

80. Fig. 5-24. Example of contact potential for heavily doped p-n junction
(a) Thermal Equilibrium
            (b) Near the maximum forward bias V=V0 80

81. below the bandgap of the material (Eq. 5-68) .
▶ Therefore, no diode current until the forward bias voltage, which is just
below the bandgap of the material (Eq. 5-68) .
▶ For the case of actual diode, the limit of the forward bias voltage is the
contact  potential.
▶ Comparison : Due to simple theory of a diode, increase in current follows
to exponential form. The assumption at that time was low level
injection). ( ) 81

82. compared to the majority concentration at thermal equilibrium
▶ High level injection condition: excess minority carrier can’t be ignored
compared to the majority concentration at thermal equilibrium
( comparable).
For high level injection;
(5-70) 82

83. (a) Low-level Injection (b) High-level Injection
▶ For V << V0 (low-level injection) & pp, nn >> ni, → simple eqn. (5-36)
(a) Low-level Injection                (b) High-level Injection 83

84. Fig. 5-23. I-V characteristic curves in heavily-doped p-n
junction diode (effects of contact potential at forward bias)
(a) Ge, Eg≈0.7 eV; (b) Si, Eg≈1.1 eV;
(c) GaAs, Eg≈1.5 eV; (d) GaAsP, Eg≈2.0 eV 84

85. Recombination and Generation in the Transition Region
▶ For the ideal diode equation, it was assumed that net generation
   -recombination in the depletion region was zero.
▶ Recombination with forward bias;
      - A new diode equation :
                             
where n is the ideality factor (n=1~2).
(n depends on the material and temperature.)
▶ Within transition region (W), recombination current
                85

86. Recombination in the Transition Region (Cont.)
▶ For the neutral regions (n , p), recombination current
▶ The ratio of the two currents ; 86

87. Recombination in the Transition Region (Cont.)
Since If
, 
Then, the effect on the recombination current ( ) within transition region becomes increased.
Ex) 87

88. Generation in the Transition Region
▶  Generation with reverse bias
; Since carrier concentration in depletion region at reverse bias is smaller than
that of thermally generated EHP, generation becomes dominant. 88

89. Generation in the Transition Region (Cont.)
Thermal generation of EHPs within a diffusion length & diffuse to
the  transition region (fall down)       swept to the other side of the
junction by E
(b) Within transition region, generation of carriers through
recombination center   
 In reverse bias condition,
       generation rate >    recomb. rate 89

90. Generation in the Transition Region (Cont.)
   
    For a large bandgap material
    
 Band-to-band thermal generation in neutral region can be
nearly neglected.
 Carrier generation at Er within W becomes dominant.
 Reverse saturation current in neutral region is nearly independent
of bias voltage.
 Generation current within W       increase with reverse bias 90

91. Generation in the Transition Region (Cont.)
(a) Ideal & (b) Real      91

92. Fig. 5-26. Carrier Capture & Generation in Recombination Center
(Extra)
Fig Carrier Capture & Generation in Recombination Center 92

93. 5.6.3. Ohmic Losses * Rp or Rn : series resistance of the P and N
                voltage drop in neutral region or at external contacts  93

94. Ohmic Losses (Cont.) Va : external voltage applied to the device
▶ Junction Voltage ;  V = Va - I[Rp(I) +Rn(I)]   ( 5-73)
                Va : external voltage applied to the device 94

95.  Overall real I-V Characteristic of p-n junction95

96. 5.6.4. Linearly Graded Junctions96

97. Linearly Graded Junctions (Cont.)
  Poisson Eq ;
Boundary Condition; 97

98. Linearly Graded Junctions (Cont.)
▶ V(x) = ? 98

99. Linearly Graded Junctions (Cont.)
Boundary Condition; 99

100. Linearly Graded Junctions (Cont.)
100

101. Linearly Graded Junctions (Cont.)
101

102. 5.7. Metal-Semiconductor Junctions
Schottky Barriers & Rectifying Contacts
102

103. Schottky Barriers (Cont.)
Work function of metal
Work function of s/c
Electron affinity
103

104. Schottky Barriers (Cont.)
104

105. Table. Electrical Nature of Ideal MS Contacts
105

106. Fig. 5-33. Effects of Forward- and Reverse-bias at Schottky barrier
(5-77)
106

107. For the case of P-type Semiconductor
107

108. Ohmic Contacts
108

109. Ohmic Contacts (Cont.)
▶ Easy flow of majority carriers from S/C to metal.
▶ No depletion region
▶ A low impedance contact (heavy doping between Metal and S/C;
   For example, n+ doping on n-type semiconductor before
metalization)
▶ Linear I-V characteristics
109

110. Ohmic Contact Formation
110

111. Ohmic Contact (Cont.)
▶ Heavy doping of S/C beneath the MS contact to facilitate ohmic contact  formation
▶ Over 1017/cm3, significant tunneling can take place through the
thin upper  portion of the barrier.
  ▶ For doping exceeding 1019/cm3, the entire barrier becomes so
narrow that even low energy majority carriers can readily
transfer between the  semiconductor and metal via tunneling process.
111

112. 5.8. Hetero Junctions
In ideal case,
112

113. Hetero Junctions (Cont.)
How to draw the band diagram in Hetero-junction
   (Assume that we already knew the band offsets, )
113

114. Hetero Junctions (Cont.)
Step 1. Equalize the Fermi level of the two S/C (with different
bandgap)  do not draw the region of transition area.
Step 2. at the point of x=0, mark the band offset with maintaining
band gap
Step 3. Just connect each level of conduction and valence band.
Ex. 5-6) Hetero-junction (GaAs-AlxGa1-xAs)
114

115. Hetero Junctions (Cont.)
▶ Draw the band diagrams,  i) N+-Al0.3Ga0.7As/n-GaAs
                                ii) N+- Al0.3Ga0.7As/p+-GaAs
sol)   
115

116. Hetero Junctions (Cont.)
116