半导体器件物理复习课件leture19_review

21
What causes scattering?
• • • • • Phonon Scattering Ionized Impurity Scattering Neutral Atom/Defect Scattering Carrier-Carrier Scattering Piezoelectric Scattering
7
Law of Mass-Action
8
Carrier Density with Doping
9
Temperature Dependent Concentration
10
R-G for Direct Bandgap
Conserve momentum and Energy
1. Eg = hn
2. Dk = kphoton = 2pn/c
47
High Frequency Response
48
Putting the Terms Together
49
HBT
• The use of a wide bandgap emitter has two benefits:
• The use of a wide bandgap collector has benefits:
cn c p n p o
R
Then net recombination becomes:
pn n
2 i
Normalized R
ET Ei o p n 2ni cosh kT
R is large for ET close to Ei and then drops off rapidly. Traps near mid-gap are much more efficient as recombination centers. 15
No scattering
25
Diffusion
26
Drift v.s Diffusion
x
E2 > E1 E1
x
t
<x> ~ mEt <x2> ~ Dt
t
27
Einstein Relationship
m and D are connected !!
Jn
drift
+ Jn
diff
= qnmnE + qDndn/dx = 0
22
Velocity Saturation in Si/Ge
23
Velocity Overshoot & Inter-valley Transfer
24
Ballistic Transport
Random scattering events (R-G centers)
1 2 3 mvth kT 2 2 vth 107 cm / sec
12
Indirect (Trap-assisted) Recombination
Phonons
Phonons
Energy space
Real space
Nonradiative Recombination (Ge, Si FETs, solar cells ) 13
Steady State Recombination Rate R
(ET-Ei)/kT
Auger Recombination
Phonon(heat)
Phonon
X Energy space X
Real space
III-Vs, highly doped samples (Opposite process is impact ionization)
16
Impact Ionization
compositionally graded bases elimination of band spikes
50
MOS
51
Exact Solution…
52
Small Signal Equivalent Circuit
On the order of kHz
53
Small Signal Equivalent Circuit
46
BJT Design
• While basic transistor operation is simple, its optimum design is not • In general, good transistor gain requires that the emitter doping be larger than base doping, which in turn should be larger than collector doping • Base doping low: current crowding, early effect • Collector doping low: kirk effect (base push out) • Emitter Doping high: gain is reduced
57
Nonideal case
• Flat band voltage • Threshold voltage shift due to trapped charges • Physics of interface traps
58
Grand Challenges in Electronics
59
Thin Film Organic Transistors
Metal
Metal or Semi-Metal
Semiconductor
Insulator
For materials with odd number of electrons per atom, they must be metal. 5
Carrier Distribution
6
Boltzmann vs. Fermi-Dirac Statistics
n(x)= Nce-[EC(x) - EF]/kT = Nce-[EC -EF - qV(x)]/kT
dn/dx = -(qE/kT)n
qnmnE - qDn(qE/kT)n = 0
Dn/mn = kT/q
28
Minority Carrier Diffusion Equations
∂Dnp ∂t ∂2Dnp ∂x2 ∂2Dpn ∂x2 Dnp n
33
Junction Capacitance
34
Dielectric Relaxation Time (Majority Side)
35
Diffusion Capacitance for Minority Carriers
36
Schottky Diode
37
AC Response
38
No Diffusion Capacitance in Schottky Diodes
symmetrical device reduced charge storage in saturation reduced collector offset voltage higher collector breakdown voltage allows heavy base doping allows moderate emitter doping
= Eg/ħc Eg ~ 1.2 eV Dk ~ 6/mm << BZ = 2p/a [Å ] Optical transitions almost vertical !!
11
Indirect Bandgap
Since photons make vertical transitions, they won’t conserve momentum for indirect band-gaps (Si, Ge)
39
Schottky contacts
40
Ohmic Contact
41
Ohmic Contact vs. Schottky Contacts
42
BJT
43
Gummel Plot and Output Characteristics
44
Current Gain
45
How to Make a Good Silicong events (R-G centers)
The field gives a net drift superposed on top
1 2 3 mvth kT 2 2 vth 107 cm / sec
105 cm(100nm) c 1012 sec(THz )
• Bandgap engineering has potential benefits: • HBTs have the potential for THz cutoff frequencies. However, it has yield issues and heating and contact R problems.
The field gives a net drift superposed on top
Ballistic Transport happens when the total travel distance is smaller than the mean free path
105 cm(100nm) c 1012 sec(THz )
14
Steady State Recombination Rate R
To get more of a physical feel for how R depends on ET it’s useful to make the assumption that electron and hole capture cross sections are equal: