department of physics,john bardeen, william shockley, walter brattain 1948 bell labs. bipolar...
TRANSCRIPT
Shingo Katsumoto
Department of Physics,
Institute for Solid State Physics
University of Tokyo
Physics of Semiconductors
8th 2016.6.6
Outline today
Review of pn junction
Estimation of built-in potential
Depletion layer width
Injection of minority carriers
Bipolar junction transistor Base-Collector characteristics
Collector-Emitter characteristics
Depletion layer with reverse bias voltage
Effective capacitance and reverse bias voltage
pn junction FET
Schottky barrier
MES FET
MOS FET
Review of pn junctions
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p n
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−𝑤𝑝 𝑤𝑛
E x
Balance of diffusion and
drift currents.
Minimize 𝐹 = 𝑈 − 𝑇𝑆
Depletion layer
Space charge
Built-in electric field
Built-in potential 𝑉bi 𝐸F
Estimation of built-in potential concentration
electrons holes
n-layer
p-layer
number of sites: N number of sites: N
particle number: 𝑁1 particle number: 𝑁2
Number of cases:
Estimation of built-in potential (2)
Stirling approximation: ln 𝑁! ≈ 𝑁ln𝑁 − 𝑁
:Mixing entropy
Depletion layer width E x −𝑤𝑝 𝑤𝑛
𝑁A 𝑁D
Current voltage characteristics
External voltage V
Forward bias (against 𝑉𝑏𝑖 ) : lowers barrier for diffusion current 𝑛𝑛
Equilibrium
Electrons
Current balance
Injection of minority carriers
0
0
V
J
minority carrier
current Barrier overflow
Fate of injected minority carriers:
Radiative recombination
Non-radiative recombination
ℎ𝜈 light emitting
diode
phonon
electron Diffusion with lifetime:
Minority carrier
diffusion length
A question for you
0
0
V
J
Consider an ideal light emitting
diode, which has no non-radiative
recombination. Every injected
carrier emits a photon with the
energy 𝐸g. Now apply a voltage
𝑉1 < 𝐸g/𝑒 and a current 𝐽1 flows.
The power of light emission is
𝑃L = 𝐸g𝐽1/𝑒 . 𝐸g
𝑒
𝑉1
𝐽1
On the other hand, the electric power source gives the power
𝑃S = 𝐽1𝑉1, which is smaller than 𝑃𝐿! Does the LED create
energy? Or what is happening inside the LED?
External injection of minority carriers: Solar Cells
V
J
0
0
dark
illuminated
𝑒𝑣𝑛Δ𝑛𝑝
External injection
Two types of transistors
John Bardeen, William Shockley,
Walter Brattain 1948 Bell Labs.
Bipolar junction transistor
n n p
Field effect transistor
p
n
Bipolar transistor structures and symbols
Bipolar transistor structures and symbols
PNP type NPN type
Similar characteristics PNP and NPN: complementary
Base-Collector characteristics
n n p
E B C
−𝐽C
−𝐽 C
𝑉BC
𝐽E
𝑉BC
𝐽E
Base-Collector characteristics
n
p n
𝑉BC
e-
e- e-
e-
e-
e- e+
e+ e+
e+
e+
𝐽𝐸 𝐽𝐶
Collector-Emitter characteristics n n p
E B C 𝐽𝐶
Current amplification : Linearize with quantity selection
𝐽𝐶 = ℎ𝐹𝐸 𝐽𝐵
Emitter-common current gain
Linear approximation of bipolar transistor
⋃ ≖ ∱ ≊ ∲
∡ ∽ ⋃ ≈ ∱ ∱ ≈ ∱ ∲ ≈ ∲ ∱ ≈ ∲ ∲
∡ ⋃ ≊ ∱ ≖ ∲
∡ ∺
𝑗1
𝑉1
𝑉2
⋃ ≶ ∱ ≪ ∲
∡ ∽ ⋃ ≨ ∱ ∱ ≨ ∱ ∲ ≨ ∲ ∱ ≨ ∲ ∲
∡ ⋃ ≪ ∱ ≶ ∲
∡ ∽ ⋃ ≨ ≩ ≨ ≲ ≨ ≦ ≨ ≯
∡ ⋃ ≪ ∱ ≶ ∲
∡
(lower case:
local linear approximation)
Hybrid matrix
h-parameters
𝑗2
Depletion layer width with reverse bias voltage
+ - + +
+
- - -
p n
−𝑤𝑝 𝑤𝑛
𝑉𝑏𝑖 + 𝑉 Poisson equation
Depletion layer width with reverse bias voltage (2)
Charge per unit area:
Effective capacitance and reverse bias voltage
V
−𝑉𝑏𝑖
Doping profiler
Varicap diode
KB505 Frequency modulation
Phase lock loop
pn junction field effect transistor (JFET)
Circuit symbols
D
G
S
D
G
S
n-channel p-channel
pn junction FET
y
L
wd (y)
n
p+
2wt S D
G
p+ G
-NDe
Vg
Vch(y)
pinch off (internal) voltage:
Only valid for wd < wt/2.
conductivity
electric field
channel width
I-V characteristics of JFET
2N5459
From Wikipedia
R(Vg) is non-linear
Schottky barrier
𝐸F
𝑒𝜙𝑀
𝑒𝜙𝑆
𝐸D 𝐸F
𝐸c
𝐸v
𝐸F
𝐸c
𝐸v
𝑤𝑑
metal semiconductor
x 0
- Q
Walter Schottky
1886-1976
Charge balance:
Voltage V --> barrier height e(Vs-V)
MES-FET
MOS-FET
enhancement
depletion
inversion
Simplified
CMOS inverter
circuit
Low leakage
current
Single gate input
both on/off switch
Exercise A
A-1. p-Ge has Seebeck coefficient of 300mV/K and n-type
Bi2Te3 -230mV/K. If one makes a thermocouple from these
two materials, how high is the voltage caused by the
temperature difference of 50K.
A-2. Obtain expressions for electron mobility and for
diffusion constant in terms of the conductivity and the Hall
coefficient.
Submission deadline: 2016.6.20