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