Temperature Sensors
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Thermo-Mechanical Sensors
Thermoresistive Sensors
Thermocouples
Junction-Based Thermal Sensors
Thermo-Mechanical Sensors
αL =
1 ∆L
∆T L
Coefficient of thermal expansion
Operating principle of thermal bimorph switch
Thermoresistive Sensors
Thermoresistive temperature transducers are based on the fact that the
resistance (or resistivity) of most materials changes with temperature.
αR =
1 ∆R
∆T R
Temperature Coefficient of Resistance
Thermistor
A form of resistive device that possesses a large
temperature coefficient of resistance over an
extended temperature range.
Typical: 40000-60000ppm/K for NTC thermistor
Classification:
• negative temperature coefficient (NTC) thermistor
• positive temperature coefficient (PTC) thermistor
Resistivity and TCR of some metals
NTC Thermistor
Material:
Sintered mixture of metal oxides of Mn, Ni, Co, Cu, Fe...
Electrical Characteristics:
σ = Nq µ
N = density of charge carriers
µ = mobility of the carriers
σ ∝ e(-E /kT)
a
R = R∞ e ( E
α=
a
Ea: activation energy
/ kT )
E
1 dR
= − a2
R dT
kT
TCR
PTC Thermistor
Material: Metals, Single-crystal silicon, polysilicon
1. Freeze-out Region
1/ 2
⎛ EC − E D ⎞
⎟
2 kT ⎠
⎛ N DN C ⎞ ⎜⎝ −
n=⎜
⎟ e
⎝ 2 ⎠
⎛ EC − E D ⎞
⎟
kT ⎠
⎜−
⎛ N D− N A ⎞
⎜
⎟
or ⎜
N C e⎝
⎟
⎝ 2N A ⎠
(Depending on compensation conditions)
2. Extrinsic Region
(Saturation Region)
n = N D , p = ni2 / N D ≈ 0
3. Intrinsic Region
n = p = ni = ( N C NV ) e
1/ 2
⎛ Eg ⎞
⎜−
⎟
⎝ 2 kT ⎠
Electron Concentration - Temperature relationship
Resistivity of Single Crystal Silicon
ρ = (nqµ n + pqµ p ) −1
Fermi level as a function of temperature
and impurity concentration.
µ n ∝ T −2.5 ,µ p ∝ T −2.7
( for lightly doped silicon)
Resistivity of Silicon (Nd=1015cm-3)
TCR for single-crystal
silicon with usual
doping levels: in the
order of 0.5%K-1
Junction-Based Thermal Sensors
⎛ qVD ⎞
⎡ ⎛⎜ qVkTD ⎞⎟ ⎤
⎜
⎟
⎝
⎠
⎝ kT ⎠
− 1⎥ ≈ I S e
I D = I S ⎢e
⎢⎣
⎥⎦
⎛ Dn ni2 D p ni2 ⎞
⎟
+
I S = qA⎜
⎜L N
⎟
⎝ n a Lp N d ⎠
ni2 = N C NV e
−
Eg
kT
IS doubles per 5 °C
kT02
ln(2)
∆T = T − T0 =
Eg
⎛ 26mV
≈⎜
⎝ 1.12V
, N C NV ∝ T 3
3
⎛ 1
1 ⎞
⎞
⎟(300 K ) ln(2) ≈ 4.83K
⎠
Neglect temperature
⎛ T ⎞ − E g ⎜⎜⎝ kT − kT0 ⎟⎟⎠ dependence of D/L Practical circuit configuration:
I S (T ) / I S (T0 ) = ⎜⎜ ⎟⎟ e
to measure the voltage across the
⎝ T0 ⎠
I S (T ), I S (T0 ) : reverse saturation currents at T and T0 diode when operated at fixed ID
Approximation : (exponential term dominates)
I S (T ) / I S (T0 ) ≈ e
⎛ 1
1
− E g ⎜⎜
−
kT
kT
0
⎝
⎞
⎟⎟
⎠
I S (T ) E g ⎛ 1 1 ⎞ E g
⎜⎜ − ⎟⎟ ≈ 2 (T − T0 )
=
ln
I S (T0 ) k ⎝ T0 T ⎠ kT0
VD (T ) =
kT
I
ln D
q
I S (T )
Blackbody Radiation
Planck Radiation law:
2πε hc 2
M λ (T ) = 5 hc / λ kT
(W .cm −2 .µ m −1 )
− 1)
λ (e
+∞
Stephan-Boltzmann law: M (T ) =
∫ M λ (T )d λ = εσ T
4
(W .cm −2 ) M (293.15K ) = 41.9mW .cm −2
0
Wien Displacement law: λmax
2897.8
( µ m)
=
T (K )
Spectral Exitance of a blackbody at Room
temperature
λmax = 9.9 µ m
λmax = 9.3µ m
for T=293.15K (20o C)
for T=310.15K (37 o C)
Material
Emissivity
Al foil
0.04
Steel (polished)
0.07
Brick
0.93
Glass
0.95
Human skin
0.98
Water
0.96
Wood
0.9
Concrete
0.95
Infrared Wavelength
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Near Infrared (NIR): 0.7 to 1.5 µm.
Short Wavelength Infrared (SWIR): 1.5 to 3 µm.
Mid Wavelength Infrared (MWIR): 3 to 8 µm.
Long Wavelength Infrared (LWIR): 8 to 15 µm.
• Far Infrared (FIR): longer than 15 µm
Photon Detectors Materials
Material Name
Symbol
Eg (eV)
λc
(µm)
Operating Temp. (K)
Silicon
Si
1.12
1.1
163 - 300
Mer-Cad-Tel
HgCdTe
Indium Antimonide
InSb
0.23
5.9
30
Arsenic doped Silicon
Si:As
0.05
24
4
1.00 – 0.09 1.24 – 14
hc
1.24eV
=
E=
λ λ ( µm)
20 - 80
Photon detectors
E=
hc
λ
=
1.24
eV < 0.15eV for thermal infrared Wavelengths
λ ( µ m)
Absorption coef.cient for various photodetector materials in
spectral range of 1–14 um (from Rogalski)
LWIR Imaging: Applications
•Night vision
•Perimeter surveillance
•Vehicule/personnel detection
•Chemical Agents detection
•Firefighting
•Industrial Process Monitoring
•Law enforcement
•Driver’s vision enhancement
LWIR Thermal Detectors
Thermal detectors first converts the radiation to heat, then
measure the temperature increase
•William Herschel, 1800
‘‘Thermometer No. 1 rose 7 degrees in 10 minutes by
an exposure to the full red coloured rays. I drew back
the stand....... thermometer No. 1 rose, in 16 minutes, 8
3/8 degrees when its centre was 1/2 inch out of the
visible rays.’’
•Golay cell
Gas Expansion
•Bimorph
Mechanical Deflection
•Thermoelectric
Voltage
•Pyroelectric
Electrical Polarization
•Bolometer
Resistance change
Bolometers
A Bolometer uses a thermistor to measure radiation-induced
temperature increase on a thermally insulated absorber.
I bias