LOW FREQUENCY NOISE
CHARACTERIZATION AND MODELING AT
CRYOGENIC TEMPERATURES OF SI-GE
BIPOLAR TRANSISTORS
C.Arnaboldi, G.Boella, G.Pessina
Istituto Nazionale di Fisica Nucleare
INFN e Dip. di Fisica della Bicocca
U2
P.za della Scienza 3, 20126 Milano, Italy
Istituto Nazionale di Fisica Nucleare
Sez. di Milano
Università degli Studi di Milano-Bicocca
Facoltà di Fisica
SUMMARY
1.
MOTIVATIONS FOR SiGe STUDY;
2.
Heterojunction-Bipolar-Transistor PRINCIPLE OF OPERATION AT COLD;
3.
STATIC CHARACTERISTICS VS TEMPERATURE;
4.
SERIES NOISE IN THE LOW FREQUENCY REGION VS TEMPERATURE;
5.
PARALLEL NOISE IN THE LOW FREQUENCY REGION VS TEMPERATURE.
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ARGUMENT
1.
MOTIVATIONS FOR SiGe STUDY;
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FIELDS OF APPLICATION
IT EXISTS A LARGE CLASS OF CRYOGENIC DETECTORS THAT SHOULD TAKE
ADVANTAGE BY THE USE OF A COLD FRONT-END.
HERE WE HAVE A FEW EXAMPLES:
•
BOLOMETERS;
•
TRANSITION EDGE DETECTORS;
•
TUNNEL JUNCTIONS;
•
….
IN ADDITION, MANY CONVENTIONAL DETECTORS CAN IMPROVE THEIR
ENERGY RESOLUTION BY LOWERING THEIR PARALLEL NOISE:
•
•
•
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Ge DETECTORS;
Si DETECTORS;
…
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PRINCIPLE OF OPERATION OF CRYOGENIC DETECTORS
AT COLD THE HEAT CAPACITY IS VERY SMALL AND THE ENERGY LEFT BY A
PARTICLE MAY DETERMINE A MEASURABLE TEMPERATURE INCREASE.
(ABSORBING
CRYSTAL)
∆T =
U
CT
RL
IMPINGING
PARTICLE
OF
ENERGY U
vBIAS
PREFERRED
SOLUTION: COLD
FRONT-END
VO
(THERMISTOR OR ANY
OTHER CRYOGENIC SENSOR)
CTOT
KTOT
HEAT SINK:
10mK TO 150mK
THE TIME CONSTANTS ARE DOMINATED BY THE THERMAL CONDUCTANCES
COMBINED WITH THE HEAT CAPACITIES. THE SPEED OF SOUND IS THE MAXIMUM
RATE AT WHICH THE THERMAL SIGNALS ARE TRANSMITTED.
CRYOGENIC DETECTORS ARE NOT FAST. THEIR BANDWIDTH EXTENDS AT
MOST TO A FEW HUNDRED OF KHz.
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FRONT-END REQUIREMENTS FOR CRYOGENIC DETECTORS
FOR THE PARTICULAR CASE THE DETECTORS HAS A LARGE IMPEDANCE
(FOR INSTANCE µ-BOLOMETERS), THE FRONT-END SHOULD WORK AT
CRYOGENIC TEMPERATURE, TO REDUCE PARASITIC EFFECTS.
THE SMALL FREQUENCY BANDWIDTH IS A STRONG
REQUIREMENT FOR A LOW NOISE AT SMALL FREQUENCIES.
STRINGENT REQUIREMENTS SUMMARY
LOW SERIES NOISE AT LOW FREQUENCIES
LOW PARALLEL NOISE AT LOW FREQUENCIES
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PERFORMANCE EXAMPLE
100
nV/√Hz
103 k
121 k
CGS≈6 pF
10
MX11BD
T= 111 K
IDS=1 mA
VDS=1 V
UP TO NOW BEST NOISE
PERFORMANCES HAS BEEN
OBTAINED WITH Si-JFET
TRANSISTORS, THAT ARE ABLE TO
WORK WITH ADEQUATE RESPONSE
DOWN TO ABOUT 100 K.
1
131 K
Hz
0.1
1
10
100
1000
10000
100000
THE ENERGY RESOLUTION IS LIMITED
ONLY BY THERMODYNAMIC: THE
PHONON ENERGY IS ONLY A FEW µ eV
AT A FEW TENS OF mK.
WHEN THE REQUIREMENTS ARE
SATISFIED, VERY GOOD RESULTS ARE
OBTAINED.
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SUMMARY
1.
2.
Heterojunction-Bipolar-Transistor PRINCIPLE OF OPERATION AT COLD.
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CURRENT GAIN OF A HOMO-JUNCTION BIPOLAR TRANSISTOR
B-C=REVERSE BIASED
THE COLLECTOR CURRENT IS
CONTROLLABLE BY THE BASE
CURRENT.
IE
IB
IC
E-B=FORWARD BIASED
Le=DIFFUSION LENGTH
Ne=ELECTRON CONCENTRATION IN THE E
BY SUPPOSING ABSENT THE
RECOMBINATION CURRENT WITHIN THE
BASE WE CAN APPROXIMATE THE
CURRENT GAIN AS:
2
n
I
L N
⇒ β = h FE = C ÷ e e ib
2
I B Wb N b n ie
nie=INTRINSIC CONCENTRATION IN THE E REGION
Wb=BASE WIDTH
Nb=HOLE CONCENTRATION IN THE B
nib=INTRINSIC CONCENTRATION IN THE B REGION
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CURRENT GAIN OF A HOMO-JUNCTION BIPOLAR TRANSISTOR
2
Le N e n ib
⇒ β = h FE =
÷
2
I B Wb N b n ie
IC
TO INCREASE THE CURRENT GAIN:
DRAWBACKS:
DRAWBACKS
MAKE Wb << Le
BASE CROWDING
MAKE Nb SMALL
BASE SPREADING RESISTANCE INCREASE
MAKE Ne >> Nb
BAND-GAP NARROWING
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