non gaussian noise in quantum wells answers and upon questions
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Soreq. Non Gaussian Noise in Quantum Wells Answers and UPON Questions. Yossi Paltiel and Grzegorz Jung Solid State Physics Group, Soreq NRC Department of Physics, Ben Gurion University. Contents. Quantum wells and QWIPs Noise in wells Non Gaussian noise in wells - PowerPoint PPT PresentationTRANSCRIPT
Non Gaussian Noise in Quantum Wells
Answers and UPON Questions
SoreqYossi Paltiel and Grzegorz Jung
Solid State Physics Group, Soreq NRCDepartment of Physics, Ben Gurion University
Contents
• Quantum wells and QWIPs
• Noise in wells
• Non Gaussian noise in wells
• Our simple model (what we think we understand)
• UPON Open issues
This work is a part of M.Sc. thesis of Noam Snapy and Avi Ben Simon
Quantum well infrared photodetectorsQWIPs
e- Voltage bias
E = hν
x50
Photon excites an electron to produce a measurable current
The detection of different wavelengths can be easily controlled by changing the well width Lw, and the energy barrier height h.
h - barrier height, changes with Al concentrationLw - width of the well, changes with the thickness of the layer
Lw
h
22*
22
2n
LmE
wn
m* effective mass,
n - an integer
Quantum well
(a)
(b)
(c)
-
Continuum
Conductionband
Bound state
Z
Energy
-
-
E��������������
Current Transport in QWs
(d)
(a) Thermionic emission(b)Thermally assisted tunneling(c) Ground state sequential tunneling(d) photocurrent
Mechanisms contributing charge carriers to the current flow in the conduction band.
Doping can be n or p
Noise in QWs
• Generation-recombination (GR) noise is accepted as the dominant noise source in bound to continuum QWs.
• GR noise is Gaussian.
• A general theoretical formula for the PSD of the GR noise at low frequencies was provided by Beck:
Shot noise
( ) 4 12
ci
PS V qIg
gIqVSiPc4)(
1
GR noise
12)(
cPi gIqVS
22
2
1
14
gqIfIS ni
Noise one expects to see in quantum wells
Gaussian noise…and white noise at low frequencies
Lorentzian power spectral density of the GR noise is frequency independent up to a cutoff frequency, located in the GHz range, above which it decays as 1/f2
Measurement system
Our samples system consist of 5 wells with the same structure in both n and p type
AlGaAsGaAs
QWIP StructureGaAs semi insulating substratep+ GaAs Buffer 500 nm 2 x 1018 cm-3
GaAs Spacer 100 nm undopedBarrier AlGaAs 30% 50 nm undoped QW GaAs p+ 4.6 nm 5 x 1017 cm-3
Barrier AlGaAs 30% 50 nm undopedGaAs Spacer 100 nm undopedp+ GaAs contact 500 nm 2 x 1018 cm-3
Shielded Dewar
grounded to TI
77K
Home made or Femto transimpedance amplifier
Blackbody radiation
Grounded Out shield
Battery
Kithley 6487 picoampermeter
Dual channel spectrum analyzer SR785
Computer
PSD of n and p-QWs at 77K
100 1000 100001E-28
1E-26
1E-24
1E-22
1 V
1/f2
4 V
3.5 V
2.5 V2 V
3V
PS
D [
A2 /H
z]Frequency [Hz]
Si=S
0e2.7V
1000 100001E-27
1E-26
1E-25 Si=S
0e1.23V
PS
D (
A2 /H
z)
Frequency (Hz)
-3.8V
-1.6V
-2.2V
-3V
-3.4V
1/f1.5
The high frequency plateau represents the GR noise level, while the low frequency plateau represents the excess noise.
n type wells p type wells
Additional noise at certain voltages
Going to 1/f2 AT LOW FREQUENCIES in both cases – Open question
Time Domain Measurements in p-QWs
RTN -like noise
-1x10-8
0
1x10-8
-5V
(c)
-5x10-10
05x10-10
Cur
rent
[A] -2.5V
(b)
-5x10-11
0
5x10-11
Time [ms]
-0.5V
30 0 1800
Count
(a)
Non Gaussian noise appears at intermediate bias levels
Discreet noise???
Gaussian noise
T=77 K
Time domain analysis
0.0 0.5 1.0100
101
102
1 2 3 4 510-11
10-10
10-9
SD
[A
]
Voltage [V]
SDdown
up0.28ms
down
Cou
nt
Time [ms]
down0.16ms
100
101
102
1 2 3 4 510-11
10-10
10-9 SDup
SD
[A
]
Voltage [V]
up
-2.5 V
-0.5
0.0
0.5
1 2
-2.5V(a)
Am
plitu
de (
nA)
0 0 500 1000 1500Time (ms)
Time (ms)
(b)
Counts
0.0 0.5 1.01
10
100 down0.16ms up0.28ms
down
Cou
nts
Time (ms)
0.0 0.5 1.0
up
Normalized skewness of the noise
33/ 2
1
1( )
n
ii
skewness x xnD
-4 -3 -2 -1
-0.05
0.00
0.05
Ske
wne
ss
Voltage (V)
77K
-5 -4 -3 -2 -1 0
-0.01
0.00
0.01
Volage (V)
Ske
wn
ess
1000K
The amount of asymmetry in the noise amplitude distribution is characterized by the third moment, skewness.
Gaussian noise has no third moment – non Gaussian noise
n
ii xx
nD
1
2)(1
P type N type
Trying to understand…
• New type of noise in quantum wells.
• Appears in both n-type and p-type wells. More pronounced in p-type systems.
• Lorenzian spectra with the cutoff at low frequencies.
• Non Gaussian.
I-V for n- and p-QWs
n-type QWs :
Characterized by very low capture probability, therefore more widely used in devices.
-6 -4 -2 0 2 4 6
1E-9
1E-7
1E-5
Cu
rre
nt
[A]
Voltage (V)
1000K 300K 77K
-3 -2 -1 0 1 2 3
1E-9
1E-7
1E-5
e-2.5 Ve-1.8 V
Cu
rre
nt (
A)
Voltage (V)
p-type QWs:
Characterized by very high capture probability. Strong tunneling effects.
non exponential increase of the current
Low frequency cutoff p type
Frequency domain:
102 103 10410-28
10-26
10-24
10-22
1/f2
4.5V
3.5V
2.5V1.5V
0.5V
Si [A
2/H
z]
Frequency [Hz]
Dark current noise spectrum for different positive voltages at 77K.
Bias dependence of the cut-off frequency determined from the spectra.
VfVf cc exp0
Exponential growth with different exponents a = 0.6 and a = 1.45 below and above 2.5 V, respectively.
1 2 3 4102
103
104
105
Cut
-off
Fre
quen
cy [H
z]
Voltage [V]
Non Gaussian noise level and I-V
-4 -2 0
0.6
1.2
-4 -2 0
0.6
1.2 77K
Gai
n
Voltage (V)
300K
1E7
1E9
1E11
-5 -4 -3 -2 -1 0
2
3
4 (b)
Voltage (V)
Diff
ere
ntia
l R
esi
sta
nce
(
)
1000K 300K 77K
No
rma
lize
d
PS
D (
1/T
Hz)
(a)
Gainthe probability for electron to be collected
There is a clear correlation between I-V shape and noise levels
Non Gaussian noise in N-type wells vs. I-V
-6 -4 -2 0 2 4 6
1E-8
1E-6
0.02
0.04
0.06
10000c background radiation
Dark current
ST
D
I[A]
V [volts]
77k
plateau
STD
-4 -2 0
-0.01
0.00
0.01
skewness gain
V [volts]
ske
wn
ess
0.4
0.8
1.2
gain
Conclusions so far…
• Experiments suggest the same, or at least very similar, mechanism of excess non-Gaussian current noise in n and p-QWs. But is it true?
• Non Gaussian noise can be associated with two, or more, possible solutions to the current continuity equation.
• Each solution is associated with a different potential distribution, corresponding to a different resistance, and consequently different currents flowing in the system at the same voltage bias.
• The potential distributions are metastable and random switching between them results in non-Gaussian excess current noise.
Simple model
Possible mechanisms for NDR
• N type:– Intervallic scattering– Impact ionization
• P type:– Different tunnel rate of light and heavy holes ?– Impact ionization
Intervalley scattering“Quantum Gunn effect”
• NDC in bulk GaAs appears as a result of intervalley scattering between Γ, L and X conduction energy subbands.
• In n-QWs, at intermediate voltages under illumination, intervalley scattering results in current plateau and NDC in the homogenic equation of the current.
• The homogenic equation is composed of the dark current and the photocurrent.
hom [ ( ) ] ( )thc
L PI q n F g F
h
Open questions• Difference between N and P
– P more pronounced– Random telegraph noise only in P wells– Difference in high moments
– Due to difference in capture probability? Light/heavy holes?
• Discreet levels of noise – no real explanation
• No real match between I-V kink and noise kink in p type
• 5 wells system
• Difference between dark and under illumination noise
Summary
• Non Gaussian noise in both n and p type wells
• More preannounce in P type wells
• Attributed to nonlinear I-V and gain
• Two solutions to the continuity equation allow existence of metastable voltage states
• Some open questions; your suggestions are welcomed!
Nanodots crackling noise?
4 8 12 16-0.01
0.00
0.01
0.02
0.03
1 10 100 10001E-18
1E-17
1E-16
1E-15
1E-14
Si [
A2 /
Hz
]
Frequency [Hz]
1/ f 1.5
300K3V
I [A
/cm
2 ]Time [sec]
Crackling avalanche noise as measured in transport through transistor coupled to a nanodots system
internal avalanche dynamics with widely distributed amplitudes
crackling noise
n-GaAsGaAs
GaAs semi-insulating substrate
5nm
50nm
AlGaAs semi-insulating
Au Au
GaAs
Mathematically, Gaussianity means that every multipoint correlation function can be obtained by summing all factorizations into two-point products, each of which is replaced by the two-point correlation.
The most familiar functions characterizing noise records of some variable x( t ) are:
two-point correlation function
power spectral density
( ) ( ) ( )xC x t x t
0
( ) 4 ( )cos( )xS C d
1 2 3 1 3 2 2 3 1 3 2 1( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )x t x t x t x t C C C C C C
For Gaussian noise all higher order time correlation functions and any of their Fourier relatives are fully determined by S().
For example, assuming <x>=0,
Gaussian noise
•In the non-Gaussian noise higher moments are important and proper analysis requires measurements of multipoint correlations:
( ) , 2n
x t x n
Non-Gaussian noise
All the information contained in a record of a Gaussian noise is obtainable from S(). For Gaussian systems all the information can be
obtained from the response measurements.
Only non-Gaussian fluctuations provide information which is not available otherwise.
Just the mere non-Gaussian character of the noise indicates that it cannot be due to a combined action of many elementary fluctuators.
Random Telegraph Noise downupcf 112 Where: τup and τdown are the average life times at the up and down levels respectively.
Proposed model
2 QWs
E2E2
I in
Lp
"up" state"dn" state
Pc Iin IwIw Iw
E2
E1 =V/L p -E 2LogI in
Iw
E2
E1pc <<1
Two voltage distributions
pc ~1
Iin Iw
Lp
1 QW
)1-P c (I in
Pc I inLp E1 +L p E2 =V
LogI w
Iw =P c I in
No NDCPc Iin Iw
With NDC
Single State