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