Excess Noise Properties of GaN Nanowires

Presented by Liang-Chen Li

2006/12/22

Introduction

Random process[1]:

For a stationary random process X(t):

Cross spectrum :

For two signals X(t) and Y(t):

2

dttjtXfS

tjatX

x

nn

)exp()(2)(

)exp()(

2

dssjstYtXfS

tjbtYtjatX

xy

nn

nn

)exp()()(2)(

)exp()(;)exp()(

Introduction

1/f Noise: The power spectrum density of the fluctuation varies inversely as frequency.[2]

For semiconductors, the 1/f noise may arise due to the relaxation of the defects or the dynamics of groups of defects in a finite relaxation time.[3]

3

Lorentzian Noise: The Lorentzian noise is also known as “Burst noise”. [2]

When the kinetics of the fluctuation is characterized by a single

relaxation time, the spectral density is a Lorentzian function of

frequency.[4]

Sample -- Growth

The nanowires are grown by the Vapor-Liquid-Solid (VLS） process.[5]

In the quartz tube: Molten Ga + Catalyst:Au

From room temperature to the reaction temperature, 910 : at ℃a rate of 50 / min.℃

Kept constant for about 12 hours with the ammonia flow rate at 18 sccm.

Grown GaN nanowires are collected in the catalyst substrate.

4

SEM image of GaN nanowires. The diameter of the wire is 80.3 nm. (This image was provided by Mr. L. T. Liu from the laboratory of Prof. C. C. Chen in the Department of Chemistry, National Taiwan Normal University.)

Sample -- Fabrication

Al, Al/Ti, or Ti/Au electrodes of the nanowires are defined by the e-beam lithography.

SEM image is the sample J.

5

Sample -- Electrical properties

Two-wire I-V plots of the sample I at room temperature. The contacts of the wire are ohmic.

6

Sample Resistance () dw

A 4.0k 45nm

B 8.8k 160nm

C 11.2 k 72nm

D 17.7k 76nm

E 15.6k 80nm

F 23.4k 127nm

G 26.2k 133nm

H 28.4k 150nm

I 34.4k 137nm

J 44.3 k 144nm -4.0x10-4 -3.0x10-4 -2.0x10-4 -1.0x10-4 0.0 1.0x10-4 2.0x10-4 3.0x10-4 4.0x10-4-10.0n

-5.0n

0.0

5.0n

10.0n

GaN Nanowire with R = 34.4 k Linear fitting

Cur

rent

(A)

Voltage (V)

Table of resistance and diameter of

the sample

Instrumentation and measurement methods -- Instrument specification 7

The specification of our instruments: 1.Homemade JFET-input ultra low-noise voltage preamplifier[6]: Noise: (with very high Input impedance)

If the cross spectrum technique is used, the noise will be down to 2.SR560 Low-noise preamplifier: Noise 3.SR780 Spectrum Analyzer: Frequency range : 1 mHz ~ 102.4 kHz Noise

kHz 1atHznV/95.1

kHz 1atHznV/4

kHz1atHznV/3.0

kHz1atHznV/10

Instrumentation and measurement methods -- Spectrum of homemade preamplifier 8

0.01 0.1 1 10 100 1000 10000 100000

330 thermal noise

1.4 k thermal noise

10-12

10-14

10-16

10-18

S

V (

V2 /H

z)

Frequency (Hz)

Instrumentation and measurement methods -- direct FFT measurement

We use a balanced circuit to measure the noise of an GaN nanowire. In the direct FFT measurement, the amplified signal from the sample is fed into the FFT dynamic signal analyzer . SR780 measures the power spectrum density directly.

9

3

1

2

R c 1

R c 2

R c 3

R s

R s '

R s ' '4

R c 4

A

B

( S R 5 6 0 )

Instrumentation and measurement methods -- Cross-spectrum technique

We use a balanced circuit to measure the noise of an GaN nanowire. In the direct FFT measurement, the amplified signal from the sample is fed into the FFT dynamic signal analyzer . SR780 measures the power spectrum density directly.

10

C o r r e l a t o r

( S R 7 8 0 )

( S R 5 6 0 )

A

B

( )x 2

Instrumentation and measurement methods -- Time domain sampling

We use a balanced circuit to measure the noise of an GaN nanowire. In the

11

1/f Noise -- Introduction

Hooge’s phenomenal equation [7]:

Simplified equation[8]:

Fitting equation of our experiment:

12

fN

VSV

tot

2

f

VASV

2

thermalV Sf

VAS

2

where Ntot is the number of the mobile carriers,

= 2 × 10-3, and = 1.

Where A is the noise amplitude.

Where Sthemal is the background thermal noise of samples.

1/f Noise --Experiments of carbon nanotubes

Collins et al (2000):[8]

1. Experiment of the 1/f noiseof singlewalled carbon nanotubes (SWCNTs).

2. A=10-11R and =1~1.1

3. SV of the GaN nanowire is smaller than that of SWCNTs with similar resistance at the same bias current.

Ouacha et al (2002)[9]:1. Experiment of the 1/f noiseof mult

iwalled carbon nanotubes (MWCNTs)

2. An individual MWCNT:=1.02.

3. Tow crossing MWCNT: =1.56.

13

Spectrum of the work of collins et al (2000)[8]

Results -- Spectrum of a two-wire sample

The 1/f excess noise raises up when the current through the GaN-nanowire increases. The red straight line in the plot is the background thermal noise (4kTR).

14

10-2 10-1 100 101 102 103 104

10-16

10-14

10-12

10-10

fcorner

I=1.05x10-8A

I=4.39x10-9A

I=7.80x10-9A

I=1.67x10-9A

I=5.01x10-10A I=0

S

v(V

2 /Hz)

Frequncy(Hz)

Results -- versus bias currents

The scattering range of is between 0.87 to 1.3. The orange line is=1.11 ± 0.09 in average

15

10-9 10-8 10-7 10-60.8

0.9

1.0

1.1

1.2

1.3 R=11.2k R=15.6k R=17.7k R=26.2k R=31.2k R=49.5k

I (A)

Results -- Noise amplitude versus bias current

The noise magnitude is around the same value for each individual nanowire.

16

10-9 10-8 10-7 10-610-9

10-8

10-7

10-6

R=11.2k R=15.6k R=17.7k R=26.2k R=31.2k R=49.5k

N

ois

e A

mp

litu

de

I (A)

Results -- and Noise amplitude versus resistances

and the noise amplitude, A versus resistance of the GaN nanowires. = 1.11 ± 0.09 for different samples.

17

0.8

0.9

1.0

1.1

1.2

1.3

1.4

5.0k 10.0k 15.0k 20.0k 25.0k 30.0k 35.0k 40.0k 45.0k 50.0k 55.0k 60.0k

10-8

10-7

10-6

10-5

A

Resistant ( )

56.114104.4 RA

Results -- Corner Frequency of Samples

The slope of the corner frequency (fc) vs the current in logarithmic scale is close to 2. fc is not clearly related to resistances.

18

10-9 10-8 10-7 10-6

101

102

103

R=8.88k R=11.2k R=15.6k R=17.7k R=22.6k R=26.2k R=31.1k R=44.1k R=49.5k

Co

rner

Fre

qu

ency

(H

z)

Current (A)

Results -- Spectrum of a four-wire sample

Spectrum of a four-wire a sample with R4W =1.53 k, and R2W = 32.60 k. The contact resistance of the two voltage probes is 6.58k and 26.13 k, respectively

19

10-2 10-1 100 101 102 103 10410-16

10-15

10-14

10-13

10-12

I=6.3nA I=4.8nA I=0nA

S

V (

V2 /H

z)

Frequency (Hz)

Lorentzian noise -- Introduction

Lorentzian noise expression:[10]

20

2

0

)(1

)0(

ff

SS V

V

where SV(0) is the Lorentzian plateau .

f0 is the characteristic frequency.

Lorentzian time constant L=(2f0)-1.

Lorentzian noise -- Experiments of diodes and transistor

Deen et al (1999)[11]:1. The noise measurement of polysilicon

emitter bipolar transistors .

2. From 8 Hz to 10 kHz, there exists Lorentzian feature.

Bychikhin et al (2005) [12] :1. The noise measurements of GaN-bas

ed light-emitting diodes.

2. From 10 Hz to 100 Hz, there exists Lorentzian feature.

Rumyantsev et al (2004) [13] :1. Fluctuations of ligh sources of LEDs a

nd laser diodes.

2. For f<1 Hz, there exists Lorentzian feature.

21

Spectrum of the work of Deen et al (1999)[11]

Results -- Lorentzian noise of a two-wire sample

Two-wire power spectrum density of GaN nanowire with different bias current I at room temperature. The Lorentzian feature are observed at the large enough driving current.

22

10-2 10-1 100 101 102 103 10410-16

10-11

10-12

10-15

10-14

10-13

I=6.3nA I=4.8nA I=0nA

S

V(V

2 /Hz)

Frequency (Hz)

0.1 1 10

Frequency (Hz)

Results -- Lorentzian noise of a four-wire sample

Spectrum of a sample with R4W= 230 , and R2W = 1.2 k at 303 K at I=7nA.The resistances of the two voltage probes are 3.1 k and 14.1 k, respectively.

23

10-2 10-1 100 101 102 103 10410-16

10-15

10-14

10-13

10-12

S

V(V

2 /Hz)

Frequency (Hz)

0.1 1 10

T-dependence of Lorentzian Noise -- Introduction

Arrhenius law[4]:

24

)exp(10 Tk

E

B

aL

where Ea is the activation energy, and 0 is an attempt frequency which is in the order of the atomic vibration frequency.

Model of Levinshtein et al[14]:

1000

10

10

)(

)exp(

)exp(

Tc

Bcc

B

n

Tk

E

Tk

E

where is the cross section, n0 is the carrier concentration, c is the capturing characteristic time, and T is the thermal velocity.

E c

EE

E

E v

N c

N t

n0

0

dF

T-dependence of Lorentzian Noise -- Experiments of semiconductor material

Muller et al (2006)[15]:

1. The 1/f noise measurement of AlGaAs/GaAs Hall device .

2. Below 50 K, there exists Lorentzian feature.

3. From Arrhenius plot, Ea = 88 meV, 0 = 6 × 109 Hz

25

Model of Levinshtein et al[16]:

1. The 1/f noise measurement of GaNÕAlGaN heterostructure field-effect transistors

2. From 150 K to 50 K, there exists Lorentzian feature.

3. From Arrhenius plot, Ea = 1~3meV,

Arrhenius plot of Muller et al (2006)[1

5]

Results-- Lorentzian noise below room temperature

Spectrum of a two-wire GaN nanowire device at 175 K with 58 k.

26

10-2 10-1 100 101 102 103 10410-16

10-15

10-14

10-13

10-12

10-11

I=10nA I=8nA I=6nA I=4nA I=3nA I=2nA I=1nA I=0nA

S

V (

V2 /H

z)

Frequency (Hz)

Results -- Temperature dependence of SI(0)/I2

SI(0)/I2 vs temerature. At the same temperature, SI(0)/I2 is around the same order of magnitude relative with the current I.

27

100 150 200 250 300 3501E-8

1E-7

1E-6

1E-5

1E-4

1E-3

I2nA I3nA I4nA I6nA I8nA I10nA

SI(0

)/I2 (

1/H

z)

Temperture(K)

Results -- SI(0)/I2 versus L

SI(0)/I2 versus the characteristic time L for the different bias currents.

28

10-3 10-2 10-1 100 10110-8

10-7

10-6

10-5

10-4

10-3

I=2nA I=3nA I=4nA I=6nA I=8nA I=10nA

S

I(0)/

I2 (A

rb.U

nit

)

Time(s)

Results -- T-dependence of a four-wire device

Temperature dependence of the characteristic time and SI(0)/I2 at I=7nA.

29

0.0044 0.0042 0.0040 0.0038 0.0036 0.0034 0.0032

10-1

6.0x10-2 8.0x10-2 1.0x10-1

Tim

e (s

)

1/T (K-1)

10-8

10-7

SI(0

)/I2 (

1/H

z)

Time(s)

Results-- Activation energy of the two-wire device

Activation energy versus the bias current. The activation energy at the high temperature regime is larger than that at the low temperature regime.

30

2.0n 4.0n 6.0n 8.0n 10.0n

10-2

10-1

E0in high temperature region

E0 effect in low temperature region

E1 in high temperature region

E1 in low temperature region

Act

ivat

ion

En

erg

y (e

V)

Current (A)

Results-- Activation energy of the four-wire device

From Arrhenius plot: Ea = 41.69 meV.

From the model of Levinstein et al[2], E0 = 37.7 meV and E1 = 41.69 meV.

For nanowires, it is close to the ionization energy, 30 meV[2] of the wutzite GaN bulk material.

31

Results -- Contact noise

Averaged cross spectrum between the port 12 and port 23.

32

10-2 10-1 100 101 102 103

10-16

10-15

10-14

10-13

I=0nA I=3.1nA I=4.2nA I=6.2nA

S

V(V

2 /Hz)

Frequency (Hz)

Results -- Correlation Coefficient

Averaged Cf under different applied bias current versus frequency f. The error bars indicate the size of the 95% confidence band.

33

1 10 100 1000-4

-3

-2

-1

0

1

I=6.3nA I=4.8nA I=3.1nA I=0nA

C

Frequency (Hz)

Conclusion

1. So far, there is no experimental investigation about semiconductor nanowires.

2. GaN nanowires exhibit the 1/f-like excess noise from room temperature to 77 K in the frequency below 200 Hz.

3. Lorentzian-like feature is observed embedded in the 1/f noise when the applied bias current is large enough.

4. From the results of two-wire and four-wire measurement, the GaN nanowire do exhibit the excess noise itself, but the excess noise of the two-wire measurement come from the metal-semiconductor contact region rather than from the nanowires directly.

5. The nanoscale correlation might be caused by the strong voltage fluctuations under the contact region, which may contain complicated alloy or defects consisting of GaN and the Al or Ti/Au.

6. GaN nanowires is with lower 1/f noise in the lower frequency region than carbon nanotubes. It makes GaN nanowires a potential material for nanodevices, such as photo-detector, sensor and low frequency transistors.

34

References

1. A. Van der Ziel. Noise: Source, Characterization, Measurements. Prentice Hall Inc., Englewood Cliffs, NJ, (1970).

2. D. A. Bell, Noise and the solid state, Pentech Press Ltd., Devon, UK, (1985).3. P. Dutta and P. M. Horn, Rev. Mod. Phys. 53, 497 (1981).4. Sh. Kogan, Electronic noise and fluctuations in solids, Cambridge university pre

ss, Cambridge, UK (1996)

5. C.C.Chen, C.C.Yeh, C.H.Chen, M.Y.Yu, H.L.Liu, J.J.Wu, K.H.Chen, J.Y.Peng, Y.F.Chen, J. Am. Chem. Soc. 123, 2791. (2001)

6. W. K. Wang, The noise measurement with the homemade low-noise preamplifiers, B.S Thesis, National Chung Hsing University (2001)

7. Hooge, Phys. Lett. A 29, 139 (1969).8. P. G. Collins, M. S. Fuhrer, and A. Zettl, Appl. Phys. Lett. 76, 894 (2000). 9. H. Ouacha, M. Willander, H. Y. Yu, Y. W. Park, M. S. Kabir, S. H. Magnus Pe

rsson, L. B. Kish, and A. Ouacha, Appl. Phys. Lett. 80, 1055 (2002). 10. N. B. Lukyanchikova, M. V. Petrichuk, N. P. Garbar, A. Mercha, E. Simoen, an

d C. Claeys, J. Appl. Phys. 94, 4461 (2003).

35

References

11. M. J. Deen, S. L. Rumyantsev, and M. Schroter. J. Appl. Phys., 85, 1192, (1999).

12. S. Bychikhin, D. Pogany, L. K. J. Vandamme, G. Meneghesso, and E. Zanoni. J. Appl. Phys., 97, 123714, (2005).

13. S. L. Rumyantsev, M. S. Shur, Yu. Bilenko, P. V. Kosterin, and B. M. Salzberg. J. Appl. Phys., 96, 966, (2004).

14. M. E. Levinshtein and S. L. Rumyantsev. Semicond. Sci. Technol., 9, 1183, (1994).

15. J. Muller, S. von Molnar, Y. Ohno, and H. Ohno. Phys. Rev. Lett., 96, 186601, (2006).

16. S. L. Rumyantsev, Y. Deng, E. Borovitskaya, A. Dmitriev, W. Knap, N. Pala, M. S. Shur, M. E. Levinshtein, M. Asif Khan, G. Simin, J. Yang, and X. Hu. J. Appl. Phys., 92, 4726, (2002).

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