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Fluctuation and Noise Letters
Vol. 12, No. 3 (2013) 1350014 (14 pages)
c World Scientific Publishing Company
DOI: 10.1142/S0219477513500144
ANALYSIS OF NOISE CHARACTERISTICS
OF GaAs TUNNEL DIODES
Fluct. Noise Lett. 2013.12. Downloaded from www.worldscientific.com
by Dr. Sandra Pralgauskait on 10/01/13. For personal use only.
VILIUS PALENSKIS∗ , JONAS MATUKAS, JUOZAS VYŠNIAUSKAS
and SANDRA PRALGAUSKAITĖ
Radiophysics Department, Vilnius University
LT-10222 Vilnius, Lithuania
∗vilius.palenskis@ff.vu.lt
HADAS SHTRIKMAN
Department of Condensed Matter Physics
Weizmann Institute of Science
Rehovot 76100, Israel
DALIUS SELIUTA, IRMANTAS KAŠALYNAS
and GINTARAS VALUŠIS
Optoelectronics Department
Center for Physical Sciences and Technology
LT-01108 Vilnius, Lithuania
Received 14 December 2012
Accepted 26 June 2013
Published 19 August 2013
Communicated by Francois Danneville
An analysis and investigation of noises of GaAs tunnel diodes, which abrupt p+ -n+ profile was obtained by using amphoteric nature of silicon, were performed. The main scope
of this work was to verify the concepts of the explanation of white noise characteristics
on the ground of shot noise and on the ground of the Gupta theorem of thermal noise in
resistive elements. The other scope was to investigate the peculiarities of low frequency
noise in p+ -n+ junctions formed by using amphoteric silicon nature.
Keywords: Generation-recombination noise; Gupta theorem; shot noise; thermal noise;
tunnel GaAs diode noise.
1. Introduction
Though the tunnel diode is known many decades ago, at present there is a variety
of applications of tunnel diode structures in combination with different semiconductor devices. The tunnel diode contact is used to improve the characteristics of the
MOSFET transistors [1], of the laser diodes by integration of multi-quantum-well
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V. Palenskis et al.
tunnel diode [2], of the multi-junction solar cells by incorporation of cascade tunnel diode structure to InAs/GaSb interface to enhance the performance of such
cells [3, 4]. The tunnel diodes are used for detection of very small powers (about
several picowatts) of millimeter and submillimeter waves [5–7]. They are also used
in measurement technique: for surface impedance measurement of superconductors
[8], a gated tunnel diode has been introduced into a waveguide oscillator circuit [9,
10] to tune the oscillation frequency and to turn the oscillator on and off [10]. A
very attractive is investigation of electronic transport in GaSb/InAs(Sb) nanowire
tunnel diodes [11] for developing tunnel-field-effect transistors.
The relation between charge carrier scattering and fluctuations at equilibrium
conditions was determined over a decade ago: the fluctuations cause the scattering
mechanism of energy, and the dissipative systems are influenced by the thermal
fluctuations. The relation between the diffusion coefficient and mobility of randomly moving charge carriers and the Nyquist theorem for thermal noise confirm
this relation [12, 13]. The relation with nonlinearity of resistive systems was defined
by Gupta only 50 years later than the Nyquist theorem [14, 15]. Gupta related the
thermal noise spectral density with phenomenological characteristics of nonlinear
resistive system. At low frequencies the tunnel diode also as p-n junction and Schottky diodes can be presented as nonlinear resistor with particular current–voltage
characteristic. In many cases it is stated that the tunneling component of current
produces the shot noise, which is described by Schottky formula [16–19]. In [20]
and [21], it has been shown, that the p-n junction diodes and the Schottky-barrier
diodes in the range of the white spectrum is consistent with the idea of thermal
noise in nonlinear resistive elements independently of technology and non-ideality of
current–voltage characteristics, and is well described by Gupta formula. The Schottky formula is applicable only for ideal exponential current–voltage characteristics,
caused due to diffusion process. Considering that these two ways for explanation
of the white noise sources are different, it is very interesting to verify, which one is
more near to experimental results for tunnel diodes. In this paper we present a detail
investigation of noise characteristics of GaAs tunnel diodes. The other scope was
to investigate the low-frequency noise characteristics of GaAs tunnel diodes, which
p+ -n+ junction abrupt doping profile was achieved by using amphoteric nature of
silicon on GaAs surface.
2. Samples and the Measurement Technique
The investigated p+ -n+ structures were grown by molecular beam epitaxy on semiinsulating GaAs substrates. High carrier densities as well as abrupt doping profile
were achieved by using amphoteric nature of silicon on (311)A GaAs substrate [22].
Technologically, at high growth temperatures (>660◦C) and low As/Ga flux ratio
(≈ 1), Si atoms predominantly incorporate on As sublattice sites and behave as
uncompensated acceptors, while at low growth temperature (<500◦ C) and at high
As/Ga flux ratio (>2.5) Si atoms occupy Ga sublattice sites and act as donors.
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Analysis of Noise Characteristics of GaAs Tunnel Diodes
Fig. 1. A view of the quadratic mesa structure of the GaAs tunnel diode. The upper Ni-Au-Ge
alloy electrode layer area is (100 µm × 100 µm), n+ = 3 · 1018 cm−3 layer thickness is 0.4 µm, and
the area is (120 µm × 120 µm); p+ = 5 · 1019 cm−3 layer thickness is 0.6 µm. Round the mesa
structure there is the ohmic contact: the side stripline of the square is equal 1.2 mm, and the
stripline width is 0.15 mm.
PC
ADC
LNA
A
+
¯
RL1
E
Ret
C
V
TD
Fig. 2. The measurement circuit: TD is the GaAs tunnel diode; RL1 is the load resistance, which
assures the constant direct current regime; LNA is the very low noise amplifier; PC is the personal
computer; ADC is the analog-to-digital converter (National InstrumentTM PCI 6115 board); E
is the storage battery; Ret is the standard resistor; C is the capacitor for shunting the noise from
supply system.
The samples were with alloyed Ni-Au-Ge contacts. A view of measured samples is
shown in Fig. 1.
The tunnel diode noise measurement circuit is presented in Fig. 2. The tunnel
diode noise properties were investigated at low forward voltages up to peak current
and at backward voltages in order to verify the Gupta theorem. For noise measurement there was designed very low noise amplifier. The comparison of the noise levels
between own measurement system to that of tunnel diode at zero bias is presented
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V. Palenskis et al.
V d=0
-18
2
S u, V s
10
syst.
10
-19
10
3
10
4
10
5
10
6
Fluct. Noise Lett. 2013.12. Downloaded from www.worldscientific.com
by Dr. Sandra Pralgauskait on 10/01/13. For personal use only.
f, Hz
Fig. 3. Comparison of the noise levels between the own measurement system to that of tunnel
diode at Vd = 0.
in Fig. 3. It is seen that the white noise level of the measurement system is about
an order smaller than that of tunnel diode at zero bias voltage. The spectral density
of tunnel diode noise was evaluated by comparison with thermal noise of standard
resistor Ret :
SV =
2 −V2
Vtd
syst
2
Vet2 − Vsyst
· 4kT 0 Ret ,
(1)
2,V 2
2
where Vtd
syst and Vet respectively are the tunnel diode, the measuring system,
and the standard resistor thermal noise variances in the narrow frequency band
∆f ; T0 is the absolute temperature of the standard resistor.
3. Experimental Results and Their Analysis
3.1. Investigation of white noise characteristics
of GaAs tunnel diode
As was mentioned in introduction, in literature there are two concepts (on the
ground of shot noise, and on thermal noise of nonlinear resistive elements) for explanation of the white noise sources in different p-n junctions, it was very interesting
to verify, which one is more near to experimental results for GaAs tunnel diodes.
A schematic energy diagram of the tunnel diode is shown in Fig. 4. The position
of the Fermi energy for electrons ∆EFn and for holes ∆EFp of high degenerated
materials can be evaluated from these expressions [23, 24]:
∆EFn = (2 /2m∗dn ) · (3π 2 n)2/3
and ∆EFp = (2 /2m∗dp ) · (3π 2 p)2/3 ,
(2)
where n is the density of free electrons in conduction band; p is the free holes
density in valence band; = h/2π is the Plank’s constant; the effective mass of
density of states for electrons in GaAs mdn ≈ 0.064m0 [25] and the position of the
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Analysis of Noise Characteristics of GaAs Tunnel Diodes
p
+
n
Ec
Eg
Ev
E Fp
+
"Tails" of density
of states
eVp
eVn
EFn
Ec
Fig. 4. Schematic energy diagram of the tunnel diode. The potentials Vn and Vp reflect the degrees
of the degeneracy of n+ -region and p+ -region, respectively.
6
Imax
Exp.
4
Calc.
2
I, mA
Fluct. Noise Lett. 2013.12. Downloaded from www.worldscientific.com
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Ev
0
Vp
-2
Vpexp
-4
-6
-600
-300
0
300
600
900
1200
V d, mV
Fig. 5. Current–voltage characteristic of GaAs tunnel diode. Exp. is the direct measurement curve,
and Calc. is the calculated curve by eliminating the voltage Ir ser due to serial resistance rser of
the tunnel diode.
Fermi energy ∆EFn ≈ 0.12 eV, and the effective mass of density of states for holes
mdh ≈ 0.61m0 [25] and ∆EFp ≈ 0.08 eV; here m0 is the free electron mass.
The typical current–voltage characteristic of the investigated GaAs tunnel
diodes is presented in Fig. 5. The current peak of the directly measured results
shows that it happens at higher bias voltage Vpexp than it follows from the tunnel
diode diagram: the current peak has to occur at bias voltage when the Fermi energy
∆EFn coincides with the top of the valence band [26], i.e., when Vd = Vp ≈ 0.08 V.
For investigated tunnel diodes the voltage difference (Vpexp − Vp ) is due to serial
resistance rser = (Vpexp − Vp )/Imax of the tunnel diode structure. In Fig. 5, it is also
shown the calculated current–voltage characteristic (curve Calc.) by eliminating the
voltage Ir ser due to serial resistance. The spectral density of voltage fluctuations
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10
-11
10
-13
10
-15
10
-17
V d, V:
0.53
0.60 0.80
1.00 1.15
1/f
2
S v, V s
V. Palenskis et al.
Vd, mV:
0 66
10
1
105 183
10
2
300
10
3
341
10
4
Fig. 6. Spectral density of voltage fluctuations dependence on frequency (in the frequency range
from 10 Hz to 20 kHz) at different forward voltages of tunnel diode.
dependence on frequency at different forward biases in the frequency band from
10 Hz to 20 kHz is presented in Fig. 6. It is seen that in this frequency band at
biases lower than that for current peak prevails the generation-recombination noise,
but at higher voltages (>0.53 V, i.e., when energy Ec in n+ region is larger than
Ev in p+ region) there is 1/f -type noise due to localized centers of defects in the
forbidden energy gap near the interfaces of p+ -n+ junction [26], which cause the
leakage current due to charge carrier tunneling to these centers and subsequent
their recombination.
As it can be seen from Fig. 6, in order to measure the white noise level, it is
needed to measure the noise at higher frequencies. For this purpose, the very low
noise amplifier was designed that led to the investigation of the tunnel diode noise
characteristics of up to 2 MHz (Fig. 3). The noise spectra of GaAs tunnel diode at
different forward and backward biases at room temperature are shown in Fig. 7.
10
-16
10
-17
10
-18
10
-19
10
101.5
V d, mV:
125.1
151.9
200.2
250.2
306.4
341.7
381.6
407.3
0 25.1 75.1
50.3
10
3
10
-17
V d , mV: -152.2
-201.4
-250.8
-303.8
-350.4
-404.5
2
-15
S V, V s
10
2
S V, V s
Fluct. Noise Lett. 2013.12. Downloaded from www.worldscientific.com
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f, Hz
10
-18
0
-25.2
-50.6
-102.3
syst.
syst.
4
10
5
10
6
f, Hz
10
-19
10
3
10
4
10
5
10
6
f, Hz
Fig. 7. Noise spectra of GaAs tunnel diode at different forward (on the left) and backward (on
the right) biases at room temperature T = 293 K.
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Analysis of Noise Characteristics of GaAs Tunnel Diodes
The differential resistance of Exp. curve (Fig. 5) Rd = dV/dI = rser + rd , where
rd is differential resistance of Calc. curve (Fig. 5). These differential resistances are
presented in Fig. 8.
The spectral density of voltage thermal noise calculated from Eq. (3) is presented
in Fig. 9 by dashed line. The measurement results are also shown in this figure
by black dots. These investigations directly show that though the Gupta theorem
gives good coincidence for white noise level in the case of exponential current–
voltage characteristics for p-n junctions [20, 21], but for investigated GaAs tunnel
diodes here coincidence is only at backward currents where the current–voltage
characteristic is caused by the serial resistance. In the case of forward currents the
white noise level cannot be explained on the ground of thermal noise of nonlinear
resistive elements.
From the equivalent circuit (Fig. 10) follows that spectral density of voltage
fluctuations of real GaAs tunnel diode for white noise can be expressed as
SV = 4kTR d + 2qIr 2d = 4kT (rser + rd ) + 2qIr 2d .
(4)
This expression of spectral density is presented in Fig. 9 by solid line. Thus,
the spectral density of white noise of investigated GaAs tunnel diodes consists
100
Rd
R d, r d , Ω
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The white noise exceeds the generation-recombination noise level at frequencies
higher than 100 kHz. It is interesting to note that white noise level at backward
currents almost does not depend on the current magnitude. It is very strange from
the view of tunneling, because one believes that there will be shot noise, which has
to increase with current increase.
According to the Gupta theorem [14, 15], the spectral density SV of voltage
thermal fluctuations of nonlinear resistive elements can be presented as
1 d2 V
dV
+ I 2
.
(3)
SV = 4kT
dI
2 dI I=const
rd
10
-6
-4
-2
0
2
4
6
I, mA
Fig. 8. The differential resistances of investigated GaAs tunnel diodes. Rd = rser + rd ; rser is
the serial resistance, and rd is differential resistance due to charge carriers tunneling through the
p+ -n+ potential barrier.
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V. Palenskis et al.
10
-17
2
S V, V s
Thermal+
shot noises
Gupta
10
-18
-6
-4
-2
0
2
4
6
Fluct. Noise Lett. 2013.12. Downloaded from www.worldscientific.com
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I, mA
Fig. 9. The white noise level dependence on the forward and backward currents of the GaAs tunnel
diode. Black dots are the measurement results; dashed line is calculated by Eq. (3); solid line is
calculated by Eq. (4).
of two components: thermal noise due to differential resistance of the tunnel diode,
and shot noise caused by the tunneling of the charge carriers through the p+ -n+
junction. These investigations show that white noise of tunnel diodes cannot be
explained on the ground of Gupta theory [14, 15] for nonlinear resistive elements.
Thus, the experimental result that shot noise often is not observed at backward
currents and sometimes at forward currents can be explained in such a way: a
real tunnel junction differential resistance rd is many times smaller than the total
differential resistance of the tunnel diode, and the shot noise is shunted by rd
(Fig. 10).
3.2. Investigation of generation-recombination noise
characteristics of GaAs tunnel diodes
The other scope was to investigate the low-frequency noise characteristics of
GaAs tunnel diodes, which p+ -n+ junction abrupt doping profile was achieved by
using amphoteric nature of silicon on GaAs. A detail pattern of the generationrecombination noise spectra of investigated tunnel diodes at forward currents is
shown in Fig. 11. They have the Lorentzian type spectrum. The fact that at higher
frequencies generation-recombination noise decreases as 1/f shows, that there is
rd
rser
e(t)
i(t)
Fig. 10. The equivalent white noise circuit of the investigated GaAs tunnel diodes. The voltage
noise source e(t) is caused by the thermal noises of resistances rser and rd ; the current noise source
i(t) is due to charge carriers tunneling through the p+ -n+ potential barrier.
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Analysis of Noise Characteristics of GaAs Tunnel Diodes
10
-15
10
-16
V d, mV: 391
~1/f
300
2
S V gr, V s
349
252
10
-17
10
-18
200
153
101
51
10
0
1
10
2
10
3
10
4
Fig. 11. Generation-recombination noise spectra at different forward bias voltages at room temperature T = 293 K.
10
-12
10
-13
10
-14
10
-15
10
-16
10
-17
2
SV gr *f , V
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f, Hz
V d, mV:
391
349
300
252
200
153
101
51
10
1
10
2
10
3
10
4
f, Hz
Fig. 12. Normalized generation-recombination noise spectra SV
voltages at room temperature T = 293 K.
gr
· f at different forward bias
a distribution of relaxation times. In order to evaluate the distribution of these
relaxation times it is convenient to present the normalized spectral density SV gr · f
of this noise (Fig. 12). The flat part of the normalized spectral density SV gr · f
over the frequency 1 kHz shows that relaxation times for generation-recombination
noise at room temperature are distributed in wide time range: approximately from
0.2 ms to about 7 µs. It is interesting to note that this distribution of relaxation
times does not depend on the forward current up to the peak current.
The spectral density of voltage fluctuations in the above mentioned frequency
band at backward biases also has relaxation behavior (Fig. 13). Usually the level
of generation-recombination noise in materials is proportional to the square of
current (or voltage) [27]. The intensity of generation-recombination noise at backward biases is approximately proportional to the square of current as in the case
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V. Palenskis et al.
10
-16
2
S V gr , V s
V d, mV:
-300
10
-17
-185
-106
-66,5
10
0
-18
10
1
10
2
10
3
10
4
Fig. 13. Generation-recombination noise spectra at different backward bias voltages at room temperature T = 293 K.
10-13
Exp.
(SV gr/Vrd2 )0*(rd/rd 0)
Sv gr/Vrd2 , s
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f, Hz
(SV gr/Vrd2)0
10-14
0
20
40
60
80
100
Vrd, mV
2 dependence on
Fig. 14. The intensity of normalized generation-recombination noise SV gr0 /Vrd
forward bias voltage Vrd = Vd − Ir ser of p+ -n+ junction (black dots). The open circles represent
2 ) ∗ (r /r ), where r
the quantity (SV gr0 /Vrd
0
d d0
d0 is equal rd at Vrd = 0.
of material, but at forward currents the noise intensity increases more steeply. It
shows that generation-recombination noise is related with p+ -n+ junction. Normalized with respect to voltage Vrd generation-recombination noise spectral density
2
dependence on forward voltage Vrd = Vd − Ir ser is presented in Fig. 14
SV /Vrd
by black dots. When the forward voltage increases, the differential resistance rd
of the p+ -n+ junction increases, i.e., the effective number of free carriers Neff in
the p+ -n+ junction range decreases with increasing of the differential resistance
2
has to increase as a
rd . So, if this effect take place, the spectral density SV /Vrd
relative differential resistance rd /rd0 , where rd0 is the differential resistance rd at
2
)0 ∗(rd /rd0 ) is presented in Fig. 14
Vrd = 0. The normalized spectral density (SV /Vrd
by open circles. It is seen that there is a sufficiently good agreement between the
2
2
and the calculated (SV /Vrd
)0 ∗ (rd /rd0 ) quantities.
experimental values of SV /Vrd
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10
-15
10
-16
10
-17
10
-18
10
-19
T, K: 249.7
262.7
275.5
288.0
2
S V, V s
Analysis of Noise Characteristics of GaAs Tunnel Diodes
300.9
313.6
327.6
10
1
10
2
339.8
10
3
10
4
Fig. 15. Generation-recombination noise spectra of GaAs tunnel diode at different temperatures
and at constant current 3.3 mA.
262.7
288.0
275.5
249.7
10
-14
10
-15
2
S Vf , V
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f, Hz
10
238.6
300.9
313.6
327.6
339.8
-16
10
1
10
2
10
T , K:
3
10
4
f, Hz
Fig. 16. Normalized generation-recombination noise spectra SV gr f at different temperatures
(white noise level was eliminated), and at constant current 3.3 mA.
The typical generation-recombination noise spectra of investigated GaAs tunnel
diodes at different temperatures are shown in Fig. 15. The maximum of the normalized spectral density SV gr · f function (Fig. 16) is at ω0 τ = 1. The flat maximum shows that relaxation times are distributed in wide time range: τ1 /τ2 ≈ 30.
The relaxation times of generation-recombination noise and its distribution dependence on temperature are presented in Fig. 17. The temperature dependence of
relaxation times can be presented as τ = τ0 exp( ∆E
kT ) with the activation energy
∆E ≈ Eg min /2 ≈ 0.53 eV.
The energy gap Eg narrows in the p+ -n+ interface to Eg min due to high doping
of GaAs, and due to formation of “tails” of density of states below the bottom of
conduction band and above the top of valence band (Fig. 4) [24, 25]. The every “tail”
of density of states occupies about (0.1–0.15) eV energy range. It is expected that
activation energy ∆E and its independence on forward current up to peak value
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τ , ms
V. Palenskis et al.
10
1
10
0
∆ E =0.53 eV
10
-1
10
-2
10
-3
τ
2.8
3.0
3.2
3.4
3.6
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1000/T , K
3.8
4.0
-1
Fig. 17. The relaxation time of generation-recombination noise dependence on temperature at
constant current 3.3 mA.
and intensive charge carrier recombination noise is related due to recombination
process in states of the “tails” in p+ -n+ interface.
4. Conclusion
It is shown that GaAs tunnel diodes, grown by molecular beam epitaxy on semiinsulating GaAs substrates with abrupt p+ -n+ profile by using amphoteric nature
of silicon have at low frequencies intensive relaxation type noise. The distribution
of the relaxation times and their dependence on temperature show that this noise
is related with the charge carrier tunneling and recombination processes in states
of “tails”. There is presented the equivalent circuit of white noise sources. The
performed investigations show that white noise of tunnel diodes cannot be explained
on the ground of Gupta theory for nonlinear resistive elements. The spectral density
of white noise of investigated GaAs tunnel diodes consists of two components:
thermal noise caused by the total differential resistance of the tunnel diode, and
shot noise due to the tunneling of the charge carriers through the p+ -n+ junction.
The shot noise is shunted by differential resistance of the tunneling junction.
Acknowledgments
The study was funded in part from the European Community’s social foundation
under Grant Agreement No. VP1-3.1-ŠMM-08-K-01-004/KS-120000-1756.
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by Dr. Sandra Pralgauskait on 10/01/13. For personal use only.
Analysis of Noise Characteristics of GaAs Tunnel Diodes
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Fluct. Noise Lett. 2013.12. Downloaded from www.worldscientific.com
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