ACTIVITIES
Plasmonically Enhanced Nanopillar Single Photon Avalanche Diodes
REU Student: Benjamin Sandoval
Graduate Mentor: David Ramirez
Faculty Mentor: Dr. Majeed Hayat
1.A. Introduction
A Single Photon Avalanche Diode (SPAD) is a semiconductor device that operates as a
photodetector. This particular photodetector is a sensor which is capable of sensing light of a
specific wavelength of 730nm. This plasmonically enhanced nanopillar is composed of gallium
arsenide (GaAs) material fabricated by means of a molecular beam epitaxy machine. GaAs is
considered to be a metamaterial, which is not found in nature.
1.B. Background
A photon can best be described as a quantum of light or quantum of electromagnetic energy of a
single mode. This can best be described as a single wavelength ( λ ), single direction and single
polarization[9]. The photoelectric effect is described as photons of light having a certain energy
associated with it.
E=
hc
λ
−34
where E is the energy of the photon, h is plank’s constant which holds a value of 6.62607x10 J⋅ s, c is
the speed of light which holds 2.998x10 m/s and λ is the wavelength of light measured in meters [1].
Photoconductivity occurs as a result of a photon of light striking the surface of the metal, which then
excites an electron above the bandgap energy to conduct electricity (Figure 1.1).
8
Figure 1.1 – Schematic depicting the photoelectron emission associated with the photoelectric effect exciting a free
electron. The Fermi Level describes the electron bandgap energy when must be overcome to reach the conduction band.
Source: [1]
The internal photoeffect is what affects the operation of the photodetector (Figure 1.2). The
internal photoeffect is described as the holes and electrons remaining within the metal itself.
Figure 1.3 – Schematic showing multiplicative gain associated with the avalanche effect. As electrons collide and free
other electrons, the holes drift in the opposite direction. Source: [1]
Figure 1.2 – Visual schematic depicting the Internal Photoeffect taking place within the p-n junction inside the
photodetector. Source: [1]
A specific metamaterial known as gallium arsenide [GaAs] is commonly used in the areas of
optoelectronics and nanotechnology. Gallium Arsenide is a material, which has excellent electric
properties such as higher electron mobility and a higher saturated electron velocity than that of
silicon. GaAs also has the direct bandgap property, which allows the material to absorb and emit
light efficiently. The avalanche photodiode relies on the avalanche effect for optimum performance.
As light is absorbed within the depletion layer the kinetic energy absorbed by the electrons promote
the electrons above the bandgap energy into the conduction band. As the electrons cross the bandgap
energy and into the conduction band, they are accelerated as a result of the reverse bias voltage
applied across the p-n junction. As the electrons are accelerated they collide with other electrons in
the atomic lattice causing those newly created electrons to then accelerate thus causing more
electrons to break free into the conduction band. This effect causes the holes to accelerate in the
opposite direction contributing to the electric flow of current. This effect is referred to as the
avalanche effect [2]. The avalanche effect contributes the gain of the device. As the electron is
injected into the conduction band, the gain can be observed as a result of the avalanche effect
(Figure 1.3).
The avalanche gain of avalanche photodiodes (APD’s) is dependant on the three step process
mentioned
above which
is known
andspace
Amplification.
Thethegeneration phase
Figure 1.4 – Position/time
graph
showingas
theGeneration,
time associatedTransport
with the dead
occurring within
consists of the
photonsthe
generating
free
electrons
due to the
wavelength
dependent kinetic
photodetector.
Theabsorbed
solid lies represent
electrons and
dashed
lines represent
the holes.
Source [1]
energy associated with the photon of light absorbed in the depletion layer. The transport phase
consists of the electric force applied from the reverse bias condition to the free electron and hole
carriers contributing to their movement and acceleration. Finally the amplification phase consists of
the applied reverse bias voltage imparting enough kinetic energy to the electron to cause further
ionization of more electrons. The avalanche effect is due to this impact ionization [1].
Dead Space
The kinetic energy associated with the electrons inside the PN junction causes the electrons to
accelerate in the depletion region and collide with other electrons to create more electron-hole pairs.
The distance the electrons travel before they impact ionize with other electrons and excite those
electrons into the conduction band is referred to as dead space. These dead space effects are
employed to correctly predict the gain/noise characteristics of devices such as these nanopillars [5].
Figure 1.4 shows a graph associated with the time involved with the dead space effects. As an
electron is “injected” into the depletion layer it is accelerated due to the reverse bias field. The graph
accurately depicts the electron accelerating within the absorption region. Impact ionization then
occurs within the multiplication region. In this multiplication region is where the electron-hole pairs
are made. The graph shows the positively charged holes being drawn to the left as the electrons are
drawn to the right. An injected electron in this case involves an electron being freed from the valence
band into the conduction band as a result of a photon with energy E = hf exciting the electron above
the work function of the material.
Response Time
From the graph in figure 1.4 above, the transit time involved for the distance for the electron to
w
travel through the absorption region from point 1 to point 2 in the graph is
, where w is the ve
a
a
width of the absorption region and v is the velocity of the electron. In the multiplication region the
electron also travels with the velocity v which impaction ionizes and forms more electron-hole pairs.
The holes travel with a velocity v in the opposite direction as the electrons. The hole
w
wa wa
transit time is found to be . The total time is found to be τ =
+τ where τ is the
+
vh vevh multiplication time. The multiplication time is known to be random since
it relies on the multiplication process, which is random in itself.
e
e
h
a
m
m
Responsivity
The responsivity relates the electric current which flows in the device to the incident optical power
[1]. A photon flux (photons/second) produces an electron flux Φ as each incident photon generates a
single photoelectron. This principle corresponds to the short circuit electric current of ip = eΦ. Optical
power is defined as P = hfΦ, where h is plank’s constant, f is the frequency of the
incident photon and Φ is the electron flux. Using substitution from the previous two equations,
eP
the electric current then becomes i = = ℜP , where ℜ is the proportionality factor between the
p
hf
optical power and the electric current and is termed the responsivity of the device. ℜ =
ip
P
and has
ηe λ0
=η
. The responsivity ℜ increases with
h
1.24
λ0 because these detectors are responsive to the photonf flux rather than to the optical power. As the
units of A/W (amps/watt) and is also given by ℜ
=
wavelength of the photon is increased then the optical power s carried by more photons which
product more electrons. Figure 1.5 below shows a graph of the responsivity as a function of
wavelength.
Figure 1.5 – Graph depicting the responsivity ℜ as a dependence of wavelength λ0 using the quantum efficiency
η as a parameter. As at a wavelength of λ0 = 1.24 µm and quantum efficiency η = 1, the responsivity ℜ = 1A/W.
Source [1]
Noise
Noise, which is best described as unwanted interference is usually produced when photon
detection occurs. Several different types of noise are Photon Noise, Photoelectron Noise, Gain
Noise, Receiver Circuit Noise, Background Noise and dark-current noise.
Photon noise arises as a result of random arrivals of individual photons. This type of noise is best
described through Poisson statistics. Photoelectron noise is involved with the randomness of
carrier generation. Unwanted carrier generation is associated with photoelectron noise. Each detected
photon generates a random number of carriers (electrons and holes) with an average value. This value
has an uncertainty that is dependent on the nature of the amplification mechanism. The latter is what
best describes gain noise. Receiver circuit noise is associated with the various components within the
optical receiver. These components such as transistors and receivers contribute to receiver circuit
noise. Background noise is photon noise that arises as a result of various unwanted sources of light
such as sunlight or starlight reaching the detector. Dark current noise is noise that is present even in
the absence of light. This happens as a result of random electron-hole pairs that may be generated
either by tunneling or by thermal excitation [1].
Figure 1.6 - Signal and various noise sources associated with a photodetector with gain such as an APD. Source: [1]
The four sources of noise are shown in figure 1.6. When the input signal enters the detector it has its
own intrinsic photon noise associated with it. As a result of the photoeffect, photons are converted
into photoelectrons. This causes the average signal to decrease by a factor of the quantum efficiency
η. The noise also decreases however it is by a lesser amount than the input photon signal. This causes
the signal to noise ratio of the photoelectrons to be lower than that of the incident photons. Both the
signal and the photoelectron noise are amplified if a photodetector gain mechanism is present. This
amplification also causes its own gain noise. The schematic also shows where the circuit noise enters
where the current collection occurs [1].
1.C. Research Objective
The objective of this research is to offer a new theoretical investigation, which will focus on a new
platform for the single photon avalanche diodes (SPADs). This will utilize the 3dimensional
plasmonic grating, which is self-aligned to a patterned nanopillar array (figure 1.5). The expectation
is that it will produce enhanced absorption along with enhanced avalanche multiplication inside the
nanopillar. This research also focuses on a localized 3-dimensional electric field due to a core shell
PN-junction inside the nanopillar which will act as the
multiplication region all while efficient light absorption via surface plasmon polariton Bloch wave is
taking place at the surface due to the self-aligned metal nanohole lattice as seen in figure
1.7. This research will also observe the capacitance-voltage characteristics associated with the
device along with temperature-dependent breakdown measurements and detailed device modeling
that the avalanche region is on the order of the ionization path length, such that dead space effects
can be observed.
This particular avalanche photodetector is constructed as an array of nanopillar structures as
depicted in figure 1.6 with nanoholes aligned next to each structure which are used to enhance the
absorption of light into the structure [2].
Figure 1.7 – Scanning Electron Micrograph (SEM) of the Nanopillar lattice with the observable nanoholes aligned next
to the nanopillars. Source: [2]
Figure 1.8 – Schematic of one individual structure of the nanopillar array showing where the p-n junction lies inside the
multiplication avalanche diode. Source: [2]
One particular nanopillar structure is shown in figure 1.8. The width and height of the structure are 150nm and 900nm
respectively. The core of the N-GaAs is 80nm in width and 800nm in height. Surrounding the N-GaAs core is a 35nm
thick P-GaAs shell. Each nanopillar is encapsulated with a high bandgap passivation layer of In 0.5Ga0.5P material. The
purpose of the high bandgap passivation layer is to mitigate the effects of surface states, which would cause interference
with the performance of the avalanche photodetector [2]. The high bandgap
passivation layer material has a bandgap associated with it so unwanted photon energy will not
interfere with the device. This interference will cause noise in the device, which would lower its
efficiency. The aligned nanoholes as seen in figure 1.7 have dimensions of (150x200)x10 m at a pitch of
−9
600nm. This is ideal for peak absorption within the specific bandgap of the GaAs material [2]. The doping concentrations for the n-core and p-shell are intended to be
18
−3
~10 cm . The particular observed gain will be the multiplication gain which arises as a result of the avalanche effect. Figure 1.9 below shows a schematic of a nanopillar
structure, which is used for 3D modeling of the capacitance.
Figure 1.10 – Shows where the plasmonic absorption occurs (730nm). This contributes to enhanced photogeneration inside
the nanopillar. Source: [2]
Figure 1.9 – Schematic of a nanopillar structure showing the doping concentrations associated with the p+ GaAs shell
and n+ GaAs base. Source: [2]
Plasmon
Plasma oscillations are rapid oscillations of the electron density in conducting media such as
plasmas and metals. The plasmon is the quasiparticle which results form the quantization of these
oscillations of free electron gas density at optical frequencies for example. A photon can couple
with a plasmon which would create another quasiparticle called a plasma polariton[4].
Plasmonically enhanced absorption can be attained by engineering the geometry of the 3dimensinoal nanopillar antennae which can excite the surface plasmon polariton Bloch waves
(SPP-BWs) [2]. Figure 1.10 shows where the plasmonic absorption occurs. The self-aligned nano
holes channel the light into the device for better efficiency.
A particular device referred to as a Molecular Beam Epitaxy Machine (MBE machine) is used to
construct these particular nanopillar arrays. Epitaxy signifies layers and molecular beam signifies
that specific layers can be created with molecular precision. An MBE machine has a chamber with a
very high vacuum, which is intended to replicate conditions such as in outer space. This is empty
space with no matter inside. To ensure maximum precision, the center of the chamber is super cooled
with liquid nitrogen to cause the impurities to stick to the cooled surface in order to create the high
vacuum needed to fabricate the nanopillar arrays with molecular precision. The MBE machine is
widely used to manufacture semiconductor devices [6].
1.D. Methodology
The fundamental principles and methods described in the introduction such as the photoelectric
effect, responsivity, gain, noise, and the energy behavior of the photon are used to model the
behavior of the single photon nanopillar avalanche photodiodes. Graphical approaches along with
schematics are used to interpret the behavior of these principles.
1.E. Description of Experiments
This research experiment will model the effects of avalanche multiplication using dead space
multiplication theory, also known as DSMT along with carrier multiplication theory which are
described in the results. The DSMT determines the mean gain, excess noise factor and the
probability distribution of the gain [5].
References
[1] Bahaa, E. A. Saleh. & Malvin Carl Teich, (1991), Fundamentals of Photonics. n:p John
Wiley & Sons. Inc.
[2] P. Senanayake, C-H. Hung, A. Farrell, D. A. Ramirez, J. Shapiro, C-K. Li, Y-R. Wu, M. M.
Hayat, and D. L. Huffaker, ``Thin 3D Multiplication Regions in Plasmonically Enhanced
Nanopillar Avalanche Detectors,'' Nano Lett., vol. 12, pp. 6448--6452, 2012.
[3] Wolfram Alpha LLC. 2009. Wolfram|Alpha. http://www.wolframalpha.com/input/?i=2%2B2
(access April 06, 2013).
[4] Wikipedia contributors, 'Plasma oscillation', Wikipedia, The Free Encyclopedia, 26 February
2013, 15:57 UTC,
<http://en.wikipedia.org/w/index.php?title=Plasma_oscillation&oldid=540659122> [accessed 09
April 2013]
[5] M. A. Saleh, M. M. Hayat, B. E. A. Saleh, and M. C. Teich, "Dead-space-based theory
correctly predicts excess noise factor for thin GaAs and AlGaAs avalanche photodiodes," IEEE
Trans. Electron Devices, vol. 47, pp.625-633, March 2000.
[6] Mohamed Henini. (2012). Molecular Beam Epitaxy: From Research to Mass Production.
(p.744). Waltham, MA: Elsevier Inc..
[7] Donald Neamen. (2002). Semiconductor Physics and Devices. (3rd ed., p.768). New York,
NY: McGraw-Hill/Science/Engineering/Math.
[8] Graham, R; Miller, C.; Oh, E.; Yu, D. Nano Letters 2010, 11 (2), 171-722
[9] Photonics Dictionary. (1999). (45th ed.). Pittsfield, MA: Layton Publishing Co. Inc.
[10] M. M. Hayat and D. A. Ramirez,`` Multiplication theory for dynamically biased avalanche
photodiodes: new limits for gain bandwidth product,'' Optics Express, Vol. 20, No. 7, pp. 80258040,
2012.
2. Plasmonically Enhanced Nanopillar Single Photon Avalanche Diodes
REU Student: Benjamin Sandoval
Graduate Mentor: David Ramirez
Faculty Mentor: Dr. Majeed Hayat
2.A. Results
2
At a room temperature of 300K the nanopillar with the active surface area of 53700 µm , which
contains a total of 149160 nanopillars exhibits its typical light and dark current-voltage (I-V)
characteristics. These characteristics are shown in figure 2.1.
Figure 2.1 – Graph showing the light and dark I-V characteristics of NP array contacting ~149160 NPs at 300K.
Source: [2]
The curves shown in figure 2.1 can be fit to the ideal diode equation:
q(V −IRs
nkT)
I = I0 ⋅e
−12
From this equation, I is the current, I is the saturation current having a value of 3×10 A, q is the
elementary charge, V is the bias voltage, R is the series resistance, which holds a value of ~ 40 Ω, T is
the temperature in Kelvin, V is the bias voltage and n is the ideality factor [7]. Typically the ideality
factor n will have a value of 1 if recombination is limited by the minority carriers. The ideality factor
n will hold a value of 2 if recombination is limited by both carrier types (electrons and holes). These
recombinations produce ideality factors, which deviate from the ideal. This gives the term ideality
factor. For this experiment the ideality factor n holds a value of 1.6. From the values given above of
the saturation current, saturation resistance, ideality
0
s
factor and temperature demonstrate excellent diode characteristics. This means that within the
nanopillar device there exists a high quality PN-junction formed. Under light conditions at zero bias
there exists an extremely low photocurrent of 20nA, which typically indicates a short diffusion
length (below 1 µm) resulting in the photogenerated carriers not being extracted by the core-shell
electric field. As the reverse bias voltage is increased, the photocurrent in increased which
corresponds to an increase in the field dependent diffusion length of photogenerated carriers along
with an extension of the depletion region into the low field absorber [8] [2].
Figure 2.3 – capacitance-voltage (C-V) characteristics as a function of area of nanopillar arrays with different
number of nanopillars. Source: [2]
Figure 2.2 - Graph showing plateau region where the punch through voltage occurs at -3V. Source: [2]
When the reverse bias voltage reaches -3V all the photogenerated carriers (holes and electrons) are
extracted in the nanopillar. The graph in figure 2.2 shows the punch through voltage occurring at the
reverse bias voltage of -3V, which indicates maximum expansion of the depletion region within the
PN-junction. The mean gain shown in figure 2.2 is calculated by subtracting the dark current from the
light current, which are shown in figure 2.1. The resulting responsivity shown from this reverse bias
voltage is 0.27 A/W at 730nm. Upon further reverse biasing the device causes the photocurrent to be
multiplied beyond the primary photocurrent. This is contributed by the avalanche multiplication
process. This increased reverse bias causes an increase in avalanche gain up to gains as high as ~216
and a reverse bias voltage of -12V [2]. The doping and the geometry of the nanopillar as seen from
figure 1.9 are used for modeling the capacitance-voltage (C-V) characteristics. The capacitance
characteristics are shown in figure 2.3 as a function of area with a frequency of 1MHz. The
capacitance characteristics and frequency are used to sample the junction capacitance within the
PN-junction in the device.
2
Figure
2.4bias
– Contour
plot showing within
the electric
through junction
the center of
individual
nanopillar
the abreakdown
At zero
the capacitance
thefield
core-shell
is an
around
0.347
fF /µm atand
small reverse
voltage of -10V. Source [2]
bias of -1V results in around a 50% drop in the capacitance. Higher reverse biases result in the
saturation of the capacitance to around 0.05 fF /µm . It is estimated that the ultrasmall saturation
capacitance would allow these nanopillar arrays to have an RC limited bandwidth that would exceed
40GHz. This would take place with as few as 3000 nanopillars. Figure 2.4 below shows a contour
plot of the electric field within an individual nanopillar. This electric field results at the breakdown
voltage of -10V in the device. The electric field shown in the contour plot is a high electric field
above 5×10 V /cm. This electric field is confined to within 310 nm of the tip of the core-shell junction.
The resulting impact ionization as a result of this electric field is also confined to a very small
volume. The dotted white line in the figure marks the center of the nanopillar.
2
5
The axial electric field profile as a function of the reverse bias voltage through the center of the
nanopillar is shown below in figure 2.5. An axial region of around 310 nm is where the electric field
is confined. The plot below shows the confined electric field to be located from ~590nm to ~900nm.
A highly localized field of around 1MV/cm is also seen in the plot, which is taking place at the tip of
the core within the nanopillar.
Figure 2.5 – Plot showing the axial electric field profile along the pillar as a function of the reverse voltage bias.
Source [2]
The expected gain is modeled as a result of the bias dependent electric field using both local
carrier multiplication theory and carrier multiplication theory. For local theory, the mean
multiplication (M) is calculated using the equation 1 below.
x
0
M (x0)
=
∫
exp[
(α(x)−β(x))dx]
0
Wx
1−∫α(x)exp[−∫ (α(x')−β (x'))dx']dx
00
From equation 1 above, M is the mean multiplication, α is the electron-ionization coefficient, β is the
hole-ionization coefficient. The data is evaluated at x = W where W is the position of the depletion
edge. Figure 2.6 shows the plot of the temperature-dependent I-V characteristics of the core-shell
nanopillar diodes. The high reverse biases range from 77K up to 300K as shown within the plot.
0
Figure 2.6 – Plot showing the temperature dependence of avalanche breakdown. Source [2]
2.B. Conclusion
This research has experimented with the position controlled plasmonically enhanced avalanche
diodes, which have thin avalanche regions. Avalanche gains as high as ~216 were observed as a
result of the engineered 3-dimensional geometric shape of the core-shell junction within the
nanopillar. A junction capacitance as low as 0.05fF /µm is observed. The core-shell PN diodes exhibit
diode characteristics with ideality factors of 1.6 [2]. The temperature-dependent CV measurements
show a breakdown voltage shift of +3.3mV/K, which confirms that the gain mechanism is shown to
occur from avalanche breakdown [2]. DSMT was used to model the avalanche multiplication and
shows that the dead space effects are shown to be dominant in the avalanche characteristics of the
thin regions which avalanche multiplication occurs. [2]
2
2.C. Future Work
The engineering work associated with the 3-dimensional confined multiplication regions in these
...............................................................................................................................
plasmonically enhanced nanopillar avalanche diodes presents a clear path in the engineering of the
dead
space effects in these devices.
High performance avalanche diode detectors will transform the
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performance
of detection efficiency in the use of single photon
for applications in
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........... detection
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telecommunications along with future works in quantum communications and direct-detection
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high-speed lightwave communication systems [10].
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䘀椀最甀爀攀
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