The value of the ionization ratio \(k\) for this structure is thus substantially reduced in comparison to a conventional structure of the same material.

“Every element [of this project] worked like in an orchestra,” Meretska says. “Both sample fabrication and measurement processes are incredibly challenging and knowing everything worked as designed was very satisfying.”

Academics, Applied Physics, Alumni, Bioengineering, Diversity / Inclusion

Extreme UVmeaning

In principle, a p-n or p-i-n diode biased near its breakdown voltage can have an avalanche multiplication gain, thus functioning as an APD.

Find the 3-dB cutoff frequency and the gain-bandwidth product of this APD when it operates at a multiplication gain of \(G=10\) with a load resistance of \(R_\text{L}=50\) Ω.

Sophisticated heterostructures, including those using quantum wells and graded-gap layers, have been developed to improve the performance characteristics of APDs.

This acrylic Frensel lens magnifier provides 3.5X magnification. It is large enough to magnify a full page. There are Grasp-bars on the side of the Fresnel Lens ...

A new perforated metalens proves it is possible to use nano-optics to focus beams of extreme ultraviolet light (EUV) and could open new doors in microscopy, sensing, holography, and fundamental physics research. The advance is reported in Science.

Because \(k\gt1\) in InP, hole injection, rather than electron injection, into the avalanche region for multiplication is desired in this device. Therefore, it is the \(\text{n}^--\)InP layer that is placed on the \(\text{p}^+\) side next to the \(\text{p}^+-\)InP layer.

In the reach-through structure shown in Figure 14-28, photons are absorbed to generate electron-hole pairs mainly in the thick \(\pi\) region. The photogenerated electrons, which are minority carriers in the \(\pi\) region, are accelerated and injected into the thin \(\text{p}-\text{n}^+\) junction where avalanche multiplication takes place in the presence of a high electric field.

The breakthrough will have implications for attosecond physics, as the metalens can be used to better understand light and matter interactions on the nanoparticle scale. Capasso says the semiconducting industry will also benefit from EUV metalens technology because it will enable the fabrication of smaller and smaller transistors and processors. But, perhaps most exciting, Capasso says there are likely many future applications that haven’t yet been thought of.

In the avalanche region, the multiplication process is not instantaneous but takes time to build up. The avalanche buildup time is a function of the gain, the ionization ratio, and the thickness of the avalanche region.

At a certain value of \(\alpha_\text{e}d_\text{m}\) and its corresponding value of \(\alpha_\text{h}d_\text{m}\) for a given \(k\), however, \(G\) increases quickly to approach infinity. The consequence is an instability leading to avalanche breakdown.

The energy drop at each conduction-band step is larger than the threshold impact-ionization energy for electrons. The electrons drift through a low-field region without multiplication, but they impact ionize when passing through an abrupt conduction-band step.

The excess noise degrades the SNR of an APD when compared with an ordinary photodiode of the same quantum efficiency. Therefore, the use of an APD instead of an ordinary photodiode such as a p-i-n photodiode makes sense only when amplifiers are needed in the use of an ordinary photodiode for the detection of low-power optical signals.

The Capasso group’s latest breakthrough – fabricating a metalens that uses nano-sized holes to vacuum-guide EUV -- introduces a game-changing workaround. “This work will revolutionize optics in a spectral region (extreme UV) where, until now, there were no lenses or viable optics for high-performance or high-volume applications,” says Capasso, co-corresponding author, who is the Robert L. Wallace Professor of Applied Physics and Vinton Hayes Senior Research Fellow in Electrical Engineering at SEAS. The new work was in collaboration with Martin Schultze’s lab at Graz University of Technology.

The idea was originally conceived by Marcus Ossiander, a postdoctoral fellow in Capasso’s group, whose background is in attosecond physics, or the study of how light and matter interact on the inconceivably-small timescale of quintillionths of a second. “The only way you can create laser pulses on the attosecond scale is using these very short wavelengths of ultraviolet light,” Ossiander says. “I had this big dream, a bit of a moonshot, really, to create a metalens that could control EUV. And Federico will never stop you from pursuing a dream.”

For Si, \(k\lt1\), and the value of \(k\) can be as small as 0.01, depending on the field strength. Therefore, impact ionization in Si is completely dominated by electrons.

The signal-current frequency response of an APD has the form of (14-93) [refer to the junction photodiodes tutorial] but with the time constant \(\tau\) given in (14-115):

where \(v_\text{e}^\text{a}\) and \(v_\text{h}^\text{a}\) are, respectively, the electron and hole drift velocities in the absorption region.

Since that initial metalens demonstration, researchers far and wide have been adopting the technique to create metalens designs that exert increasingly complex control over visible and infrared light – but harnessing such metasurfaces to control light in the EUV range has remained out of reach. EUV wavelengths are extremely small, around the 50-nanometer range, which is much smaller than visible wavelengths of light, which are 400 to 700 nanometers in size. At such a small wavelength, EUV is absorbed by all materials, preventing that light from being refracted and controlled by transmissive optics.

“Fabrication, in general, requires a lot of perseverance,” Meretska says. “It took many attempts to realize the working sample. We learned something new about the process with every attempt, and that kept me going.”

A superlattice InGaAs/InP SAM APD designed for optical detection in the infrared spectral range covering 1.3 and 1.55 μm wavelengths has the structure shown in Figure 14-29(b).

Small Bracket. 8621 likes · 9 talking about this · 27 were here. Small Bracket is a Children's brand with an aim to provide one stop solution to parents...

The absorption coefficients of the InGaAs absorption layer at 1.3 and 1.55 μm wavelengths are \(\alpha=1.2\times10^6\text{ m}^{-1}\) and \(\alpha=6.6\times10^5\text{ m}^{-1}\), respectively.

Part of this work was performed at Harvard’s Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Coordinated Infrastructure (NNCI), which is supported by the NSF under award no. ECCS-2025158. Computations were run on the FASRC Cannon cluster supported by the FAS Division of Science Research Computing Group at Harvard University. This research was supported by the Alexander von Humboldt Foundation (Feodor-Lynen Fellowship), the Austrian Science Fund (FWF, Start Grant Y1525), the European Union (grant agreement 01076933 EUVORAM), A*STAR Singapore through the National Science Scholarship Scheme, and the Air Force Office of Scientific Research (AFOSR) under award Number FA9550-21-1- 0312.

Ultravioletlightexamples

At the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS), Federico Capasso’s lab unveiled in 2011 the groundbreaking concept of refracting metasurfaces, or sub-wavelength-spaced arrays of nanostructures, with a Science paper that has since been cited 7,000 times. In 2016, another Science paper reported the use of high-performance flat lenses made up of nanopillars and fabricated using lithography techniques, which unlocked a new strategy to focus light. That work was a major leap forward for conventional optical devices that had historically been fabricated by molding, making them thick and bulky.

Because these superlattice materials have \(k\lt1\), electron injection, rather than hole injection, is desired. Consequently, this superlattice multiplication layer is place on the \(\text{n}^+\) side of the structure, and the InGaAs absorption layer is now on the \(\text{p}^+\) side.

A detailed analysis of the time response of an APD is very complicated because it has to take into account the spatial variations of the field strength and the carrier distribution in each region, as well as the spatial variations in \(\alpha_\text{e}\), \(\alpha_\text{h}\), and \(k\) in the avalanche region. However, by taking these parameters to be constants of their respectively spatially averaged values, a simplified analysis yields results that are very good approximations to accurate values.

When the diffusion time of carriers in the diffusion regions is minimized, the intrinsic time constant for the signal current in an APD is the sum of the transit time and the avalanche buildup time:

\[\tag{14-114}\tau_\text{av}\approx\frac{G}{k}\frac{d_\text{m}}{v_\text{h}^\text{m}}+\frac{d_\text{m}}{v_\text{e}^\text{m}}\]

In an APD, the average drift velocities of electrons and holes remain at the saturation velocities, but high-energy carriers at the tail of the energy distribution can have kinetic energies higher than the threshold energies for impact ionization.

Like any photodiode, the response time of an APD is determined by both the response time of its signal current and the time constant of its equivalent circuit.

The avalanche photodiode (APD) is the solid-state counterpart of the PMT (photomultiplier tube) [refer to the photoemissive detectors tutorial]. An APD versus an ordinary junction photodiode [refer to the junction photodiodes tutorial] is similar to a PMT versus a vacuum photodiode [refer to the photoemissive detectors tutorial].

The photogenerated holes in the \(\pi\) region are collected in the \(\text{p}^+\) region without multiplication because of the low field in that region.

“We don’t currently know all the fields that might benefit from EUV metalenses, because no one expected that this type of technology would be possible anytime soon,” Ossiander says.

The bandgap in each layer increases linearly from a small value of \(E_\text{g1}\) to a large value of \(E_\text{g2}\) with an abrupt drop back to \(E_\text{g1}\) at the end of the layer.

where \(V_\text{r}\) is the reverse voltage on the APD, \(V_\text{br}\) is the avalanche breakdown voltage, and \(n\) is an empirically fitted parameter typically in the range of \(3-6\). The values of \(V_\text{br}\) and \(n\) depend strongly on the device structure and operating temperature.

To reduce the noise caused by the leakage current at the edges of the \(\text{p}-\text{n}^+\) junction and to avoid local breakdown at these edges, a guard ring around the edges is often incorporated into a reach-through Si APD, as also shown in Figure 14-28.

“This work really pushed the limits of what’s possible in nanotechnology today,” Capasso says. “We needed impeccable fabrication methods to make this metalens with features small enough to interact with EUV wavelengths, which means the features must be smaller than those wavelengths. It pushed us to shrink the metalens features by a factor of 10 compared to what’s been done before – it was really a very large leap.”

Figure 14-28 shows the structure and the field distribution in reverse bias of a Si SAM APD consisting of \(\text{p}^+-\pi-\text{p}-\text{n}^+\) layers.

We see from the above two relations that the multiplication gain \(G\) increases nonlinearly with an increase in the value of \(\alpha_\text{e}d_\text{m}\), with a corresponding increase in that of \(\alpha_\text{h}d_\text{m}\), for any given value of \(k\).

At the operating bias voltage of the device, the energy band has a pattern like that shown in Figure 14-30(b). Photogenerated electrons in the \(\text{p}^+\) region are injected into successive stages of alternating low-field graded-gap regions and high-field conduction-band steps.

where \(v_\text{e}^\text{m}\) and \(v_\text{h}^\text{m}\) are, respectively, the electron and hole drift velocities in the avalanche multiplication region.

A superlattice InGaAs/InP APD, which is described in further detail in Example 14-16 below, has an avalanche multiplication region that consists of an InAlGaAs/InAlAs superlattice layer of \(d_\text{m}=231\text{ nm}\). It has an ionization ratio of \(k=0.25\). When an average electric field of \(E_\text{m}=63\text{ MV m}^{-1}\) is established by a reverse bias voltage in this avalanche multiplication layer, the electron ionization coefficient is \(\alpha_\text{e}=6.5\times10^6\text{ m}^{-1}\).

The absorption layer of an APD is equivalent to the intrinsic region of a p-i-n photodiode. It is either intrinsic or very lightly doped and is depleted to maintain a sufficiently high field in this region for a short carrier transit time.

The impact ionization process is characterized quantitatively by the ionization coefficients, \(\alpha_\text{e}\) for electrons and \(\alpha_\text{h}\) for holes (quoted per meter, but also often quoted per centimeter).

Harvard’s Office of Technology Development has protected the intellectual property arising from this study and is exploring commercialization opportunities.

In the photon-counting mode of operation, the reverse bias voltage is set above the breakdown voltage. In this situation, a single photon can trigger a constant flow of photocurrent because \(G\rightarrow\infty\) for \(V_\text{r}\gt{V}_\text{br}\), according to (14-107).

A concept for optimizing both photogeneration and avalanche multiplication in an APD is to use a separate absorption and multiplication (SAM) structure, which has separate regions for the two functions.

We see that \(F_\text{h}\) is about nine times \(F_\text{e}\). Clearly, the avalanche multiplication process in this device of \(k\lt1\) has to be initiated by electrons, not by holes. in order to minimize the excess noise. If holes are injected instead, the excess noise factor would be enhanced by as much as nine times, resulting in a significant increase in the APD noise.

May 15, 2023 — Focal length is measured in millimeters, and the higher the number, the longer the focal length. A lens with a focal length of 50mm is ...

Magnification, 5x, 10x ; Numerical Aperture, 0.1, 0.25 ; Wavelength Range, 400-700 nm, 400-700 nm ; Effective Focal Length (EFL), 25.4 mm, 16.5 mm ; Working ...

\[\tag{14-111}\overline{i_\text{n}^2}=2eBGF(\overline{i_\text{s}}+\overline{i_\text{b}}+\overline{i_\text{d}})+\frac{4k_\text{B}TB}{R_\text{L}}\]

The threshold kinetic energies for an electron or hole to initiate impact ionization in a semiconductor of a bandgap \(E_\text{g}\) fall between \(E_\text{g}\) and \(2E_\text{g}\), depending on the effective electron and hole masses and the details of the band structure.

With the given parameters, we have \(\alpha_\text{e}d_\text{m}=6.5\times10^6\times231\times10^{-9}=1.5\). The multiplication gain is obtained by using (14-105)

Because the field strengths in these two regions are different, and their material compositions can also be different in heterostructure APDs, the carrier velocities in these two regions can be different even when they are all close to or at their respective saturation values.

The gain of an APD is very sensitive to both reverse bias voltage and temperature. Voltage and temperature stabilization is often required for the operation of an APD at a constant gain.

The avalanche multiplication layer requires an even higher field. Thus, it is also intrinsic or very lightly doped. Besides, it is much thinner than the absorption layer: \(d_\text{m}\ll{d}_\text{a}\).

In normal operation, an APD is biased at a fixed voltage below, but close to, the breakdown voltage. Typical gains range from 10 to 20 for Ge and InGaAs APDs, and from 50 to 200 for Si APDs.

Holes do not contribute to avalanche multiplication but are quickly swept away because the moderately high field in the valence-band is not large enough to cause impact ionization by holes.

\[\tag{14-120}f_\text{3dB}\approx\frac{0.443}{[\tau^2+(2.78\tau_\text{RC})^2]^{1/2}}=\frac{1}{2\pi[\tau_\text{RC}^2+(0.36\tau)^2]^{1/2}}\]

In this structure, the avalanche region consists of either an InGaAsP/InAlAs superlattice or an InAlGaAs/InAlAs superlattice that is lattice matched to InP.

In the presence of a high electric field, the newly generated electron and hole can be accelerated to gain sufficient kinetic energies for impact ionization to generate more electron-hole pairs. A cascade of these events leads to avalanche multiplication of the photogenerated carriers.

Because of the noise from the amplifiers, an APD can have a better SNR than a photodiode-amplifier combination to justify the use of the APD. This situation occurs when detecting high-frequency signals at very low power levels because the amplifier noise dominates the detector noise at high frequencies.

Because this device has a very small \(k\) value and a small excess noise factor, it has improved performance characteristics in terms of optimized gain, reduced noise, and increased speed.

P&R Infrared offers a comprehensive selection of thermal rifle scopes, thermal cameras, and thermal gun sights to let you see in complete darkness and ...

From (14-108) and (14-109), we see that it is important to have the correct type of carriers injected into the avalanche regions in order to minimize the excess noise because injection of the wrong type of carriers will lead to a very large value of \(F\).

All APDs generate excess noise because of the statistical nature of the avalanche multiplication process. The excess noise factor \(F\) for an APD is a function of the avalanche multiplication gain \(G\) and the ionization ratio \(k\).

Extreme uv lightlithography

For typical III-V semiconductors, most of the heterostructure bandgap difference occurs in the conduction band. In reverse bias, the voltage applied to the device drops almost entirely across the nearly intrinsic multilayer graded-gap region.

The secondary hole then takes a time of \(\tau_\text{tr}^\text{h}\) to drift back to the \(\text{p}^+\) side  where it is collected. Because the drift of a secondary hole follows the drift of its primary electron, the transit time in an APD is twice as long as that in an ordinary photodiode of the same intrinsic absorption-layer thickness:

Find the excess noise factor for the APD considered in Example 14-14 if electrons are injected into its avalanche region to initiate the avalanche multiplication process. What is its excess noise factor if holes are injected instead?

The impact ionization ratio is \(k=0.25\). The active area of this APD has a diameter of \(2r=40\) μm. It has a total capacitance, including its internal capacitance and parasitic capacitance, of \(C=300\) fF and a parasitic series resistance of \(R_\text{s}=10\) Ω.

For an APD that has a uniform field across its avalanche multiplication region of thickness \(d_\text{m}\), the field-dependent parameters \(\alpha_\text{e}\), \(\alpha_\text{h}\), and \(k\) have spatially independent, constant values over the thickness \(d_\text{m}\).

\[\tau_\text{tr}=\frac{d_\text{a}}{v_\text{e}^\text{a}}+\frac{d_\text{a}}{v_\text{h}^\text{a}}=\left(\frac{1\times10^{-6}}{8\times10^4}+\frac{1\times10^{-6}}{6\times10^4}\right)\text{ s}=29\text{ ps}\]

Extreme uv lightuses

In this mode of operation, an APD is capable of counting single photons, like a PMT (photomultiplier tube) [refer to the photoemissive detectors tutorial].

We find that \(2.78\tau_\text{RC}=50\) ps, which is the same as \(\tau\). Thus the bandwidth of this APD in the given operating condition is equally determined by both its intrinsic time constant and its RC time constant. We have

The avalanche multiplication in this APD is initiated by electrons. With \(d_\text{m}=231\) nm, \(k=0.25\), and \(G=10\), the avalanche buildup time in the multiplication layer is

Extreme UVwavelength

The ionization coefficient for an electron or hole represents the probability for an electron or hole that travels a unit distance to create an electron-hole pair through impact ionization.

The operation of an APD in this mode is controlled by an external circuit to quench the breakdown current by reducing the voltage on the APD to below the breakdown voltage after a photon triggers the breakdown. The APD is then ready to respond to the next incoming photon.

Typical metalenses rely on the fabrication of nanopillars that – sticking up like the skyscrapers of the Manhattan skyline – refract visible light and focus it in desired ways. But with EUV light being absorbed by all materials it reaches, Ossiander knew that strategy would not work. As he contemplated the way materials interact with light that oscillates incredibly fast, a creative new idea struck him.

The excess noise factor of a staircase APD is also much reduced due to the fact that impact ionization in this device is localized at the conduction-band steps.

An internal gain is built into an APD to multiply the photogenerated electrons and holes. The physical process responsible for the internal gain in an APD is avalanche multiplication of charge carriers through impact ionization, as illustrated in Figure 14-16.

Extremeultraviolet lithography machine

In the normal operating condition of the APD, the electron and hole drift velocities are \(v_\text{e}^\text{a}=8\times10^4\text{ m s}^{-1}\) and \(v_\text{h}^\text{a}=6\times10^4\text{ m s}^{-1}\) in the InGaAs absorption layer and \(v_\text{e}^\text{m}=4.2\times10^4\text{ m s}^{-1}\) and \(v_\text{h}^\text{m}=3.2\times10^4\text{ m s}^{-1}\) in the InAlGaAs/InAlAs superlattice multiplication layer.

These kinetic threshold energies are much higher than the kinetic energies of electron and holes at their respective saturation velocities. Therefore, no avalanche multiplication takes place in an ordinary photodiode even when the photogenerated electrons and holes in the device are accelerated to reach their respective saturation velocities, such as in a high-speed p-i-n photodiode.

\[\tag{14-105}G=\frac{1-k}{\text{e}^{-(1-k)\alpha_\text{e}d_\text{m}}-k}=\frac{1-1/k}{\text{e}^{-(1-1/k)\alpha_\text{h}d_\text{m}}-1/k}\]

\[\tau_\text{av}\approx{Gk}\frac{d_\text{m}}{v_\text{e}^\text{m}}+\frac{d_\text{m}}{v_\text{h}^\text{m}}=\left(10\times0.25\times\frac{231\times10^{-9}}{4.2\times10^4}+\frac{231\times10^{-9}}{3.2\times10^4}\right)\text{ s}=21\text{ ps}\]

We have \(k=0.25\) and \(G=10\) from Example 14-14. If electrons are injected, the excess noise factor is found using (14-108) to be

This structure is the solid-state equivalent of the PMT (photomultiplier tube) [refer to the photoemissive detectors tutorial], with each graded-gap layer functioning as an electron multiplication state equivalent to a dynode in a PMT.

In an APD where electron multiplication dominates the avalanche process, an electron generated on the \(\text{p}^+\) side of the absorption layer can generate a secondary electron-hole pair in the avalanche region located on the \(\text{n}^+\) side of the absorption layer after taking a time of \(\tau_\text{tr}^\text{e}\) to drift through the absorption layer.

Amazon.com: WEITOL Wall Mounted Makeup Mirror, 1X＆3X/5X/7X/10X Magnification Vanity Mirrors, Bathroom 8 Inch Double Sided Extendable Swivel Shaving Mirrors ...

At each potential step, each electron acquires only enough energy to generate one secondary electron-hole pair. The only excess noise comes from the probability that an electron, though having enough energy, may or may not impact ionize at a given potential step.

Neutral gray McCrone linear polarizing film has applications ranging from microscopy to large aperture optical systems.

Its response speed, or time resolution, in counting successive photons is determined by the speed of the external circuit. With a passive current-quenching circuit that consists of current-limiting resistors, the time resolution is on the order of a few nanoseconds, limited by the RC time constant of the circuit. With an active current-quenching circuit consisting of a current-switching transistor, the time resolution can be as high as 20 ps, limited by the switching speed of the transistor in the circuit.

It consists of a nearly intrinsic \(\pi-\)InGaAs absorption layer of \(d_\text{a}=1\) μm, an undoped InAlGaAs/InAlAs superlattice multiplication layer of \(d_\text{m}=231\) nm, and a heavily doped \(\text{p}^+-\)InP buffer layer of a very small thickness of 30-50 nm between these two layers.

“Why not flip the design… to make transmissive pillars… out of air?” he says. By making holes in the surface of a material with a lower refractive index than air itself, he hypothesized that EUV could be guided and focused using the vacuum inside the holes. When computer simulations suggested it might actually work, he teamed up with nanofabrication expert Maryna Leonidivna Meretska, a postdoctoral researcher in Capasso’s lab, to develop a prototype.

The shot noise of an APD has the form given in (14-25) [refer to the photodetector noise tutorial] for a photodetector that has an internal gain.

The absorption region in this \(\text{P}^+-\text{N}^--\nu-\text{n}^+\) heterostructure is the InGaAs \(\nu\) region, which has a smaller bandgap than the InP layers. Holes that are photogenerated in this region are injected into the avalanche region at the InP \(\text{p}^+-\text{n}^-\) junction for avalanche multiplication. Photogenerated electrons are collected in the InGaAs \(\text{n}^+\) region without multiplication.

The spectral response of an APD is similar to that of an ordinary photodiode with a threshold photon energy of \(E_\text{th}=E_\text{g}\) determined by the bandgap of the absorption region where electron-hole pairs are photogenerated.

\[f_\text{3dB}=\frac{0.443}{[\tau^2+(2.78\tau_\text{RC})^2]^{1/2}}=\frac{0.443}{[50^2+50^2]^{1/2}\times10^{-12}}\text{ Hz}=6.26\text{ GHz}\]

We find that \(\tau_\text{tr}\) is comparable to but somewhat larger than \(\tau_\text{av}\) for this APD in the given operating condition. Thus, the intrinsic time constant

\[\tag{14-116}\mathcal{R}_\text{s}^2(f)=\left|\frac{i_\text{s}(f)}{P_\text{s}(f)}\right|^2\approx\mathcal{R}_\text{s}^2(0)\left(\frac{\sin\pi{f\tau}}{\pi{f}\tau}\right)^2\]

Because we do not have the information on the parameter \(n\), we can only calculate the limits of the reverse bias voltage to be \(19.31\text{ V}\le{V_\text{r}}\le19.65\text{ V}\) by assuming that \(3\le{n}\le6\).

The excess noise of an APD is minimized if \(k\lt1\) when only electrons contribute to avalanche multiplication, or if \(k\gt1\) when only holes contribute to avalanche multiplication. The theoretical minimum of the excess noise factor for an APD is \(F=2-1/G\) for \(k=0\) in (14-108) or \(k=\infty\) in (14-109).

Extremeultraviolet lithography

An ordinary p-n or p-i-n structure is not ideal for an APD because both photogeneration and avalanche multiplication of carriers take place in its depletion layer. Some Ge APDs have \(\text{n}^+-\text{p}\), \(\text{n}^+-\text{n}-\text{p}\), or \(\text{p}^+-\text{n}\) structures, which are acceptable but not optimum.

The avalanche buildup time is unique to APDs. The other three factors are common to all photodiodes, but the transit time in an APD is different from that in an ordinary photodiode.

The small-signal equivalent circuit of an APD is shown in Figure 14-27(a). It is similar to that of an ordinary junction photodiode [refer to the junction photodiode tutorial], except that the avalanche multiplication gain is included in the signal current \(i_\text{s}=Gi_\text{ph}\) for an APD. Figure 14-27(b) shows the noise equivalent circuit of an APD.

Jan 5, 2021 — Use the condenser diaphragm to reduce the amount of light and increase the contrast of the image. Condenser Focusing Knob - This control is used ...

In such a structure, photogeneration takes place in a relatively thick region of a moderately high field to reduce the carrier transit time, whereas the ionizing carriers are injected into a thin region of a very high field for avalanche multiplication.

\[\tag{14-112}\tau_\text{tr}=\tau_\text{tr}^\text{e}+\tau_\text{tr}^\text{h}=\frac{d_\text{a}}{v_\text{e}^\text{a}}+\frac{d_\text{a}}{v_\text{h}^\text{a}}\]

Extreme UVweather

This structure is called the reach-through structure because the depletion layer under a large reverse bias voltage in the operating condition of this device reaches through the \(\pi\) and \(\text{p}\) regions from the \(\text{p}^+\) region to the \(\text{n}^+\) region.

For this reason, an avalanche region consisting of a material with \(k\lt1\) is placed on the \(\text{n}^+\) side opposite to an absorption layer on the \(\text{p}^+\) side so that electrons are injected into the avalanche region in reverse bias, whereas an avalanche region consisting of a material with \(k\gt1\) is placed on the \(\text{p}^+\) side opposite to an absorption layer on the \(\text{n}^+\) side so that holes are injected into the avalanche region in reverse bias. This point can be clearly seen in the two structures shown later in Figure 14-29.

Because of the internal gain, the responsivity of an APD is \(\mathcal{R}=G\mathcal{R}_0\), where \(\mathcal{R}_0\) is the intrinsic responsivity of an equivalent photodiode without an internal gain.

Sep 12, 2022 — Waves having such a direction are said to be polarized. For an EM wave, we define the direction of polarization to be the direction parallel to ...

In the impact ionization process, an electron or hole of a sufficiently high kinetic energy can create a secondary electron-hole pair by transferring its kinetic energy to the excitation of the secondary carriers through collision with the lattice.

The total current gain, \(G=i_\text{s}/i_\text{ph}\) as defined in (14-23) [refer to the photodetector noise tutorial], of an APD is the avalanche multiplication factor of photogenerated carriers. It depends on the thickness and the structure of the avalanche region in the APD, as well as on the reverse voltage applied to the APD.

Once the prototype was complete, Ossiander flew to the Institute of Experimental Physics at Graz University of Technology in Austria, one of few labs in the world that can create EUV. There, researchers led by attosecond physicist Martin Schultze (a co-corresponding author on the study) sent EUV radiation through the metalens prototype. After many experiments, the team saw what they had long dreamed of: a small spot, indicating the concentration of light, detected by a special camera.

Because \(V_\text{r}\) is very close to \(V_\text{br}\), the multiplication gain is very sensitive to the reverse bias voltage. For example, if we take \(n=3\) but use \(V_\text{r}=19.65\text{ V}\), which is obtained for \(n=6\), we find a gain of \(G=19.4\) instead of \(10\). This example shows that stabilization of both voltage and temperature is very important for an APD to function at a constant gain as both \(V_\text{br}\) and \(n\) vary sensitively with temperature.

The ionization ratio is a function of field strength and temperature. It also varies among different semiconductors. When \(k\lt1\), impact ionization by electrons dominates. When \(k\gt1\), impact ionization by holes dominates.

There is also a thin \(\text{p}^+-\)InP buffer layer in this structure. This heavily doped buffer layer allows a sharp transition from a very high field strength in the avalanche region to a lower field in the absorption region so that relatively constant, but very different, field strengths can be maintained in both regions. Its purpose is to suppress undesirable tunneling dark current generation and avalanche multiplication in the absorption layer.

The 3-dB cutoff frequency of an APD can be approximated by a relation similar to that given in (14-99) [refer to the junction photodiodes tutorial]:

\[\tag{14-119}\mathcal{R}^2(f)=\mathcal{R}_\text{s}^2(f)\mathcal{R}_\text{ckt}^2(f)=\frac{\mathcal{R}^2(0)}{1+4\pi^2f^2\tau_\text{RC}^2}\left(\frac{\sin\pi{f\tau}}{\pi{f\tau}}\right)^2\]

The SNR of an APD has the form given in (14-33) [refer to the photodetector noise tutorial] for a photodetector that has an internal gain.

Figure 14-30(a) and (b) show, respectively, the unbiased and biased band diagrams of a staircase APD, which consists of multiple nearly intrinsic, or lightly doped, graded-gap layers between the \(\text{p}^+\) and \(\text{n}^+\) regions.

As we shall see below, to maximize the avalanche gain and minimize the excess noise, an ideal APD must have only electrons initiating impact ionization, thus \(k\ll1\), or only holes initiating impact ionization, thus \(k\gg1\). A \(k\) value close to unity is not desirable because it limits the avalanche gain due to a large excess noise.

The graded gap in this structure is made by varying the composition of a semiconductor material, such as the composition \(x\) in AlxGa1-xAs.

Both \(\alpha_\text{e}\) and \(\alpha_\text{h}\) are characteristics of a semiconductor and are strong functions of both electric field strength and temperature. They increase rapidly with an increasing electric field strength but decrease with increasing temperature.

In this ideal situation, the avalanche multiplication gain for electron or hole injection into the avalanche region can be expressed as

In practice, however, the structure of an APD is designed to optimize both the quantum efficiency and the avalanche multiplication gain of the device.

There are two modes of operation for an APD. In the normal mode of operation discussed above, the bias voltage is set at a fixed value just below the breakdown voltage. As can be seen from (14-107), the device has a fixed gain at a given operating temperature for \(V_\text{r}\lt{V}_\text{br}\).

Linear and Circular Polarized 3D Glasses & Clip-Ons. From the world leader in high end passive polarized 3D eyewear comes 3DLUX®, an acrylic laminated circular ...