Multiplication Region Width Research Articles

Theoretical Analysis of AlAs₀.₅₆Sb₀.₄₄ Single Photon Avalanche Diodes With High Breakdown Probability

Single photon avalanche diodes (SPADs) are key enabling technologies for a wide range of applications in the near-infrared wavelength range. Recently, AlAs <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.56</sub> Sb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.44</sub> (hereafter AlAsSb) lattice-matched to InP has been demonstrated for extremely low excess noise avalanche photodiodes (APDs) due to its large disparity between electron and hole ionization coefficients ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> respectively). The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha /\beta $ </tex-math></inline-formula> ratio also plays a role in Geiger mode operation as it affects the avalanche breakdown probability and hence detection efficiency. In this work, we theoretically investigate the performance of AlAsSb based SPADs. The probability of breakdown for electron-initiated Geiger mode operation increases more sharply with multiplication region width due to progressively more dissimilar ionization coefficients. In comparison with other common avalanche materials, such as InAlAs, InP and Si, our result also suggests that SPADs based on AlAsSb have a sharper breakdown probability than the other three materials under similar low overbias ratio. The calculated breakdown probability of 0.81 in AlAsSb is 0.18 and 0.28 higher than that of InAlAs/Si and InP respectively at 5% overbias ratio and with avalanche region width of 1500 nm.

Analytical Formulas for Mean Gain and Excess Noise Factor in InAs Avalanche Photodiodes

It has been known that McIntyre’s local multiplication theory for avalanche photodiodes (APDs) does not fully explain the experimental results for single-carrier InAs APDs, which exhibit excess noise factor values below 2. While it has been established that the inclusion of the dead-space effect in the nonlocal multiplication theory resolves this discrepancy, no closed-form formulas for the mean gain and excess noise factor have been specialized to InAs APDs in a nonlocal setting. Upon utilizing prior analytical formulation of single-carrier avalanche multiplication based on age-dependent branching theory in conjunction with nonlocal ionization coefficients and thresholds for InAs, closed-form solutions of the mean gain and the excess noise factor for InAs APDs are provided here for the first time. The formulas are validated against published experimental data from InAs APDs across a variety of multiplication region widths and are shown to be applicable for devices with multiplication widths of 500 nm and larger.

Avalanche Noise in Al0.52In0.48P Diodes

Multiplication and avalanche excess noise measurements have been undertaken on a series of AlInP homo-junction p-i-n and n-i-p diodes with $i$ region widths ranging from 0.04 to 0.89 $\mu \text{m}$ , using 442 and 460 nm wavelength light. Low dark currents of $^{\mathrm {-2}}$ at 95% of breakdown voltage were obtained in all the devices because of its wide bandgap and there was no tunneling dark current present even at high fields >1000 kV/cm. For a given multiplication factor, the excess noise decreased as the avalanche width decreased due to the dead-space effect. Using 460 nm wavelength light, measurements showed that a separate absorption multiplication avalanche photodiode with a nominal multiplication region width of 0.2 $\mu \text{m}$ had an effective $k$ (hole to electron ionization coefficient ratio) of $\sim 0.3$ .

Full-band Monte Carlo simulation of high-energy carrier transport in single photon avalanche diodes: Computation of breakdown probability, time to avalanche breakdown, and jitter

The high-energy charge transport of electrons and holes in GaAs single photon avalanche diodes with multiplication region widths of 55 nm to 500 nm is investigated by means of the full-band Monte Carlo technique incorporating computationally efficient full-band phonon scattering rates. Compared to previous works, the solution of the Boltzmann transport equation and the incorporation of the full-band structure put the evaluation of the breakdown probability, the time to avalanche breakdown, and the jitter on deeper theoretical grounds. As a main result, the breakdown probability exhibits a steeper rise versus reverse bias for smaller multiplicator sizes. The time to avalanche breakdown and jitter decrease for smaller multiplicator widths.

NUMERICAL ANALYSIS OF HOMOJUNCTION AVALANCHE PHOTODIODES (APDS)

In this paper we introduce a rigorous numerical analysis to investigate the characteristics of double carrier multiplication homojunction avalanche photodiodes (APDs) considering the nonlocal nature of the ionization process in the wide range of multiplication region width. Also in our calculations the effects of dead space has been considered. Our analyses based on the history dependent multiplication theory (HDMT) and width independent ionization coefficient.

NUMERICAL ANALYSIS OF HOMOJUNCTION GALLIUM ARSENIDE AVALANCHE PHOTODIODES (GAAS-APDS)

In our earlier work we introduce a numerical analysis to investigate the excess noise and performance factor of double carrier multiplication homojunction avalanche photodiodes (APDs) considering the nonlocal nature of the ionization process. In this paper we investigate the gain, breakdown voltage and carrier injection breakdown probability of homojunction avalanche photodiode in the wide range of multiplication region width. Also in our calculations the efiects of dead space has been considered. Our analyses based on the history dependent multiplication theory (HDMT) and width independent ionization coe-cient.

Computation of bit-error probabilities for optical receivers using thin avalanche photodiodes

The large-deviation-based asymptotic-analysis and importance-sampling methods for computing bit-error probabilities for avalanche-photodiode (APD) based optical receivers, developed by Letaief and Sadowsky [IEEE Trans. Inform. Theory, vol. 38, pp. 1162-1169, 1992], are extended to include the effect of dead space, which is significant in high-speed APDs with thin multiplication regions. It is shown that the receiver's bit-error probability is reduced as the magnitude of dead space increases relative to the APD's multiplication-region width. The calculated error probabilities and receiver sensitivities are also compared with those obtained from the Chernoff bound.

Information-theoretic criterion for the performance of single-photon avalanche photodiodes

A channel-capacity metric is introduced for assessing the performance of single-photon avalanche photodiodes (SPADs) when used as detectors in laser communication systems. This metric is employed to theoretically optimize, with respect to the device structure and operating voltage, the performance of SPADs with simple InP or In/sub 0.52/Al/sub 0.48/As-InP heterojunction multiplication regions. As the multiplication-region width increases, an increase is predicted in both the peak and the full-width at half-maximum of the channel capacity curve versus the normalized excess voltage. Calculations also show the existence of an optimal In/sub 0.52/Al/sub 0.48/As-InP heterojunction multiplication region that maximizes the peak channel capacity beyond that of InP.

Impact-ionization and noise characteristics of thin III-V avalanche photodiodes

It is, by now, well known that McIntyre's localized carrier-multiplication theory cannot explain the suppression of excess noise factor observed in avalanche photodiodes (APDs) that make use of thin multiplication regions. We demonstrate that a carrier multiplication model that incorporates the effects of dead space, as developed earlier by Hayat et al. provides excellent agreement with the impact-ionization and noise characteristics of thin InP, In/sub 0.52/Al/sub 0.48/As, GaAs, and Al/sub 0.2/Ga/sub 0.8/As APDs, with multiplication regions of different widths. We outline a general technique that facilitates the calculation of ionization coefficients for carriers that have traveled a distance exceeding the dead space (enabled carriers), directly from experimental excess-noise-factor data. These coefficients depend on the electric field in exponential fashion and are independent of multiplication width, as expected on physical grounds. The procedure for obtaining the ionization coefficients is used in conjunction with the dead-space-multiplication theory (DSMT) to predict excess noise factor versus mean-gain curves that are in excellent accord with experimental data for thin III-V APDs, for all multiplication-region widths.

Avalanche multiplication in submicron AlxGa1−xAs/GaAs multilayer structures

A systematic study of the role of band edge discontinuities on ionization rates in periodic AlxGa1−xAs/GaAs structures has been performed by measuring the electron and hole multiplication characteristics in a series of submicron AlxGa1−xAs/GaAs multilayer p–i–n and n–i–p structures. These structures comprise alternating 500Å AlxGa1−xAs and GaAs layers in the intrinsic multiplication regions, with a total thickness of up to 0.5 μm. The results show little dependence on initiating carrier type for multiplication region widths above 0.3 μm, nor on whether they originate in GaAs or AlxGa1−xAs. Only alloy-like behavior is observed at all values of multiplication up to the breakdown voltage in contrast to earlier work on single heterojunction structures where a large difference was seen at low values of multiplication between carriers starting in GaAs and AlxGa1−xAs. The microscopic aspects of hot carrier transport in these devices were studied numerically using a simple Monte Carlo model. Simulations suggest that the energy gained from the conduction band edge discontinuity from AlxGa1−xAs to GaAs is offset by the increased energy loss via the higher phonon scattering rate in the preceding AlxGa1−xAs layer. We conclude that AlxGa1−xAs/GaAs multilayer structures offer no electron ionization enhancement.

Dead-space-based theory correctly predicts excess noise factor for thin GaAs and AlGaAs avalanche photodiodes

The conventional McIntyre carrier multiplication theory for avalanche photodiodes (APDs) does not adequately describe the experimental results obtained from APDs with thin multiplication-regions. Using published data for thin GaAs and Al/sub 0.2/Ga/sub 0.8/As APDs, collected from multiplication-regions of different widths, we show that incorporating dead-space in the model resolves the discrepancy. The ionization coefficients of enabled carriers that have traveled the dead space are determined as functions of the electric field, within the confines of a single exponential model for each device, independent of multiplication-region width. The model parameters are determined directly from experimental data. The use of these physically based ionization coefficients in the dead-space multiplication theory, developed earlier by Hayat et al. provide excess noise factor versus mean gain curves that accord very closely with those measured for each device, regardless of multiplication-region width. It is verified that the ratio of the dead-space to the multiplication-region width increases, for a fixed mean gain, as the width is reduced. This behavior, too, is in accord with the reduction of the excess noise factor predicted by the dead-space multiplication theory.

Thin multiplication region InAlAs homojunction avalanche photodiodes

Low excess noise in avalanche photodetectors (APDs) is desired for improved sensitivity and high-frequency performance. Gain and noise characteristics are measured for InAlAs p-i-n homojunction APDs that were grown with varying i-region widths on InP by molecular beam epitaxy. The effective ionization ratio k (β/α) determined by noise measurements shows a dependence on multiplication region width, reducing from 0.31 to 0.18 for multiplication region thicknesses of 1600–200 nm. This trend follows previously shown results in AlGaAs-based APDs, which exhibit reduced excess noise due to nonlocal multiplication effects. These results show that this effect is a characteristic of thin avalanche regions and is not a material-specific phenomenon.

Theoretical analysis of the -3/4 power law in semiconductor avalanche breakdown

The -3/4 power law giving a relationship between carrier concentration and breakdown voltage, is studied by analytical procedures using a quasi-ionisation rate and connected to an equivalent multiplication region. It is found that the -3/4 power law originates from a fact that the ratio of the equivalent multiplication region width to the depletion region width is 1/8. Such a relationship was traced back to the effect of the electric field dependence of the quasi-ionisation rate in the general case. The power law is relatively independent of the material, the breakdown voltage and the carrier concentration.