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In this study, separate absorption, grading, charge, and multiplication (SAGCM) avalanche photodiode (APD) with double heterojunction AlN/Al
_{x}Ga
_{1-x}N/GaN in multiplication region were designed to reduce excess noise using Monte Carlo simulation. The multiplication region was broken to three different regions and tried to enhance localization of the first and second impact ionization events at near the heterojunctions. The excess noise of the proposed structure, for high gains, was 64% smaller than that of the fabricated standard AlGaN-APDs.

Avalanche photodiodes (APDs) fabricated on AlGaN materials are suitable for ultraviolet (UV) wavelengths detections, enjoying advantages such as low dark current density, high receiver sensitivity, high gain, low noise, and cut-off wavelengths around 280 nm [

Tut et al. [_{0.4}Ga_{0.6}N, and reversed biased at about 70 V [^{2}E) multiplication region [^{2}E, to demonstrate optimal excess noise reduction in thin heterojunction Al_{0.6}Ga_{0.4} As-GaAs APDs. Chen et al. [

Possibility of fabricating Al_{x}Ga_{1−x}N based hetero-interfaces with large band-gap discontinuities in one hand and having direct band-gap material for the whole 0 ≤ x ≤ 1 range on the other hand made us to propose a new separate absorption, grading, charge, and multiplication (SAGCM) APD , based on Al_{x}Ga_{1−x}N alloys. SAGM-APDs based on III-As alloys have already been employed for carrier build-up in multiplication region and reduction of dark current and excess noise factor [

A schematic representation of the conduction band for the proposed SAGCM- APD is illustrated in _{0.4}Ga_{0.6}N and AlN (~1.68 eV), as well as the lattice mismatch between these two materials. Whereas, the AlN charge layer that is a highly p^{+} doped thin AlN layer separates the absorption and multiplication layer, providing high electric field in the multiplication layer and relatively low electric field in the absorption layer.

Using ensemble Monte Carlo (EMC) simulation, we have obtained the optimized values for thicknesses of layers constituting the absorption, grading and multiplication regions; as well as the Al mole fraction, x, in various Al_{x}Ga_{1−x}N layers, all of which, in turn, lead to an optimized value for the device excess noise factor. In optimizing the layers thicknesses in the AlN/Al_{x}Ga_{1−x}N/GaN multiplication region, we have aimed the impact ionization (II) events to be

localized as close as possible to both AlN/Al_{x}Ga_{1-x}N and Al_{x}Ga_{1-x}N/GaN hetero-interfaces, in the multiplication region, but within the narrower hand-gap sides of each interface. In an optimized double heterostructure multiplication region, such as AlN/Al_{x}Ga_{1−x}N/GaN, AlN should be thick enough for electrons, just before crossing over the heterointerface, to have the chance of attaining mean energies, E_{M-AlN}, very close but smaller than their corresponding ionization threshold energy, E_{TH-AlN}, and yet larger than the carriers’ ionization threshold energy in the narrower band-gap material; i.e., E_{TH-AlN} > E_{M-AlN} > E_{TH} (Al_{x}Ga_{1-x}N). Hence, such electrons, upon entering Al_{x}Ga_{1-x}N, have enough energy to get involved in an II event without a need to traverse the dead space in that region. In this manner the first ionization event is localized to the hetero interface within Al_{x}Ga_{1-x}N. In the same manner, Al_{x}Ga_{1-x}N also should be thick enough to localize the next ionization event adjacent to the next heterointerface and yet within the GaN. Eliminating the carriers’ dead spaces in both Al_{x}Ga_{1-x}N and GaN regions, in this manner, reduces the device excess noise factor, in effect.

As we have already mentioned, there is a relatively large band-gap discontinuity between the Al_{0.4}Ga_{0.6}N (E_{G} = 4.52 eV) used for the absorption region and AlN (E_{G} = 6.2 eV) as the starting material for the proposed APD structure. For electrons to overcome such a large barrier height, one needs to use an optimum grading region through which electrons pass with minimal transit time minimal total reflection. In one hand, for electrons to cross over a grading region with minimal reflections number of steps/layer making up the region should be maximized. On the other hand, to keep electrons transit time as short as possible, total thickness of such region should be minimized. Therefore, there are two critical design parameters by which an optimum grading region can be designed. Those are, thickness of each layer, w_{g}, and the barrier (step) height between to adjacent layers, ΔE_{cg}, through which optimum number layers with optimum thicknesses can be obtained.

As the number of steps increases, the total reflection is reduced. Besides, if the length of grading region increases causes one can use more steps in grading region to reduce total reflection. However, as the length of grading region is increased, electron transit time cross the grading region is increased and distribution of energy is more broaden due to more scattering. So, we reduce length of the grading region until electrons can pass through the barriers and enter in multiplication region.

Our Monte Carlo model uses an analytical approximation for the band structure involving spherical, non-parabolic for two conduction bands and two sub-bands in valence bands. Impurity, Acoustic, non-polar, polar optical phonon, and alloy scattering processes are included for carriers. II rate is described by the Keldysh approach using ionization threshold energy and softness coefficients as fitting parameters to the experimental ionization coefficient data [

To validate our MC model, we calculate electron impact ionization coefficients (α) and compare to calculated electron impact ionization coefficients by Bulutay for Al_{x}Ga_{1-x}N ( x = 0 , 0.2 , 0.4 , ⋯ , 1 ) as shown in

As the Al mole fraction is increasing in Al_{x}Ga_{1-x}N, electron impact ionization coefficient is reduced. More Al mole fraction results in the heavier carriers and wider band-gap material. So, the threshold energy for impact ionization and dead space are increased. The obtained threshold energy for electron II has given in

According to mentioned modeling, we design and simulate the DH AlN/Al_{0.4}Ga_{0.6}N/GaN multiplication region SAGCM-APD (see _{0.4}Ga_{0.6}N region where distances of photon absorption from illuminated edge are distributed exponentially. We select W_{a} = 200 nm results in more than 90% of entering photons is absorbed in Al_{0.4}Ga_{0.6}N. Details of different layers are given for proposed SAGCM-APD in _{m}_{1} and W_{m}_{2} are calculated for different charge layers.

As the length of the grading region shrinks, mean transit time through the barriers reduces and distribution of energy of electrons becomes almost narrow. However, one can shrink grading regions until the electrons can pass the grading region. So, the number of steps (N_{step}) and length of the grading region (W_{G}) are key parameters. We considered the different lengths of grading layer and grading region, which our simulations demonstrated the minimum length of the grading region is 88 nm with N_{step} = 9 where electrons could inject to charge region. Also, our simulations demonstrated the full width at half maximum (FWHM) in distribution of energy for electrons at end of the grading region is almost increased ~0.011 ev and 0.002 ev for each 1 nm increasing in grading

Al content (x) in Al_{x}Ga_{1-x}N | 0 | 0.2 | 0.4 | 0.6 | 0.8 | 1 |
---|---|---|---|---|---|---|

E_{TH} (eV) | 4 | 4.5 | 5.2 | 5.7 | 6.3 | 6.8 |

n^{+}-GaN | Multiplication [N_{A} = 10^{16} (cm^{−3})] | Charge | 9-steps Grading | Absorption | ||||||
---|---|---|---|---|---|---|---|---|---|---|

p^{−} GaN | p^{−} Al_{0.4}Ga_{0.6}N | p^{−} AlN | p^{+}-AlN | p^{−}-Al_{x}G_{1−x}N (0.4 ≤ x ≤1) | p^{−} Al_{0.4}Ga_{0.6}N | |||||

N D + | W | W_{m}_{3} | W_{m}_{2} (nm) | W_{m}_{1} (nm) | N_{A} (10^{17} cm^{−3}) | W_{C} (nm) | N_{A} | W_{G} | N_{A} | W_{a} |

2 × 10^{18} cm^{−3} | 30 nm | 250 nm | 50 | 78 | 5 | 30 | 10^{16} cm^{−3} | 88 nm | 10^{16} cm^{−3} | 200 nm |

50 | 74 | 4.6 | 35 | |||||||

48 | 72 | 4 | 40 | |||||||

46 | 70 | 3.6 | 45 | |||||||

46 | 66 | 3.1 | 50 |

layers and each one step decreasing respectively. As the FWHM is larger, the distribution of energy is more broaden.

To compare different charge layers (that are tabulated in

Injected energized electrons from charge to multiplication region need to almost short dead space to gain the threshold energy for II in AlN. Maximum electric field in multiplication region is lower than 2.7 MV∙cm^{−1} to breakdown is not occurred in GaN. We select mean distance of first II events in Al_{x}Ga_{1-x}N

W_{C} (nm) | 30 | 35 | 40 | 45 | 50 |
---|---|---|---|---|---|

FWHM (eV) | 1.06 | 1.09 | 1.12 | 1.16 | 1.21 |

from AlN/Al_{x}Ga_{1-x}N hetero-interface (<δ_{1}>) as a criterion to study the localization of first II events in Al_{x}Ga_{1-x}N. The minimum value for δ_{1} is obtained with W_{m1} = 78 nm, and Al mole fraction, x = 0.4. _{1} with different Al mole fractions.

Existence of an optimum value for Al mole fraction (x) is due to two issues whose effects on δ_{1} are in opposite direct; 1) reflection from hetero-interface, and 2) access to more energy due to discontinuity of energy at hetero-interface. In one hand, As the Al content in Al_{x}Ga_{1-x}N is reduced, reflection from hetero-interface AlN/Al_{x}Ga_{1-x}N is increased. Some reflected electrons can gain the more energy from electric field to ionize in AlN region. After the ionization event, they have low energy when are injected (transmitted) to Al_{x}Ga_{1-x}N region. Also, scattering processes can reduce the energy of other reflected electrons. So, they need to long dead space to can be ionized in Al_{x}Ga_{1-x}N region. This issue degrades the localization of impact ionization events at near the hetero-interface.

On the other hand, As the Al content in Al_{x}Ga_{1-x}N is reduced, discontinuity of energy at hetero-interface is increased. So, the probability of II occurrence for transmitted electrons to Al_{x}Ga_{1-x}N is increased and transmitted electrons are ionized near the hetero-interface in Al_{x}Ga_{1-x}N. Knowing all these, we deduce from _{1} for x ≥ 0.4 while reflection from hetero-interface increases δ_{1} for x < 0.4.

After first II events in Al_{0.4}Ga_{0.6}N, electrons with different initial energies drift to GaN region and can gain the threshold energy to ionization. _{2}> for Al_{0.4}Ga_{0.6}N/GaN with different lengths of Al_{0.4}Ga_{0.6}N region.

One can see the minimum δ_{2} is obtained when the length of Al_{0.4}Ga_{0.6}N (W_{m}_{2}) region is 50 nm. Our simulations demonstrates II events in Al_{0.4}Ga_{0.6}N occur for W_{m}_{2} > 50 nm. This issue degrades localization of second II events in GaN for W_{m}_{2} > 50 nm, because after II in Al_{0.4}Ga_{0.6}N, electrons have low energy and need to long dead space to ionized in GaN. Now, we calculate excess noise factor (F) for two different devices: a) a fabricated homojunction Al_{0.4}Ga_{0.6}N pin-APD [_{C} = 30 nm (see

Our simulation demonstrates the proposed SAGCM can reduce excess noise ~64% than a fabricated device for M ≈ 900 [^{+} GaN region, τ_{d}, for two mentioned devices in

Our simulations demonstrate the delay time for SAGCM is almost reduced exponentially with gain and it’s ~65 fs longer than a fabricated pin-APD [

In this study, we presented and designed a wide band gap SAGCM-APD with Al_{0.4}Ga_{0.6}N in absorption region and a DH AlN/Al_{0.4}Ga_{0.6}N/GaN in multiplication region to reduce excess noise. Our study demonstrated that the large amount of conduction band discontinuity, always, did not enhance localization of impact ionization events near the hetero-interface. In fact, less Al content (x) in Al_{x}Ga_{1-x}N (or more discontinuity in AlN/Al_{x}Ga_{1-x}N) results in more reflection which destroys the localization of first impact ionization events in Al_{x}Ga_{1-x}N and has dominant effect on excess noise for x < 0.4. We divided the large discontinuity between AlN and GaN in two smaller discontinuities to enhance the first and second localizations. Length of grading layer, number and size of steps in grading layer are key parameters to design. Our simulation demonstrates that one can shrink the length of grading region until 88 nm (with 9 steps) where the carriers can pass the grading layers. We showed that 30 nm for length and 5 × 10^{17} cm^{−3} for doping concentration of charge layer are good choice. Using these issues, we could mainly reduce excess noise than a fabricated pin-APD for high gains.

Bagheriyeh- Behbahani, M., Soroosh, M. and Farshidi, E. (2017) A Double Heterostructure Multi- plication Region in AlGaN Based SAGCM Avalanche Photodiode. Optics and Photonics Journal, 7, 151-159. https://doi.org/10.4236/opj.2017.710015