Demonstration of large ionization coefficient ratio in AlAs0.56Sb0.44 lattice matched to InP

The electron and hole avalanche multiplication characteristics have been measured in bulk AlAs0.56Sb0.44 p-i-n and n-i-p homojunction diodes, lattice matched to InP, with nominal avalanche region thicknesses of ~0.6 μm, 1.0 μm and 1.5 μm. From these and data from two much thinner devices, the bulk electron and hole impact ionization coefficients (α and β respectively), have been determined over an electric-field range from 220–1250 kV/cm for α and from 360–1250 kV/cm for β for the first time. The α/β ratio is found to vary from 1000 to 2 over this field range, making it the first report of a wide band-gap III-V semiconductor with ionization coefficient ratios similar to or larger than that observed in silicon.

effect of the dead-space [15][16][17] which can become significant in thin avalanching regions as wavelength dependent multiplication indicated that α/β~1 in these structures. An accurate determination of the α and β in this material ideally requires pure electron and hole initiated multiplication characteristics from p-i-n and n-i-p diodes with a range of avalanching widths where the effect of the dead-space is likely to be relatively insignificant.
In this work, we report for the first time the α and β in AlAsSb covering a wide range of electric fields. These α and β are not only capable of fitting the multiplication characteristics in our devices with ~660 nm-1550 nm thick p-i-n and n-i-p structures but also structures with avalanching widths as thin as 230 nm 14 .

Results
A series of p-i-n and n-i-p AlAsSb photodiode structures (P1-P3, N1-N2) were grown by solid-source molecular beam epitaxy (MBE) lattice matched to InP substrates using a digital alloy growth technique and then fabricated into mesa diodes by wet chemical etching. The details of the layer thicknesses are given in Table 1 and P4, P5 refer to thin avalanching layers investigated previously. The growth and the fabrication details are given in the Methods section.
The forward and reverse bias currents in these devices were measured in the dark and are shown in Fig. 1(a). At low forward bias, the dark currents scaled with device perimeter suggesting the presence of large surface currents while at higher forward biases they scaled with area with ideality factors of ~2. The high reverse dark currents seen here are not indicative of the bulk dark currents in this material system as they too appear to scale with perimeter. In all the structures, a clear breakdown voltage could be seen.
The capacitance as a function of reverse bias for all the layers is shown in Fig. 1(b). After an initial rapid decrease in capacitance with bias, the capacitance remains approximately constant suggesting that the intrinsic region is fully depleted and there is negligible depletion in the heavily doped cladding regions. The depletion widths and doping levels obtained from these measurements are summarized in Table 1. The doping density varies between 5 × 10 15 -10 × 10 15 cm −3 resulting in a tapered electric-field profile in the intrinsic region (shown in Fig. 1 in Supplementary Information).
The photocurrent versus reverse bias was obtained using light at 405-and 633-nm wavelength lasers, focussed onto the top of the 420 μm diameter devices (shown in Fig. 2 in Supplementary Information). Due to the relatively high surface dark currents, the photocurrent measurements were undertaken by modulating the laser light and using phase sensitive detection techniques. The 405-nm light is assumed to be almost fully absorbed in the top doped cladding layers so will provide single carrier injection into the avalanching region (giving us M e on the p-i-n's or M h on the n-i-p's) while the 633 nm light should only be weakly absorbed and will generate carriers  uniformly throughout the structure, providing a 'mixed' injection multiplication characteristic (M mix ). The determination of the absorption coefficients at these wavelengths is given in the Methods section. Measurements were undertaken on at least 3 different devices for each structure at different laser powers to ensure the repeatability of results. The multiplication in these structures was determined by looking at the increase in photocurrent once the intrinsic layer was fully depleted and correcting for any increase in the primary photocurrent due to small movement of the depletion edges in the heavily doped cladding regions 18 . Figure 2 shows the multiplication characteristics from these structures and indicates that α > β in this material because the M mix ≤ M e in the p-i-n structures and M mix ≥ M h in the n-i-p structures. The M mix results (obtained using 633 nm illumination) for P1 and N1, and P2 and N2 are very similar as each pair has very similar intrinsic layer thicknesses and doping profiles. The M e from the three p-i-n structures are shown on a log plot in Fig. 4 in Supplementary information.

Discussion
The ionization coefficients as a function of electric-field were extracted from the multiplication results of P1-5 and N1-2 taking into consideration any tapered electric-field profile but ignoring any dead-space effects 19 by using a trial and error fitting technique which minimised the difference between the experimental and modelled data. The parameterized ionization coefficients cover a wide electric field range from 220-1250 kV/cm for α and from 360-1250 kV/cm for β and are given by; E E ( ) 5 5 10 exp 12 1 10 cm (1) for 220 KV/cm ≤ E ≤ 500 KV/cm and   for 360 KV/cm ≤ E ≤ 1250 KV/cm. These ionization coefficients are shown graphically in Fig. 3(a), as is the α/β ratio as a function of inverse electric-field. These coefficients are capable of reproducing the measured M e and M h for the different avalanche layer structures accurately as shown by the plot of (M-1) on a logarithmic scale in Fig. 3(b). Excellent agreement was achieved even at very low gain values of M~1.01. Figure 3(a) shows that an α/β ratio of >100 can be achieved at electric fields below 460 kV/cm and this ratio can exceed 1000 at electric fields below 360 kV/cm. The onset of measurable M e occurs well below the breakdown voltage in P1-P3, in contrast to the M h in N1 and N2 as shown in Fig. 3(b). This is because in our samples we can accurately measure multiplication values down to 1.01 and at the electric-field where M e gives us 1.01, the value of β is too low to give any measurable M h . Although the M h could only be experimentally obtained over a limited range in N1, the good agreement with the model down to values of M h = 1.01 suggests that the low electric-field data for β is correct.
These coefficients can also replicate the M e in P4 reasonably well if we use the parameters given in Table 1 but the fit to M e in P5 is slightly worse at higher values of multiplication, even when allowing for the depletion into the p + and n + cladding regions. The reason for this is likely to be due to the fact that at very high electric fields in very thin structures, the ionization coefficients are not simple functions of electric-field 20 and more sophisticated modelling techniques are required to fit to the experimental data.
To further emphasis how much larger the α/β ratio in AlAsSb is compared to normal III-V materials and silicon, Fig. 4 presents the ionization coefficients of AlAsSb, together with those of InP, InAlAs and silicon as a function of inverse electric field. AlAsSb can be seen to have a significantly larger α/β ratio so this should give rise to APDs with very low excess noise. For example, an ideal 1 μm p-i-n structure operating at a gain of 10, would have an α/β ratio of >40.
The rapidly increasing α/β ratio as the electric field decreases also explains the unusual result observed by Xie et al. 14 , whereby the excess noise decreased significantly as the avalanche thickness increased from 80 nm to 230 nm, contrary to results observed in InAlAs 21 and Si 22 . The α in all three III-V avalanche materials shown in Fig. 4 appear to be almost identical, despite quite different conduction band structures but the most interesting observation is that the β is significantly lower in AlAsSb, giving rise to the large α/β ratio.
In summary, the avalanche multiplication characteristics of AlAsSb have been measured in a series of diodes with avalanche region widths from 1.55 μm down to ~80 nm. From these, the ionization coefficients as a function of electric-field have been extracted and the α/β ratio is found to much larger than any other wide band-gap III-V semiconductor material with values of >100 for electric fields below 460 kV/cm. This makes AlAsSb ideal for the multiplication region in InP based telecommunication SAM-APDs.

Methods
The AlAsSb p-i-n and n-i-p structures are grown on epi-ready n-InP (001) and p-InP (001) substrates, respectively, via digital alloy growth technology in a Veeco GEN930 MBE reactor, in which both As 2 and Sb 2 fluxes are supplied using valved cracker cells. Due to the wide miscibility band gap, growth of thick high-quality and lattice-matched AlAsSb alloy is extremely challenging because of the non-unity sticking coefficient of group-V species 23,24 . Both fast fluctuations and slow drifts in group-V cell temperatures can also result in composition fluctuations and departure from the exact lattice-matched condition. In order to get the precise lattice-matched AlAsSb alloy with high crystalline quality, digitally grown AlAsSb is realized by periodically alternating the As  [10], InP [6] and silicon [5]. α of InAlAs and InP are almost identical to that of AlAsSb and are difficult to separate in the figure.
A schematic diagram of the device structure is shown in Fig. 5. The i-region is sandwiched between a 300-nm p + /n + AlAsSb and a 100-nm p + /n + AlAsSb cladding layers with Be and Te doping concentrations of 2.0 × 10 18 cm −3 . The structure also has a highly doped (1.0 × 10 19 cm −3 ) top 20-nm and bottom 500-nm InGaAs contact layers. Mesa devices were fabricated by standard lithography and wet chemical etching where a 2: 1 mixture of citric acid (1 g citric acid powder to 1 ml of de-ionised water (DIW)) and hydrogen peroxide (H 2 O 2 ) is used for the removal of the InGaAs cap layer and a 1: 2: 10 mixture of hydrochloric acid, diluted H 2 O 2 (with a ratio of 1 part peroxide to 9 parts DIW) and DIW to etch the AlAsSb layer into circular mesa diodes with diameters of 70, 120, 220, and 420 μm. Ti-Au was used to form the top and bottom metal contacts.
A HP4275A LCR meter was used to perform capacitance-voltage measurements at a frequency of 1 MHz. A static dielectric constant, ε r , of 10.95 was used to determine the depletion widths and background doping concentration. Dark current-voltage measurements were undertaken using a HP4140B picoammeter and a probe station.
The multiplication characteristics, M, as a function of reverse bias were determined from modulated photocurrent measurements obtained using a lock-in amplifier with phase-sensitive detection to remove the dc leakage currents. The impact ionization coefficients were determined by fitting to the experimentally determined multiplication data using the equation below 27 with the doping density and i-region thickness as shown in Table 1. Different wavelength light was used to generate pure carrier or mixed carrier multiplication in the diodes. As no published absorption coefficient of AlAsSb is available, we linearly interpolate between the absorption coefficients of AlAs and AlSb 28,29 to obtain values of 2.0 × 10 5 cm −1 at 405 nm and 3.6 × 10 2 cm −1 at 633 nm. Due to the large InGaAs/AlAsSb conduction band offset 30,31 carriers created in the top 20 nm InGaAs cap layer do not contribute to the photocurrent.