Atomistic transport modeling, design principles and empirical rules for Low Noise III-V Digital Alloy Avalanche Photodiodes

The demand for efficient optical detectors is constantly growing due to rapid developments in telecommunication, light imaging, detection and ranging (LIDAR) systems and other military and research fields [1, 2, 3, 4, 5, 6, 7]. Photodetectors are increasingly being incorporated in photonic integrated circuits for Internet of Things and 5G communications [8, 9, 10]. These applications require higher sensitivity in comparison to traditional p-i-n photodiodes [11]. Avalanche photodiodes (APDs) are often deployed instead due to their higher sensitivity, enabled by their intrinsic gain mechanism. However, the stochastic nature of the impact ionization process of APDs adds an excess noise factor $F(M)=\langle m^{2}\rangle/\langle m\rangle^{2}=kM+(1-k)(2-1/M)$ to the shot noise current, $\langle i_{shot}^{2}\rangle=2qIM^{2}F(M)\Delta f$ [12, 13, 14]. Here, $q$ is the electron charge, $I$ is the total photo plus dark current, $m$ is the per primary electron avalanche gain, $M=\langle m\rangle$ the average multiplication gain and $\Delta f$ is the bandwidth. A low value of $k$, which is the ratio of hole ionization coefficient $\beta$ to the electron ionization coefficient, $\alpha$, is desirable for designing low-noise n-type APDs. This ratio stipulates that for pure electron injection, a significantly lower hole ionization than the electron ionization rate leads to reduced shot noise. If impact ionization is caused by pure hole injection, $k$ in the equation will be replaced by $1/k$.

Recently, several III-V digital alloys, i.e., short-period superlattices with binary components stacked alternately in a periodic manner, were found to exhibit extremely low noise currents and a high gain-bandwidth product in the short-infrared wavelength spectrum [15, 16, 17]. Characterization of InAlAs, AlInAsSb and AlAsSb digital alloy APDs have shown very small values of $k$, [15, 16, 17] whereas other digital alloys, like InGaAs and AlGaAs, demonstrate much higher $k$ value [18, 19]. Based on previous full-band Monte Carlo simulations, [20, 21, 22] the low $k$ has been attributed to the presence of superlattice minigaps inside the valence band of the material bandstructure, along with an enhanced effective mass arising from the lower band-width available to the holes. Such valence band minigaps often co-exist with similar (but not symmetrical) minigaps in the conduction band. However, electrons in the conduction band typically have very low effective mass, which allows quantum tunneling and enhanced phonon scattering to circumvent minigaps in the conduction band. Furthermore certain digital alloys showing mini-gaps do not exhibit low noise, and the reason behind that has not yet been addressed. Our postulate is that a combination of valence band minigap, a large separation between tight-hole and split-off bands, and corresponding enhanced hole effective mass tend to limit hole ionization coefficient. A comprehensive analysis is clearly necessary to understand the carrier impact ionization in these materials.

In this paper, we employ a fully atomistic, Environment-Dependent Tight Bindng (EDTB) model, [23] calibrated to Density Functional Theory (DFT) bandstructure as well as wavefunctions, to compute the bandstructures of several III-V digital alloys. Using a full three-dimensional quantum kinetic Non-Equilibrium Green’s Method (NEGF) formalism with the EDTB Hamiltonian as input, we compute the ballistic transmission across these digital alloys that accounts for intraband quantum tunneling across minigaps and light-hole/split-off bands offset. Additionally, a full-band Boltzmann transport solver is employed to determine the energy resolved carrier occupation probability under the influence of an electric field in order to study the effect of optical phonon scattering in these short-period superlattices. The calculations are performed using computational resources at University of Virginia and XSEDE [24]. Using these transport formalisms, we elucidate the impact of minigap sizes, light-hole/split-off band offset and effective masses on carrier transport in the valence band.

Our simulations demonstrate that the squashing of subbands into tighter band-widths, such as arising from minigap formation, or the engineering of large light-hole/split-off band offset lead to the suppression in transport of one carrier type, by resisting quantum tunneling or phonon-assisted thermal jumps. For InAlAs, the improved performance is primarily due to the minigaps generated by the digital alloy periodicity and the corresponding enhanced effective mass. For AlInAsSb and AlAsSb, the gain is a combination of minigaps, large effective mass and LH/SO offset. The LH/SO offsets in these two alloys results arise from the strong spin-orbit coupling due to the Sb atoms, a characteristic which is also observed in their random alloy counterparts that exhibit low noise. A quantitative comparison of the various alloy gains measured is presented in the last two columns of Table IV.

The unique superlattice structure of the digital alloys opens the possibility for designing new low-noise alloy combinations for detection of other frequency ranges. Ideally, it is easier and cheaper to at first computationally study the suitability of the alloys for achieving low noise before actually fabricating these. For this purpose, we need a set of design criteria for judging the alloy performance using theoretically calculated parameters. Based on our simulations, we propose five simple inequalities that can be used to judge the suitability of digital alloys for use in low-noise APDs. We judge the aptness of five existing digital alloys- InAlAs, InGaAs, AlGaAs, AlInAsSb and AlAsSb. We observe that the inequalities provide a good benchmark for gauging the applicability of digital alloys for use in low-noise APDs.

There are three common ways to achieve low noise and high gain-bandwidth product - selecting a semiconductor with favorable impact ionization coefficients, scaling the multiplication region to exploit the non-local aspect of impact ionization, and impact ionization engineering using appropriately designed heterojunctions [11]. Typically, the lower hole impact ionization coefficient in semiconductors is due to stronger scattering in the valence bands, as depicted in Fig. 2(a). Previously, the lowest noise with favorable impact ionization characteristics were realized with Si in the visible and near-infrared range, [36, 37, 38, 39] and InAs [40, 41, 42, 43, 44] and HgCdTe [45, 46] in the mid-infrared spectrum. In comparison, InGaAs/InAlAs [47, 48] random alloy APDs exhibit significantly higher noise than Si, HgCdTe or InAs, which are the highest performance telecommunications APDs. In the recent past, digital alloy InAlAs APDs have demonstrated lower noise compared to their random alloy counterpart [15]. This seems a surprise, as the suppression of one carrier type (the opposite of ballistic flow expected in an ordered structure) is necessary for low excess noise. Initially, the low value of $k$ in InAlAs was attributed to the presence of minigaps [22]. However, minigaps were also observed in InGaAs digital alloy APDs which have higher excess noise[49, 18]. So, a clearer understanding of the minigap physics was needed and hence a comprehensive study was required.

Our recent results suggest that well defined minigaps introduced in the valence band of digital alloys suppress the density of high energy holes and thereby reduce the impact ionization greatly, as shown in Fig. 2(b). In a regular low-noise electron-injected APD, the electron ionization coefficient is much higher than the hole ionization coefficient. Thus, electrons can easily climb to higher kinetic energies in the conduction band, depicted in Fig. 2(c), and participate in the impact ionization process by gaining the impact ionization threshold energy. On the other hand holes lose energy by various inelastic scattering processes (Fig. 2(d)), collectively known as thermalization. Thermalization prevents holes from reaching their secondary impact ionization threshold. In superlattice APDs, minigaps provide an additional filter mechanism that prevents holes from reaching the threshold energy required to initiate secondary impact ionization.

The effect of minigaps is shown in Fig. 2(e). However, not all digital alloy APDs exhibit low noise. The excess noise $F(M)$ vs. multiplication gain characteristics of experimental InGaAs, AlGaAs, InAlAs, AlInAsSb and AlAsSb digital alloy APDs are shown in Fig. 3 [15, 18, 19, 16, 17]. InGaAs APDs have the highest excess noise while AlAsSb has the lowest. The dotted lines represent the theoretical $F(M)$ vs. $M$ calculated using the well known McIntyre’s formula [12], introduced in the first paragraph of this paper. In order to understand the underlying physics in these digital alloys, an in-depth analysis of the material bandstructure and its effect on the carrier transport is required.

We calculate the atomistic DFT-calibrated EDTB bandstructure of these materials and unfold their bands using the techniques described in section II.1, to understand the underlying physics of their noise performance. In Fig. 4, we show the periods of the different digital alloys considered- (a) 6ML InGaAs, (b) 6ML AlGaAs, (c) 6ML InAlAs, (d) 10ML Al_0.7In_0.3AsSb and (e) 5ML AlAsSb. Here, 6ML InGaAs includes 3ML InAs and 3ML GaAs, 6ML AlGaAs has 3ML AlAs and 3ML GaAs, and 6 ML InAlAs has 3ML InAs and 3ML AlAs. 10ML Al_0.7In_0.3AsSb consists of 3ML AlSb, 1ML AlAs, 3ML AlAs and 3ML InAs in its period. AlAsSb has 4ML AlSb and 1ML AlAs. The unfolded bandstructures of these alloys are shown in Fig. 5. We observe that minigaps exist in at least one of the valence bands (heavy-hole, light-hole or split-off) for all the material combinations. The InAlAs valence band structure is magnified in Fig. 6. The minigap between the LH and SO band is denoted in the figure. Additionally, the large separation between the LH and SO bands at the $\Gamma$ point is highlighted.

The role of the minigaps on hole localization is not identical across different alloys. For instance, the presence of minigaps in material bandstructure is not sufficient to realize low noise in APDs. Taking a closer look at the bandstructures, we observe that the positions in energy of the minigaps with respect to the valence band edge differ from one material to another. Additionally, the minigap sizes of the different alloys vary in magnitude. A complimentary effect of the minigap size is the flattening of the energy bands, i.e., a large minigap size results in flatter bands around the gap. This in turn results in an increased effective mass which tends to inhibit carrier transport. Table 1 lists the energy location of the minigap with respect to the valence band edge $\Delta E_{b}$, the minigap size $\Delta E_{m}$, the light-hole (LH) and split-off (SO) band effective masses and the energy difference between the LH and SO bands $\Delta E_{LS}$ at the $\Gamma$ point for the digital alloys studied.

We can see in the table that there are significant variations in minigap size and position between different materials. At first glance, there seems to be no direct correlation between these variations and the excess noise, prompting us to do added transport analyses. Under high electric field, a carrier must gain at least the threshold energy, $E_{TH}$, in order to impact ionize. Typically, $E_{TH}$ is assumed to be approximately 1.5 times the material bandgap, $E_{G}$. Thus, in the presence of minigaps, electrons/holes must bypass these gaps by some transport mechanism in order to gain energy equivalent to $E_{TH}$. The two such major transport mechanisms are quantum mechanical tunneling and optical phonon scattering. Our transport study must incorporate these two mechanisms to understand the effectiveness of minigaps on the APD excess noise.

We employ the NEGF formalism described in Section II.2 to compute the ballistic transmission in the valence band as a function of energy, $T(E)$, dominated by tunneling processes. The effect of different minigap sizes is highlighted in Fig. 7. For our simulation, we set the quasi-Fermi level of the left contact at $-qV$ below the valence band edge and quasi-Fermi level of the right contact at another $-qV$ below. This is done in order to only observe the intraband tunneling inside the valence band which is responsible for overcoming minigaps under ballistic conditions. In Fig. 7 (a), We demonstrate that a small minigap in the valence band creates a small tunneling barrier for the holes. A hole with a small enough effective mass will be able to tunnel across this barrier and render it ineffective. That is the case for InGaAs which has a LH effective mass of $0.13m_{0}$ and $\Delta E_{m}=0.03eV$. The spectral current density for InGaAs under a bias $V=0.25V$ is shown in Fig. 7 (b). We observe that the current spectrum in the valence band is continuous in the Fermi energy window and there is no drop in transmission due to the minigap. For a large minigap, the holes encounter a larger tunneling barrier, as shown in Fig. 7 (c), preventing them from gaining the threshold energy $E_{TH}$ for secondary impact ionization. This case is operational in InAlAs digital alloys, as shown in the spectral density plot in Fig. 7 (d). InAlAs has a minigap size of $0.12eV$ and LH effective mass of $0.4m_{0}$. Within the Fermi window we see that there are regions with extremely low current due to low tunneling probability across the minigap. This is further demonstrated by the $T(E)$ vs. $E$ plot in Fig. 7 (e). Here, it is observed that there are regions of low transmission for InAlAs whereas the InGaAs transmission is continuous. This signifies that the minigaps in the InAlAs valence band are large enough to prevent holes from gaining in kinetic energy, resulting in a low hole ionization coefficient.

In order to investigate the role of minigaps in the remaining digital alloys, we look at the transmission vs. energy plots for all the alloys. The $T(E)$ vs. $E$ characteristics for the five digital alloys are shown in Fig. 8 for two bias conditions, (a) $V=0.25V$ and (b) $V=0.5V$. We use a $21\times 21$ grid for the transverse wavevectors ($k_{x},k_{y}$) within the first Brillouin zone. For this simulation, the structure length for InGaAs, AlGaAs, InAlAs and AlAsSb is considered to be two periods. For AlInAsSb we consider one period length. This allows us to keep the structure lengths as close as possible. We consider lengths of $3.48nm$ InGaAs, $3.42nm$ AlGaAs, $3.54nm$ InAlAs, $3.06nm$ AlInAsSb and $3.08nm$ AlAsSb channels. The channel sizes chosen are small compared to actual device lengths in order to keep the computation tractable. For both the bias conditions in Fig. 8 we see there are energy ranges for InAlAs, AlInAsSb and AlAsSb in which the transmission probability drops drastically. This low tunneling probability can be attributed to two factors. The first factor is the presence of a sizeable minigap in all directions in the material bandstructure. The other contributing factor is the separation between the LH and SO bands. This factor is partly responsible for the low transmission regions in AlInAsSb and AlAsSb, whose minigap sizes (from Table 1) are smaller than InAlAs but also demonstrate lower excess noise. InGaAs and AlGaAs do not have any large drop in transmission for both biases. This characteristic implies that either the minigap size is too small to affect the carrier transport like in InGaAs or there is no minigap at all as in AlGaAs.

For further confirmation of these observations, we compute the spectral current density for the case of constant total period length of all the structures. The period size of each unit cell stays the same but the number of unit cells is increased to make the total period length the same for all alloys. We consider the case with total period of 30MLs and voltage bias of $0.25V$. The current spectral density plots for the five digital alloys using a $15\times 15$ transverse wavevector grid are shown in Fig. 9. Smaller number of grid points are used here to save computation time. In the figure, a very small minigap is observed for InGaAs within the Fermi window and a continuous spectrum is seen for AlGaAs. Regions of low transmission/current are observed for InAlAs, AlInAsSb and AlAsSb. These observations are consistent with our previous calculations. We can thus infer that at least under fully coherent transport including tunneling, holes will not be able to gain sufficient kinetic energy to achieve impact ionization.

Besides tunneling processes it is possible for carriers to jump across energy gaps through inelastic scattering. In APDs, the dominant scattering mechanism is intervalley optical phonon scattering. Using the BTE model described in Section II.3, the effect of phonon scattering in digital alloys is studied. The carrier mobilities and optical phonon energies of the binary constituents of the alloys used in the BTE simulations are listed in Table  2. An effective scattering strength $H_{\vec{p},\vec{p}^{\prime}}$ is obtained from the mobility values as described in Section II.3. For our BTE simulations, we use the heavy-hole effective masses outlined in Table. 1. We compute the carrier occupation probability in the valence band under a high electric field of $1MV/cm$, by solving the three-dimensional Boltzmann equation with the entire set of tight binding energy bands within the Brillouin zone of the digital alloy. The optical phonon energy and mobilities of each alloy are taken to be the average of the binary constituent optical phonon energies and their mobilities. The energy resolved carrier occupation probability for all the alloys is shown in Fig. 10. The valence band plot in Fig. 10 shows that the occupation probability for InAlAs, AlInAsSb and AlAsAsb is lower than the other two alloys at high energies. The optical phonon energies of these alloys are not sufficiently large to overcome their minigaps and thus prevent holes from ramping their kinetic energies up to $E_{TH}$.

The top few valence bands of InGaAs are shown on the left side of Fig. 11(a) and the valence band carrier density distribution is projected onto the bottom. The bands are inverted for better view. For clearer understanding, the InGaAs carrier density distribution contour is also shown on the right. The valence band carrier distributions for the other alloys are shown in Fig. 11(b) AlGaAs, (c) InAlAs, (d) AlInAsSb and (e) AlAsSb. By studying the contours of each material, we observe that the densities for InAlAs, AlInAsSb and AlAsSb are more localized compared to thåt of AlGaAs and InGaAs. This is once again consistent with the lower hole impact ionization of InAlAs, AlInAsSb and AlAsSb.

For InGaAs and AlGaAs, the bandwidths are large enough to allow both holes and electrons to reach $E_{TH}$ easily. The resulting values of $k$ for these materials are quite high. Correspondingly, these two alloys have higher excess noise. In contrast in InAlAs, AlInAsSb and AlAsSb, it is easy for electrons to reach the threshold energy, but the holes are confined close to the valence band edge. This results in asymmetric ionization coefficients which give a low $k$, leading in turn to low excess noise.

Armed with these results, we attempt to paint a clearer picture on how the minigaps and band splitting can reduce the excess noise in APDs. Specifically, we propose a set of empirical inequalities that can used to judge the excess noise performance of a digital alloy.

Based on our experimental results and theoretical calculations, five inequalities are proposed that use only material parameters like effective mass and minigap size obtained from our material bandstructures as inputs. In this paper, the transport is in the $[001]$ direction. Since the minigaps considered lie in the LH band, we use the unfolded LH effective mass value in the $\Gamma-[001]$ direction for the inequalities. The masses are obtained using the relationship $\hbar^{2}k^{2}/2m^{*}=E(1+\alpha E)$ where $\alpha=[(1-m^{*}/m_{0})^{2}]/E_{G}$ [52]. In reality, the effective masses are complicated tensors that cannot be included in these empirical inequalities but are captured by the NEGF simulations described in Section. II.2. A digital alloy material should favor low noise if it satisfies the majority of these inequalities. The four main inequalities are:

Here, $\Delta E_{b}$ represents the energy difference between the VB maximum and the first minigap edge in the VB, $E_{opt}$ is the optical phonon energy and $\Delta E_{m}$ gives the size of the minigap. The longitudinal effective mass of the band in which the minigap exists is represented by $m_{l}$. $\Delta E_{LS}$ signifies the energy difference between the LH and SO bands at the $\Gamma$ point. A pictorial view of the different energy differences and inequalities mentioned above is shown in Fig. 12.

The first inequality, Inequality (1), states that the energy bandwidth $\Delta E_{b}$ must be less than the ionization threshold energy $E_{TH}$. This means a carrier cannot gain sufficient kinetic energy to impact ionize before reaching the minigap. When a carrier reaches a minigap it faces a barrier (Fig. 12), which it can overcome by phonon scattering or quantum tunneling. Inequality (2) sets the condition for phonon scattering across the minigap. If the $E_{opt}$ of the material is less than $\Delta E_{m}$, then the phonon scattering of the carriers across the minigap is inhibited because carriers cannot gain sufficient energy to jump across the gap. It is possible for the carrier to still overcome the minigap by tunneling, and the condition for that is given in Inequality (3), in terms of the tunneling probability across the minigap under the influence of an electric field. To compute the tunneling probability we consider a triangular barrier in the minigap region and use the well-known Fowler-Nordheim equation. Together Inequalities (2) and (3) give the effectiveness of the minigap in limiting hole ionization in digital alloys.

Electron injected digital alloys can in fact achieve low noise even in the absence of minigaps, for instance in a material with a large separation $\Delta E_{LS}$ between the LH and SO bands, like AlAsSb. Holes within HH/LH bands are limited near the valence band edge by thermalization (hole-phonon scattering) due to the heavy effective masses in these bands, preventing them from reaching the ionization threshold energy within the band. An alternate pathway to ionization involves the split-off band. Since the split-off band has a low effective mass, holes require much smaller momentum to reach higher energies in this band, so that holes entering this band from HH/LH can quickly gain their ionization threshold energy. The separation between HH/LH and SO bands is controlled by spin-orbit coupling, as shown in Fig. 13. Strong spin-orbit coupling due to inclusion of heavy elements, like antimony or bismuth, can increase the separation $\Delta E_{LS}$, as shown in Fig. 13(b). When $\Delta E_{LS}$ is large it becomes very difficult for holes to reach the threshold energy. Inequality (4) is accordingly important for APDs in which electron impact ionization is the dominant process, and is a measure of hole tunneling from the light-hole to the split-off band.

An inherent fifth inequality, satisfied by these five alloys, is

$E_{SC}$ is the energy gained by a hole between successive phonon scattering events, expressed as $E_{SC}=\lambda_{mfp}/F$. The z-directed mean free path, $\lambda_{mfp}=v_{sat}\tau_{SC}/2$, where $v_{sat}$ is the saturation velocity and $\tau_{SC}$ is the scattering lifetime. $E_{SC}$ values of the five alloys at electric fields of $100kV/cm$ and $500kV/cm$ are given in Table. 3. We extract $\tau_{SC}$ for an alloy by assuming a virtual crystal approximation of the component binary alloy scattering times. $\tau_{SC}$ values for InAs, GaAs, AlAs and AlSb are $0.08ps$, $0.09$, $0.08ps$ and $0.11ps$, respectively [53]. A similar average is done for the ternary alloy saturation velocities. Due to unavailability of AlSb $v_{sat}$, InAs $v_{sat}$ is used for AlInAsSb and AlAs $v_{sat}$ for AlAsSb. InAs, GaAs and AlAs $v_{sat}$ values used are $5\times 10^{4}m/s$, $9\times 10^{4}m/s$ and $8\times 10^{4}m/s$, respectively [54].

In order to validate these inequalities as design criteria, we apply them to the set of digital alloys mentioned in this paper. We consider a high electric field of $1MV/cm$ for Inequalities (3) and (4). The values of the left sides of the inequalities for the five alloys- InGaAs, AlGaAs, InAlAs, AlInAsSb and AlAsSb, are given in the first four columns of Table 3, while the measured $k$ is provided as reference in column 5. The table cells are colored green or red. Green cells aid in noise suppression (left sides of the inequalities are relatively small) and red is detrimental to reducing noise (left sides larger and corresponding inequalities not satisfied). Additionally, the color intensities highlight the strength of that inequality (how far the left side is from equality with the right side). A lighter shade represents a smaller impact while a darker shade means that condition has a greater effect on the impact ionization noise. For example, in the case of InGaAs, Inequality (1) is shaded light green which means it does not effect noise performance significantly. However, the remaining inequalities for InGaAs are shaded dark red, indicating their key role in the high noise and hence high $k$ of InGaAs. The inequalities for AlGaAs, which has a slightly lower $k$, have a lighter shade of red. There are no minigaps for AlGaAs in the light-hole band. There is a minigap in the SO band of AlGaAs which is very deep in the valence band and there are other available states at that energy. Thus, holes can gain sufficient momentum to jump to other bands and bypass the minigap. So, we consider $\Delta E_{m}=0$ for it. We accordingly expect that AlGaAs has a lower noise. However, since the LH effective mass for AlGaAs is greater than InGaAs, it has lower hole impact ionization and thus lower noise compared to InGaAs. The remaining alloys have significantly lower noise compared to these two.

The boxes for InAlAs, AlInAsSb and AlAsSb are all green. This means these three alloys are quite favorable for attaining low excess performance. InAlAs has a minigap size $\Delta E_{m}=0.12eV$ which is larger than its optical phonon energy. It also has a large LH effective mass which prevents quantum tunneling across the minigap, as well as the LH-SO separation $\Delta E_{LS}$ which is comparable to that of AlGaAs and InGaAs. AlInAsSb has a low value for Inqequality (1), so that box is shaded dark green. However, for Inequalities (2) and (3) the values for AlInAsSb are higher than that of InAlAs and are thus shaded in a lighter color. AlInAsSb has a larger LH-SO separation than InAlAs and hence its Inequality (4) has a darker shade. In AlAsSb, the values for Inequalities (1)-(3) have medium shades as they lie between the maximum and minimum values in each of these columns for the corresponding inequalities. However, AlAsSb has a large $\Delta E_{LS}=0.54eV$, so its Inequality (4) is shaded dark green. Based on the inequality values it would seem InAlAs would have the lowest noise since it has the darkest shades. However, looking at the Inequality (4) values for these three materials we can infer that the LH-SO separation plays a critical role in reducing noise. Here, AlAsSb has the lowest $k=0.005$ and also the largest $\Delta E_{LS}$. On the contrary, InAlAs has the highest $k=0.1$ and the smallest $\Delta E_{LS}$. Finally, inequality 5, discussed in the context of split-off states (Eq. 17), is trivially satisfied by all five studied alloys. While important, it is thus not tabulated here, as it does not alter the status quo.

In short, the values of the inequalities in Table 3 give a fairly good understanding of the excess noise performance of the set of digital alloys considered in this paper. They can potentially serve as empirical design criteria for judging new digital alloys in consideration as potential material candidates for digital alloy superlattice APDs.

In this paper, we have studied the digital alloy valence band carrier transport using NEGF and BTE formalisms. Based on our simulation results, we explain how minigaps and LH/SO offset impede hole impact ionization in APDs and improve their excess noise performance. When these gaps/offsets are sufficiently large they cannot bridged across by quantum tunneling or phonon scattering processes. Furthermore, we propose five inequalities as empirical design criteria for digital alloys with low noise performance capabilities. Material parameters calculated computationally are used as inputs for these. We validate these criteria by explaining the excess noise performance of several experimentally fabricated digital alloy APDs. The design criteria can be used to computationally design new digital alloy structures and benchmark them before actually fabricating these.

This work was funded by National Science Foundation grant NSF 1936016. The authors thank Dr. John P David of University of Sheffield and Dr. Seth R. Bank of University of Texas-Austin for important discussions and insights. The calculations are done using the computational resources from High-Performance Computing systems at the University of Virginia (Rivanna) and the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562.