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Abstract
Al0.85Ga0.15As0.56Sb0.44 is a promising avalanche material for near infrared avalanche photodiodes (APDs) because they exhibit very low excess noise factors. However electric field dependence of ionization coefficients in this material have not been reported. We report a Simple Monte Carlo model for Al0.85Ga0.15As0.56Sb0.44, which was validated using reported experimental results of capacitance-voltage, avalanche multiplication and excess noise factors from five APDs. The model was used to produce effective ionization coefficients and threshold energies between 400–1200 kV.cm-1 at room temperature, which are suitable for use with less complex APD simulation models.
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1. Introduction
Avalanche photodiodes (APDs) are widely used in high-speed optical communication [1] and laser ranging applications [2], which require detection of weak optical signals. In these applications, the detection system’s signal-to-noise ratio is often limited by the electronic noise. An APD provides internal gain, termed avalanche multiplication, M, amplifying the optical signals before the electronics. This reduces the significance of electronic noise and increases the system’s signal-to-noise ratio, making APDs advantageous compared to photodiodes.
Avalanche multiplication of an APD is the end product of successive impact ionization events taking place in its avalanche region. Impact ionization events are stochastic so there are fluctuations around a mean value of M for a given APD’s reverse bias, V. This gives rise to APD’s excess noise factor, F, which generally increases with M. The exact F(M) characteristics depend on the avalanche material, operating temperature, and the avalanche region width, w.
Near infrared APDs grown on InP substrates usually have InP [3] or In0.52Al0.48As [4–6] as their avalanche material. In recent years, the material Al0.85Ga0.15As0.56Sb0.44 (hereafter referred to as AlGaAsSb) has shown much potential as an alternative avalanche material, following reports of very low F(M) characteristics [7–9], compared to other common avalanche materials [3–6]. There are however no accurate impact ionization coefficients for electrons and holes, α and β, for this material in the literature. It is therefore problematic to accurately simulate M(V) and F(M) characteristics as well as avalanche breakdown voltage, Vbd, for AlGaAsSb APDs.
Extracting impact ionization coefficients from experimental results of M(V) and F(M) usually require experimental samples with uniform electric fields across the avalanche regions. The AlGaAsSb diodes in Refs. [7,8] unfortunately possess relatively graded doping profiles, producing non-uniform electric field profiles. Commonly used APD simulation models, such as local model [10], recurrence model [11], and Random Path Length (RPL) model [12], are unsuitable for non-uniform electric field profiles [13]. Obtaining electric field dependences of α and β for AlGaAsSb therefore requires a more complex method and APD simulation model.
In this work, we present a Simple Monte Carlo (SMC) simulation model for AlGaAsSb APDs, which was validated with extensive, published room temperature data of M(V) and F(M) [7,8]. Using the AlGaAsSb SMC model, electric field dependences of impact ionization coefficients and threshold energies were extracted. These could be used with simpler, more accessible simulation models, such as recurrence model and RPL model, provided the APD designs have well-defined doping profiles.
2. Model
The SMC model used in this work is largely based on Ref. [14] and has been shown to work with InP [15] a III-V material and Si [16] an indirect bandgap material like AlGaAsSb. This work does contain a notable difference, with alloy scattering included as an additional scattering mechanism for the carriers as in an In0.52Al0.48As SMC model [13]. In the simulation, each carrier drifts across an avalanche region, under an electric field, for a random distance before undergoing one of four possible scattering mechanisms: intervalley phonon emission, intervalley phonon absorption, impact ionization or alloy scattering. Carriers are tracked until they exit the avalanche region. A simulation ends when all carriers have left the avalanche region. When simulating an APD at a given reverse bias, the electric field profile was calculated using a 1-D Poisson’s field solver.
The rate of intervalley phonon emission (Rem) and absorption (Rab) is given by
Value of ħω was obtained by linear interpolation of values from the binary materials [19–21]. Value of Eth was similarly obtained. Value of the binary material’s threshold energy was given by the weighted average [22] ${E_{th}} = \; ({{E_0} + 3{E_x} + 4{E_L}} )/8$, where E0, Ex, and EL [19,23–26] are the energy bandgap for Γ, X and L valleys, respectively.
3. Validation
Values of Cii, Eth and Calloy were adjusted so that the SMC results agree with published M(V) and F(M) results. The relative permittivity for this material was from [27] and built-in voltage was extracted from experimental Capacitance-Voltage (C-V) data. The AlGaAsSb SMC model parameter set is summarized in Table 1. The SMC predicts saturation velocities of 7.6 × 104 and 6.6 × 104 m.s-1 for electrons and holes respectively, close to those of GaAs.
Table 1. Al0.85Ga0.15As0.56Sb0.44 SMC model parameter set
The experimental data used in the SMC model validation were from three p-i-n wafers (A, C, and E) and two n-i-p wafers (B and D) of various AlGaAsSb avalanche widths, w, reported in Refs. [7,8]. Nominal w values, Vbd values, and data types of the wafers are summarized in Table 2. The p-i-n wafers provided validation data for electron-initiated avalanche multiplication and excess noise factor, Me(V) and Fe(Me), respectively. Similarly the n-i-p wafers provided hole-initiated avalanche multiplication and excess noise factor, Mh(V) and Fh(Mh).
Table 2. AlGaAsSb APDs used to validate the SMC model
The doping profiles for wafer A-D used were estimated from C-V data and Secondary Ion Mass Spectroscopy. For each of the five wafers, the C-V data used cover multiple devices with at least three device diameters. In addition, C-V data analyses included slight reductions in device area to account for device fabrication tolerances.
The C-V data and fitting using the 1-D Poisson’s field solver for wafer C (109.3 µm device diameter) are shown as examples in Fig. 1(left). The doping profile used for C-V fitting (and subsequently SMC simulations) was extracted from SIMS data, both of which are shown in Fig. 1(middle). This process was applied to all other wafers, with the exception of wafer E whose C-V data were fitted satisfactorily using a 3-region fitting. Examples of electric field profiles of wafers A-D (at 98% of their breakdown voltages) are shown in Fig. 1 (right).
Fig. 1. (Left) Experimental C-V characteristics and fitting using 1-D Poisson’s field solver for wafer C with device diameter of 109.3 µm. (Middle) Doping profiles used in C-V fitting and from SIMS results. (Right) Electric field profiles of wafer A-D at 98% of their breakdown voltages.
Using our SMC model, avalanche multiplication and excess noise characteristics were simulated for wafers A, C and E (electron-initiated) as well as wafers B and D (hole-initiated). The simulated results are in agreement with the validation data (experimental results), as shown in Fig. 2.
Fig. 2. (Left) M(V) and (Right) F(M) from the SMC model (symbols) are in agreement with the validation data from Refs. [3,4] (lines). Dotted lines indicate the McIntrye’s local excess noise model [10], where k is ionization ratio.
4. Results
Using the AlGaAsSb SMC model, another series of simulations were carried out to extract impact ionization coefficients as functions of electric field (ξ) from 400 to 1200 kV.cm-1. For this, each simulation tracked a single carrier (electron or hole) under a constant electric field of infinite length and recorded distances between each consecutive impact ionisation events (i.e. ionization path lengths). These statistics yielded probability density functions (PDFs) of the ionization path lengths for electrons and holes, he(x) and hh(x) [28]. Effective ionization coefficient (α* and β*) and deadspace (de and dh) for electrons and holes were obtained from fittings to these PDFs, using the hard deadspace assumption [11], where
Example he(x) and hh(x) as well as their fittings at ξ = 800 kV.cm-1 are shown in Fig. 3(left). For each electric field, values of α* (or β*) and de (or dh) were extracted by fitting to the gradient of he(x) at large x and the he(x) region before the peak, respectively. The deadspaces were given by ${d_{e(h )}} = {E_{the(h )}}/q\xi $, where Ethe and Ethh are threshold energy for electrons and holes, respectively.
Fig. 3. (Left) Probability density function of ionization path length from SMC (symbols) and fittings (lines) at 800 kV.cm-1. (Right) α* and β* obtained from the SMC model (symbols) and the parameterized expressions (lines).
The values for Ethe and Ethh are 3.6 eV. The extracted α* and β* are plotted versus inverse electric field in Fig. 3(right). They can be parametrized using
To confirm the validity of Eqn. (1) and (2), avalanche multiplication and excess noise factors of a series of AlGaAsSb ideal p-i-n diodes were simulated using both the AlGaAsSb SMC model and an RPL model. Inputs to the latter are Eqn. (6) and (7) as well as our Ethe and Ethh values. The ideal p-i-n diodes, labelled as D1, D2, D3, D4, D5, and D6, have w of 100, 200, 500, 800, 1000, and 1500 nm, respectively. Results from SMC and RPL simulations are in good agreement, as shown in Fig. 4, confirming the validity of our expressions for α*(ξ), β*(ξ), Ethe, and Ethh.
Fig. 4. Comparisons of (left) M(V), (middle) Fe(Me), and (right) Fe(Me) simulated using SMC (triangle for electron- and circles for hole-initiated conditions) and RPL (solid lines for electron- and dashed lines for hole-initiated conditions). D1, D2, D3, D4, D5, and D6 have w of 100, 200 500, 800, 1000, and 1500 nm, respectively.
Simulation results for D5 (w = 1000 nm) indicate Vbd of 54 V, which is consistent with the 1000 nm AlGaAsSb APD reported in [9]. It is however lower than the 58 V reported in [29] for a w = 910 nm AlGaAsSb APD, possibly due to experimental uncertainties in the APD structure.
5. Conclusion
We have presented an SMC model for Al0.85Ga0.15As0.56Sb0.44 APDs at room temperature. The model was validated using comprehensive experimental results of capacitance-voltage, avalanche multiplication, and excess noise factor from earlier reports on Al0.85Ga0.15As0.56Sb0.44 APDs. Using this validated model, we have extracted room temperature electric field dependences of effective impact ionization coefficients and threshold energies for Al0.85Ga0.15As0.56Sb0.44 at electric field range of 400–1200 kV.cm-1. These parameters can be used with RPL model and recurrence equations for Al0.85Ga0.15As0.56Sb0.44 APD simulations of avalanche multiplication and excess noise factors.
Funding
UK Engineering and Physical Sciences Research Council (EP/N509735/1).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in Ref. [30].
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30. ORDA digital repository, doi: 10.15131/shef.data.19299665
