Physical modelling and experimental characterisation of InAlAs/InGaAs avalanche photodiode for 10 Gb/s data rates and higher

InAlAs/InGaAs avalanche photodiodes (APD) were simulated using physical device models, then designed and fabricated to detect light in the wavelength range from 1.3 to 1.55 μm. DC characterisation under dark and light conditions were performed at room temperature to measure and investigate the performance of the APD. High-frequency characterisation was carried out on the device to extract the diode intrinsic and extrinsic parameters. The work reported here focuses on the dark and light physical device simulations (both under DC and AC conditions) which were accomplished using Atlas SILVACO tool. The effect of electron velocity overshoot was considered for accurate bandwidth modelling. All measured data are in excellent agreement with the modelled ones. The internal device gain of the APD is 45 at −23.5 V leading to a ∼220 GHz gain–bandwidth product. This successful APD model can be exploited to further improve the diode structure for higher data rate applications beyond 10 Gb/s.


Introduction
The avalanche photodiode (APD) is the preferred photodiode receiver device in telecommunication detection systems due to its internal gain which leads to high sensitivity at low optical power.However, the random nature of the impact ionisation process in the APD generally introduces excess noise which depends on exact semiconductor materials used in the device [1].In practice, the APD is always used in tandem with a trans-impedance amplifier can be incorporated to adjust the gain, improve the signal-to-noise ratio and the bandwidth of the optical receiver system [2].APD based on InP and InAlAs multiplication layers have been extensively studied by many groups [1,[3][4][5][6].The InAlAs material is an electron multiplication material with a k-ratio of 0.29-0.5 [7], while InP is a hole multiplication material with a k-ratio of 0.4-0.5 [8].Moreover, an APD with InAlAs multiplication layer has better stability compared with the one based on InP multiplication layer [3].The lowest reported k-ratio material is silicon with k = 0.03-0.1 [9].However, silicon is not lattice matched with InGaAs material, which limits its use for 1.3-1.55wavelength telecommunication applications, even though attempts at using mismatched Si-Ge are underway [10].
The work reported here can be summarised as follow.Firstly, an InGaAs-InAlAs APD with a light window size of 30 µm was designed and then experimentally fabricated and characterised in terms of its DC and high-frequency optical characteristics.Secondly, high-frequency equivalent circuits from fabricated devices were built up to 40 GHz to extract key diode parameters, including junction capacitance, series resistance, and junction resistance utilising Advanced Design System (ADS) software from Keysight Technologies.Extracting the APD parameters is necessary to calculate its cut-off frequency and predict its performance for high-frequency applications.Finally, physical models of the APD structure, using the Atlas SILVACO simulation tool, including dark current, photocurrent current, C-V characteristics, optical 3 dB bandwidth, and gain, are developed and validated by an experimental APD epi-layer structure.To the best of the authors knowledge, this is the first full virtual wafer fabrication physical modelling (DC and C-V characteristics, and optical 3 dB bandwidth) of an InGaAs-InAlAs APD in SILVACO using the concept of electron velocity overshoot.The simulated results for both models, i.e. high-frequency small-signal equivalent circuit model and SILVACO physical model, showed high correlation with the measured data which validates the models used.Specifically, the junction capacitance at different bias voltages was extracted from both models and the obtained values show excellent agreements with the measured ones.
The structure reported in this work was grown using molecular beam epitaxy on a 620 µm thick semi-insulating InP substrate as shown in Fig.  cm −3 ) and 1 × 10 19 cm −3 with thicknesses of ∼100 and 500 nm, respectively.The highly doped contacts help to reduce the series resistance (R S ) which leads to improvements in the frequency response of the device.The absorber is relatively thick (∼1.5 µm), but this makes the APD efficient at absorbing light in the 1.3-1.6 µm wavelength region.The grading layer thickness is 50 nm which improves the frequency response of the APD by reducing the band discontinuity at the interface with the charge layer.The charge layer has a doping profile of ∼1 × 10 18 cm −3 with a thickness of 50 nm.The main function of this layer is adjusting the electric field of the device.Finally, the multiplication layer with a thickness of 200 nm is buried under the charge layer.

Experimental and simulation characterisation details
The APD was experimentally characterised to determine its electrical and optical characteristics.The electrical characterisation was performed under dark conditions and at room temperature to measure the dark current, capacitance-voltage (C-V) characteristics, and high-frequency s-parameter measurements up to 40 GHz at different bias voltages.An Anritsu VNA was used to collect the s-parameter data as well as measuring the C-V characteristics.For the optical characterisation, a 1.55 µm wavelength laser with −30 dBm output power (1 µW) was utilised to illuminate the device.The laser diameter was 5 µm.A Lightwave Component Analyser (HP 8703A) was employed to measure the 3 dB optical bandwidth of the device.The bias voltage IET Optoelectron., 2018, Vol. 12 Iss. 1, pp. [5][6][7][8][9][10] This is an open access article published by the IET under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/) is applied using a DC supply HP4142B connected to the Analyser through a bias-T.
The main objective of this work was to build a quantitative and predictive physical model for the APD photo-detector to validate the measured electrical and optical characteristics and which can then be used for further device improvements.Therefore, numerical simulations of the InAlAs/InGaAs APD photodetector under dark and light conditions and at room temperature were carried out using the Atlas SILVACO tool.Device structure and type determines the required physical models to use.To model the impact ionisation process of the APD, an IMPACT SELBER model was used as will be discussed later in Section 4. As the SILVACO library does not contain material parameters for InGaAs, InAlAs, and InAlGaAs, all III-V material parameters were obtained both from the literatures and from validation from a number of devices studied over the years in our lab [4,[11][12][13][14].

S-parameter measurement and small-signal radio frequency equivalent circuit extraction of the APD
The device was fabricated into a circular mesa form with an aperture window of 30 µm as shown in Fig. 2. High-frequency characterisation plays an important role in determining the intrinsic and extrinsic component of the device such as series resistance (R S ), junction resistance (R J ), junction capacitance (C J ), pad capacitance (C P ), and pad inductance (L P ).The parasitic components are introduced by the GSG coplanar waveguide configuration.The optimisation of the CPW dimensions is required to further reduce the parasitic capacitance caused by fringing effect without increase in conductor losses or change in the designated characteristic impedance (50 Ω) [15][16][17].High-frequency sparameter measurements were performed for the open, short, and actual structures from 40 MHz to 40 GHz at different bias voltages.Fig. 2 depicts the GSG coplanar waveguide one-port structure of the APD.
The dimension of the GSG coplanar waveguide was optimised to give an impedance of 50 Ω.All measurements were performed in the dark at room temperature.As there is no standard model for the APD in ADS, an equivalent circuit model was built and the fitting was made with measured data to validate this model and extract the intrinsic and extrinsic components of the InAlAs/ InGaAs APD.The equivalent circuit for the open structure was built in ADS and is represented by a capacitor only (C P ), while the short structure is represented by an inductor (L P ).The simulated sparameters of the equivalent circuits were fitted with the measured ones to extract C P and L P .The measured and simulated sparameters represented on a Smith chart for the open and short devices are shown in Fig. 3.The excellent agreement between the measured and simulated data validates the equivalent circuits used to extract C P and L P .The extracted C P and L P are 8 fF and 40 pH, respectively.The small parasitic capacitance (C P ) comes from the optimised coplanar waveguide design process.In the same manner, the equivalent circuit for the actual structure was built at different bias voltages and its s-parameters were compared with the measured ones to extract the intrinsic components (R S , C J , and R J ) of the device as shown in Fig. 4. C P and L P were de-embedded from the total equivalent circuit.Fig. 4 depicts the measured and equivalent circuit s-parameters of the device at −15 V.The equivalent circuit s-parameters agree extremely well with the measured ones over the frequency range 40 MHz-40 GHz with simulated and measured curves being essentially identical (Figs. 3  and 4).Table 1 lists the extracted component at different bias voltages.
The fully depleted junction capacitance of the APD is 162 fF.The small R S (10 Ω) of the APD is due to the highly doped profile of the top and bottom contact layers.The series resistance (R S ) is mainly due to contributions from the top contact resistance and spreading and epi-layer resistances [18].Reducing the separation between the top and bottom contact also helps minimise the series resistance of the APD.When the reverse bias voltage increased beyond punch-through, a voltage drop occurs through the series and load resistances.At higher gain levels, a large photocurrent flows in the series resistance resulting in undesired behaviour leading to a non-linear relationship between output current and applied light [19].The intrinsic cut-off frequency calculated using the usual expression 1/2πR S C J is 105 GHz and the extrinsic cut-off frequency is 16 GHz when used in a 50 Ω load as would be the case for an APD.Extracting the junction capacitance of the APD using the high-frequency small-signal equivalent circuit model is necessary to validate the SILVACO physical model which exhibits almost the same value when the APD is fully depleted as will be discussed in Section 4.

Experimental and physical modelling results
The APD was modelled using the same dimensions as the fabricated structure such as aperture window size, mesa size, anode and cathode diameter sizes, anode to cathode separation, and region thicknesses.Fig. 5 depicts the three-dimensional (3D) APD configuration and its 2D sectional view in the Atlas SILVACO tool.
The dark current of the device was measured up to −25 V reverse bias voltage using a probe station under dark room conditions and at room temperature.The fitting process of the dark current is crucial to validate the model and material parameters used.This model was then used to simulate the C-V characteristics, photocurrent, and optical 3 dB bandwidth.In SILVACO, a bias voltage was applied as shown in Fig. 5 and the device simulated to extract the dark current under the same conditions.Fig. 6 shows the measured and simulated dark currents of the InAlAs/InGaAs APD.The modelling process of the APD photodetector was performed using two assumptions.The first assumption was based on the dark current characterisation, where no electron-hole generation is defined in the absorber layer, and where the multiplication region has a low electric field distribution.Therefore, electrons travel with their normal velocity in both multiplication and charge sheet layers.According to that, the electron velocity was set to 2.5 × 10 6 and 1 × 10 7 cm/s in the charge and multiplication layers, respectively.The electron velocity in the absorption layer was set to 1.5 × 10 7 cm/s.The key fitting parameters used in SILVACO modelling are shown in Table 2.
The electron mobilities of each layer (InGaAs, InAlAs, and InAlGaAs) are different depending upon the doping profile of each layer.All required values were obtained from the literatures in [12][13][14].For the simulation of the dark current, several models have to be considered.The Shockley-Read-Hall (SRH) model and Fermi-Dirac statistics were used to model the generation-recombination and carrier drift-diffusion processes both of which make large contributions to the total dark current.The basic analytical expression of these models can be found in details in [20].The band-to-band tunnelling current was not considered due to the inclusion of the graded and charge sheet layers which provide enough electric field separation between the absorber and multiplication layers.Band-to-band tunnelling current starts to dominate the dark current of the APD when the multiplication region is smaller than 100 nm [21].The most important phenomena to take in account for accurate physical simulation of the dark    current is the impact ionisation process which is described by the following equation [20]: where G is the generation rate of the electron-hole pairs, α n and α p are the electron and hole impact ionisation coefficients, and J n and J p the electron and hole current densities.In SILVACO, FLDMOB, and a local field, IMPACT SELBER models were used to model the electric field mobility dependency and impact ionisation rate of electron and hole in the multiplication region, respectively.Both models are necessary to fit the dark current and breakdown voltage (V BR ).The IMPACT SELBER model which is a variation of the classical Chynoweth model was used to determine the ionisation coefficients (α n and α p ) using the following equations: where E is the electric field across the structure.AN, AP, BN, BP, BETAN, and BETAP are the impact statement parameters [20].Through the simulation, SILVACO calculates these parameters according to the material parameters of the charge sheet multiplication regions (lattice temperature and energy gap) as well as the required model for the impact ionisation process.The calculation process of the parameters can be found in details in [20].The output window of the SILVACO resulted in values of 8.6 × 10 6 cm −1 , 2.3 × 10 7 cm −1 , 3.5 × 10 6 cm −1 , 4.5 × 10 6 cm −1 , 1, and 1 for AN, AP, BN, BP, BETAN, and BETAP, respectively.From Fig. 6, it is clear that there is excellent fit between experimental and simulated data which validates the physical models used.The excellent agreement is due to the appropriate material parameters and models used.The breakdown voltage is −24 V (defined at 0.1 mA dark current).In Silvaco, the doping profile and the thickness of the charge sheet layer are the key factors in adjusting the V BR of the device to be fitted with the measured one and this therefore allows for a determination of the actual doping and thickness of the specified layer for further improvements.The dark current for the device is <14 nA at (90%V BR ), which makes the device efficient for high-sensitivity receivers.
Similarly, the measurement of the device capacitance-voltage (C-V) characteristic is important in determining the actual doping profile and layers thicknesses of the fabricated device.The total capacitance including the junction and parasitic capacitances was measured at different bias.The parasitic capacitance comes from the GSG coplanar waveguide pad.The junction capacitance of the device was then extracted as shown in Fig. 7 which depicts the measured and simulated junction capacitances at different reverse bias voltages.The doping profile of the charge sheet layer is a critical factor in fitting the simulated junction capacitance to the measured one.The fitting process indicated that the doping of this layer is ∼6.2 × 10 17 cm −3 .The simulated junction capacitance is in an excellent agreement with the measured one except for a difference of ∼12% from −18 to −21 V bias voltages.This difference could be due to the wider simulated depletion region in the SILVACO tool, resulting in a smaller capacitance value.
The device has a wide margin voltage range where the punchthrough voltage (V PT ) occurs at (−12.5 V), which is far enough from the breakdown voltage (V BR = −24 V).At the punch-through voltage (V PT ), the junction capacitance value starts to drop due to the expansion of the depletion region.The fully depleted junction capacitance is 160 fF which matches the extracted value from the high-frequency small-signal equivalent circuit.The junction capacitance can be further minimised by enlarging the absorber thickness, but this would lead to increasing the carrier transient time and as a result degrading the bandwidth.
The second assumption in the modelling process was based on the light characterisation which takes into account the generation process of the electron-hole pair in the absorber layer and the high electric field distribution in the charge and multiplication layers.The optical generation rate is calculated in SILVACO using the formula [20]: where η 0 is the material quantum efficiency, P* represents the effect of absorption losses and transmission and reflection factors, λ is the light wavelength, α the material absorption coefficient, h the Planck constant, and c the speed of light.The photo-response characteristics of the InAlAs/InGaAs were measured and modelled.
A laser light was utilised with a wavelength of 1.55 µm to generate electron-hole pairs in the absorption layer.The laser power was 1 µW as shown in Fig. 5.In the photocurrent simulation process, the same models (SRH, Fermi-Dirac statistics, IMPAT SELBER, and FLDMOB) and fitting parameters of the dark current and C-V characteristics were used except that the electron velocity in the absorption and charge sheet layers were set to 2 × 10 7 and 5 × 10 7 cm/s, respectively, as the electric field is higher under light conditions.In [4], a Monte Carlo model was used to simulate the optical characteristics of the APD.In [9], it was shown that in thin multiplication regions and high electric fields, the electron can travel with a speed that is much higher than its saturation velocity.This was also confirmed in [22], where the carrier velocity used in the model was much higher than the saturation velocity for an APD with a 200 nm InAlAs multiplication region.This concept was further explored in our model where the charge sheet and multiplication layers have a high electric field profile as shown in Fig. 8.As can be clearly seen, the electric field is ∼690 and 700 kV/cm at −18 and −20 V bias voltages, respectively.At higher electric field, the newly generated electrons, due to the impact ionisation process, tend to populate the Г valley where the electrons have lighter effective mass.This then lead to a carrier velocity overshot behaviour.The measured and simulated dark and photocurrents are shown in Fig. 9a.The appropriate material parameter and models used resulted in excellent agreement between the measured and simulated results.Thereafter, this model was used to simulate the frequency response of the InGaAs/InAlAs APD by only changing the electron velocity in the charge sheet layer according to the gain value.Under dark conditions, there is no electron-hole pair generation and no injected electron into the multiplication region and as a result, the dark current does not change much before and after the punch-through voltage (V PT ).For this reason, V PT cannot be determined from the dark current.However, V PT can easily be determined from the photocurrent curve (Fig. 9a) and is around −12.5 V which matches well with the value obtained from the C-V characteristics.The photocurrent is equal to the dark current for voltages < punch trough voltage (V PT ).
For voltages >V PT , the carrier starts to be injected into the multiplication region, which leads to an increase in the photocurrent.At the breakdown voltage (V BR = −24 V), a large number of impact ionisation events occur resulting in a large photocurrent exceeding 0.1 mA.The measured and simulated multiplication gain is given by the ratio of the photocurrent to the injected primary photocurrent at −13.4 bias voltage as depicted in Fig. 9b.The internal gain increases with increasing the bias voltage after the punch-through voltage where it is clear that the APD can provide a gain >10 at 90%V BR .High-sensitivity receivers require the high gain that an APD provides.However, the excess noise factor increases at high multiplication gain which in turn degrades the signal-to-noise ratio.The 3 dB optical bandwidth of the device was calculated from the measured S21 frequency response.S21 response represents the ratio of the measured current signal at the GSG probe to the applied laser power.S21 frequency response was measured at different bias voltages at 1 µW input laser power.The simulation process of the S21 frequency response was performed using the same model used to simulate the photocurrent.The fitting parameter (charge sheet layer electron velocity) was changed according to the gain values because of the field-velocity dependency.The charge sheet layer electron velocity was adjusted to fit the simulated optical bandwidth with the measured one at different bias voltages according to the velocity overshot in the thin multiplication layer.At gain values of 5-10, the electron velocity in the absorption layer and multiplication layer were set to 2 × 10 7 and 1 × 10 7 cm/s, respectively.The effect of the velocity overshoot was applied on the electron velocity in the charge sheet layer.Therefore, the electron velocity of the charge sheet layer was varied according to the applied bias voltage and it was set to 6 × 10 7 , 5.5 × 10 7 , 5 × 10 7 , and 4 × 10 7 cm/s at −18, −19, −20, and −21 V bias voltage, respectively.Fig. 10a shows the measured and simulated S21 response at −20 V bias voltage and Fig. 10b shows the variation of bandwidth with applied bias.The excellent fit between the measured and simulated results validates the SILVACO APD models developed which should then provide further predictive behaviour of the device characteristics under different epitaxial layers and device layout configurations for 25 G/s applications and above.The device has an optical bandwidth of 6.7 GHz at −20 V bias voltage, which can be used for 10 G/s applications.At higher bias voltage close to the breakdown voltage, the electrons start to scatter from Г to L and X valleys where the effective masses are higher.Therefore, the electrons travel with lower speeds resulting in a reduced operating bandwidth as can be seen in Fig. 10b.In our model at −22 V bias voltage, the electron velocity of the charge sheet layer was reduced to 1 × 10 7 cm/s.The measured gain-bandwidth of the device is 220 GHz at −23.5 V bias voltage (for a gain of 45).

Conclusion
In this work, detailed physical modelling of an InAlAs/InGaAs avalanche photodetector including dark and light DC characteristics, frequency response, and C-V simulation using Atlas SILVACO were presented which agreed extremely well with measured data.The intrinsic and extrinsic diode parameters were accurately extracted up to 40 GHz using a small-signal equivalent circuit technique.The velocity overshoot of electron gave an optimal modelled bandwidth which fits the measured data at different bias voltages.This successful physical model provides excellent quantitative predictions of the APD characteristics which can be useful to further improve the device performances.This model represents a platform to design APDs operating at high data rates, e.g. 25 Gb/s receiver systems and higher.

Fig. 4
Fig. 4 Measured and simulated s-parameters Smith charts and equivalent circuit of the APD at −15 V bias voltage

Fig. 7
Fig. 7 Measured and simulated C-V characteristic of the InAlAs/InGaAs APD

Fig. 10
Fig. 10 Measured and simulated (a) S21 response, (b) Bandwidth versus bias voltages of the InAlAs/InGaAs APD 1.It comprises p-type In 0.53 Ga 0.47 As top and n-type In 0.53 Ga 0.47 As bottom contacts, p-type In 0.53 Ga 0.47 As top and ntype In 0.52 Al 0.48 As bottom cladding layers, undoped In 0.53 Ga 0.47 As absorber layer, p-type In 0.52 Al 0.22 Ga 0.25 As grading layer, p-type In 0.52 Al 0.48 As charge sheet layer, and undoped In 0.52 Al 0.48 As multiplication layer.The top and bottom contacts are heavily doped (>2 × 10 19