Development of photodetectors with high sensitivity, high speed, and low power consumption has been a main goal in device research for optical communication applications. Metal–semiconductor–metal (MSM) and p–i–n photodetectors can provide high speed, low noise operation but no internal gain.^[1–4] Avalanche photodiodes (APDs) can achieve high sensitivity due to the large internal gain, however, they need high operation voltages.^[5] It is therefore expected that heterojunction phototransistors (HPTs) can provide an exciting alternative to p–i–n photodetectors or APDs for the optical communication application. An HPT basically is a heterojunction bipolar transistor with a light-sensitive collector and base region; the incoming light is absorbed in the narrow bandgap collector and base region, producing electron–hole pairs. The amplification process is the same as that in a transistor, except that the base–emitter forward bias is provided by the optical absorption process rather than a metal contact.^[6,7]

Spectral response is a key performance parameter for many photoelectric devices. Even though many reports involving spectral response models have emerged recently for photodiodes,^[8–10] analytical models for HPTs are still rather limited. Chand et al. formulated the expressions for the flux-dependent current,^[11] but the boundary conditions were taken from the p–i–n photodetectors, which were not effective for the HPTs, in addition, no experimental data were used to verify the theory they proposed. Several others tried to predict the spectral response of HPTs, but the absorption coefficients in those studies were taken as unity for all the layers in the HPTs, which may not be the case for every detector.^[12–14] Khan et al. optimized the necessary analytical expressions of the spectral response model using the doping-dependent collection efficency with the incident light radiated at the base region directly.^[15] However, according to the theory of Chand,^[11] the diffusion current coming from the neutral portion sub-collector should be taken into consideration in calculating the depleted-collector current, which was neglected by Khan owing to the relatively small diffusion coefficients of the minority-carrier holes in the n-type sub-collecter. Furthermore, there are many integrated devices currently employing HPTs with a floating base such as HPTs/OLEDs optical up-converter^[16,17] and HPTs/LDs,^[18,19] which require the light radiated from the emitter of the HPTs. Moreover, in the optical up-converter, the p–n–p InGaAs/InP HPTs are usually chosen to be integrated with the anode of OLEDs. Thus, the establishment of the spectral response model for the p–n–p HPTs is necessary.

In this paper, we present a back illuminated p–n–p In_0.53Ga_0.47As/InP HPT along with a corresponding spectral response model. The epitaxial layer structure of this device consists of a p-type InP layer as emitter, a thin n-type In_0.53Ga_0.47As layer as base, and a p-type In_0.53Ga_0.47As layer as collector. Unlike the structure of Khan et al.,^[15,20,21] the emitter/base junction and the collector/sub-collector junction in our model are neither exposed to the air nor contacted to the metal. So not only the photo-generated minority carriers but also the thermal equilibrium minority carriers electrons (holes) in these regions should be taken into account in the boundary conditions of the spectral response model. The main aim of this study is to determine the spectral response model for the p–n–p HPT which has a perfect agreement with the measurements. Moreover, a nearly proportional relationship between the response and the base width is found in this paper.

The In_0.53Ga_0.47As/InP HPT was grown by metal-organic chemical vapor deposition (MOCVD) on a semi-insulated InP substrate. The epitaxy structure is as follows: 500 nm InP emitter contact (p⁺, 1 × 10¹⁸ cm⁻³), 300 nm InP emitter layer (p, 5 × 10¹⁷ cm⁻³), 100 nm InGaAs base layer (n⁺, 1 × 10¹⁸ cm⁻³), 1 μm InGaAs collector layer (p, 5 × 10¹⁷ cm⁻³). The HPT was capped with a 500 nm InGaAs contact layer (p⁺, 1 × 10¹⁸ cm⁻³). The first step of the device fabrication was to pattern and etch square mesas (1 mm × 1 mm). The solution of H₂SO₄:H₂O₂:H₂O (1:8:160) was used to etch the InGaAs layer (∼1.6 μm thick), and the solution of H₃PO₄:HCl (10:1) was used to etch part of the p-InP layer (∼0.5 μm thick) to complete the square mesas (Fig. 1). Subsequently, metal (Ti/Pt/Au) contacts were deposited on the top and bottom of the device by electron beam evaporation. The spectral response measurements were carried out using a BOMEM spectrometer over 900–1700 nm.

Fig. 1.

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	Fig. 1. Schematic cross section of the In0.53Ga0.47As/InP HPT. Note that the top and bottom metal contacts consist of 25 nm Ti, 55 nm Pt, and 120 nm Au.

When the p–n–p HPT is exposed to the incoming near-infrared (NIR) light, electron–hole pairs will be generated in the base, depleted-collector, and sub-collector regions. These electrons and holes will be driven to the contrary directions (electrons drifting towards the n-type base region and holes to the p-type sub-collector). The photo-generated electrons will accumulate in the base region due to a large potential barrier in the conduction band at the base–emitter heterojunction until they recombine with the injected holes from the emitter. Thus a large amount of holes inject from the emitter into the base to maintain the charge-neutrality condition in the base layer, leading to a large hole current.

The spectral response model is based on the steady state continuity equations with suitable boundary conditions. The distributions of minority-carriers (electrons and holes) at the low-injection state in the base and sub-collector regions respectively obey

The electron current in the sub-collector region I_x=wb+wdep+wc can be similarly derived as

The current in the depleted-collector layer I_dr consists of photo-generated current I_ph and diffusion current I_x=wb+wdep. The former is owing to the optical-flux absorption, the latter is the result of the electrons diffusion from the neutral portion, which are respectively given as

The optical-flux profiles of the active regions in the p–n–p In_0.53Ga_0.47As/InP HPT at 980 nm, 1310 nm, and 1550 nm are given numerically in Fig. 2 with the incident light power of 1 mV, which are modeled by

The total current I_total of this HPT is the sum of the hole current at the base/depeted-collecter junction I_x=wb, the electron current in the sub-collector region I_x=wb+wdep+wc, and the current in the depleted-collector region I_dr. The responsivity can be obtained by I_total/P_in, where P_in is the incident light power. As shown in Fig. 3, the calculated responsivities for this In_0.53Ga_0.47As/InP HPT at 980 nm, 1310 nm, and 1550 nm are 6.34 A/W, 25.7 A/W, and 28.1 A/W, respectively, which are in good agreement with the measured values.

Fig. 2.

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	Fig. 2. The calculated optical-flux profiles for the In0.53Ga0.47As/InP HPT.

Table 1.

Table 1.

Table 1. Material parameters used for In0.53Ga0.47As/InP HPT simulation. . Parameter Value Unit Reference Dn, DP 90, 6 cm2·s− 1 [25] τn, τp 4.3 × 10−9, 4.3 × 10−9 s [26] Ln = (τnDn)1/2, Lp = (τpDp)1/2 6.3 × 10− 4, 1.6 × 10−4 cm [22] Sn, Sp 1 × 104, ∼106 cm·s−1 [27] 2 × 104, 2 × 104 cm−3 [28] αb(980 nm), αb(1310 nm), αb(1550 nm) 2.80 × 104, 1.20 × 104, 0.70 × 104 cm−1 [23], [29] αdep(980 nm), αdep(1310 nm), αdep(1550 nm) 2.80 × 104, 1.28 × 104, 0.88 × 104 cm− 1 [23], [29] αc(980 nm), αc(1310 nm), αc(1550 nm) 2.80 × 104, 1.59 × 104, 0.78 × 104 cm−1 [23], [29]

Table 1. Material parameters used for In0.53Ga0.47As/InP HPT simulation. .

Fig. 3.

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	Fig. 3. Calculated and measured responsivities as a function of wavelength for the In0.53Ga0.47As/InP HPT.

We assume that the InP substrate and the emitter region are transparent to NIR light, i.e., light absorption starts from the base layer. For a constant incident light power, the optical flux increases with the increase of the wavelength, resulting in increasing photo-generated electron–hole pairs. While the absorption coefficient is opposite, thus, leading to a responsivity peak at about 1420 nm, and the responsivity tends to drop at longer wavelengths owing to the lower absorption coefficient, which causes a cut-off wavelength around 1700 nm.

For various base widths, the corresponding responsivities are shown in Fig. 4. As observed in this figure, the responsivity has a near linear falling with the increase of the base width. It is common knowledge that an increase in the base width is related to an increasing recombination of the minority-carrier holes and the majority-carrier electrons in the base region, which will lead to a decreasing built-in current gain, i.e., a decreasing responsivity. However, different decreasing rates in responsivity can be found for the under-investigated In_0.53Ga_0.47As/InP HPT at 980 nm, 1310 nm, and 1550 nm due to the different absorption coefficients and optical-flux profiles in the base region. For the incident light of the wavelength of 1310 nm, the absorption coefficient is lower compared to that of 980 nm, and the optical flux is fewer compared to that of 1550 nm, leading to the fewest photo-generated carriers compared to those at 980 nm and 1550 nm, hence, the falling rate is highest at 1310 nm.

Fig. 4.

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	Fig. 4. Calculated responsivities versus the base width for the In0.53Ga0.47As/InP HPT at various incident wavelengths.

An accurate spectral response model for the back-illuminated p–n–p In_0.53Ga_0.47As/InP HPT has been established by applying the semiconductor continuity equations with the exacted boundary conditions which contain the thermal equilibrium minority-carrier electrons (holes). Twice Fresnel reflection and the diffusion current of the electrons from the sub-collector have been taken into consideration in this model. The calculated responsivity is close to the measured one, which has a peak at about 1420 nm. Furthermore, a nearly proportional relationship between the responsivity and the base width has been found in this work.