1.
Introduction
Due to the advantages of optical power transmission in electrical insulation of source, immunity to electromagnetic pulses and radio-frequency, laser power converters (LPCs) are attracting more attention[1–6]. Semiconductor materials Si, GaSb, GaAs and GaInP have been used to fabricate LPCs, while GaAs LPCs converting the power of near-infrared laser light (790–850 nm) demonstrate the highest efficiency[7, 8]. A single-junction GaAs LPC produces an open circuit voltage (Voc) of approximately 1 V, while typical higher operating voltages, e.g., 5, 6, and 12 V, are expected for real applications. An output voltage of 4 V GaAs LPCs has been realized using metal wires to connect multiple GaAs single-junction cells placed side by side in series, whereas a large light receiving area of this type of LPC is a disadvantage[9]. A maximum conversion efficiency (ηc) of 42.7% has been achieved at a laser power density of 22 W/cm2 by connecting multiple pie-shaped sub-cells isolated by etched trenches on a semi-insulating substrate in series, and the operating voltage at the maximum power point achieves 6.03 V[7]. However, the fabrication processes are relatively complex, and light shining on the trench area leads to higher losses. The performance of LPCs has improved in the past four years with the breakthrough implementation of the vertically-stacked heterostructure. The mechanism of vertically-stacked LPCs is similar to multi-junction solar cells[10–11]. Five-volt vertically-stacked GaAs LPCs were demonstrated, and an ηc of 60% was obtained at a power density of 11 W/cm2 at a wavelength of 835 nm[12]. The vertically-stacked LPC can not only get rid of the problems caused by isolation trenches, but also achieve a lower series resistance and a higher ηc.
In this paper, monolithic six-junction vertically-stacked GaAs LPCs have been designed and fabricated. A maximum ηc is demonstrated for an LPC with an aperture diameter of 2 mm at an input laser power of 0.5 W (power density of 15.92 W/cm2). In addition, the key parameters of the LPC, i.e., the reverse saturation current (Is), ideality factor (n), series resistance (Rs) and shunt resistance (Rsh) are obtained by fitting the experimental current–voltage (I–V) curves with a standard equivalent-circuit (SEC) model. Variations of the six-junction GaAs LPC parameters with illumination intensity are investigated based on the SEC model.
2.
LPC structure and model of N-junction photovoltaic devices
Vertically-stacked multi-junction GaAs LPCs need to be carefully designed to achieve current-matching, that is, equal photocurrent generation in each sub-cell. Each GaAs sub-cell thickness can be calculated by Beer-Lambert law[13].
$$I = {I_0}exp ( - alpha (lambda )x),$$  | (1) |
where I, I0, α(λ), and x are the transmitted light intensity in the GaAs absorption layer, light intensity at the surface of the GaAs, absorption coefficient at a given wavelength λ and transmitted depth of photons from the surface, respectively, e.g., the measured value for α(808 nm) is ~1.24 × 104 cm?1[13]. Fig. 1 shows the schematic structure of an LPC with neighboring sub-cells connected via an n+-GaAs/p+-Al0.37Ga0.63As TJ. In six-junction GaAs LPC, the percentage of the incident light absorbed by each sub-cell is ~15.3% and the thickness of cell 1, 2, 3, 4, 5, and 6 is 124, 156, 206, 295, 504, and 2000 nm, respectively.
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Figure1.
Schematic cross-section of an LPC structure.
The I–V characteristics of a photovoltaic (PV) converter can be modeled by an ideal diode model[14, 15], as shown in Fig. 2. The model includes a light generated current source, a diode, Rs and Rsh. Therefore, the I–V characteristics of a PV converter can be expressed by
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Figure2.
Equivalent circuit of a PV converter.
$$I = {I_{ m {ph}}} - {I_{ m s}}[exp ((V + I{R_{ m s}})/(n{V_{ m t}})) - 1] - (V + I{R_{ m s}})/{R_{ m {sh}}},$$  | (2) |
$${V_{ m t}} = kT/q,$$  | (3) |
where Iph is the photocurrent, Is the reverse saturation current, V the output voltage, Ithe output current, Vt the thermal voltage[16] (~25.9 mV at 300 K), k the Boltzmann’s constant, T the temperature and q the electron charge, respectively.
Fig. 3 shows the SEC model of series-connected N-junction PV converters[17]. Therefore, the I–V characteristics of a PV converter formed by connecting PV sub-cells in-series can be described by[17, 18]:
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Figure3.
SEC of series-connected N-junction PV cells.
$$I = {I_{ m {ph}}} - {I_{ m s}}[exp ((V/N + I{R_{ m s}})/(n{V_{ m t}})) - 1] - (V/N + I{R_{ m s}})/{R_{ m {sh}}},$$  | (4) |
where N is the number of cells in series, Rs and Rsh the series and shunt resistance of each cell, respectively.
For a vertically-stacked multi-junction GaAs LPC, we assume all sub-cells have the same electric voltage and current values. Therefore, the SEC model can be used for a six-junction LPC with N of 6.
Commonly, Iph can be approximated by the short circuit current Isc in Eq. (4). In an open-circuit condition, the I–V characteristics of a six-junction LPC can then be written as:
$$0 = {I_{ m {sc}}} - {I_{ m s}}left[ {exp (q{V_{ m {oc}}}/(6nkT)) - 1} ight] - {V_{ m {oc}}}/(6{R_{ m {sh}}}),$$  | (5) |
and Eq. (5) can be rewritten as:
$$q/(6nkT) = ln ({I_{ m {sc}}}/{I_{ m s}} - {V_{ m {oc}}}/(6{R_{ m {sh}}}{I_{ m s}}) + 1)/{V_{ m {oc}}}.$$  | (6) |
Substituting Eq. (6) into Eq. (4), thus Eq. (4) becomes
$$begin{split}I = & {I_{ m {sc}}} - {I_{ m s}}left[ {{{({I_{ m {sc}}}/{I_{ m s}} - {V_{ m { m {oc}}}}/(6{R_{ m {sh}}}{I_{ m s}}) + 1)}^{(V + 6I{R_{ m s}})/{V_{ m {oc}}}}} - 1} ight] & - (V/6 + I{R_{ m s}})/{R_{ m {sh}}}.end{split}$$  | (7) |
Eventually, Is, Rs and Rsh of a six-junction LPC can be extracted by fitting the measured I–V curve with the SEC model.
3.
Experiments
The six-junction GaAs LPC epitaxial structures were grown on 2-inch Si-doped GaAs (100) substrates with a miscut of 2° toward (111)A using an AIXTRON 200/4 horizontal low-pressure metal-organic chemical vapor deposition (MOCVD) system. The carrier gas was Pd-diffused hydrogen (H2) and the precursors included arsine (AsH3), trimethylgallium (TMGa), trimethylaluminum (TMAl), and carbon tetrabromide (CBr4) and silane (SiH4) were used as P and N type doping sources, respectively. Low-pressure growth was carried out at 100 mbar, and the growth temperature ranged between 600 and 700 °C. Each sub-cell consists of a C-doped Al0.37Ga0.63As back surface field (BSF) layer (2 × 1018 cm?3, 20 nm), C-doped base layer (5 × 1017 cm?3), Si-doped emitter layer (1 × 1018 cm?3) and Si-doped Al0.35Ga0.65As window layer (2 × 1018 cm?3, 45 nm). An n+-GaAs (20 nm)/p+-Al0.37Ga0.63As (25 nm) TJ structure has been used in the six-junction LPCs, and the doping levels in TJs are 1 × 1019 cm?3 for the n+ layer and 1 × 1020 cm?3 for the p+ layer, respectively. A cap layer of 75-nm-thick Si-doped GaAs was finally grown as the ohmic contact layer on the top of a 900-nm-thick Si-doped Al0.35Ga0.65As (2 × 1018 cm?3) current spreading layer. The epitaxial wafers of LPC were processed into chips with an aperture diameter of 2 mm by conventional photolithography, metal evaporation, etching and isolation. The antireflection coating (ARC) consists of a double layer dielectric of 90 nm-SiO2/60 nm-TiO2 optimized for minimum reflection around 808 nm.
I–V curves of the LPC chips were measured under 808 nm laser illumination, and LPC devices were mounted on Cu-plated ceramic heat sinks placed on a temperature-controlled stage maintained at 25 °C.
4.
Results and discussion
Fig. 4 shows the microscopic image of an LPC with an aperture diameter of 2 mm, and the picture of the measurement setup. The four-probe I–V measurements were performed to reduce the effects of the lead resistance.
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Figure4.
(Color online) (a) A microscopic image of a six-junction GaAs LPC, and (b) a picture of the measurement setup.
The external quantum efficiency (EQE) was measured at 25 °C to understand better the current matching behavior for the six-junction GaAs LPCs, as shown in Fig. 5. The EQE reaches a peak value of 81.52%/6 at a wavelength of 818 nm, while the EQE is 80.22%/6 at 808 nm. The results show that there is a current mismatch at 808 nm for six-junction GaAs LPCs, and this is due to the difference between the actual absorption coefficient of GaAs and the one used for LPC design, and the deviation of the sub-cells thicknesses from the designed values during the growth can also lead to current mismatch among sub-cells.
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Figure5.
Measured EQE of a six-junction GaAs LPC.
Fig. 6(a) shows the I–V curves of a six-junction LPC at varying input laser powers (up to 2 W). It can be seen that the Isc of a six-junction LPC was proportional to the input laser power (Pin) with a photocurrent generation ratio G = Isc/Pin = 0.089 ± 0.003 A/W, independent of Pin, and achieves 0.173 A at Pin = 2 W. A singularity is observed in I–V curves when the laser power is 2 W, and this is due to the current limitation effect of TJs when the photo-generated current density exceeds the peak tunneling current density[19]. The operating voltage at the maximum power point is above 6 V, and Voc increases as the Pin is increasing from 0.5 to 1.2 W, while it begins to decrease slightly due to the temperature rise of the LPC[20–23]. The fill factor (FF) and ηc of an LPC as a function of the Pin are shown in Fig. 6(b), and an output power of ~0.94 W can be achieved at an input laser power of 2 W. Besides, the maximum FF and ηc of an LPC are 85% and 53.1%, respectively, at an input laser power of 0.5 W. The performances of LPC were better than those of former LPC[24] because we optimized the structure and the order of fabrication processes of six-junction GaAs LPCs based on former measured results. For example, the LPCs were ground rather than polished after being thinned in order to increase the stickiness between electrode and GaAs. The FF drops from 85% (at 0.5 W) to 79.2% (at 2 W), which indicates that the gridline geometry can be further optimized to decrease the series resistance loss (I2Rs). The I2Rs of LPC can be further decreased by increasing the gridline thicknesses[25], which can also permit higher FF values in operation. Uncertainty in the measured ηc was estimated to be ±2% (relative) and was primarily limited by modal instability of the illuminating laser.
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Figure6.
(a) Measured I–V characteristics. (b) Output power, ηc and FF as a function of input laser power.
Fig. 7(a) shows the temperature dependence of the EQE measured with a six-junction LPC. It can be observed that the measurements of EQE are shifting consistently with the GaAs bandgap narrowing by ~0.26 nm/°C. Besides, a dVoc/dT = ?10.98 mV/°C is obtained for 0.26 W input, as shown in Fig. 7(b). The six-junction LPC exhibits temperature behaviour roughly consistent with a multijunction concentrated photovoltaic cell (typically, a dVoc/dT between ?6 and ?7 mV/°C for a triple-junction CPV cell at 1 sun[25]).
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Figure7.
The dependence of measured results on temperature: (a) EQE, and (b) Voc.
According to the SEC of six-junction GaAs LPCs, the I–V curve for an input laser power of 0.5 W (Isc = 0.046 A, Voc = 6.79 V), i.e., transcendental Eq. (7) of an LPC can be calculated by using MATLAB. The calculated values from the SEC model are evaluated against measured data from the manufacturer’s datasheet. The results are shown in Fig. 8. As can be seen, the I–V characteristics of the GaAs LPC can be fitted very well by the SEC model, and the fitting yields a Is of 9 × 10?18 A, an n of 1.2, Rs of 0.18 Ω and Rsh of 800 Ω for the sub-cells.
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Figure8.
Measured (circles) and fitting I–V characteristics of an LPC using the SEC model (solid line).
The dependence of the Rs and Rsh of the sub-cells on input laser power is shown in Fig. 9(a). It can be seen that the Rs decreases continuously with the increase of input laser power mainly due to the reduction of resistivity resulting from increased carrier density[26], while the Rsh increases with input powers. The presence of Rsh is due to the leakage current, i.e., conduction between front and back sides at the edges of the LPC or through the junction via defects inside the bulk. The reason for the Rsh increase is that the traps in the localized defect regions capture photo-generated minority carriers from neighboring regions[27], and as the input laser power increases the defect-assisted conduction becomes gradually saturated leading to an increase of the resistance.
Fig. 9(b) shows the Is and nof the sub-cell of a six-junction LPC under different incident laser powers. The Is increases from 9 × 10?18 to 3 × 10?11 A, and n increases from 1.2 to 1.94 when raising the input laser power from 0.5 to 2 W, respectively. Under higher input laser powers, the excessive photo-generated carriers result in a higher recombination (e.g., Auger, non-radiative and surface recombination) in depletion, quasi-neutral and interface regions, and therefore increase the n and Is[28–30].
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Figure9.
Dependence of the parameters of sub-cell on input laser power: (a) Rs and Rsh, and (b) Is and n.
5.
Summary
A six-junction vertically-stacked AlGaAs/GaAs power converter structure is designed and grown by MOCVD for converting 808 nm light. LPCs with an aperture diameter of 2 mm are fabricated and characterized under illumination of an 808 nm laser, and a maximum conversion efficiency of 53.1% and FF of 85% have been achieved at a laser power of 0.5 W. The ηc under higher input laser powers are expected to be further improved by refining the design of the contact grid to reduce the I2R loss. In addition, the I–V characteristics of the LPCs have been fitted using the SEC model for extraction of the n, Is, Rs and Rsh, and dependence of these parameters on input laser power is also investigated.
