1.
Introduction

Optical power transmission systems have the advantages of high temperature tolerance, good electrical insulation, strong anti-interference ability, and high η_c, and laser power converter (LPC) is the key component in the systems^[1–3]. Semiconductor materials Si, GaSb, GaAs, and GaInP have been used to fabricate LPCs, while GaAs LPCs converting the power of widely used 808 nm laser demonstrate the highest efficiencies^[4–6]. A η_c of 54.9% has been achieved for a single-junction GaAs LPC at an optical power density of 36.5 W/cm^2[7]. The output voltage of a single-junction GaAs LPC is some 1 V, while higher operating voltages, e.g., 3.3, 4, and 5 V, are expected for real applications. Aiming at a high output voltage, the first straightforward approach is to connect multiple separate single junction GaAs cells placed side-by-side in series via metal wires as demonstrated by the 4 V GaAs LPC^[8], whereas the large light receiving area of this type of LPC is a disadvantage. The second method is to series connect multiple pie-shaped sub-cells isolated by etched trenches on a semi-insulating substrate. However, the fabrication processes are relatively complex, and light shining on the trench area contributes to the efficiency losses. Vertically-stacked multi-junction LPCs can not only get rid of the problems with the above two approaches, but also achieve a high η_c while producing a high output voltage.



In this article, monolithic four-junction vertically-stacked GaAs LPCs have been designed and fabricated using n⁺-GaAs/p⁺-Al_0.37Ga_0.63 tunnel junctions (TJs) to connect the sub-cells. Calculations based on ideal diode model indicate that the η_c of the four-junction GaAs LPC can reach 59.96% at an optical power density of 100 W/cm². Experimentally, a η_c of 56.9% is obtained at an input laser power of 0.2 W for a circular aperture of 3.14 mm² (power density of 6.37 W/cm²).

2.
Structure design and experiments

The vertically-stacked multi-junction GaAs LPCs need to be carefully designed to achieve current matching, that is, equal current generation in each sub-cell. Consequently, the most important thing in LPC design is to calculate thicknesses of the sub-cells to achieve current matching. The thickness of each sub-cell can be designed by the following equation^[9]

$${I_{i + 1}} = {I_i}{{ m e}^{ - alpha (lambda ){t_i}}},$$

(1)

where α(λ) is the absorption coefficient at a given wavelength λ, t_i the thickness of the absorbing layer of the ith sub-cell from the top, I_i the light intensity entering the ith sub-cell. In this GaAs LPC, percentage of the incident light absorbed by each sub-cell is ~23.7%. Fig. 1 shows the schematic structure of an LPC with neighboring sub-cells connected by an n⁺-GaAs/p⁺-Al_0.37Ga_0.63 TJ.






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Figure1.
Schematic structure of an LPC.




The current density–voltage (J–V) characteristics of each sub-cell have been calculated using PC-1D, and the loss mechanisms such as series resistance, reflectance of surface, and surface recombination were taken into consideration during the calculation.



The characteristics of single junction GaAs LPCs are calculated using an ideal diode model^{[10, 11]}:

$$J = {J_{ m {sc}}} - {J_0}left( {{{ m e}^{frac{{qV}}{{nkT}}}} - 1} ight),$$

(2)

$${V_{ m {oc}}} = frac{{nkT}}{q}ln left( {frac{{{J_{ m {sc}}}}}{{{J_0}}} + 1} ight),$$

(3)

where J is the output current density of an LPC, V_oc the open circuit voltage, J_sc the short circuit current density, J₀ the reverse saturation current density, q the electron charge, V the output voltage, k the Boltzmann’s constant, T the temperature, and n the ideality factor of the diode. The best value of reverse saturation current density J₀ and ideality factor n are 6 × 10^–20 A/cm² and 1, respectively^[11]. In order to simplify the calculation, the ideal diode model is still used for a vertically-stacked four-junction LPC with an ideality factor of 4. J_sc could be calculated by the following formula

$${J_{ m sc}} = frac{{{P_{ m in}}qlambda QEleft( lambda ight)}}{{hcN}},$$

(4)

where P_in is the input optical power density in W/cm², QE(λ) the external quantum efficiency at λ = 808 nm, h the Planck’s constant, c the velocity of light in vacuum, and N the number of sub-cells in an LPC. The η_c of an LPC is the ratio of the maximum output power to the input power and is represented as^[12]:

$${eta _{ m c}} = frac{{{V_{ m oc}}{J_{ m sc}}{ m FF}}}{{{P_{ m in}}}},$$

(5)

where FF is the fill factor of the cell.



The four-junction LPC epitaxial structures were grown on 2-inch Si-doped (100) GaAs substrates 2° off towards (111) A by AIXTRON 200/4 MOCVD system using trimethylgallium (TMGa), trimethylaluminum (TMAl), and arsine (AsH₃) as the group III and V precursors, respectively. Carbon tetrabromide (CBr₄) and silane (SiH₄) were used as P and N type doping sources, respectively. Each sub-cell consists of 20 nm p-type Al_0.37Ga_0.63 back surface field (BSF) with a C doping of 2 × 10¹⁸ cm^–3, p-type GaAs base layer C-doped to 5 × 10¹⁷ cm^–3, n-type GaAs emitter layer Si-doped to 1 × 10¹⁸ cm^–3, and 45 nm n-type Al_0.3Ga_0.7As window layer Si-doped to 2 × 10¹⁸ cm^–3. An n⁺-GaAs (20 nm)/p⁺-Al_0.37Ga_0.63 (25 nm) TJ structure is used in the four junction LPC, and the doping levels in TJ are 1 × 10¹⁹ cm^–3 for n⁺ layer, and 1 × 10²⁰ cm^–3 for 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 Al_0.3Ga_0.7As current spreading layer with a Si doping concentration of 2 × 10¹⁸ cm^?3. The epitaxial wafers of LPC were processed into chips with a circular aperture of 3.14 mm² by conventional photolithography, ohmic contact, etching and isolation. A double layer dielectric 90 nm-SiO₂/60 nm-TiO₂ was deposited as antireflection coating (ARC) to reduce the reflectivity around the wavelength of 808 nm.



Upon completion of the four-junction GaAs LPC chip processing, the I–V characteristics were measured under 808 nm laser illumination with the LPC chips glued to a Cu-plated ceramic heat sink and placed on a temperature-controlled stage maintained at 25 °C.

3.
Results and discussion

The calculated J–V curves of the sub-cells under 808 nm illumination with an optical power density of 10 W/cm² are shown in Fig. 2(a). It can be seen that the current is nearly matched at the operating point, with a discrepancy 3.5% in J_sc between the four sub-cells, and this is due to the absorption at TJs not being taken into account during the structure design, and the V_oc decreases from 1.126 to 1.09 V from cell 1 to cell 4. The internal quantum efficiency (IQE) of each sub-cell is 99.8%. The V_oc for sub-cells are shown in the Fig. 2(b), and the V_oc of cell 4 is ~3.5% lower than that of cell 1 due to the larger base thickness of cell 4. In cell 4, the photo-generated carriers result in a higher recombination (e.g., Auger, and non-radiative) in quasi-neutral region, and therefore cause the reduction in V_oc^[13]. The overall current of a four-junction LPC is limited by the sub-cell producing the lowest current. Therefore, V_oc, the voltage of the maximum power point (V_m), J_sc and current density of maximum power point (J_m) of the four-junction LPC estimated by using four sub-cells J–V characteristics are 4.46 V, 4.07 V, 1.42 A/cm² and 1.33 A/cm², respectively, and the FF of the four-junction LPC is 85.5%.






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Figure2.
(a) Calculated J–V curves of each sub-cell under 10 W/cm² of intensity, and (b) V_oc of sub-cells at varying illumination intensities.




The parameters used for the estimation of a four-junction GaAs LPC are shown in Table 1.

J0 (A/cm2)	n	Shadowing factor	IQE	Reflectance	FF
6 × 10–20	4	0.06	0.998	0.002	0.855

Table1.
The reverse saturation current density (J₀), ideality factor (n), shadowing factor, IQE, reflectance of surface and FF used for estimation.



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J0 (A/cm2)	n	Shadowing factor	IQE	Reflectance	FF
6 × 10–20	4	0.06	0.998	0.002	0.855

The P_in dependence of the calculated V_oc and J_sc for a four-junction GaAs LPC is shown in Fig. 3(a). It can be seen that V_oc increases with P_in, and J_sc is proportional to the P_in, and the J_sc is 14.46 A/cm² at an input power density of 100 W/cm². The calculated η_c of the GaAs LPC as a function of the P_in is shown in Fig. 3(b), and it increases from 56.1% to 59.96% as the P_in increasing from 5 W/cm² to 100 W/cm².






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Figure3.
Calculated (a) V_oc and J_sc, and (b) η_c as function of input power density.




Fig. 4(a) shows the I–V curves of the fabricated LPC device, and I_sc reaches 207 mA at an input power of 1.5 W. Spikes are observed in the I–V curves when the laser power is above 1 W, and this is due to the current limitation effect of 4 TJs when the operating current density exceeds peak tunneling current density^{[14, 15]}. As the photo-generated current starts exceeding their peak tunneling current, the negative differential resistance region of the I–V curves of the respective TJs impedes the current flow. Then the I–V curve of an LPC follows the negative differential resistance behavior of the individual TJ’s as the voltage is swept across the heterostructure^[9]. The current restriction by 4 TJs is probably due to the degradation of 4 TJs caused by the annealing effect during the growth of above layers^[14]. The growth temperature of the LPC ranged between 600 and 700 °C, and the diffusion of n-type and p-type dopants may cause the difference of I–V characteristics of the TJs. The output powers of the LPC under different incident laser powers are shown in Fig. 4(b). The operating voltage at the maximum power point is between 3.8 and 4.1 V, depending on the input laser power, and an electrical output power of 0.655 W is achieved at an input laser power of 1.5 W. The FF and η_c of the LPC as a function of the input power are shown in Fig. 4(c). The maximum FF and η_c of an LPC are 83.25% and 56.9%, respectively, at an input laser power of 0.2 W, and decrease significantly as the input power increases from 0.2 to 1.5 W. The degradation in cell performance becomes increasingly evident at higher laser powers mainly due to both temperature rise of the chips and higher series resistance loss (I²R) resulting from increased current densities. The impact of the increased I²R loss is a reduction in FF and therefore a lower η_c^[16]. In addition, the reduction in FF caused by an increase in voltage drop across the TJ can also lead to a reduced η_c^[17].






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Figure4.
(Color online) (a) I–V characteristics, (b) output power of an LPC, and (c) FF and η_c as a function of input laser power. The inset shows a microscopic image of an LPC.




For an ideal photovoltaic power converter, plots of V_oc against lg P_in are invariably linear^[18]. Fig. 5 shows the plots of measured V_oc against log₁₀ P_in, and the measured V_oc increases from 4.5 to 4.7 V when raising the input laser power from 0.2 to 1.5 W. The measured V_oc shows a linear dependence on lg P_in under lower input powers, but it increases sub- linearly with input power due to temperature rise of LPC device under higher input powers^{[18, 19]}. The inset of Fig. 5 shows that the calculated and measured J_sc are basically in agreement with each other under lower input power densities (< 15 W/cm²). However, the measured J_sc is appreciably lower than the calculated one at higher input laser power densities (> 15 W/cm²), e.g., the calculated and measured J_sc at 47.77 W/cm² are 6.9 and 6.6 A/cm², respectively. Minority carrier diffusion length and carrier collection efficiency decrease at higher input optical power densities^[20], and they probably contribute to the drop of J_sc at higher input power densities compared with calculated J_sc. Furthermore, the actual absorption coefficient of GaAs may be lower than that used for LPC design，while the deviation of the sub-cells thicknesses from the designed values during the growth will also lead to current mismatch among sub-cells.






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Figure5.
Measured V_oc of an LPC as a function of lg P_in. The inset shows calculated and measured J_sc at different input laser power densities.

4.
Conclusion

Four-junction vertically-stacked AlGaAs/GaAs power converter structure is designed and grown by MOCVD for converting 808 nm light. LPCs with a circular aperture of 3.14 mm² are fabricated and characterized under illumination of an 808 nm laser, and a maximum conversion efficiency of 56.9% and FF of 83.25% have been achieved at a laser power of 0.2 W, and the LPC shows a V_oc of above 4.5 V. η_c under higher input laser powers is expected to be further increased by refining the design of the contact grid to reduce the I²R loss, and optimization of n⁺-GaAs/p⁺-Al_0.37Ga_0.63 TJ and thickness of each sub-cell will improve the performance of LPCs.