**4. Transition from 3D to 2D carrier confinement**

Nano-enhanced III-V absorbers are a specific example of optically-thin photovoltaic device structures that are being investigated as a pathway to extend infrared absorption and increase photovoltaic power conversion efficiency. In a typical III-V nano-enhanced solar cell, quantum well and/or quantum dot layers are added to the depletion region of a PIN diode. In principle, the addition of narrow band gap material to the diode structure is expected to result in an increase in the fundamental radiative dark current. In practice, non-radiative recombination both in the narrow band gap material and underlying baseline diode often obscures the radiative dark current. However, nano-enhanced absorber structures with a novel material structure have recently achieved ultra-low dark currents by employing advanced band gap engineering to suppress non-radiative recombination and expose the limiting radiative component of the dark current [19]. As the thickness of the absorber layer decreases, quantum confinement effects can begin to play a role. In this quantum confinement limit, the variation of the radiative dark current with thickness will deviate from that implied in Equation (6), as derived in the previous section.

In this section, we describe the saturation in radiative recombination with decreasing well thickness observed in both photoluminescence and dark current measurements on highvoltage, single InGaAs well structures. The observed saturation in PL intensity and radiative dark current is consistent with a transition from a three-dimensional (3D) to a two-dimensional (2D) density of states as quantum confinement effects increase with decreasing well thickness. The dependence of the radiative dark current on well thickness is described mechanistically in terms of a transition from 3D to 2D carrier recombination.

Figure 4 compares the photoluminescence spectra and diode dark currents from a set of single, square InGaAs well structures with varying well thickness but the same effective well energy. These InGaAs quantum well structures have been synthesized on semi-insulating GaAs substrates via metal-organic chemical vapor deposition (MOCVD). To minimize the diode dark current, an extended wide band gap emitter heterojunction structure has been employed, consisting of wide energy-gap InGaP and AlGaAs materials in the emitter and in the depletion region adjacent to the emitter [19]. To ensure that photogenerated carriers can overcome potential energy barriers via field-assisted thermionic emission, the InGaAs quantum wells and the transitions to higher energy-gap materials are located within the built-in field of the junction depletion region [25].

of saturated radiative dark current on absorber thickness for GaAs, as summarized in Figure 3 (c). Clearly the radiative dark current can be reduced, and the operating voltage enhanced,

Radiative recombination can also be described mechanistically in terms of carrier recombina‐ tion via the use of a radiative recombination coefficient. With this mechanist approach, the radiative saturation current density (Jo1,rad) can be related to the intrinsic carrier density (ni

and the physical absorber layer thickness (Wp) via a three-dimensional radiative recombination

where ϕ<sup>r</sup> is Asbeck's photon recycling co-factor [23-24]. Figure 3 (d) summarizes the depend‐ ence of ϕr on thickness, as inferred from fitting Equation (6) to the radiative dark current derived from detailed balance calculations as described above and summarized in Figure 3

Nano-enhanced III-V absorbers are a specific example of optically-thin photovoltaic device structures that are being investigated as a pathway to extend infrared absorption and increase photovoltaic power conversion efficiency. In a typical III-V nano-enhanced solar cell, quantum well and/or quantum dot layers are added to the depletion region of a PIN diode. In principle, the addition of narrow band gap material to the diode structure is expected to result in an increase in the fundamental radiative dark current. In practice, non-radiative recombination both in the narrow band gap material and underlying baseline diode often obscures the radiative dark current. However, nano-enhanced absorber structures with a novel material structure have recently achieved ultra-low dark currents by employing advanced band gap engineering to suppress non-radiative recombination and expose the limiting radiative component of the dark current [19]. As the thickness of the absorber layer decreases, quantum confinement effects can begin to play a role. In this quantum confinement limit, the variation of the radiative dark current with thickness will deviate from that implied in Equation (6), as

In this section, we describe the saturation in radiative recombination with decreasing well thickness observed in both photoluminescence and dark current measurements on highvoltage, single InGaAs well structures. The observed saturation in PL intensity and radiative dark current is consistent with a transition from a three-dimensional (3D) to a two-dimensional (2D) density of states as quantum confinement effects increase with decreasing well thickness. The dependence of the radiative dark current on well thickness is described mechanistically

/s, reasonably in-line with previous estimates of the radiative recombination

<sup>2</sup> (B3D / <sup>ϕ</sup>r) Wp (6)

cm-3, a typical value quoted for GaAs, the fit also implies B3D = 3.9

Jo1,rad =q ni

)

by minimizing the absorber layer thickness.

254 Solar Cells - New Approaches and Reviews

= 2.1 x 106

**4. Transition from 3D to 2D carrier confinement**

in terms of a transition from 3D to 2D carrier recombination.

coefficient (B3D):

(c). Assuming ni

coefficient in GaAs [23].

derived in the previous section.

x 10-10 cm3

The as-grown samples have been characterized by photoluminescence (PL) measurements generated with excitation from a 785 nm laser source. In Figure 4 (a), the PL intensity meas‐ ured on each sample has been normalized to the peak GaAs base layer emissions near 1.42 eV. The PL emission peak from the InGaAs well is a function of both the well composition and thickness. In the set of structures discussed in this section, the indium composition in the well is higher in the thinner wells in order to maintain a peak PL emission near 1.32 eV. Interesting‐ ly, the relative PL intensity from the InGaAs layer clearly decreases as the well thickness decreases from 30 nm to 15 nm, but is only marginally lower for the structure with the thin‐ nest well (2.5 nm).

The wafers were quartered after the PL measurements, and standard wet etch chemistry and photolithography were employed to define simple mesa test devices with junction areas as small as 75 μm x 75 μm. These devices were then characterized via illuminated current versus voltage, capacitance versus voltage, and dark current versus voltage measurements. For dark I-V measurements shown in Figure 4 (b), a test structure consisting of a device with a junction area of 200 μm x 270 μm has been employed. While some sample-to-sample scatter in the n=2 space charge recombination component of the dark current is observed, the magnitude of n=1 component of the measured dark current mimics the behavior of the relative PL intensity emitted by the InGaAs wells. Specifically, the n=1 component decreases with well thickness from 30 nm to 15 nm, but the 2.5 nm sample has a dark current that is nearly indistinguishable from the 15 nm sample. This observed near saturation in PL intensity and radiative dark current is consistent with a transition from a three-dimensional (3D) to a two-dimensional (2D) density of states as quantum confinement effects increase with decreasing well thickness.

Figure 5 compares the reverse saturation radiative current density, as derived by scaling the integrated PL spectra in Figure 4 (a), to the n=1 reverse saturation current density extracted directly from the measured dark diode current in Figure 4 (b). The comparison in Figure 5 indicates a very close correlation between the photoluminescence and dark current measure‐ ments in this sample set. By relating the radiative recombination rate to the intrinsic carrier density (ni ) via a bulk three-dimensional radiative recombination coefficient (B3D), the radiative dark current in an optically thin absorber has previously been expressed in terms of the physical absorber layer thickness (Wp) – e.g. Equation (6). However, radiative emissions from quantum-confined structures can be more appropriately described in terms of a two-dimen‐ sional radiative recombination coefficient (B2D) [26]. In particular, the rate of radiative recom‐ bination in a quantum-confined layer is proportional to the product of the electron and hole densities within the quantum well. In the limit of evenly emitting wells in which the effective carrier densities are the same within each well, the radiative current density generated by a multiple quantum well structure can be expressed as:

$$\mathbf{J}\_{\rm o1,rad} = \mathbf{q} \begin{array}{c} \mathbf{n}\_{\rm qw} \ \mathbf{p}\_{\rm qw} \ \mathbf{B}\_{2D} \mathbf{M}\_{\rm qw} \end{array} \tag{7}$$

where nqw and pqw are the effective quantum well electron and hole densities per unit area at zero bias and Mqw is the number of wells in the structure (Mqw=1in the set considered here). For any given effective well energy, equation (7) implies that the radiative component of the dark current will scale with the number of wells, independent of well thickness.

**Figure 4:** Normalized photoluminescence spectra (a) and dark current-voltage measurements (b) from a set of highvoltage InGaAs quantum well solar cell structures, all emitting at approximately 1.325 eV but with varying well thickness. **Figure 4.** Normalized photoluminescence spectra (a) and dark current-voltage measurements (b) from a set of high-volt‐ age InGaAs quantum well solar cell structures, all emitting at approximately 1.325 eV but with varying well thickness.

In Figure 5, the reverse saturation current density values inferred from both the dark diode current and photoluminescence measurements are compared to calculations using Equations (6) and (7). For the thicker samples, the variation in Jo1,rad with absorber layer thickness is well fit by a 3D representation of the carrier recombination, as given by Equation (6), assuming the radiative recombination coefficient is independent of indium composition (B3D = 3.9 x 10-10 cm3 /s) and that the intrinsic carrier combination scales inversely with the effective energy gap (ni = (NcNv) 1/2 exp(-Eg/2kT) = 1.57 x 107 cm-3). On the other hand, for the thinner samples, the variation in Jo1,rad with absorber layer thickness is well fit by a 2D representation of the carrier recombination as given by Equation (4), assuming nqw = pqw = 0.37 cm-2 and B2D = 1.3 x 10-3 cm2 /s.

11

**Figure 5:** Reverse saturation current density of the n=1 component of the diode current as derived from the measured dark diode current (solid circles) and calculated from the measured PL spectra (open diamonds). Also shown is the expected variation in the radiative dark current in the 3D and 2D regimes using Equations (6) and (7).

**Figure 5.** Reverse saturation current density of the n=1 component of the diode current as derived from the measured dark diode current (solid circles) and calculated from the measured PL spectra (open diamonds). Also shown is the expected variation in the radiative dark current in the 3D and 2D regimes using Equations (6) and (7).
