**6. High-voltage nano-enhanced devices with suppressed radiative recombination**

In the last section, we saw that light trapping is not a particularly effective means to reduce the radiative dark current of optically-thin absorber structures. However, recent experimental work indicates that it may be possible to reduce radiative recombination in thin absorber structures by manipulating the compositional profile of quantum well absorbers [19]. In particular, a compositional step-grade design has been experimentally observed to enhance the performance of high-voltage InGaAs quantum well solar cells by reducing the overall diode dark current. A comparison of square and step-graded well structures with varying well thickness but comparable well emission energy suggests a 2x reduction in the radiative recombination coefficient. Theoretically, we will show that reducing either the Urbach tail or the refractive index environment can result in a notable reduction in the radiative dark current of optically-thin structures. In addition, non-equilibrium effects, partially hot-carrier effects, can lead to even more substantial reductions in the radiative dark current.

By embedding narrow energy-gap wells within a wide energy-gap matrix, quantum well solar cells seek to harness a wide spectrum of photons at high voltages in a single-junction device. Quantum well solar cells have the potential to deliver ultra-high efficiency over a wide range of operating conditions, avoiding the limitations of current matching inherent in multijunction devices. Over the years, quantum well solar cells have been fabricated using a variety of different material systems, and the basic concept has been extended to include quantum dot absorber structures [27-29]. Clear enhancements in the infrared spectral response have been experimentally observed in both quantum well and quantum dot solar cells. Recently, GaAsbased quantum well solar cells with a novel material structure which minimizes non-radiative recombination have also achieved record-high open circuit voltages, in some cases exceeding 1 V at one-sun bias levels [19,30]. In this section, we detail the additional performance benefits resulting from the use of compositionally step-graded InGaAs well designs.

Figure 9 compares external quantum efficiency as derived from measured photoluminescence (PL) spectra and dark diode current-voltage characteristics from a single square InGaAs well photovoltaic device to a similar structure employing a compositionally step-graded well design. The baseline diode consists of an extended p-type wide band gap emitter, which minimizes non-radiative recombination, and a relatively thin (0.5 μm) GaAs base layer, synthesized on semi-insulating GaAs substrates via metal-organic chemical vapor deposition (MOCVD) [19]. In each structure the well is placed within the junction depletion region, as photogenerated carriers can then escape from the well via field-assisted thermionic emission [25]. A comparison of the simplified band structures of the square and step-graded wells is illustrated in Figure 10.

The indium content of the square and step-graded well structures compared in Figure 9 has been tuned to yield a nearly identical peak PL energy of approximately 1.325 eV. As a result, the forward emission and carrier collection characteristics are quite similar. However, the measured dark diode characteristics of the step-graded structure are notably lower than the square structure, with fits of the n=1 component yielding a factor of 2x reduction in the reverse saturation current density. These results imply that the use of a composition step-graded profile in the quantum well results in a 2x reduction in the radiative recombination coefficient.

**6. High-voltage nano-enhanced devices with suppressed radiative**

can lead to even more substantial reductions in the radiative dark current.

resulting from the use of compositionally step-graded InGaAs well designs.

In the last section, we saw that light trapping is not a particularly effective means to reduce the radiative dark current of optically-thin absorber structures. However, recent experimental work indicates that it may be possible to reduce radiative recombination in thin absorber structures by manipulating the compositional profile of quantum well absorbers [19]. In particular, a compositional step-grade design has been experimentally observed to enhance the performance of high-voltage InGaAs quantum well solar cells by reducing the overall diode dark current. A comparison of square and step-graded well structures with varying well thickness but comparable well emission energy suggests a 2x reduction in the radiative recombination coefficient. Theoretically, we will show that reducing either the Urbach tail or the refractive index environment can result in a notable reduction in the radiative dark current of optically-thin structures. In addition, non-equilibrium effects, partially hot-carrier effects,

By embedding narrow energy-gap wells within a wide energy-gap matrix, quantum well solar cells seek to harness a wide spectrum of photons at high voltages in a single-junction device. Quantum well solar cells have the potential to deliver ultra-high efficiency over a wide range of operating conditions, avoiding the limitations of current matching inherent in multijunction devices. Over the years, quantum well solar cells have been fabricated using a variety of different material systems, and the basic concept has been extended to include quantum dot absorber structures [27-29]. Clear enhancements in the infrared spectral response have been experimentally observed in both quantum well and quantum dot solar cells. Recently, GaAsbased quantum well solar cells with a novel material structure which minimizes non-radiative recombination have also achieved record-high open circuit voltages, in some cases exceeding 1 V at one-sun bias levels [19,30]. In this section, we detail the additional performance benefits

Figure 9 compares external quantum efficiency as derived from measured photoluminescence (PL) spectra and dark diode current-voltage characteristics from a single square InGaAs well photovoltaic device to a similar structure employing a compositionally step-graded well design. The baseline diode consists of an extended p-type wide band gap emitter, which minimizes non-radiative recombination, and a relatively thin (0.5 μm) GaAs base layer, synthesized on semi-insulating GaAs substrates via metal-organic chemical vapor deposition (MOCVD) [19]. In each structure the well is placed within the junction depletion region, as photogenerated carriers can then escape from the well via field-assisted thermionic emission [25]. A comparison of the simplified band structures of the square and step-graded wells is

The indium content of the square and step-graded well structures compared in Figure 9 has been tuned to yield a nearly identical peak PL energy of approximately 1.325 eV. As a result, the forward emission and carrier collection characteristics are quite similar. However, the measured dark diode characteristics of the step-graded structure are notably lower than the square structure, with fits of the n=1 component yielding a factor of 2x reduction in the reverse

**recombination**

260 Solar Cells - New Approaches and Reviews

illustrated in Figure 10.

There are several possible mechanisms by which a step-graded well profile or other device designs may reduce the radiative recombination coefficient, and thus enhance the limiting operating voltage of photovoltaic devices. For example, any shifts in the absorption profile, and in particular the sub-band gap (e.g. Urbach tail) region, can impact radiative emissions. Figure 11 compares the calculated reverse saturation current density assuming two different Urbach tail energies. As in earlier sections, the absorption spectrum is modeled using a piecewise continuous function [21]. The absorption spectrum is then used to generate an external quantum efficiency spectrum, which is in turn used to calculate the radiative dark current based upon detailed balance concepts – e.g. Equations (5) and (1). Reducing the activation energy which describes the sub-bandgap absorption profile results in a reduction in the radiative dark current, but more so in thicker absorbers. Altering in the Urbach tail absorption characteristics may thus provide some benefits, but seems unlikely to account for the 2x reduction in the radiative recombination B-coefficient observed in thin step-graded well structures.

well. The external quantum efficiency was estimated from PL measurements assuming a reciprocity relationship between spectral response characteristics and luminescent emissions in PV and LED devices [12]. The dark current was measured on mesa test structures with a junction area of 500 m x 500 m fabricated via standard photolithography and wet etch chemistry. The dashed lines depict the slope of ideal n=1 and n=2 components of the dark current. **Figure 9.** Estimated external quantum efficiency (a) and dark current-voltage measurements (b) from two high-voltage InGaAs quantum well structures, one employing a square well and the other a compositionally step-graded well. The external quantum efficiency was estimated from PL measurements assuming a reciprocity relationship between spec‐ tral response characteristics and luminescent emissions in PV and LED devices [12]. The dark current was measured on mesa test structures with a junction area of 500 μm x 500 μm fabricated via standard photolithography and wet etch chemistry. The dashed lines depict the slope of ideal n=1 and n=2 components of the dark current.

**Ec**

**electrons**

**Ev**

**holes**

**photons**

**Ec**

**Ev**

**holes**

**photons**

**Figure 9:** Estimated external quantum efficiency (a) and dark current-voltage measurements (b) from two highvoltage InGaAs quantum well structures, one employing a square well and the other a compositionally step-graded

16

  **(a) (b)** 

**electrons**

in step-graded structures.

**0.01**

**0.1**

**Estimated**

**External**

**Quantum**

**Efficiency (%)**

**1**

**10**

dark current.

**1.0E-04**

**0.60 0.70 0.80 0.90 1.00 1.10**

**Step-Graded Well Square Well**

**n = 1**

**Voltage (V)**

**1.0E-03**

**1.0E-02**

**n = 2**

**1.0E-01**

**Current Density (mA/cm2)**

**1.0E+00**

**1.0E+01**

**1.0E+02**

**Figure 9:** Estimated external quantum efficiency (a) and dark current-voltage measurements (b) from two highvoltage InGaAs quantum well structures, one employing a square well and the other a compositionally step-graded well. The external quantum efficiency was estimated from PL measurements assuming a reciprocity relationship between spectral response characteristics and luminescent emissions in PV and LED devices [12]. The dark current

photolithography and wet etch chemistry. The dashed lines depict the slope of ideal n=1 and n=2 components of the

 **(a) (b)**

**850 870 890 910 930 950 970**

**Step-Graded Well Square Well**

**Wavelength (nm)**

**Figure 10.** Simplified band structures of the (a) square and (b) step-graded well structures employed in the Figure 9 comparison, illustrating the field-assisted photogenerated carrier escape processes. **Figure 10:** Simplified band structures of the (a) square and (b) step-graded well structures employed in the Figure 9

16

comparison, illustrating the field-assisted photogenerated carrier escape processes.

**Figure 11:** (a) Absorption spectra assuming two different activation energies (Eo) for the Urbach tail sub-band gap absorption, and (b) the resulting calculated radiative saturation current density as a function of absorber thickness. **Figure 11.** (a) Absorption spectra assuming two different activation energies (Eo) for the Urbach tail sub-band gap ab‐ sorption, and (b) the resulting calculated radiative saturation current density as a function of absorber thickness.

Restricting the angular range of emissions provides another mechanism for reducing radiative dark current. The most direct means of restricting the range of angular emissions is to alter the refractive index environment in which the absorber layer is embedded. Figure 12 (a) summarizes the calculated radiative saturation dark current for several different refractive index values. Reducing the refractive index of the material above and below the absorber layer can effectively reduce the angular emissions, and lowering the refractive index from 3.5 to 2.5 can result in a 2x reduction in the radiative recombination coefficient. However, the changes in effective value of the refractive index in the step-graded structure are not Restricting the angular range of emissions provides another mechanism for reducing radiative dark current. The most direct means of restricting the range of angular emissions is to alter the refractive index environment in which the absorber layer is embedded. Figure 12 (a) summa‐ rizes the calculated radiative saturation dark current for several different refractive index values. Reducing the refractive index of the material above and below the absorber layer can

expected to be this large. Step-graded structures could also potentially alter the strain profile in the well, and strain in quantum wells has been found to result in a non-isotropic radiation profile that may reduce overall radiative recombination losses [31]. The non-isotropic radiation profile resulting from strain is in many ways similar to that resulting from a reduction in the refractive index of the barrier material, and while potentially beneficial, would seem unlikely to account for the 2x reduction in dark current observed

Step-graded structures may also provide a means of minimizing the overall recombination losses in quantum well solar cells. Faster escape rates can potentially be obtained by employing a step-graded compositional profile to allow photogenerated carriers to readily hop out of the InGaAs well [19], as illustrated in Figure 10. Enhanced extraction of hot carriers from the absorber region of a photovoltaic device has been suggested as a potential mechanism for reducing radiation losses and increasing efficiency [8]. Hot carrier effects can result in a large reduction in the radiative recombination, potentially reducing the B-coefficient by many orders of magnitude – see Figure 12 (b). Even a small effective carrier temperature difference of less than 1 kT is projected to result in more than a 2x reduction

in the radiative dark current. Hot carrier effects can potentially be further enhanced by optimizing device

16

  **(a) (b)**

**1E‐19**

**1 10 100 1,000 10,000**

**Eo = 6.7 meV**

**Eo = 11.5 meV**

**Thickness (nm)**

**1E‐18**

**Saturation**

**CurrentDensity**

**(mA/cm2)**

**1E‐17**

**1E‐16**

**Figure 11:** (a) Absorption spectra assuming two different activation energies (Eo) for the Urbach tail sub-band gap absorption,

**Figure 11.** (a) Absorption spectra assuming two different activation energies (Eo) for the Urbach tail sub-band gap ab‐ sorption, and (b) the resulting calculated radiative saturation current density as a function of absorber thickness.

Restricting the angular range of emissions provides another mechanism for reducing radiative dark current. The most direct means of restricting the range of angular emissions is to alter the refractive index environment in which the absorber layer is embedded. Figure 12 (a) summarizes the calculated radiative saturation dark current for several different refractive index values. Reducing the refractive index of the material above and below the absorber layer can effectively reduce the angular emissions, and lowering the refractive index from 3.5 to 2.5 can result in a 2x reduction in the radiative recombination coefficient. However, the changes in effective value of the refractive index in the step-graded structure are not expected to be this large. Step-graded structures could also potentially alter the strain profile in the well, and strain in quantum wells has been found to result in a non-isotropic radiation profile that may reduce overall radiative recombination losses [31]. The non-isotropic radiation profile resulting from strain is in many ways similar to that resulting from a reduction in the refractive index of the barrier material, and while potentially beneficial, would seem unlikely to account for the 2x reduction in dark current observed

Restricting the angular range of emissions provides another mechanism for reducing radiative dark current. The most direct means of restricting the range of angular emissions is to alter the refractive index environment in which the absorber layer is embedded. Figure 12 (a) summa‐ rizes the calculated radiative saturation dark current for several different refractive index values. Reducing the refractive index of the material above and below the absorber layer can

and (b) the resulting calculated radiative saturation current density as a function of absorber thickness.

**1.30 1.40 1.50 1.60**

**Energy (eV)**

**Eo = 6.7 meV**

**Eo = 11.5 meV**

**Figure 10:** Simplified band structures of the (a) square and (b) step-graded well structures employed in the Figure 9

17

Step-graded structures may also provide a means of minimizing the overall recombination losses in quantum well solar cells. Faster escape rates can potentially be obtained by employing a step-graded compositional profile to allow photogenerated carriers to readily hop out of the InGaAs well [19], as illustrated in Figure 10. Enhanced extraction of hot carriers from the absorber region of a photovoltaic device has been suggested as a potential mechanism for reducing radiation losses and increasing efficiency [8]. Hot carrier effects can result in a large reduction in the radiative recombination, potentially reducing the B-coefficient by many orders of magnitude – see Figure 12 (b). Even a small effective carrier temperature difference of less than 1 kT is projected to result in more than a 2x reduction

**Figure 10.** Simplified band structures of the (a) square and (b) step-graded well structures employed in the Figure 9

  **(a) (b)**

comparison, illustrating the field-assisted photogenerated carrier escape processes.

comparison, illustrating the field-assisted photogenerated carrier escape processes.

**1.0E-04**

**0.60 0.70 0.80 0.90 1.00 1.10**

**Step-Graded Well Square Well**

**n = 1**

**Voltage (V)**

**electrons**

**1.0E-03**

**1.0E-02**

**n = 2**

**1.0E-01**

**Current Density (mA/cm2)**

**1.0E+00**

**1.0E+01**

**1.0E+02**

**Figure 9:** Estimated external quantum efficiency (a) and dark current-voltage measurements (b) from two highvoltage InGaAs quantum well structures, one employing a square well and the other a compositionally step-graded well. The external quantum efficiency was estimated from PL measurements assuming a reciprocity relationship between spectral response characteristics and luminescent emissions in PV and LED devices [12]. The dark current was measured on mesa test structures with a junction area of 500 m x 500 m fabricated via standard photolithography and wet etch chemistry. The dashed lines depict the slope of ideal n=1 and n=2 components of the

**Ec**

**Ev**

**holes**

**photons**

 **(a) (b)**

**electrons**

**850 870 890 910 930 950 970**

**Step-Graded Well Square Well**

**Wavelength (nm)**

dark current.

**Ec**

262 Solar Cells - New Approaches and Reviews

**Ev**

**holes**

in step-graded structures.

**1.0E+00**

**1.0E+01**

**1.0E+02**

**1.0E+03**

**Absorption Coefficient (cm-1)**

**1.0E+04**

**1.0E+05**

**photons**

**0.01**

**0.1**

**Estimated**

**External**

**Quantum**

**Efficiency (%)**

**1**

**10**

**Figure 12.** (a) Projected dependence of the radiative saturation dark current as a function of the refractive index of the material surrounding the absorber layer; and (b) Projected impact of hot carrier effects on the radiative recombination coefficient as a function of the effective carrier temperature difference between the barrier and wells.

effectively reduce the angular emissions, and lowering the refractive index from 3.5 to 2.5 can result in a 2x reduction in the radiative recombination coefficient. However, the changes in effective value of the refractive index in the step-graded structure are not expected to be this 18

large. Step-graded structures could also potentially alter the strain profile in the well, and strain in quantum wells has been found to result in a non-isotropic radiation profile that may reduce overall radiative recombination losses [31]. The non-isotropic radiation profile resulting from strain is in many ways similar to that resulting from a reduction in the refractive index of the barrier material, and while potentially beneficial, would seem unlikely to account for the 2x reduction in dark current observed in step-graded structures.

Step-graded structures may also provide a means of minimizing the overall recombination losses in quantum well solar cells. Faster escape rates can potentially be obtained by employing a step-graded compositional profile to allow photogenerated carriers to readily hop out of the InGaAs well [19], as illustrated in Figure 10. Enhanced extraction of hot carriers from the absorber region of a photovoltaic device has been suggested as a potential mechanism for reducing radiation losses and increasing efficiency [8]. Hot carrier effects can result in a large reduction in the radiative recombination, potentially reducing the B-coefficient by many orders of magnitude – see Figure 12 (b). Even a small effective carrier temperature difference of less than 1 kT is projected to result in more than a 2x reduction in the radiative dark current. Hot carrier effects can potentially be further enhanced by optimizing device design and employing optical concentration [8].
