Defect-engineered GaN:Mg nanowire arrays for overall
water splitting under violet light
M. G. Kibria1, F. A. Chowdhury1, S. Zhao1, M. L. Trudeau2, H. Guo3, and Z. Mi1*
1
Department of Electrical and Computer Engineering, McGill University
3480 University Street, Montreal, Québec H3A 0E9, Canada.
2
Science des Matériaux, IREQ, Hydro-Québec
1800 Boul. Lionel-Boulet, Varennes, Québec J3X 1S1, Canada
3
Centre for the Physics of Materials, Department of Physics, McGill University
3600 University Street, Montreal, Québec H3A 2T8, Canada
*
E-mail: zetian.mi@mcgill.ca; Phone: 1 514 398 7114
Supplementary Material
1. Calculation of absorbed photon conversion efficiency (APCE):
The absorbed photon conversion efficiency (APCE) is calculated from the following approach:
The incident power on the sample can be expressed as:
𝑃𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 (𝜆) = 𝜌𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 (𝜆) × 𝐴𝑠𝑎𝑚𝑝𝑙𝑒 × 𝛽𝑓𝑓
(S1)
where 𝐴𝑠𝑎𝑚𝑝𝑙𝑒 is the sample area (~ 3.0 cm2) and 𝛽𝑓𝑓 is the nanowire fill factor on Si substrate.
The 𝛽𝑓𝑓 is calculated from top view SEM image of the nanowire arrays. The number of incident
photons per second, as a function of wavelength is calculated from,
𝑁𝑝ℎ (𝜆) =
𝑃𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 (𝜆)
𝐸𝑝ℎ (𝜆)
(S2)
ℎ𝑐
where 𝐸𝑝ℎ (𝜆) = 𝜆 is the photon energy for the corresponding wavelength. The total number of
incident photons per second within 375-450 nm, 400-450 nm, and 425-450 nm wavelength range
can be calculated as follows:
450 𝑃𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 (𝜆)×𝜆
𝑁𝑝ℎ,𝑖𝑛𝑐 (𝛿 − 450) = ∫𝛿
ℎ𝑐
𝑑𝜆
(S3)
where 𝛿 is the cut-off wavelength of the long-pass filters used for different intra-gap excitation.
The amount of absorbed power depends on the optical properties of the different layers
involved, namely, water and GaN. Considering the large refractive index mismatch between
1
GaN and water, on average ~10% of the incident power is reflected back from the nanowires-top
surface. The absorbed power can be calculated using the refractive indices and absorption
coefficients of the materials (see Ref. 9). Subsequently, the total number of absorbed photons can
be calculated from the following equation:
450 𝑃𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑,𝐺𝑎𝑁 (𝜆)×𝜆
𝑁𝑝ℎ,𝑎𝑏𝑠 (𝛿 − 450) = ∫𝛿
ℎ𝑐
𝑑𝜆
(S4)
The APCE is then derived from the following equation:
APCE = 2 ×
Number of evolved H2 molecules per hour
Number of absorbed photons per hour
× 100 %
(S5)
Note that the light trapping and scattering effect in the nanowire arrays have not been taken into
account for the estimation of APCE.
2. Calculation of energy conversion efficiency (ECE):
The energy conversion efficiency (ECE) was calculated to be ~1.34%, ~0.56% and ~0.12%,
considering the total incident power intensity in the wavelength range 375-450 nm, 400-450 nm,
and 425-450 nm, respectively from the following equation. The corresponding H2 evolution rates
were ~160 µmol h-1, ~45 µmol h-1, and ~5 µmol h-1 as shown in Fig. 3b in the main text.
𝐸𝐶𝐸 =
mmol
)×237 kJ ×1000
s
mW
𝜌𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡_𝑡𝑜𝑡𝑎𝑙 (
)×𝐴𝑠𝑎𝑚𝑝𝑙𝑒 (sq.cm)
sq.cm
𝐻2 (
× 100 %
(S6)
𝜌𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡_𝑡𝑜𝑡𝑎𝑙 is the incident power intensity on the sample in the wavelength range 375-450 nm,
400-450 nm, and 425-450 nm, which was derived by measurements using a broadband detector
(Thermopile Sensor, Newport-818P-100-55) and taking into account the power spectrum of the
lamp and optical filter, while mimicking the experimental configuration.
2