1. Theory

Definition: Gallium arsenide is a zinc-blende III-V semiconductor (lattice constant 565.315 pm) with a direct gap of 1.424 eV at 300 K, an electron mobility of 9000 cm $^{2}$ /(V s), a hole mobility of about 400 cm $^{2}$ /(V s) and a refractive index of 3.3 (Wikipedia). Its absorption coefficient near the edge is 8000 cm $^{- 1}$ with an Urbach energy of 6.7 meV, so a few micrometres absorb most of the sunlight, against about 100 µm for silicon (Miller et al.; Wikipedia). The Auger coefficient is 7 × 10 $^{- 30}$ cm $^{6}$ /s and negligible (Miller et al.).
Luminescence: The internal fluorescence yield exceeds 99 %, and 99.7 % internal with 72 % external was measured in double heterostructures (Schnitzer et al., 1993, quoted by Miller et al.); silicon stays below 20 % internal. This is why GaAs approaches its radiative limit.
Cell structure: The inverted cell of Lee et al. has an n-GaInP window of 25 nm, an n-GaAs emitter (150 nm doped, 34 nm undoped), a p-GaAs base of 2.5 µm, a p-AlGaAs back-surface layer of 100 nm and p-GaAs contact layers, with an AlAs release layer of 25 nm for epitaxial lift-off; the layer table sums to 3.77 µm and the text gives 3.574 µm for the thickest section.
Growth: Alta Devices used metalorganic chemical vapour deposition with epitaxial lift-off to make thin, flexible cells and reuse the wafer (PV Tech). Growth rates are 1 to 3 µm/h for molecular-beam epitaxy, 50 to 60 µm/h for MOCVD and 200 to 300 µm/h for dynamic hydride vapour phase epitaxy (Lee et al.). Substrates of GaAs or germanium are expensive (Wikipedia).
Records (efficiency tables, version 64): Green et al. list a GaAs thin-film cell of 29.1 ± 0.6 % (0.998 cm $^{2}$ , 1.1272 V, 29.78 mA/cm $^{2}$ , 86.7 %, Alta Devices, Fraunhofer ISE October 2018), multicrystalline GaAs on germanium 18.4 ± 0.5 % (4.011 cm $^{2}$ total area, 0.994 V, 23.2 mA/cm $^{2}$ , 79.7 %, RTI, NREL 1995), crystalline InP 24.2 ± 0.5 % (1.008 cm $^{2}$ , 0.939 V, 31.15 mA/cm $^{2}$ , 82.6 %, NREL 2013, not measured at an external lab), a GaInP thin-film cell of 22.0 ± 0.3 % (0.2502 cm $^{2}$ , 1.4695 V, 16.63 mA/cm $^{2}$ , 90.2 %, NREL 2019) and an Alta GaAs module of 25.1 ± 0.8 % (866.45 cm $^{2}$ , 11.08 V, 2.303 A, 85.3 %, Fraunhofer ISE 2017). Under 61 suns a GaAs cell of 0.0990 cm $^{2}$ reached 30.8 ± 1.9 % (NREL 2022).
Record history: 25.1 % until 2007, 26.1 % (Bauhuis et al., 2009), 26.4 % (1.03 V, 2010), 27.6 % (late 2010), 28.2 % (June 2011), 28.9 % (NREL, July 2018) and 29.1 % (Fraunhofer ISE, December 2018) (Miller et al.; Alta press reports).
Low-cost routes: Growth on spalled substrates with in-situ planarisation by hydride vapour phase epitaxy gave 24 % (NREL, 2024), cells on nanopatterned substrates stayed above 23 % against 21.5 % for the earlier CLEFT growth (NREL, 2021), and Alta reports manufacturing samples near 27 %.

2. Working Principle

Junction and surfaces: Light is absorbed in the p-type base and the carriers are collected at the n-type emitter. The wide-gap GaInP window and the AlGaAs back layer keep the carriers away from the surfaces (background knowledge; the layers are listed by Lee et al.).
Photon recycling: In a good cell the photons made by radiative recombination are reabsorbed or leave through the front. With a back mirror the voltage depends on the external yield through $V_{oc} = V_{oc, r a d} - (k_{B} T / q) ∣ ln η_{e x t} ∣$ , and only about 2 % of the internal photons fit into the escape cone ( $1/4 n^{2}$ ). Alta describes its record as the first cell based on internal luminescence extraction, which sends the photons out through the front (PV Tech).
Voltage: The record cell has 1.1272 V, 97 % of the radiative limit with a mirror at 1.42 eV (computed, assumed), a deficit of 0.293 V, an external yield of 0.30 (computed) and a fill factor of 0.971 of the ideal value (computed).
Thickness: The model of Miller et al. gives 32.8 % at 0.5 µm, 33.1 % at 1 µm and 33.4 % at 10 µm for a textured cell with a good mirror, but only 24.3 to 30.9 % for an untextured cell with a bad mirror. The thinner cell has a higher voltage, 1.14 against 1.12 V, which also saves growth time.
Current: The record collects 29.78 mA/cm $^{2}$ , 93 % of the limit at 1.42 eV (computed); the remaining loss is probably reflection, contact shading and the window (my reading).

3. Applications

Space and high altitude: Alta cells were flown on the International Space Station (MISSE-X, one year of exposure) and considered for CubeSats and other low-Earth-orbit missions (PV Tech); GaAs resists radiation damage (Wikipedia).
Unmanned aircraft: A sailplane of 4.5 m span with 1.3 m $^{2}$ of Alta cells flew for 11 h 2 min, using 587 Wh of solar and 320 Wh of battery energy, and the cells became 30 % lighter (pv magazine, 2018).
Concentrators and tandems: GaAs is the middle cell of the multi-junction stacks of the next page and reached 30.8 % at 61 suns (Green et al.).

Optics, Gap and Detailed Balance

Name	Formula	Related Formulae	Variables/Constants
Absorption edge of the direct gap	$α (E) = α_{0} (1 + \frac{E - E _{g}}{E ^{'}}), E > E_{g}$	$α (E) = α_{0} exp (\frac{E - E _{g}}{E _{0}}), E \leq E_{g}$	$α : ab sor pt i o n coe f f i c i e n t$ $E : p h o t o n e n er g y$ $E_{g} : g a p$ $α_{0} : v a l u e a t t h e e d g e$ $E_{0} : U r ba c h e n er g y b e l o w t h e g a p$ $E^{'} : s l o p e ab o v e t h e g a p, M i l l er e t a l . u se α_{0} = 8000 c m^{- 1}, E_{0} = 6.7 m e V an d E^{'} = 140 m e V w i t h E_{g} \approx 1.42 e V (t h e t e x t a l so s a y s 1.4 e V an d F i g . 10 s h o w s a t h r es h o l d n e a r 1.39 e V)$ $(co m p u t e d : α = 4 \times 1 0^{2} c m^{- 1} a t 20 m e V b e l o w t h e g a p (1/ α = 25 μ m), 8000 c m^{- 1} a t t h e g a p (1.25 μ m), 1.37 \times 1 0^{4} c m^{- 1} a t 0.1 e V ab o v e (0.73 μ m) an d 2.5 \times 1 0^{4} c m^{- 1} a t 0.3 e V ab o v e (0.40 μ m))$
Absorptance of a thin film with a mirror or a texture	$a = 1 - e^{- 2 α L}$	$a_{t e x} = \frac{4 n ^{2} α L}{4 n ^{2} α L + 1}$ $η_{esc} \approx \frac{1}{4 n ^{2}}$	$a : ab sor pt an ce$ $L : t hi c k n ess$ $n : r e f r a c t i v e in d e x$ $a_{t e x} : ab sor pt an ce w i t h a r an d o mi s in g t e x t u r e an d a p er f ec t mi r r or$ $η_{esc} : p r o babi l i t y t ha t an in t er na l l y e mi tt e d p h o t o n l e a v es t h r o ug h t h e f r o n t co n e, M i l l er e t a l . u se t h ese f or m s (pl ana r w i t h a p er f ec t mi r r or, t e x t u r e d) an d η_{esc} \approx 2 %, W ik i p e d ia g i v es n = 3.3 (an d ab o u t 3.5 f or n - t y p e ma t er ia l in t h e sc in t i l l a t i o n sec t i o n)$ $(co m p u t e d w i t h α = 8000 c m^{- 1} an d n = 3.3 : o n e p a ss ab sor b s 33 % in 0.5 μ m, 55 % in 1 μ m, 87 % in 2.5 μ m; w i t h a mi r r or 55, 80 an d 98 %; t e x t u r e d 94.6, 97.2 an d 98.9 %; 4 n^{2} = 43.6 f or n = 3.3 an d 51.8 f or 3.6, an d 1/ (4 n^{2}) = 2.3 an d 1.9 %)$
Detailed-balance limit and voltage ratio	$r_{V} = \frac{V _{oc}}{V _{oc, S Q}}$	$Δ V = \frac{E _{g}}{q} - V_{oc}, \frac{J _{sc}}{J _{sc, ma x}}, r_{η} = \frac{η}{η _{S Q}}$	$r_{V} : f r a c t i o n o f t h e r a d ia t i v e v o l t a g e$ $V_{oc, S Q} : v o l t a g e a t t h e d e t ai l e d - ba l an ce l imi t$ $Δ V : d e f i c i t$ $J_{sc, ma x} : p h o t oc u r r e n t ab o v e t h e g a p$ $r_{η} : f r a c t i o n o f t h e l imi t, t h e m e t h o d i s t h e o n e o f t h e S o l a r C e l l F u n d am e n t a l s p a g e an d t h e ce l l i s t h e A l t a D e v i ces e n t r y o f G r ee n e t a l . (1.1272 V, 29.78 m A / c m^{2}, 86.7 %), w i t h E_{g} = 1.42 e V (a ss u m e d) an d a r e a r mi r r or (a ss u m e d f r o m t h e A l t a a pp r o a c h)$ $(co m p u t e d a t 298.15 K : 1.42 e V g i v es V_{oc, S Q} = 1.1405 V, J_{sc, ma x} = 32.04 m A / c m^{2} an d 32.7 % f or e mi ss i o n f r o m b o t h f a ces, an d 1.1583 V an d 33.2 % w i t h a r e a r mi r r or; 1.39 e V g i v es 33.0 an d 33.6 %, an d 1.424 e V g i v es 32.6 an d 33.1 %; t h e r ecor d ce l l ha s r_{V} = 0.973 (mi r r or) an d 0.988 (b o t h f a ces), Δ V = 0.293 V, J_{sc} / J_{sc, ma x} = 0.929 an d r_{η} = 0.876 (mi r r or))$

Luminescence, Voltage and Cost

Name	Formula	Related Formulae	Variables/Constants
Voltage from the external luminescence yield	$V_{oc} = V_{oc, r a d} - \frac{k _{B} T}{q} ∣ ln η_{e x t} ∣$	$η_{e x t} = exp (- \frac{V _{oc, r a d} - V _{oc}}{k _{B} T / q})$	$V_{oc, r a d} : v o l t a g e o f t h e i d e a l ce l l (e v er y r eco mbina t i o n r a d ia t i v e an d e v er y p h o t o n e mi tt e d t h r o ug h t h e f r o n t)$ $η_{e x t} : e x t er na l f l u or esce n ce y i e l d (E R E), M i l l er e t a l . g i v e t h e r e l a t i o n an d an e x am pl e o f 0.9 (2.7 mV), an in t er na l y i e l d ab o v e 99 % an d f or d o u b l e h e t er os t r u c t u r es 99.7 % in t er na l an d 72 % e x t er na l (S c hni t z er e t a l ., 1993), t h e g a p o f 1.42 e V an d t h e r e a r mi r r or a r e m y a ss u m pt i o n s$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d w i t h V_{oc, r a d} = 1.1583 V (mi r r or) : t h e ce l l o f 29.1 % (1.1272 V) ha s η_{e x t} = 0.30, t h e ce l l o f 28.2 % (1.11 V, M i l l er e t a l .) 0.15 an d t h e ce l l o f 26.4 % (1.03 V) 0.007; w i t h e mi ss i o n f r o m b o t h f a ces (1.1405 V) 0.60, 0.31 an d 0.0136; t h e p e na l t y f or η_{e x t} = 0.9 i s 2.7 mV, f or 0.72 8.4 mV an d f or 0.02 100.5 mV)$
Thickness and voltage	$Δ V = \frac{k _{B} T}{q} ln \frac{L _{1}}{L _{2}}$	$Δ V_{t e x} = \frac{k _{B} T}{q} ln (4 n^{2})$	$Δ V : v o l t a g e g ain o f a t hinn er ce l l i f t h e d a r k c u r r e n t w er e p r o p or t i o na l t o t h e t hi c k n ess L$ $Δ V_{t e x} : g ain o f a t e x t u r e, M i l l er e t a l . l i s t f or a t e x t u r e d ce l l w i t h a g oo d mi r r or V_{oc} = 1.14, 1.13 an d 1.12 V a t 0.5, 1 an d 10 μ m (32.8, 33.1 an d 33.4 %), an d f or an u n t e x t u r e d ce l l w i t h a ba d mi r r or 1.08, 1.08 an d 1.07 V (24.3, 28.3 an d 30.9 %), t h e p r o p or t i o na l i t y i s ba c k g r o u n d k n o w l e d g e$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d : 0.5 a g ain s t 10 μ m w o u l d g i v e 77 mV f or p r o p or t i o na l i t y b u t t h e t ab l e g i v es 20 mV, so r ecy c l in g mak es t h e d a r k c u r r e n t n e a r l y in d e p e n d e n t o f t hi c k n ess; Δ V_{t e x} = 97 mV f or n = 3.3 an d 101 mV f or 3.6 (t h e tw o w er e s w a pp e d b e f or e t h e a u d i t); p r o d u c t s o f t h e t ab l e r o w s a g r ee w i t h t h e p r in t e d e f f i c i e n c i es t o w i t hin 0.03 t o 0.26 p o in t s, w hi c h i s t h e r o u n d in g o f t h e v o l t a g es)$
Ideal fill factor	$F F_{0} = \frac{v _{oc} - l n ( v _{oc} + 0.72 )}{v _{oc} + 1}$	$v_{oc} = \frac{q V _{oc}}{n k _{B} T}$	$F F_{0} : f i l l f a c t or w i t h o u t ser i es an d s h u n t r es i s t an ce$ $v_{oc} : n or ma l i se d v o l t a g e$ $n : i d e a l i t y f a c t or (1 a ss u m e d), t h e e m p i r i c a l e x p r ess i o n i s ba c k g r o u n d k n o w l e d g e (a s o n t h e H I T p a g e), t h e ce l l s a r e t h e e n t r i es o f G r ee n e t a l .$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d w i t h k_{B} T / q = 25.693 mV an d n = 1 : t h e G a A s ce l l (1.1272 V) ha s F F_{0} = 0.893 an d 86.7 % i s 0.971 o f i t; I n P (0.939 V, 82.6 %) 0.877 an d 0.942; G a I n P (1.4695 V, 90.2 %) 0.913 an d 0.988; m u l t i cr y s t a l l in e G a A s (0.994 V, 79.7 %) 0.882 an d 0.903)$
Cost per watt	$c_{W} = \frac{c _{A}}{η G}$	$c_{A} = c_{W} η G$	$c_{W} : cos t p er p e ak w a tt$ $c_{A} : cos t p er a r e a o f ce l l$ $η : e f f i c i e n cy$ $G : 1000 W / m^{2}, L ee e t a l . (F or r es t g r o u p) g i v e ab o u t 80 d o l l a r s p er W p f or c u r r e n t G a A s ce l l s, 24.82 f or co n v e n t i o na l m o l ec u l a r - b e am e p i t a x y, 13.63 f or a l in e a r sy s t e m (ba se c a se, 25 %) an d 3.67 w i t h s u b s t r a t e r e u se (u p s i d e, 29 %), an d co n c l u d e t ha t t h e cos t i s u n l ik e l y t o f a l l b e l o w 3 d o l l a r s p er W p$ $(co m p u t e d : 80 d o l l a r s / W p a t 25 % i s 2.0 d o l l a r s / c m^{2}; 24.82 i s 0.62; 13.63 i s 0.34; 3.67 a t 29 % i s 0.106; 3 a t 29 % i s 0.087; 2 a t 29 % i s 0.058 d o l l a r s / c m^{2})$

Efficiency Checks

Name	Formula	Related Formulae	Variables/Constants
Efficiency from the reported parameters	$η = \frac{V _{oc} J _{sc} F F}{P _{in}}, P_{in} = 100 mW/c m^{2}$	$η_{c h ec k} = \frac{V _{oc} J _{sc} F F}{1000}$ $Δ η = η_{p r in t e d} - η_{c h ec k}$	$η : e f f i c i e n cy, V_{oc} in mV, J_{sc} in m A / c m^{2}, F F a s a f r a c t i o n (η_{c h ec k} i s in p er ce n t : t h e 1000 t u r n s mV in t o V, an d 1 mW / c m^{2} i s 1 p er ce n t o f P_{in}), t h e e n t r i es a r e f r o m t h e e f f i c i e n cy t ab l es (v er s i o n 64) o f G r ee n e t a l .$ $(co m p u t e d : G a A s t hin f i l m 1127.2, 29.78, 86.7 % g i v e 29.10 % (29.1); m u l t i cr y s t a l l in e G a A s 994, 23.2, 79.7 % g i v e 18.38 % (18.4); I n P 939, 31.15, 82.6 % g i v e 24.16 % (24.2); G a I n P 1469.5, 16.63, 90.2 % g i v e 22.04 % (22.0))$
Module efficiency from voltage, current and area	$η_{m o d} = \frac{V _{oc} I _{sc} F F}{G A}$	$P_{ma x} = V_{oc} I_{sc} F F$	$η_{m o d} : m o d u l e e f f i c i e n cy$ $V_{oc}, I_{sc} : m o d u l e v o l t a g e an d c u r r e n t$ $F F : f i l l f a c t or$ $G : i r r a d ian ce o f 1000 W / m^{2}$ $A : a p er t u r e a r e a, t h e e n t r y i s t h e A l t a D e v i ces m o d u l e o f G r ee n e t a l .$ $(co m p u t e d : 11.08 V, 2.303 A, 85.3 % o n 866.45 c m^{2} g i v e 21.77 W an d 25.12 % (25.1 \pm 0.8); t h e m o d u l e e f f i c i e n cy i s 86.3 % o f t h e ce l l e f f i c i e n cy o f 29.1 % (co m p u t e d 25.12/29.10))$

Important Questions

Ques: Is the GaAs record 29.1 or 28.9 %?

Green et al. list 29.1 ± 0.6 % for the Alta Devices thin-film cell, measured at Fraunhofer ISE in October 2018 (1.1272 V, 29.78 $mA/c m^{2}$ , 86.7 %, 0.998 $c m^{2}$ ), and the product is 29.10 % (computed). PV Tech reported 28.9 % certified by NREL in July 2018, and PV Tech and pv magazine reported 29.1 % certified by Fraunhofer ISE CalLab in December 2018, 0.2 points higher. The values are two successive records of one company, not a conflict: 28.9 % is the NREL result and 29.1 % the later one. Wikipedia still gives 29.1 % as of 2019. I found no newer single-junction GaAs result, but versions 65 to 68 of the efficiency tables were not readable, so 29.1 % is the more likely current figure only as of version 64. Alta also says its manufacturing samples reach about 27 %. Reference: Green, Dunlop, Yoshita, Kopidakis, Bothe, Siefer, Hinken, Rauer, Hohl-Ebinger and Hao, ‘Solar cell efficiency tables (Version 64)’, Prog. Photovolt. 32(7), 425-441 (2024); PV Tech, ‘Alta Devices sets GaAs solar cell efficiency record at 29.1%, joins NASA space station testing’ (13 December 2018); pv magazine, ‘Efficiency record isn’t the biggest change for Alta Devices’ GaAs solar technology’ (17 December 2018); PV Tech, ‘Alta Devices sets new GaAs solar cell conversion efficiency record at 28.9%’ (3 July 2018); Wikipedia, ‘Gallium arsenide’.

Ques: What is the GaAs efficiency limit: 33.5, 33.2 or 31.1 %?

Miller et al. calculate 33.5 % for GaAs with a planar or textured front and a perfect rear mirror, 31.1 % with an absorbing mirror, and note that earlier step-function models gave 31 % or less. Alta and Semiconductor Today quote 33.5 % as the Shockley-Queisser limit. My detailed-balance calculation for the AM1.5G spectrum at 298.15 K gives 32.7 % for emission from both faces and 33.2 % with a mirror at 1.42 eV, 33.6 % at 1.39 eV (computed). The difference of 0.3 points to 33.5 % probably comes from the gap and the exact spectrum and absorptance (my reading). A record of 29.1 % is 0.869 of 33.5 % and 0.876 of my 33.2 %. For a cell with a back mirror 33.2 to 33.5 % is the more likely limit, and 31.1 % applies to an absorbing mirror. Reference: Miller, Yablonovitch and Kurtz, ‘Intense Internal and External Fluorescence as Solar Cells Approach the Shockley-Queisser Efficiency Limit’, arXiv:1106.1603 (published in IEEE J. Photovoltaics 2012 as ‘Strong Internal and External Luminescence as Solar Cells Approach the Shockley-Queisser Limit’); Semiconductor Today, Alta Devices 28.2 % (20 June 2011) and Compound Semiconductor, ‘Alta Devices advances solar efficiency basics’ (20 June 2011); Solar Cell Fundamentals page of this vault.

Ques: Is the gap of GaAs 1.424, 1.42 or 1.39 eV?

Wikipedia gives 1.424 eV at 300 K, Miller et al. give 1.42 eV in a figure caption and 1.4 eV in the text, and their Fig. 10 shows an absorption threshold near 1.39 eV; at cryogenic temperature the gap is 1.52 eV (Wikipedia). The choice changes the limit: with a mirror the voltage limit is 1.1620 V at 1.424 eV, 1.1583 V at 1.42 eV and 1.1303 V at 1.39 eV (computed). The record cell has 1.1272 V, so at 1.39 eV the external yield would be 0.89, which is not plausible, and for emission from both faces the ratio would exceed one (1.013). The values describe the nominal gap and an apparent absorption edge. The 1.42 to 1.424 eV is the more likely gap for the voltage analysis, with a yield of 0.26 to 0.30 (computed). Reference: Wikipedia, ‘Gallium arsenide’; Miller, Yablonovitch and Kurtz, ‘Intense Internal and External Fluorescence as Solar Cells Approach the Shockley-Queisser Efficiency Limit’, arXiv:1106.1603 (published in IEEE J. Photovoltaics 2012 as ‘Strong Internal and External Luminescence as Solar Cells Approach the Shockley-Queisser Limit’).

Ques: How thick is a GaAs cell: 0.5, 1, 2.5 or 3.6 µm?

Wikipedia says a few micrometres absorb most of the sunlight, Alta calls its film micron-thick, and Miller et al. model 0.5, 1 and 10 µm. The inverted cell of Lee et al. has a base of 2.5 µm, a layer table summing to 3.77 µm (computed) and a thickest section of 3.574 µm in the text. The values are for different purposes: the model assumes ideal mirror and texture, and the thicker cell is a real stack with contact layers. With 8000 $c m^{- 1}$ one pass absorbs 55 % in 1 µm and 87 % in 2.5 µm, and a mirror gives 80 and 98 % (computed). A real record cell probably has a base of 1 to 3 µm, which I take as more likely; Alta does not print its thickness. Reference: Wikipedia, ‘Gallium arsenide’; Semiconductor Today, Alta Devices 28.2 % (20 June 2011) and Compound Semiconductor, ‘Alta Devices advances solar efficiency basics’ (20 June 2011); Miller, Yablonovitch and Kurtz, ‘Intense Internal and External Fluorescence as Solar Cells Approach the Shockley-Queisser Efficiency Limit’, arXiv:1106.1603 (published in IEEE J. Photovoltaics 2012 as ‘Strong Internal and External Luminescence as Solar Cells Approach the Shockley-Queisser Limit’); Lee, Fan and Forrest, ‘A high throughput, linear molecular beam epitaxy system for reduced cost manufacturing of GaAs photovoltaic cells: Will GaAs ever be inexpensive enough?’, Sustainable Energy & Fuels (accepted manuscript SE-ART-12-2019-001255.R1, 2020).

Ques: What does GaAs cost: orders of magnitude above silicon, 80, 24.8, 3.7 dollars per Wp or ‘essentially nothing’?

Wikipedia says III-V cells cost two to three orders of magnitude more than silicon, and pv magazine repeats that GaAs products cost orders of magnitude more, while Alta says its process has lowered the material cost to essentially nothing. Lee et al. give about 80 dollars per Wp for current cells, 24.82 for conventional molecular-beam epitaxy, 13.63 for a linear system at 25 % and 3.67 with substrate reuse at 29 %, and conclude that GaAs is unlikely to fall below 3 dollars per Wp. The statements concern different items: material, whole cell and projected cost. A cell of 25 % at 80 dollars per Wp is 2.0 dollars/ $c m^{2}$ (computed). The 3 dollars per Wp floor is the more likely for cells, and ‘essentially nothing’ most likely refers to the reused substrate (my reading). Reference: Wikipedia, ‘Gallium arsenide’; pv magazine, ‘Efficiency record isn’t the biggest change for Alta Devices’ GaAs solar technology’ (17 December 2018); Lee, Fan and Forrest, ‘A high throughput, linear molecular beam epitaxy system for reduced cost manufacturing of GaAs photovoltaic cells: Will GaAs ever be inexpensive enough?’, Sustainable Energy & Fuels (accepted manuscript SE-ART-12-2019-001255.R1, 2020).

Ques: Is conventional MBE for GaAs 24.82, 23.80 or 8.8 dollars per Wp?

Lee et al. print 24.82 dollars per Wp for conventional molecular-beam epitaxy in the text, but the entries of their Table IV add up to about 23.80 (a difference of 1.02, computed) and Table V lists 8.8 as the upside case. They also give MOCVD growth rates of 50 to 60 µm/h in Table V, 60 µm/h as current status and 20 µm/h in the work of Woodhouse et al., and substrate costs of 7.52 dollars per Wp (base) and 0.76 (upside). The 8.8 is an upside value and not comparable with the base case of 24.82. The difference of about 1 dollar between the text and the table is more likely a rounding or an omitted item, and the table is the more likely of the two, but the manuscript does not explain it. The MOCVD figure of 20 µm/h is a cited lower value. Reference: Lee, Fan and Forrest, ‘A high throughput, linear molecular beam epitaxy system for reduced cost manufacturing of GaAs photovoltaic cells: Will GaAs ever be inexpensive enough?’, Sustainable Energy & Fuels (accepted manuscript SE-ART-12-2019-001255.R1, 2020).

Ques: What efficiency do low-cost GaAs cells reach: 21.5, 23, 24, 25, 27 or 29 %?

Mangum et al. report cells on nanopatterned substrates above 23 %, against 21.5 % for the earlier CLEFT growth, and NREL reported 24 % on spalled substrates planarised by hydride vapour phase epitaxy in 2024. Lee et al. assume 25 % for their base case and 29 % for the upside, and Alta says its manufacturing samples reach about 27 % against the record of 29.1 %. These values refer to different methods: 24 % is a research cell on a reused or cheaper substrate and 27 % an industrial sample. The gap between 24 and 29.1 % is 5.1 points (computed). For a low-cost route 23 to 24 % is the demonstrated range, 27 % the claim of the industrial producer and 29 % an assumption of a cost model. Reference: Mangum, Theingi, Steiner, McMahon and Warren, ‘Development of High-Efficiency GaAs Solar Cells Grown on Nanopatterned GaAs Substrates’, Cryst. Growth Des. (2021), DOI 10.1021/acs.cgd.1c00835; ‘24% Single-Junction GaAs Solar Cell Grown Directly on Growth-Planarized Facets Using Hydride Vapor Phase Epitaxy’, Adv. Energy Mater. 14(3), 2302035 (2024) (NREL publication page, authors not listed); Lee, Fan and Forrest, ‘A high throughput, linear molecular beam epitaxy system for reduced cost manufacturing of GaAs photovoltaic cells: Will GaAs ever be inexpensive enough?’, Sustainable Energy & Fuels (accepted manuscript SE-ART-12-2019-001255.R1, 2020); pv magazine, ‘Efficiency record isn’t the biggest change for Alta Devices’ GaAs solar technology’ (17 December 2018).

Ques: Is the external luminescence yield of GaAs 72 % or 30 %?

Miller et al. quote 99.7 % internal and 72 % external fluorescence yield for double heterostructures (Schnitzer et al., 1993) and say that a solar cell needs an internal yield well above 90 %. For the record cell of 29.1 % I obtain an external yield of 0.30 (computed from 1.1272 V, a limit of 1.1583 V with a mirror and 1.42 eV, all assumed), and 0.60 for emission from both faces. The numbers measure different things: the 72 % is a laboratory value of a double heterostructure, and the 0.30 is the yield at the operating voltage of a solar cell including contacts and window absorption. The assumed gap and mirror matter: with 1.424 eV the yield is 0.26. A yield of 0.3 is the more likely value for the cell, and 72 % an upper reference. Reference: Miller, Yablonovitch and Kurtz, ‘Intense Internal and External Fluorescence as Solar Cells Approach the Shockley-Queisser Efficiency Limit’, arXiv:1106.1603 (published in IEEE J. Photovoltaics 2012 as ‘Strong Internal and External Luminescence as Solar Cells Approach the Shockley-Queisser Limit’); Green, Dunlop, Yoshita, Kopidakis, Bothe, Siefer, Hinken, Rauer, Hohl-Ebinger and Hao, ‘Solar cell efficiency tables (Version 64)’, Prog. Photovolt. 32(7), 425-441 (2024).

Ques: Is the refractive index of GaAs 3.3, 3.5 or 3.6?

The infobox of Wikipedia gives a refractive index of 3.3, while the scintillation section gives about 3.5 for n-type material, and Miller et al. use an escape probability of 1/(4n $^{2}$ ) of about 2 %, which corresponds to an index near 3.6 (computed). The values change the texture limit 4n $^{2}$ to 43.6 (3.3), 49.0 (3.5) or 51.8 (3.6), and the escape probability to 2.3, 2.0 or 1.9 %, with a voltage gain of the texture of 97 mV for 3.3 and 101 mV for 3.6 (computed). The index depends on wavelength and doping (background knowledge). Near the absorption edge, where the photons are emitted, 3.5 to 3.6 is more likely, and 3.3 is the value at long wavelengths; the extracts give no wavelength for the value of Wikipedia. Reference: Wikipedia, ‘Gallium arsenide’; Miller, Yablonovitch and Kurtz, ‘Intense Internal and External Fluorescence as Solar Cells Approach the Shockley-Queisser Efficiency Limit’, arXiv:1106.1603 (published in IEEE J. Photovoltaics 2012 as ‘Strong Internal and External Luminescence as Solar Cells Approach the Shockley-Queisser Limit’).

Quartz 5

Explorer

Gallium Arsenide (GaAs) Single-Junction Solar Cell