1. Theory

Definition: The cadmium telluride (CdTe) cell is a thin-film heterojunction on glass. Light enters through the glass and a transparent conducting oxide (SnO $_{2}$ :F or FTO), passes a thin n-type window (CdS of 60 to 80 nm, or a MgZnO layer of 100 nm) and is absorbed in a polycrystalline p-type absorber of a few µm; a back contact collects the holes. CdTe is a direct-gap semiconductor with a gap of 1.45 eV (about 1.5 eV in Lingg et al.), an absorption coefficient above $1 0^{5}$ cm $^{- 1}$ below 820 nm, and the lattice mismatch to hexagonal CdS is about 9.7 % (Hajimammadov et al.).
Deposition: The absorber is deposited by close-space sublimation or vapour transport at substrate temperatures of 420 to 500 °C and sources at 555 to 620 °C, the CdTe in less than 40 s (Intal and Ebong; Hajimammadov et al.; Munshi et al.). The film is then activated with CdCl $_{2}$ (600 s in-line at 430 °C for Munshi et al.; 25 min in air at 430 °C for Hajimammadov et al.), which recrystallizes the grains to 3 to 5 µm. Munshi et al. found that the treatment raises the voltage of their cells from 387 to 842 mV, the fill factor from 34.1 to 74.5 % and the efficiency from 0.01 to 16.8 % (0.55 cm $^{2}$ ).
Selenium alloying: A front layer of CdSe $_{x}$ Te $_{1 - x}$ lowers the gap towards 1.4 eV and raises the current; the gap bows downwards with a minimum at x of 0.3 to 0.4 (Lingg et al.). Munshi et al. have 1.5 to 2.0 µm of CdSeTe (gap 1.41 eV) under 3.5 µm of CdTe, and Lingg et al. report 19.1 % against 17.9 % for CdTe alone, a gain of 2.1 mA/cm $^{2}$ . Shah finds that the selenium grading raises the conduction band and that selenium and chlorine passivate the grain boundaries.
Doping: Copper dopes CdTe to only $1 0^{14}$ to $1 0^{15}$ cm $^{- 3}$ , which limits voltage and fill factor. Metzger et al. replace it with arsenic (group V) to reach $1 0^{16}$ to $1 0^{17}$ cm $^{- 3}$ without a lower lifetime, with a photocurrent above 30 mA/cm $^{2}$ and 20.8 %. First Solar’s CuRe modules use group V doping.
Records: Green et al. list 21.0 % for a cell of 1.06 cm $^{2}$ (875.9 mV, 30.25 mA/cm $^{2}$ , 79.4 %, Newport) and 22.6 % for a cell of 0.449 cm $^{2}$ (898.1 mV, 31.56 mA/cm $^{2}$ , 79.6 %, NREL, January 2024, after 22.4 %). First Solar announced 22.1 % in February 2016 and 23.1 % (NREL) in July 2024; the DOE paper gives 23.1 % on 0.45 cm $^{2}$ . Modules: 19.9 % record (Series 6 Plus on 23932 cm $^{2}$ ) against 16.4 % on the lead lines in 2015.
Field behaviour: First Solar states a degradation of 0.2 %/year, a temperature coefficient of -0.28 %/°C (Series 6) and at least 92 % after 30 years; these are vendor claims. Intal and Ebong list a yield gain of 4 to 6 % over mono-crystalline silicon in desert climates and a bifaciality of 0.30 in pilots.
Supply: The DOE paper gives a world tellurium production of about 640 t in 2022, 10 to 15 % of the module cost for tellurium and a U.S. share of about 34 % for CdTe in 2022; First Solar shipped 12.1 GW in 2024 (Intal and Ebong).

2. Working Principle

Collection: Light is absorbed within a few µm; the carriers generated in the depletion region are swept out by the field and those in the neutral region reach it by diffusion. The depletion width is 3.1 µm for $1 0^{14}$ cm $^{- 3}$ and 0.31 µm for $1 0^{16}$ cm $^{- 3}$ (computed, assumed permittivity and built-in voltage), so with copper doping the absorber is nearly depleted.
Alloy and grading: The CdSeTe layer next to the window has the lowest gap and collects the long wavelengths, and Lingg et al. state that the voltage stays high, which I read as the voltage being set by the CdTe behind it. The measured current of 31.56 mA/cm $^{2}$ is above the limit for 1.45 eV (30.83) and for 1.5 eV (28.94), and below that for 1.41 eV (32.44; all computed).
Voltage: The record cell has 898 mV, 270 mV below the radiative limit of 1.168 V at 1.45 eV (computed). Onno et al. find with luminescence that arsenic-doped First Solar cells have a voltage equal to the internal voltage (above 840 mV) and so nearly ideal selectivity, whereas the CSU arsenic cells with Al $_{2}$ O $_{3}$ have an external radiative efficiency above 1 % and an internal voltage above 970 mV but a poor back contact. A factor of 100 in hole density is worth 118 mV (computed).
CdCl $_{2}$ activation: The CdCl $_{2}$ -CdTe eutectic melts near 508 °C and lets the grains recrystallize; chlorine forms Cl $_{T e}$ -V $_{C d}$ acceptors and passivates the grain boundaries, but an excess lowers the efficiency (Hajimammadov et al.: 1.2 % without, 10.3 % at the optimum and 5.5 % for the thickest layer of CdCl $_{2}$ ).
Back contact: The p-type CdTe has a high work function, so the metal forms a barrier (background knowledge); the contact uses Cu-Te compounds (CuCl with a tellurium film in Munshi et al., CuTe/HgTe in Hajimammadov et al.). The resistance grows by a factor of 48 for each 0.1 eV of barrier (computed, assumed constant).
Temperature: The voltage term alone gives -0.27 %/K at 898 mV (computed), close to the -0.28 %/°C of the vendor.

3. Applications

Utility-scale power: Modules of 19.9 % on large glass area in solar farms; First Solar reports a share of about 34 % of U.S. utility-scale modules in 2022 (DOE) and 12.1 GW shipped in 2024.
Hot climates and trackers: The temperature coefficient and the spectral response are claimed to give a 4 to 6 % annual yield gain over silicon in deserts, and bifacial CdTe trackers of 400 MW operate in a 2 GW park in Dubai (Intal and Ebong).
Recycling: Closed-loop recycling recovers more than 90 % of cadmium and tellurium (Intal and Ebong), and the DOE paper gives the same figure for the module material.
Next steps: The CTAC targets in the DOE paper are cell efficiencies above 24 % by the end of 2025 and above 26 % by 2030; the thin-film pages continue with CIGS.

Absorber, Gap and Depletion Region

Name	Formula	Related Formulae	Variables/Constants
Detailed-balance limit at the gap of the absorber	$J_{0, r a d} = \frac{4 π q}{c ^{2} h ^{3}} \int_{E_{g}}^{\infty} \frac{E ^{2} d E}{e ^{E / k_{B} T} - 1}$	$V_{oc, S Q} = \frac{k _{B} T}{q} ln (\frac{J _{sc, ma x}}{J _{0, r a d}} + 1)$ $Δ V = V_{oc, S Q} - V_{oc}$	$J_{0, r a d} : r a d ia t i v e s a t u r a t i o n c u r r e n t d e n s i t y f or e mi ss i o n f r o m b o t h f a ces (2 π t im es t h e b l a c k b o d y f l ux 2 E^{2} / (h^{3} c^{2}); 2 π q w i t h a r e a r mi r r or; t h e p r e f a c t or w a s p r in t e d a s 2 π b e f or e t h e a u d i t, t h e n u mb er s u se d 4 π)$ $E_{g} : g a p$ $J_{sc, ma x} : p h o t oc u r r e n t o f t h e A M 1.5 G s p ec t r u m ab o v e t h e g a p$ $V_{oc, S Q} : v o l t a g e a t t h e r a d ia t i v e l imi t$ $Δ V : v o l t a g e d e f i c i t, t h e m e t h o d i s t h e o n e o f t h e S o l a r C e l l F u n d am e n t a l s p a g e, t h e so u r ces q u o t e l imi t s b u t d o n o t p r in t t h e in t e g r a l$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d a t 298.15 K w i t h t h e A M 1.5 G s p ec t r u m : E_{g} = 1.45 e V g i v es J_{sc, ma x} = 30.83 m A / c m^{2}, V_{oc, S Q} = 1.168 V (1.186 V w i t h a r e a r r e f l ec t or), F F = 89.6 % an d η = 32.3 % (32.8 %); 1.41 e V g i v es 32.44 m A / c m^{2}, 1.131 V an d 32.8 % (33.3 %); 1.50 e V g i v es 28.94 m A / c m^{2}, 1.215 V an d 31.6 %; t h e ce l l o f G r ee n e t a l . w i t h 898.1 mV ha s Δ V = 270 mV (E_{g} = 1.45 e V) an d E_{g} / q - V_{oc} = 552 mV; J_{0, r a d} = 5.5 \times 1 0^{- 7} f A / c m^{2} a t 1.45 e V)$
Optical gap of the cadmium selenide telluride alloy	$E_{g} (x) = x E_{C d S e} + (1 - x) E_{C d T e} - b x (1 - x)$	$x_{min} = \frac{1}{2} (1 - \frac{E _{C d S e} - E _{C d T e}}{b})$	$x : se l e ni u m f r a c t i o n o f C d S e_{x} T e_{1 - x}$ $E_{C d S e}, E_{C d T e} : g a p s o f t h e tw o co m p o u n d s$ $b : b o w in g p a r am e t er$ $x_{min} : co m p os i t i o n o f t h e minim u m g a p, C i r i s e t a l . g i v e b = 0.678 w i t h a minim u m o f ab o u t 1.4 e V a t ab o u t 45 % S e n e a r t h e t o p s u r f a ce, L in g g e t a l . g i v e b = 0.56 t o 0.97 w i t h t h e minim u m a t x = 0.3 t o 0.4 an d 1.35 t o 1.44 e V (t h e f or m u l a i s t h e u s u a l q u a d r a t i c f or m, n o t p r in t e d in t h e e x t r a c t s)$ $(co m p u t e d w i t h E_{C d T e} = 1.5 e V (L in g g e t a l .) an d E_{C d S e} = 1.74 e V (a ss u m e d f r o m ba c k g r o u n d) : b = 0.56 g i v es x_{min} = 0.29 an d 1.454 e V, b = 0.678 g i v es 0.32 an d 1.429 e V, b = 0.97 g i v es 0.38 an d 1.363 e V; f or x = 0.2 (t h e f r o n t l a y er o f M u n s hi e t a l .) t h e g a p i s 1.458, 1.440 an d 1.393 e V; M u n s hi e t a l . m e a s u r e ab o u t 1.41 e V)$
Absorption in the absorber	$A = 1 - e^{- α t}$	$t_{90%} = \frac{l n 10}{α}$	$A : ab sor b e d f r a c t i o n in o n e p a ss$ $α : ab sor pt i o n coe f f i c i e n t$ $t : t hi c k n ess$ $t_{90%} : t hi c k n ess f or 90 % ab sor pt i o n, t h e B eer - L amb er t f or m i s ba c k g r o u n d k n o w l e d g e, I n t a l an d E b o n g g i v e α > 1 0^{5} c m^{- 1} b e l o w 820 nm an d s a y t ha t 1 t o 2 μ m ab sor b m or e t han 90 % o f t h e A M 1.5 l i g h t$ $(co m p u t e d : α = 1 0^{5} c m^{- 1} g i v es t_{90%} = 0.23 μ m an d 99.995 % in 1 μ m; n e a r t h e e d g e α i s l o w er, f or 1 0^{4} c m^{- 1} t_{90%} = 2.3 μ m; t h e ce l l s in t h e so u r ces ha v e 3.5 μ m o f C d T e o n 1.5 t o 2.0 μ m o f C d S e T e (M u n s hi e t a l .) an d 6 t o 8 μ m (H aj imamma d o v e t a l .))$
Depletion width and hole density	$W = \frac{2 ε _{s} V _{bi}}{q p}$	$V_{bi} = \frac{k _{B} T}{q} ln \frac{N _{D} p}{n _{i}^{2}} (abrupt junction)$	$W : w i d t h o f t h e d e pl e t i o n r e g i o n in t h e ab sor b er$ $ε_{s} : p er mi tt i v i t y$ $V_{bi} : b u i l t - in v o l t a g e$ $p : h o l e d e n s i t y$ $N_{D} : d o n or d e n s i t y o f t h e w in d o w, t h e o n e - s i d e d ab r u pt - j u n c t i o n f or m i s ba c k g r o u n d k n o w l e d g e an d i s n o t p r in t e d b y t h e so u r ces, t h e so u r ces g i v e t h e h o l e d e n s i t y o n l y$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d w i t h ε_{s} = 10.4 ε_{0} an d V_{bi} = 0.85 V (b o t h a ss u m e d) : p = 1 0^{14} c m^{- 3} g i v es W = 3.1 μ m, 1 0^{15} 0.99 μ m, 2 \times 1 0^{15} 0.70 μ m, 1 0^{16} 0.31 μ m an d 1 0^{17} 0.10 μ m; so u r ces : co pp er d o p in g 1 0^{14} (M e t z g er e t a l ., M ey er s) or 1 0^{14} t o 1 0^{15} (D ani e l so n), a r se ni c 1 0^{16} t o 1 0^{17} (M e t z g er e t a l .))$

Voltage, Diode and Contact

Name	Formula	Related Formulae	Variables/Constants
Voltage from the hole density	$i V_{oc} = \frac{k _{B} T}{q} ln \frac{Δ n ( p + Δ n )}{n _{i}^{2}}$	$Δ i V_{oc} = \frac{k _{B} T}{q} ln \frac{p _{2}}{p _{1}} (Δ n ≪ p)$	$i V_{oc} : im pl i e d o p e n - c i r c u i t v o l t a g e$ $Δ n : e x cess c a r r i er d e n s i t y$ $p : h o l e d e n s i t y in t h e d a r k$ $n_{i} : in t r in s i c co n ce n t r a t i o n$ $p_{1}, p_{2} : tw o h o l e d e n s i t i es a t t h e s am e Δ n, t h e e x p r ess i o n i s t h e s t an d a r d o n e f r o m t h e S o l a r C e l l F u n d am e n t a l s p a g e, M e t z g er e t a l . s t a t e t ha t a h o l e d e n s i t y o f 1 0^{14} c m^{- 3} l imi t s t h e v o l t a g e an d t h e f i l l f a c t or$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d : a f a c t or o f 10 in p g i v es + 59.2 mV an d a f a c t or o f 100 g i v es + 118 mV f or t h e s am e Δ n; t hi s i s t h e or d er o f t h e g ain e x p ec t e d in g o in g f r o m 1 0^{14} t o 1 0^{16} c m^{- 3}; t h e s am e l i f e t im e i s a ss u m e d, a s M e t z g er e t a l . r e p or t t ha t t h e a r se ni c d oes n o t r e d u ce i t)$
Voltage from the external radiative efficiency	$V_{oc} = V_{oc, r a d} + \frac{k _{B} T}{q} ln Q_{e}$	$Δ V_{n r} = - \frac{k _{B} T}{q} ln Q_{e}$	$V_{oc, r a d} : v o l t a g e a t t h e r a d ia t i v e l imi t$ $Q_{e} : e x t er na l r a d ia t i v e e f f i c i e n cy (E R E)$ $Δ V_{n r} : l oss f r o m n o n - r a d ia t i v e r eco mbina t i o n, t h e r e l a t i o n i s t h e s t an d a r d o n e (ba c k g r o u n d k n o w l e d g e), O nn o e t a l . an d D ani e l so n m e a s u r e t h e E R E an d t h e in t er na l v o l t a g e, an d O nn o e t a l . f in d V oc = iV oc f or t h e F i r s t S o l a r ce l l s$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d : E R E = 0.1, 1 an d 4 % g i v e - 177, - 118 an d - 83 mV; w i t h V_{oc, r a d} = 1.131 V (1.41 e V) t hi s i s 1.013 V f or 1 % an d 1.048 V f or 4 %; f or 1.45 e V 1.050 an d 1.086 V; O nn o e t a l . : E R E ab o v e 1 % an d i V_{oc} ab o v e 970 mV (C S U, a r se ni c, A l_{2} O_{3}); D ani e l so n : E R E ab o v e 4 % an d n e a r l y 1 V)$
Diode parameters and ideality factor	$V_{oc} = \frac{n k _{B} T}{q} ln (\frac{J _{sc}}{J _{0}})$	$n = \frac{q V _{oc}}{k _{B} T l n ( J _{sc} / J _{0} )}$ $J_{0} = \frac{J _{sc}}{e ^{q V_{oc} / k_{B} T} - 1}$	$n : i d e a l i t y f a c t or$ $J_{0} : s a t u r a t i o n c u r r e n t d e n s i t y o f t h e r e a l ce l l$ $J_{sc} : s h or t - c i r c u i t c u r r e n t d e n s i t y, H aj imamma d o v e t a l . p r in t J_{0} an d t h e d i o d e f a c t or f or t h e i r ce l l s, t h e r e l a t i o n i s t h e o n e - d i o d e e q u a t i o n$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d : t h e b es t e v a p or a t e d ce l l (773 mV, 20.1 m A / c m^{2}, J_{0} = 8.2 \times 1 0^{- 8} A / c m^{2}) g i v es n = 2.42 a g ain s t 2.5 p r in t e d; t h e u n t r e a t e d ce l l (400 mV, 1.2 %, F F = 0.28, so J_{sc} = 10.7 m A / c m^{2}, J_{0} = 7.3 \times 1 0^{- 3} A / c m^{2}) g i v es n = 41 a g ain s t 7.0 p r in t e d; t h e s in g l e - d i o d e r e l a t i o n i g n or es t h e ser i es r es i s t an ce o f 28 Ω c m^{2}; t h e r ecor d ce l l s o f G r ee n e t a l . im pl y J_{0} = 0.047 f A / c m^{2} (21.0 %) an d 0.021 f A / c m^{2} (22.6 %) f or n = 1)$
Back-contact barrier	$R_{c} = \frac{k}{q A ^{*} T} e^{q φ_{B} / k_{B} T}$	$A^{} = \frac{4 π q m ^{} k _{B}^{2}}{h ^{3}}$	$R_{c} : s p ec i f i c r es i s t an ce o f t h e co n t a c t$ $A^{} : R i c ha r d so n co n s t an t$ $φ_{B} : ba r r i er h e i g h t f or h o l es$ $m^{} : e f f ec t i v e ma ss, t h e t h er mi o ni c - e mi ss i o n f or m i s ba c k g r o u n d k n o w l e d g e, t h e so u r ces d o n o t g i v e a ba r r i er, I n t a l an d E b o n g c i t e a ba c k - co n t a c t r eco mbina t i o n v e l oc i t y b e l o w 1 0^{3} c m / s (B r i tt an d F er e k i d es), M u n s hi e t a l . u se C u C l a t 140 C ann e a l e d a t 220 C w i t h a 30 nm t e l l u r i u m f i l m$ $k_{B} : B o l t z mann co n s t an t$ $(a ss u m e d A^{*} = 100 A / c m^{2} K^{2} an d T = 300 K : φ_{B} = 0.3, 0.4, 0.5 an d 0.6 e V g i v e R_{c} = 0.0003, 0.015, 0.72 an d 34 Ω c m^{2}, co m p u t e d; t h e r es i s t an ce g r o w s b y a f a c t or o f 48 f or e a c h 0.1 e V)$

Efficiency and Field Performance

Name	Formula	Related Formulae	Variables/Constants
Temperature coefficient of the voltage and of the power	$\frac{d V _{oc}}{d T} = - \frac{E _{g 0} / q - V _{oc} + γ k _{B} T / q}{T}$	$P (T) = P_{25} [1 + β (T - 25)]$ $β_{V} = \frac{1}{V _{oc}} \frac{d V _{oc}}{d T}$	$E_{g 0} : g a p e x t r a p o l a t e d t o 0 K$ $γ : e x p o n e n t o f t h e t e m p er a t u r e d e p e n d e n ce o f J_{0}$ $β : r e l a t i v e p o w er coe f f i c i e n t in 1/ K, t h e v o l t a g e r e l a t i o n i s s t an d a r d (ba c k g r o u n d k n o w l e d g e), F i r s t S o l a r (v ia P V T ec h) g i v es - 0.28 %/ C f or t h e S er i es 6 a g ain s t - 0.35 f or a C ana d ian S o l a r s i l i co n m o d u l e, I n t a l an d E b o n g g i v e - 0.18 %/ K$ $k_{B} : B o l t z mann co n s t an t$ $(co m p u t e d w i t h E_{g 0} / q = 1.55 V an d γ = 3 (b o t h a ss u m e d) a t 298.15 K : 898.1 mV g i v es - 2.45 mV / K an d β_{V} = - 0.272 %/ K, 875.9 mV g i v es - 0.288 %/ K; a t 65 C t h e p o w er i s 88.8 % f or - 0.28, 92.8 % f or - 0.18 an d 86.0 % f or - 0.35 %/ K)$
Efficiency from the reported parameters	$η = \frac{V _{oc} J _{sc} F F}{P _{in}}, P_{in} = 100 mW/c m^{2}$	$η_{c h ec k} = \frac{V _{oc} J _{sc} F F}{1000}$ $\frac{η}{η _{S Q}}$	$η : e f f i c i e n cy, V_{oc} in mV, J_{sc} in m A / c m^{2}, F F a s a f r a c t i o n (η_{c h ec k} i s in p er ce n t : t h e 1000 t u r n s mV in t o V, an d 1 mW / c m^{2} i s 1 p er ce n t o f P_{in})$ $η_{S Q} : d e t ai l e d - ba l an ce e f f i c i e n cy a t t h e g a p, G r ee n e t a l . (e f f i c i e n cy t ab l es 64) p r in t t h e p a r am e t er s o f tw o ce l l s$ $(co m p u t e d : 875.9, 30.25, 79.4 % g i v e 21.04 % (21.0 \pm 0.4, 1.0623 c m^{2}); 898.1, 31.56, 79.6 % g i v e 22.56 % (22.6 \pm 0.3, 0.4486 c m^{2}); M u n s hi e t a l . 842, 26.8, 74.5 % g i v e 16.81 % (16.8); H aj imamma d o v e t a l . 773, 20.1, 67 % g i v e 10.41 % (10.3) an d 773, 23.92, 68.7 % g i v e 12.70 % (12.71); 22.6 % i s 70 % an d 23.1 % i s 72 % o f 32.3 %)$
Module power from efficiency and area	$P_{ma x} = η_{m o d} G A$	$ρ_{P} = η_{m o d} G$	$P_{ma x} : ma x im u m p o w er o f t h e m o d u l e$ $η_{m o d} : m o d u l e e f f i c i e n cy$ $G : i r r a d ian ce o f 1000 W / m^{2}$ $A : m o d u l e a r e a$ $ρ_{P} : p o w er d e n s i t y, I n t a l an d E b o n g l i s t t h e S er i es 6 P l u s w i t h 19.9 % an d an a r e a o f 23932 c m^{2}$ $(co m p u t e d : 0.199 \times 1000 \times 2.3932 = 476 W an d 199 W / m^{2}; t h e D O E p er s p ec t i v e p a p er g i v es a m o d u l e r ecor d o f 19.9 % an d, in an o t h er sec t i o n, 18.5 % a s t h e b es t m o d u l e)$
Power retention in the field	$\frac{P ( t )}{P _{0}} = 1 - d_{1} - d (t - 1)$	$d_{e q} = \frac{1 - P ( t ) / P _{0}}{t}$	$P (t) / P_{0} : r e l a t i v e p o w er a f t er t y e a r s$ $d_{1} : l oss o f t h e f i r s t y e a r$ $d : ann u a l l oss a f t er w a r d s$ $d_{e q} : e q u i v a l e n t l in e a r r a t e, t h e l in e a r f or m i s m y s im pl i f i c a t i o n, F i r s t S o l a r (a v e n d or, v ia P V T ec h an d t h e S o l a r M o d u l e S u p er L e a g u e) s t a t es 0.2 %/ y e a r an d a t l e a s t 92 % a f t er 30 y e a r s$ $(co m p u t e d : 0.2 %/ y e a r f or 30 y e a r s g i v es 94.0 %; 92 % n ee d s 0.267 %/ y e a r w i t h o u t a f i r s t - y e a r l oss, or d_{1} = 2 % an d 0.2 %/ y e a r a f t er w a r d s (92.2 %), an a ss u m pt i o n t ha t t h e a r t i c l es d o n o t s t a t e)$

Important Questions

Ques: Which CdTe cell record is right: 21.0, 22.1, 22.6 or 23.1 %?

Green et al. list 21.0 ± 0.4 % in Table 1 for a cell of 1.06 $c m^{2}$ (Newport) and 22.6 ± 0.3 % in Table 2 for 0.449 $c m^{2}$ (NREL, January 2024, after 22.4 %). First Solar announced 22.1 % in February 2016 and 23.1 % in July 2024, and the DOE paper gives 23.1 % on 0.45 $c m^{2}$ ; the thesis of Danielson (2022) calls 21.0 % the current world record. Their products are 21.04 and 22.56 % (computed). The numbers describe different dates and areas: a class record needs more than 1 $c m^{2}$ , so 21.0 % is the large-area entry and 22.6 % the notable exception. The 23.1 % is more likely the newest small-area value, but I found no Voc, Jsc or FF for it. For comparison I use 22.6 %, because its parameters are printed. 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, ‘First Solar pushes CdTe cell efficiency to record 22.1%’ (23 February 2016); PV Tech, ‘First Solar opens Ohio R&D centre, sets new CdTe cell efficiency record’ (18 July 2024); U.S. Department of Energy, ‘Cadmium Telluride Photovoltaics Perspective Paper’ (January 2025); Danielson, ‘Investigation of Group V doping and passivating oxides to reduce the voltage deficit in CdTe solar cells’, PhD thesis, Colorado State University (2022) (abstract page).

Ques: Is the efficiency limit of CdTe 33.1 or 32.3 %?

Danielson gives a theoretical maximum of 33.1 % for CdTe. The detailed-balance calculation of this vault with the AM1.5G spectrum gives 32.3 % for 1.45 eV with emission from both faces and 32.8 % with a rear reflector, 31.6 % for 1.5 eV, and 32.8 and 33.3 % for 1.41 eV (computed). The Solar Cell Fundamentals page finds 33.1 and 33.7 % at the optimum gap of 1.34 eV. The 33.1 % of the thesis equals the optimum of the whole spectrum, and I could not read the thesis to see which gap it uses. For 1.45 eV the limit of 32.3 % is more likely, and for the graded CdSeTe of about 1.4 eV 32.8 %. The cells at 22.6 % reach about 70 % of that limit. Reference: Danielson, ‘Investigation of Group V doping and passivating oxides to reduce the voltage deficit in CdTe solar cells’, PhD thesis, Colorado State University (2022) (abstract page); Solar Cell Fundamentals page of this vault.

Ques: Is the voltage deficit of CdTe 250, 270 or 550 mV?

Danielson states that the voltage deficiency of CdTe exceeds 250 mV compared with silicon technologies. The cell of Green et al. has 898.1 mV, which is 552 mV below the gap of 1.45 eV, 270 mV below the radiative limit of 1.168 V and 290 mV below the 1.186 V with a reflector (computed). The deficit relative to the gap and relative to the radiative limit are different measures, and the thesis does not say which it uses. The radiative one is the physical deficit, and 270 mV agrees with ‘exceeds 250 mV’, so I take it to be the meaning. External radiative efficiency explains it: an ERE of 1 % costs 118 mV and 4 % costs 83 mV (computed), while Onno et al. find an internal voltage above 970 mV, close to 1 V at best. Reference: Danielson, ‘Investigation of Group V doping and passivating oxides to reduce the voltage deficit in CdTe solar cells’, PhD thesis, Colorado State University (2022) (abstract page); 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); Onno et al., ‘Understanding what limits the voltage of polycrystalline CdSeTe solar cells’, Nature Energy 7, 400-408 (2022) (abstract page).

Ques: Is the bowing parameter of CdSeTe 0.678 or between 0.56 and 0.97?

Ciris et al. fit a bowing parameter of 0.678 to films grown from mixed powders, with a minimum of about 1.4 eV at about 45 % selenium near the top. Lingg et al. collect 0.56 to 0.97 from experimental and theoretical sources and place the minimum at x of 0.3 to 0.4 with 1.35 to 1.44 eV. With 1.5 and 1.74 eV for the end points, 0.678 gives a minimum of 1.429 eV at x = 0.32, and 0.56 and 0.97 give 1.454 eV at 0.29 and 1.363 eV at 0.38 (computed), so the review range agrees with the formula. The 45 % of Ciris et al. is higher than 0.32 because their films are graded, with the top richer in selenium. A value near 0.7 is more likely for films, and the real device gap, 1.41 eV in Munshi et al., depends on the grading. Reference: Ciris, Basol, Atasoy, Karaca, Kuckomeroglu, Tomakin and Bacaksiz, ‘Deposition of CdSeTe alloys using CdTe-CdSe mixed powder source material in a close-space sublimation process’, J. Mater. Sci.: Mater. Electron. 32, 9685-9693 (2021) (abstract page); Lingg, Buecheler and Tiwari, ‘Review of CdTe1-xSex Thin Films in Solar Cell Applications’, Coatings 9(8), 520 (2019); Munshi, Kephart, Abbas, Danielson, Gelinas, Beaudry, Barth, Walls and Sampath, ‘Effect of CdCl2 passivation treatment on microstructure and performance of CdSeTe/CdTe thin-film photovoltaic devices’, Sol. Energy Mater. Sol. Cells 186, 259-265 (2018).

Ques: Is the gap of the absorber 1.45, 1.5 or 1.41 eV, given a current of 31.56 mA/cm2?

Intal and Ebong give 1.45 eV for CdTe, Lingg et al. about 1.5 eV, and Munshi et al. measure about 1.41 eV for CdSeTe. The record cell of Green et al. has 31.56 $mA/c m^{2}$ , but the AM1.5G photocurrent above the gap is 28.94 $mA/c m^{2}$ at 1.5 eV, 30.83 at 1.45 eV and 32.44 at 1.41 eV (computed). The measured current therefore exceeds the limit of the pure CdTe gaps and can only be reached if the absorber has a lower effective gap near 1.41 eV, the graded CdSeTe, with about 97 % of its limit. The gap of CdTe alone is 1.45 to 1.5 eV. I could not check which gap Intal and Ebong used, so for the cell I use 1.41 eV and for the CdTe layer 1.45 to 1.5 eV. Reference: Intal and Ebong, ‘Thin-Film Solar Photovoltaics: Trends and Future Directions’, arXiv:2508.05589 (2025); Lingg, Buecheler and Tiwari, ‘Review of CdTe1-xSex Thin Films in Solar Cell Applications’, Coatings 9(8), 520 (2019); Munshi, Kephart, Abbas, Danielson, Gelinas, Beaudry, Barth, Walls and Sampath, ‘Effect of CdCl2 passivation treatment on microstructure and performance of CdSeTe/CdTe thin-film photovoltaic devices’, Sol. Energy Mater. Sol. Cells 186, 259-265 (2018); 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 hole density of arsenic-doped CdTe above 10^16, 2 x 10^15 or 10^15?

Intal and Ebong give a hole density above 10 $^{16}$ $c m^{- 3}$ in one section and above 2 × 10 $^{15}$ $c m^{- 3}$ in another, Metzger et al. give 10 $^{16}$ to 10 $^{17}$ $c m^{- 3}$ for the abstract of the 20.8 % work, and Danielson reports arsenic densities above 10 $^{15}$ $c m^{- 3}$ . Copper gives 10 $^{14}$ (Metzger et al., Meyers) or 10 $^{14}$ to 10 $^{15}$ (Danielson). They refer to different films and years, and Danielson says that models need 10 $^{16}$ to 10 $^{17}$ . A factor of ten in hole density is worth 59 mV at the same excess density and a factor of 100 is worth 118 mV (computed). The 10 $^{16}$ to 10 $^{17}$ of the original paper is the best case and 10 $^{15}$ is the typical result of later work, so I take 10 $^{15}$ to 10 $^{16}$ as the likely range for production material. Reference: Intal and Ebong, ‘Thin-Film Solar Photovoltaics: Trends and Future Directions’, arXiv:2508.05589 (2025); Metzger et al., ‘Exceeding 20% efficiency with in situ group V doping in polycrystalline CdTe solar cells’, Nature Energy 4, 837-845 (2019) (abstract page); Danielson, ‘Investigation of Group V doping and passivating oxides to reduce the voltage deficit in CdTe solar cells’, PhD thesis, Colorado State University (2022) (abstract page).

Ques: How thick must the CdTe absorber be: 1 to 2 µm, below 3 µm or 3.5 to 8 µm?

Intal and Ebong state that 1 to 2 µm absorb more than 90 % of the light in one section and sub-3 µm in the conclusions, whereas Munshi et al. have a stack of about 5 µm (1.5 to 2.0 µm of CdSeTe and 3.5 µm of CdTe) and Hajimammadov et al. use 6 to 8 µm by close-space sublimation and 4 µm by evaporation. For an absorption coefficient of 10 $^{5}$ $c m^{- 1}$ only 0.23 µm gives 90 %, and 2.3 µm are needed at 10 $^{4}$ $c m^{- 1}$ near the edge (computed). The optical need is therefore 1 to 2 µm. The cells are thicker because of the grain size, the depletion width of 0.3 to 3 µm and the processing. For the research cells 3 to 5 µm is more likely; a thickness below 3 µm is a goal that the sources do not demonstrate. Reference: Intal and Ebong, ‘Thin-Film Solar Photovoltaics: Trends and Future Directions’, arXiv:2508.05589 (2025); Munshi, Kephart, Abbas, Danielson, Gelinas, Beaudry, Barth, Walls and Sampath, ‘Effect of CdCl2 passivation treatment on microstructure and performance of CdSeTe/CdTe thin-film photovoltaic devices’, Sol. Energy Mater. Sol. Cells 186, 259-265 (2018); Hajimammadov, Fathi, Bayramov, Khrypunov, Klochko and Li, ‘Effect of CdCl2 Treatment on Properties of CdTe-Based Solar Cells Prepared by Physical Vapor Deposition and Close-Spaced Sublimation Methods’, Jpn. J. Appl. Phys. 50, 05FH01 (2011).

Ques: Is the temperature coefficient of CdTe -0.28 or -0.18 %/°C?

First Solar gives -0.28 %/°C for the Series 6 (against -0.35 for a silicon module from Canadian Solar, PV Tech), and Intal and Ebong give -0.18 %/K in a section on field performance. With an extrapolated gap of 1.55 V and an exponent of 3 (assumed) the voltage term alone is -0.27 %/K at 898 mV and -0.29 %/K at 876 mV (computed). A coefficient of -0.18 would need the current and the fill factor to add +0.09 %/K, which I would not expect. The -0.28 agrees with the voltage term and is a product value, so it is more likely for modules. The -0.18 could be a different quantity (for instance an energy-yield gain or a coefficient of the current), but the source does not say; at 65 °C the two give 88.8 and 92.8 % of the power. Reference: PV Tech, ‘First Solar touts its CuRe technology delivering module degradation rates of only 0.2% per year’ (16 April 2021); Intal and Ebong, ‘Thin-Film Solar Photovoltaics: Trends and Future Directions’, arXiv:2508.05589 (2025).

Ques: Does the vendor’s 0.2 %/year degradation match 92 % after 30 years?

First Solar states a warranted degradation of 0.2 %/year for the Series 6 CuRe and, with the Solar Module Super League, at least 92 % of the power after 30 years; Intal and Ebong repeat 0.2 %/year. Linear loss of 0.2 %/year for 30 years leaves 94.0 %, while 92 % needs 0.267 %/year, or a first-year loss of about 2 % followed by 0.2 %/year (92.2 %, computed). The articles give no first-year loss, so I cannot confirm the second reading; a warranty with a first-year step would be consistent. The DOE paper gives a module record of 19.9 % and elsewhere 18.5 %; 19.9 % is more likely the newer (my reading), and equals 476 W on 23932 $c m^{2}$ (computed). Reference: PV Tech, ‘First Solar touts its CuRe technology delivering module degradation rates of only 0.2% per year’ (16 April 2021); Intal and Ebong, ‘Thin-Film Solar Photovoltaics: Trends and Future Directions’, arXiv:2508.05589 (2025); U.S. Department of Energy, ‘Cadmium Telluride Photovoltaics Perspective Paper’ (January 2025).

Ques: Are the diode parameters of the CdCl2 study consistent?

Hajimammadov et al. print for the best evaporated cell 773 mV, 20.1 $mA/c m^{2}$ , a saturation current of 8.2 × 10 $^{- 8}$ $A/c m^{2}$ and a diode factor of 2.5. The one-diode relation gives 2.42 (computed), so these agree. For the untreated cell they print 400 mV, an efficiency of 1.2 %, a fill factor of 0.28, a saturation current of 7.3 × 10 $^{- 3}$ $A/c m^{2}$ and a diode factor of 7.0; the current is then 10.7 $mA/c m^{2}$ and the relation gives 41, not 7.0 (computed), because the series resistance of 28 $Ω$ cm $^{2}$ distorts the fit. The efficiency product of the best cell is 10.41 % against 10.3 % printed. The diode factor of 2.5 is more likely reliable and the 7.0 is a fit parameter of a very resistive cell; both cells of the paper also have the same voltage of 773 mV, which may be a typing repeat. Reference: Hajimammadov, Fathi, Bayramov, Khrypunov, Klochko and Li, ‘Effect of CdCl2 Treatment on Properties of CdTe-Based Solar Cells Prepared by Physical Vapor Deposition and Close-Spaced Sublimation Methods’, Jpn. J. Appl. Phys. 50, 05FH01 (2011).

Ques: Is the lifetime of CdSeTe 430 ns or 8 µs?

Lingg et al. give 430 ns for passivated CdTe0.8Se0.2, about ten times the value of CdTe, Shah gives 430 ns for alumina double heterostructures of CdSeTe, and Danielson reports excess-carrier lifetimes of up to 8 µs with Al $_{2}$ O $_{3}$ passivation, the highest for polycrystalline Cd(Se)Te, and microsecond values for arsenic doping with alumina. The values differ by a factor of 19 but describe different samples: passivated double heterostructures against a stack with arsenic and a later optimized oxide. The thesis does not give its thickness or measurement, and I could not read the details. The 8 µs is the best value of later work and 430 ns the earlier reference. For production cells neither applies, because the lifetime of finished devices is lower; the radiative efficiency of 1 to 4 % is the more useful measure. Reference: Shah, ‘Experimental and theoretical investigations of selenium graded cadmium telluride-based solar cells’, PhD dissertation, Colorado State University (2022) (abstract page); Lingg, Buecheler and Tiwari, ‘Review of CdTe1-xSex Thin Films in Solar Cell Applications’, Coatings 9(8), 520 (2019); Danielson, ‘Investigation of Group V doping and passivating oxides to reduce the voltage deficit in CdTe solar cells’, PhD thesis, Colorado State University (2022) (abstract page).

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Cadmium Telluride (CdTe) Thin-Film Solar Cell