1. Theory

Definition: The passivated emitter and rear cell (PERC) keeps the front of the Al-BSF cell (a POCl $_{3}$ emitter of about 90 $Ω/ sq$ , a silicon nitride coating and a screen-printed silver grid) but replaces the full-area aluminium contact on the rear by a dielectric stack of aluminium oxide capped with silicon nitride, through which a laser opens small local contacts; a full-area aluminium paste is printed and fired, and it alloys with the silicon only at the openings.
PERT and PERL: The pv-manufacturing.org page lists 24.5 % for a PERT cell on magnetic Czochralski silicon and 24.7 % for a PERL cell on float-zone silicon, and an efficiency of 25 % of the UNSW PERL cell in 1999 after recalibration. PERL means a rear that is locally diffused and PERT one that is diffused over the whole area (the acronyms are not spelled out in the sources I read, so this is background knowledge). The industrial n-PERT cell has an n-type Czochralski wafer, a boron emitter on the front (diffused or implanted), a phosphorus-doped rear over the whole area, passivation on both sides and screen-printed contacts on both sides, which makes it bifacial.
History: UNSW introduced PERC in 1983 and held a record of 22.8 % in 1989; Knobloch et al. proposed aluminium-alloyed local contacts in 1989. pv-manufacturing.org says the industry began to change to PERC from 2013, Lohmuller et al. that mass production began in 2012 and that PERC dominated the production in 2018; pv Europe reports that TOPCon was set to overtake PERC as the market leader in 2024.
Rear stack: The Aalto document deposits about 10 nm of Al $_{2}$ O $_{3}$ by thermal ALD (trimethylaluminium and ozone, 200 °C) under 100 nm of PECVD silicon nitride; Lohmuller et al. use 6 nm by spatial ALD, an outgassing at 550 °C and 150 nm of silicon nitride, and in 2024 a thermal oxide followed by AlO $_{x}$ , SiO $_{x}$ N $_{y}$ and SiN $_{x}$ . The aluminium oxide has a negative fixed charge, up to $- (1 \pm 0.4) \times 1 0^{12}$ $c m^{- 2}$ , and an interface-state density of about $2 \times 1 0^{10}$ eV $^{- 1}$ cm $^{- 2}$ (Saynova et al.).
Contacts: The Aalto cell has 180 lines of about 30 µm opened by a 532 nm picosecond laser (rear aluminium fraction 3.25 %, local aluminium layer of about 10 µm, fired for 2 to 3 s at a peak of 760 °C); Lohmuller et al. use dots at a pitch of 500 µm (boron-doped) or 425 µm (gallium-doped) in 2020 and 600 µm in 2024.
Performance: The Aalto cells reach 20.22 % on average (about 2000 cells, before degradation) with a voltage of about 652 mV; Fraunhofer ISE reached 22.1 and 22.2 % (680 mV) in 2020 and 23.4 % (693 mV, 41.5 $mA/c m^{2}$ , 81.5 %) for a gallium-doped champion cell; reported records are 23.6 % (LONGi), 23.39 % (Trina, bifacial, 252 cm $^{2}$ ) and 23.83 % for a LONGi cell. The n-PERT cell has 21.0 % (664.6 mV) with a bifaciality of 97.3 %.
Degradation: Boron-doped cells show the boron-oxygen degradation, which gallium doping removes; the light and elevated temperature induced degradation (LeTID) was first seen in multicrystalline PERC cells and is related to hydrogen.

2. Working Principle

Passivation: The aluminium oxide passivates chemically, by hydrogen and a low density of interface states, and by the field effect, because its negative charge repels the electrons from the surface of p-type silicon and keeps the holes at it; the passivated area reaches a velocity of about 10 $cm/s$ or less.
Local contacts: The recombination at the contacts remains high, so the rear velocity seen by the base is the sum of the passivated part and a contact part that is limited by the diffusion of the electrons to the contacts; this is the reason why a metallized fraction of a few percent is enough, and why a local back-surface field at the contacts helps.
Current path: The holes have to flow laterally to the contacts, which adds a spreading resistance that grows with the pitch and falls with the contact size; the contact size is chosen between the loss in the fill factor and the loss in voltage.
Optics: The dielectric stack with the aluminium behind it is a better mirror than the alloyed aluminium (Zanuccoli et al. use 0.9 for the passivated area and 0.65 for the full metal; the Al-BSF page gives 65 % against 93 % for PERC), which raises the current.
Shunting: A silicon nitride layer on p-type silicon has a positive charge that can form an inversion layer under the rear and shunt the contacts (Cesar et al.: current losses of up to 3.5 $mA/c m^{2}$ in the literature), which is one reason for the negative charge of the aluminium oxide.
Degradation: The firing drives hydrogen from the nitride into the silicon; with the wrong firing and cooling it is released later and forms the LeTID defects, and the boron-oxygen defects form under light in boron-doped Czochralski silicon.

3. Applications

Mass production: The mono-PERC cell was the standard industrial cell from about 2018, mostly in bifacial form, and it can be made by adding the rear stack, the laser and the final treatment to an Al-BSF line.
Bifacial modules: The n-PERT cell with a bifaciality of more than 97 % serves modules that profit from rear-side light.
Reference: The cell is the baseline for the comparison with the TOPCon, heterojunction and back-contact cells on the following pages; the pilot line of Fraunhofer ISE gained 0.4 points per year since 2007.

Rear Passivation and Local Contacts

Name	Formula	Related Formulae	Variables/Constants
Effective recombination velocity of a locally contacted rear	$S_{e f f} = (1 - f) S_{p a ss} + [\frac{1}{f S _{co n t}} + \frac{L _{s p}}{D}]^{- 1}$	$f = \frac{π}{4} (\frac{d}{p})^{2} (points), f = \frac{w}{p} (lines)$ $L_{s p} \approx \frac{p ^{2}}{2 d} (d ≪ p)$	$S_{e f f} : e f f ec t i v e r eco mbina t i o n v e l oc i t y o f t h e r e a r a s see n b y t h e ba se$ $f : m e t a l l i z e d f r a c t i o n o f t h e r e a r$ $S_{p a ss} : v e l oc i t y o f t h e p a ss i v a t e d a r e a$ $S_{co n t} : v e l oc i t y a t t h e co n t a c t s (a l l oy e d A l / p + r e g i o n)$ $L_{s p} : s p r e a d in g l e n g t h o f t h e e l ec t r o n s (s p r e a d in g r es i s t an ce o f t h e ba se d i v i d e d b y i t s r es i s t i v i t y, g eo m e t r y o n l y)$ $D : e l ec t r o n d i f f u s i v i t y o f t h e ba se$ $d : d iam e t er o f a p o in t co n t a c t$ $w : w i d t h o f a l in e co n t a c t$ $p : p i t c h, t h e s t r u c t u r e (S_{co n t}, S_{p a ss}, f an d a d i f f u s i o n r es i s t an ce) i s t ha t o f t h e F i sc h er m o d e l a s d escr ib e d b y S ain t - C a s t e t a l ., w h ose p r in t e d e q u a t i o n s w er e g a r b l e d, so t h e f or m h er e i s ba c k g r o u n d k n o w l e d g e t ha t I c h ec k e d a g ain s t t h e n u m er i c a l so l u t i o n b e l o w$ $(co m p u t e d w i t h a f ini t e - d i f f er e n ce so l u t i o n o f t h e s t e a d y d i f f u s i o n e q u a t i o n in t h e u ni t ce l l, D = 30 c m^{2} / s a ss u m e d, S_{p a ss} = 10 c m / s (S ain t - C a s t e t a l .), S_{co n t} = 1 0^{5} c m / s (L a u er mann e t a l .), p = 500 μ m : d = 40, 60, 80 an d 100 μ m g i v e S_{e f f} = 94, 151, 216 an d 289 c m / s, an d 15, 20, 28 an d 38 c m / s f or S_{co n t} = 1 0^{3} c m / s; l in es o f 30 μ m a t 870 μ m p i t c h (f = 3.45 %) g i v e ab o u t 330 an d 39 c m / s; m es h er r or 1 t o 4 %; t h e i so l a t e d - co n t a c t L_{s p} i s 7 % (d = 40 μ m) t o 32 % (d = 100 μ m) ab o v e t h e n u m er i c a l o n e)$
Contact fraction and rear reflectance	$f = \frac{π}{4} (\frac{d}{p})^{2}, R_{bi} = R_{bi, m} - 0.25 f$	$f = \frac{N w}{L} (N lines of width w across a length L)$	$f : m e t a l l i z e d f r a c t i o n o f t h e r e a r (0 t o 1)$ $d : co n t a c t d iam e t er$ $p : p i t c h o f t h e s q u a r e g r i d$ $R_{bi} : in t er na l r e f l ec t an ce o f t h e r e a r$ $R_{bi, m} : v a l u e o f t h e p a ss i v a t e d a r e a (0.9 in t h e s im u l a t i o n o f Z an u cco l i e t a l .), t h e l in e a r r e l a t i o n an d i t s v a l u e 0.65 a t f = 1 a r e p r in t e d in t h e p a p er, t h e f or m u l a f or f w a s g a r b l e d in t h e e x t r a c t i o n an d i s r eco n s t r u c t e d so t ha t i t r e p r o d u ces t h e i r t ab l e$ $(Z an u cco l i e t a l . : p, d = 200, 25; 500, 75; 1000, 200 μ m g i v e f = 1.23, 1.77 an d 3.14 % (t h e t ab l e p r in t s 3.08 f or t h e l a s t, t h e t e x t 3.14); t h e A a l t o d oc u m e n t : 180 l in es o f ab o u t 30 μ m a cr oss 156 mm (w i d t h a ss u m e d) g i v e 3.46 % a g ain s t 3.25 % p r in t e d f or t h e r e a r A l f r a c t i o n; R_{bi} = 0.892 f or f = 3.25 %; a l l co m p u t e d)$
Chemical and field-effect passivation by aluminium oxide	$S_{e f f} = \frac{n _{s} p _{s} - n _{i}^{2}}{\frac{n _{s} + n _{1}}{S _{p 0}} + \frac{p _{s} + p _{1}}{S _{n 0}}}, S_{n 0} = σ_{n} v_{t h} N_{i t}$	$n_{s} = n_{b} e^{q ψ_{s} / k_{B} T}, p_{s} = p_{b} e^{- q ψ_{s} / k_{B} T}$ $S_{e f f, ma x} \leq \frac{W}{2 τ _{e f f}}$	$n_{s}, p_{s} : e l ec t r o n an d h o l e d e n s i t i es a t t h e s u r f a ce$ $n_{b}, p_{b} : d e n s i t i es in t h e b u l k u n d er inj ec t i o n$ $n_{1}, p_{1} : S R H d e n s i t i es o f t h e t r a p l e v e l (mi d - g a p : n_{1} = p_{1} = n_{i})$ $S_{n 0}, S_{p 0} : c a pt u r e - l imi t e d v e l oc i t i es$ $σ : c a pt u r e cr oss sec t i o n$ $v_{t h} : t h er ma l v e l oc i t y$ $N_{i t} : a r e a l d e n s i t y o f in t er f a ce t r a p s$ $ψ_{s} : ban d b e n d in g (n e g a t i v e f or t h e n e g a t i v e c ha r g e o f A l 2 O 3 o n p - t y p e s i l i co n)$ $W : w a f er t hi c k n ess$ $τ_{e f f} : m e a s u r e d e f f ec t i v e l i f e t im e, S a y n o v a e t a l . p r in t t h e l a s t r e l a t i o n an d S_{n} = σ_{n} v_{t h} N_{i t} w i t h g a r b l e d sy mb o l s (r e a d h er e a s cr oss sec t i o n s, m y r e a d in g), t h e s in g l e - l e v e l S R H f or m w i t h t h e f i e l d t er m i s t h e s t an d a r d r es u l t an d ba c k g r o u n d k n o w l e d g e$ $k_{B} : B o l t z mann co n s t an t$ $(S a y n o v a e t a l . : v_{t h} = 1 0^{7} c m / s, σ ab o u t 6 \times 1 0^{- 16} c m^{2}, Q_{f} f r o m + 1 t o - 1 \times 1 0^{12} c m^{- 2} a f t er t h e ann e a l (b es t - (1 \pm 0.4) \times 1 0^{12}), D_{i t} ab o u t 2 \times 1 0^{10} e V^{- 1} c m^{- 2}; an a ss u m e d N_{i t} = 5 \times 1 0^{9} c m^{- 2} g i v es S_{n 0} = 30 c m / s; w i t h S_{p 0} = S_{n 0}, N_{A} = 1.8 \times 1 0^{16} an d Δ n = 1 0^{15} c m^{- 3} (a ss u m e d), S_{e f f} = 28.5, 0.61 an d 0.012 c m / s f or ψ_{s} = 0, - 0.1 an d - 0.2 V; τ_{e f f} = 1.2 m s an d W = 200 μ m (a ss u m e d) g i v e S_{e f f, ma x} = 8.3 c m / s; co m p u t e d)$
Thickness of the atomic-layer-deposited aluminium oxide	$d_{A l_{2} O_{3}} = N_{cy c} g$	$N_{cy c} = \frac{d _{A l_{2} O_{3}}}{g}$	$d : f i l m t hi c k n ess$ $N_{cy c} : n u mb er o f A L D cy c l es$ $g : g r o w t h p er cy c l e (S a y n o v a e t a l . : 1.0 A a t 100 C an d 1.1 A a t 150 t o 200 C f or t h er ma l A L D w i t h T M A an d w a t er), t h e A a l t o d oc u m e n t u ses T M A an d oz o n e a t 200 C (w in d o w 200 t o 240 C, p a ss i v a t i o n d r o p s s ha r pl y a t 275 C)$ $(g = 1.1 A / cy c l e i s a ss u m e d f or a l l t oo l s : 3.5, 6 an d 10 nm n ee d 32, 55 an d 91 cy c l es, co m p u t e d; A a l t o d oc u m e n t : o pt im u m ab o u t 10 nm (r an g e 3.5 t o 16 nm), 3.5 nm s t i l l g i v es 652 mV an d 20.3 %; L o hm u l l er e t a l . : 6 nm b y s p a t ia l A L D, o u t g a sse d a t 550 C f or 10 min, c a pp e d w i t h 150 nm S i N x)$
Spreading resistance of the base towards the local contacts	$R_{s, s p} = ρ L_{s p}, R_{s, ba se + s p} = ρ (W + L_{s p})$	$L_{s p} \approx \frac{p ^{2}}{2 d} (d ≪ p)$	$R_{s, s p} : a r e a - n or ma l i z e d s p r e a d in g r es i s t an ce o f t h e ba se$ $ρ : ba se r es i s t i v i t y$ $W : w a f er t hi c k n ess$ $L_{s p} : s am e s p r e a d in g l e n g t h a s in t h e f i r s t r o w, Z an u cco l i e t a l . s t a t e t ha t t h e s p r e a d in g r es i s t an ce d e p e n d s o n t h e s i z e an d t h e p i t c h o f t h e co n t a c t s, t h e l ink w i t h L_{s p} f o l l o w s f r o m t h e ana l o g y b e tw ee n co n d u c t i o n an d d i f f u s i o n an d i s ba c k g r o u n d k n o w l e d g e$ $(co m p u t e d w i t h t h e s am e so l v er f or i d e a l co n t a c t s, W = 170 μ m : p = 500 μ m an d d = 40, 60, 80, 100 μ m g i v e L_{s p} = 2.92, 1.81, 1.27 an d 0.95 mm, so R_{s, s p} = 0.23 an d 0.076 Ω c m^{2} f or d = 40 an d 100 μ m a t ρ = 0.8 Ω c m; l in es o f 30 μ m a t 870 μ m g i v e 0.80 mm; t h e r e a r s i l i co n s p r e a d in g o f t h e A a l t o ce l l, 12.51 % o f 0.5967 Ω c m^{2} = 0.0746 Ω c m^{2}, t h e n n ee d s ρ = 0.94 Ω c m)$

Saturation Current, Series Resistance and Efficiency

Name	Formula	Related Formulae	Variables/Constants
Saturation current density from the open-circuit voltage	$j_{01} = \frac{j _{sc}}{e ^{q V_{oc} / k_{B} T} - 1}$	$j_{01} = j_{0 e} + j_{0, ba se + r e a r}$ $j_{0, r e a r} \approx \frac{q n _{i}^{2}}{N _{A}} S_{e f f} (S_{e f f} ≪ \frac{D}{W})$	$j_{01} : s a t u r a t i o n c u r r e n t d e n s i t y o f t h e s in g l e - d i o d e m o d e l$ $j_{sc} : s h or t - c i r c u i t c u r r e n t d e n s i t y$ $V_{oc} : o p e n - c i r c u i t v o l t a g e$ $j_{0 e} : e mi tt er t er m$ $j_{0, ba se + r e a r} : ba se w i t h t h e r e a r s u r f a ce$ $n_{i} : in t r in s i c co n ce n t r a t i o n$ $N_{A} : ba se d o p in g$ $D : e l ec t r o n d i f f u s i v i t y$ $W : w a f er t hi c k n ess, t h e seco n d r e l a t i o n i s t h e t hin - ba se l imi t o f t h e f ini t e - w a f er e x p r ess i o n o f t h e A l - B S F p a g e$ $k_{B} : B o l t z mann co n s t an t$ $(25 C, n_{i} = 8.70 \times 1 0^{9} c m^{- 3}, N_{A} = 1.8 \times 1 0^{16} c m^{- 3} f or 0.8 Ω c m (m o bi l i t y 430 c m^{2} / V s a ss u m e d) : q n_{i}^{2} / N_{A} = 0.67 f A / c m^{2} p er c m / s; L o hm u l l er e t a l . (B - d o p e d, 680 mV, 40.3 m A / c m^{2}) g i v e j_{01} = 129 f A / c m^{2}, t h e im pl i e d 688 mV g i v es 95 f A / c m^{2}, an d w i t h j_{0 e} = 56 f A / c m^{2} t h e ba se an d r e a r a r e a t m os t 39 f A / c m^{2}, i . e . S_{e f f} o f a t m os t 58 c m / s; t h e c ham p i o n ce l l (693 mV, 41.5 m A / c m^{2}) g i v es 80 f A / c m^{2}; a l l co m p u t e d)$
Series resistance of the PERC cell and the contact-size trade-off	$R_{s} = R_{s, ba se} + R_{s, s p} + R_{s, e mi tt er} + R_{s, g r i d} + R_{s, co n t a c t} + R_{s, r e a r}$	$R_{s, e mi tt er} = \frac{ρ _{□} S ^{2}}{12}$ $Δ η \approx \frac{J _{m p}^{2} Δ R _{s}}{P _{in}}, Δ η \approx \frac{Δ V _{oc} J _{sc} F F}{P _{in}}$	$R_{s, ba se} : v er t i c a l r es i s t an ce ρ W$ $R_{s, s p} : s p r e a d in g t er m o f t h e p r e v i o u s sec t i o n$ $R_{s, e mi tt er}, R_{s, g r i d}, R_{s, co n t a c t} : f r o n t t er m s$ $R_{s, r e a r} : r e a r a l u mini u m$ $ρ_{□} : s h ee t r es i s t an ce o f t h e e mi tt er$ $S : f in g er s p a c in g$ $J_{m p} : c u r r e n t d e n s i t y a t ma x im u m p o w er$ $P_{in} : in c i d e n t p o w er, t h e tw o e f f i c i e n cy r e l a t i o n s a r e m y f i r s t - or d er es t ima t es o f t h e o hmi c an d t h e v o l t a g e l oss$ $(A a l t o d oc u m e n t, 0.5967 Ω c m^{2} : e mi tt er 0.197, g r i d 0.220, r e a r A l 0.042, r e a r S i s p r e a d in g 0.075, r es t 0.063 (ba se, co n t a c t s, b u s ba r s), f r o m t h e p r in t e d p er ce n t a g es; t h e e mi tt er f or m u l a w i t h 90 Ω/ s q an d 156 mm /96 f in g er s = 1.625 mm g i v es 0.198 Ω c m^{2}; L o hm u l l er e t a l . : r_{S} = 0.40 an d 0.39 Ω c m^{2}; t r a d e - o f f a t p = 500 μ m, ρ = 0.8 Ω c m, J_{m p} = 38 m A / c m^{2}, s t a r t in g f r o m 129 f A / c m^{2} : d = 40 t o 100 μ m l o w er s R_{s} b y 0.157 Ω c m^{2} (+ 0.23 p o in t s), b u t S_{e f f} r i ses f r o m 94 t o 289 c m / s f or S_{co n t} = 1 0^{5} c m / s (- 17.9 mV, - 0.59 p o in t s) or f r o m 15 t o 38 c m / s f or 1 0^{3} c m / s (- 2.9 mV, - 0.09 p o in t s); a l l co m p u t e d)$
Efficiency from the reported parameters	$η = \frac{V _{oc} J _{sc} F F}{P _{in}}, P_{in} = 100 mW/c m^{2}$	$η_{c h ec k} = \frac{V _{oc} J _{sc} F F}{1000}$ $Δ η = η_{p r in t e d} - η_{c h ec k}$	$η : e f f i c i e n cy, V_{oc} in mV, J_{sc} in m A / c m^{2}, F F a s a f r a c t i o n (η_{c h ec k} i s in p er ce n t : t h e 1000 t u r n s mV in t o V, an d 1 mW / c m^{2} i s 1 p er ce n t o f P_{in}), P_{in} i s t h e s t an d a r d t es t co n d i t i o n, t h e v a l u es a r e c ham p i o n or b es t ce l l s a s l ab e l l e d b y t h e so u r ces$ $(L o hm u l l er e t a l . : 680, 40.3, 80.8 % g i v e 22.14 % (p r in t e d 22.1); 679, 40.4, 81.1 % g i v e 22.25 % (22.2); t h e c ham p i o n 693, 41.5, 81.5 % g i v es 23.44 % (23.4); n - P E R T : 664.6, 39.8, 79.3 % g i v e 20.98 % (21.0) an d 657.6, 39.9, 78.4 % g i v e 20.57 % (20.6); L a u er mann e t a l . : 638.6, 37.8, 77.2 % g i v e 18.64 % (18.6), 640.0, 37.7, 78.3 % g i v e 18.89 % (18.9), 641.8, 36.4, 72.1 % g i v e 16.84 % (16.9); co m p u t e d)$
Bifaciality and bifacial gain	$φ = \frac{η _{r e a r}}{η _{f r o n t}}, G_{E} = G_{f} + φ G_{r}$	$\frac{Δ P}{P} \approx φ \frac{G _{r}}{G _{f}}$	$φ : bi f a c ia l i t y f a c t or$ $η_{r e a r}, η_{f r o n t} : e f f i c i e n c i es w i t h i l l u mina t i o n f r o m t h e r e a r an d f r o m t h e f r o n t$ $G_{E} : e q u i v a l e n t i r r a d ian ce$ $G_{f}, G_{r} : i r r a d ian ce o n t h e f r o n t an d o n t h e r e a r, t h e g ain i s a f i r s t - or d er es t ima t e t ha t n e g l ec t s t h e c han g e o f t h e e f f i c i e n cy w i t h t h e i r r a d ian ce (ba c k g r o u n d k n o w l e d g e)$ $(n - P E R T : 97.3 % (b or o n e mi tt er) an d 97.7 % (B F_{2}), in - h o u se f r o n t an d r e a r m e a s u r e m e n t s; bi f a c ia l P E R C m o d u l e o f L O N G i : 82.15 %; t h e g ain a t G_{r} / G_{f} = 0.1 an d 0.2 i s 9.7 an d 19.5 % f or 0.973, an d 8.2 an d 16.4 % f or 0.8215, co m p u t e d)$

Material, Degradation and the n-PERT Cell

Name	Formula	Related Formulae	Variables/Constants
Boron-oxygen degradation and dopant segregation in the ingot	$N_{B O} \propto N_{A} [O_{i}]^{2}$	$C_{s} = k C_{0} (1 - g)^{k - 1}$ $ρ = \frac{1}{q μ N _{A}}$	$N_{B O} : co n ce n t r a t i o n o f t h e b or o n - o x y g e n d e f ec t (L O N G i, c i t in g S c hmi d t 2004)$ $N_{A} : b or o n co n ce n t r a t i o n$ $O_{i} : in t er s t i t ia l o x y g e n$ $C_{s} : co n ce n t r a t i o n in t h e so l i d$ $C_{0} : ini t ia l co n ce n t r a t i o n o f t h e m e l t$ $k : se g r e g a t i o n coe f f i c i e n t (b or o n 0.75, g a l l i u m 0.008)$ $g : so l i d i f i e d f r a c t i o n$ $μ : maj or i t y - c a r r i er m o bi l i t y, t h e S c h e i l r e l a t i o n i s ba c k g r o u n d k n o w l e d g e$ $(L O N G i : 12 an d 16 pp m o f o x y g e n g i v e 0.5 an d 0.7 % d e g r a d a t i o n o f b or o n - d o p e d P E R C + ce l l s, t h e s q u a r e l a w p r e d i c t s a r a t i o o f 1.78 a g ain s t 1.40 o b ser v e d; C_{s} / C_{s} (0) a t g = 0.5, 0.8, 0.9 i s 1.19, 1.50, 1.78 f or b or o n an d 1.99, 4.94, 9.82 f or g a l l i u m, so t h e r es i s t i v i t y f a l l s b y t h e s am e f a c t or s a l o n g t h e in g o t; co m p u t e d; g a l l i u m w a f er s o f 0.3 t o 1.5 Ω c m, u p t o 21 % a t 0.4 Ω c m an d m or e t han 97 % o f t h e p e ak b e tw ee n 0.25 an d 1.34 Ω c m)$
Light and elevated temperature induced degradation	$N^{*} = \frac{1}{τ ( t )} - \frac{1}{τ ( 0 )}$	$Δ η_{r e l} = 1 - \frac{η ( t )}{η ( 0 )}$	$N^{*} : n or ma l i z e d d e f ec t d e n s i t y$ $τ (t) : e f f ec t i v e l i f e t im e a f t er t h e t im e t$ $τ (0) : ini t ia l l i f e t im e$ $Δ η_{r e l} : r e l a t i v e e f f i c i e n cy l oss, t h e n or ma l i z e d d e f ec t d e n s i t y i s t h e u s u a l d e f ini t i o n an d ba c k g r o u n d k n o w l e d g e$ $(C h e n : ce l l l osses o f 4.3 t o 16 % r e l a t i v e (u p t o 10 % o n a v er a g e f or u n t r e a t e d ce l l s), m o d u l es 11 %, o u t d oor 7.5 t o 10 %, t es t co n d i t i o n s 65 t o 85 C w i t h 0.4 t o 1 s u n or c u r r e n t inj ec t i o n; f or ce l l s o f 22.1 % t h e r an g e i s 0.95 t o 3.5 p o in t s, co m p u t e d; P V M a g a z in e : t h e d r a f t I E C 61215 - 2 t es t t ak es ab o u t 800 h a t 75 C w i t h c u r r e n t inj ec t i o n)$
Saturation current budget of the n-PERT cell	$j_{01} = j_{0, e m} + j_{0, B S F} + j_{0, ba se}$	$V_{oc} = \frac{k _{B} T}{q} ln (\frac{j _{sc}}{j _{01}} + 1)$	$j_{0, e m} : b or o n e mi tt er o n t h e f r o n t (d i f f u se d or im pl an t e d)$ $j_{0, B S F} : p h os p h or u s - d o p e d r e a r o v er t h e w h o l e a r e a$ $j_{0, ba se} : n - t y p e ba se, b o t h s u r f a ces a r e p a ss i v a t e d an d co n t a c t e d b y scr ee n p r in t in g, t h e t er m s a r e n o t se p a r a t e d b y t h e so u r ces I r e a d$ $k_{B} : B o l t z mann co n s t an t$ $(t h e 21.0 % ce l l w i t h im pl an t e d b or o n (664.6 mV, 39.8 m A / c m^{2}) ha s j_{01} = 232 f A / c m^{2}, t h e B F_{2} ce l l (657.6 mV, 39.9 m A / c m^{2}) 306 f A / c m^{2}, a g ain s t 129 f A / c m^{2} f or t h e p - t y p e P E R C ce l l o f F r a u nh o f er I S E, co m p u t e d a t 25 C; t h e b es t r o u t e o f t h e M E T U s t u d y i s a b or o n - d i f f u se d e mi tt er w i t h a p h os p h or u s - im pl an t e d B S F)$

Important Questions

Ques: How much open-circuit voltage does the rear passivation add: about 20 mV or more than 40 mV?

Herguth et al. state that PERC cells reach 650 to 660 mV, which is about 20 mV above Al-BSF cells. Lauermann et al. added passivation to Al-BSF-type cells and gained 19.5 mV with point contacts (619.1 to 638.6 mV) and only 8.1 mV with line contacts (computed from their table). The saturation currents suggest more: 850 $fA/c m^{2}$ for the cells of Werner et al. against 129 $fA/c m^{2}$ for the Fraunhofer cell of 680 mV (computed at 25 °C) is 48 mV. That large figure also contains a better emitter ( $j_{0 e}$ of 56 $fA/c m^{2}$ ) and a better lifetime, so about 20 mV is more likely for the rear alone, and the 8 mV of the line contacts shows that the contact design matters. Reference: Herguth, Horbelt, Wilking, Job and Hahn, ‘Comparison of BO Regeneration dynamics in PERC and Al-BSF solar cells’, Energy Procedia 77, 75-82 (2015); Lauermann, Zuschlag, Scholz, Hahn and Terheiden, ‘The Influence of Contact Geometry and Sub-Contact Passivation on the Performance of Screen-Printed Al2O3 Passivated Solar Cells’, 26th EU PVSEC (2011); Werner, Lohmuller, Maier, Kimmerle, Spribille, Wasmer, Clement and Wolf, ‘Process Optimization for the Front Side of p-Type Silicon Solar Cells’, 29th EU PVSEC, Amsterdam (2014); Lohmuller, Greulich, Saint-Cast et al., ‘Front side optimization on boron- and gallium-doped Cz-Si PERC solar cells exceeding 22% conversion efficiency’, 37th EU PVSEC (2020).

Ques: How much efficiency does the PERC rear add: 0.3 to 0.4 points or 0.5 points?

Cesar et al. estimate 0.3 to 0.4 points for rear-passivated multicrystalline cells with local contacts, and their other paper on open-rear cells gives 0.5 points. Lauermann et al. measured 0.7 points (17.9 to 18.6 % with point contacts, 18.2 to 18.9 % with line contacts, computed from their table). Much larger numbers appear when whole cells are compared: the best Al-BSF cell of Awaah et al. has 19.7 %, the Aalto PERC cells 20.22 % on average, the Fraunhofer champion cell 23.4 %. The gap of 3.7 points to the champion contains a better front side, wafer and emitter, so 0.5 to 0.7 points is more likely for the rear step alone, and the rest is the accumulated optimization of the pilot line. Reference: Cesar, Mewe, Manshanden, Romijn, Janssen and Weeber, ‘Effect of Al Contact Pitch on Rear Passivated Solar Cells’, SiliconPV 2011, Energy Procedia (2011); Cesar, Granneman, Vermont, Khatri, Kerp, Shaikh, Manshanden, Mewe, Romijn and Weeber, ‘Industrial Application of Uncapped Al2O3 and Firing-Through Al-BSF In Open Rear Passivated Solar Cells’, ECN; Lauermann, Zuschlag, Scholz, Hahn and Terheiden, ‘The Influence of Contact Geometry and Sub-Contact Passivation on the Performance of Screen-Printed Al2O3 Passivated Solar Cells’, 26th EU PVSEC (2011); Awaah, Awaah, Apalangya and Das, ‘Investigation and Characterization of Al paste as back surface field (BSF) for High Efficiency Si Solar cell’, 2021 IEEE PES/IAS PowerAfrica; Lohmuller, Lohmuller, Saint-Cast, Greulich, Glunz and Preu, ‘Review and Highlights of More Than 30 Years Research on Ever Improving Technology for PERC Solar Cells at Fraunhofer ISE’, 41st EU PVSEC (2024); Aluminium Back-Surface-Field (Al-BSF) Silicon Cell page of this vault.

Ques: Why is the cell-level rear velocity so much higher than the passivation velocity?

Saynova et al. find at most 5 to 30 $cm/s$ on aluminium oxide, Saint-Cast et al. use 10 $cm/s$ for the passivated area, and Cesar et al. fitted more than 500 $cm/s$ on cells with a nitride rear and aluminium points at a pitch of 1 mm. The contacts explain the difference. With 10 $^{5}$ $cm/s$ at the contacts my solution of the diffusion equation gives 94 to 289 $cm/s$ for points of 40 to 100 µm at 500 µm pitch and about 330 $cm/s$ for lines of 30 µm; only lines of about 9 % of the area reach 526 $cm/s$ (computed). A local back-surface field with 10 $^{3}$ $cm/s$ gives 15 to 39 $cm/s$ . More than 500 $cm/s$ therefore needs large unpassivated contacts or the inversion-layer shunt of the nitride that Cesar et al. discuss; this is my reading. Reference: Saynova, Janssen, Burgers, Mewe, Cianci, Seguini and Perego, ‘Al2O3 passivation on c-Si surfaces for low temperature solar cell applications’, Energy Procedia 38, 872-880 (2013); Saint-Cast, Wohrle and Greulich, ‘Validation of Analytic Modelling of Local Rear Contacts in PERC/PERL Solar Cells’, 33rd EU PVSEC (2017); Cesar, Mewe, Manshanden, Romijn, Janssen and Weeber, ‘Effect of Al Contact Pitch on Rear Passivated Solar Cells’, SiliconPV 2011, Energy Procedia (2011); Lauermann, Zuschlag, Scholz, Hahn and Terheiden, ‘The Influence of Contact Geometry and Sub-Contact Passivation on the Performance of Screen-Printed Al2O3 Passivated Solar Cells’, 26th EU PVSEC (2011).

Ques: Which rear contact fraction is best: 1 to 3 %, about 3 % or 6 to 8 %?

Zanuccoli et al. simulate an optimum between 1 and 3 %, the Aalto cell has 3.25 % in lines, and Lauermann et al. used 6 % and 8 % for screen-printed aluminium. My calculation shows why the optimum moves. Enlarging the points from 40 to 100 µm at a pitch of 500 µm and 0.8 $Ω cm$ lowers the spreading resistance by 0.157 $Ω c m^{2}$ , which gains 0.23 points. With 10 $^{5}$ $cm/s$ at the contacts the voltage falls by 17.9 mV (0.59 points); with a local field of 10 $^{3}$ $cm/s$ it falls by 2.9 mV (0.09 points; all computed). So 1 to 3 % suits unpassivated alloyed contacts, 2 to 4 % is more likely for today’s industrial cells, and 6 to 8 % belongs to the earlier screen-printed contacts; this is my reading. Reference: Zanuccoli, Guo, Sangiorgi and Fiegna, ‘Three-Dimensional Numerical Simulation of Rear Point Contact Crystalline Silicon Solar Cells’, Renewable Energy and Power Quality Journal 1(9) (2011); Aluminium Back-Surface-Field (Al-BSF) Silicon Cell page of this vault; Lauermann, Zuschlag, Scholz, Hahn and Terheiden, ‘The Influence of Contact Geometry and Sub-Contact Passivation on the Performance of Screen-Printed Al2O3 Passivated Solar Cells’, 26th EU PVSEC (2011); Saint-Cast, Wohrle and Greulich, ‘Validation of Analytic Modelling of Local Rear Contacts in PERC/PERL Solar Cells’, 33rd EU PVSEC (2017).

Ques: Is the best aluminium oxide thickness 10 nm or 6 nm?

The Aalto document finds an optimum of about 10 nm in a range of 3.5 to 16 nm, but 3.5 nm still gave 652 mV and 20.3 %. Saynova et al. also use 10 nm and reach lifetimes of 1.2 ms. Lohmuller et al. use only 6 nm and reach 680 mV, with a spatial ALD tool, an outgassing at 550 °C for 10 min and a 150 nm nitride cap. At 1.1 A per cycle these are 91 and 55 cycles (computed, one growth rate assumed for both tools). The values do not contradict each other, because the passivation comes from the interface charge and hydrogen and saturates at a few nanometres; the thickness matters for the cap and for the firing. Six nanometres is more likely for a modern high-voltage cell; 10 nm is the safer choice for a temporal ALD. Reference: Industrial PERC solar cell with ALD Al2O3 rear passivation, Aalto University research portal file 1_s2.0_S2352340916307910_main.pdf (open-access article; title and authors not shown by the fetch tool); Saynova, Janssen, Burgers, Mewe, Cianci, Seguini and Perego, ‘Al2O3 passivation on c-Si surfaces for low temperature solar cell applications’, Energy Procedia 38, 872-880 (2013); Lohmuller, Greulich, Saint-Cast et al., ‘Front side optimization on boron- and gallium-doped Cz-Si PERC solar cells exceeding 22% conversion efficiency’, 37th EU PVSEC (2020).

Ques: How large is the fixed charge of aluminium oxide?

Saynova et al. measured fixed charges from +1 to $- 1 \times 1 0^{12}$ $c m^{- 2}$ after the anneal, with a best value of $- (1 \pm 0.4) \times 1 0^{12}$ $c m^{- 2}$ at a deposition temperature of 200 °C, and the sign changed from positive to negative when the post-deposition anneal went from 200 to 250 °C at the lower temperatures. The same paper quotes $(1$ to $4) \times 1 0^{12}$ $c m^{- 2}$ in one section and $(2$ to $6) \times 1 0^{12}$ $c m^{- 2}$ in its introduction. The narrower range is more likely for ALD films on silicon, and their own best film is at its lower end. A strong charge is not needed: for $N_{A}$ of $1.8 \times 1 0^{16}$ $c m^{- 3}$ a band bending of $- 0.1$ V already lowers the field-effect velocity by a factor of 47, and $- 0.2$ V by about 2300 (computed with the single-level model). Reference: Saynova, Janssen, Burgers, Mewe, Cianci, Seguini and Perego, ‘Al2O3 passivation on c-Si surfaces for low temperature solar cell applications’, Energy Procedia 38, 872-880 (2013).

Ques: How big is the light-induced degradation of a PERC cell?

It depends on the mechanism. Lohmuller et al. report 0.1 points after an ultrafast regeneration for boron-doped cells (data not shown) and none for gallium-doped cells. LONGi gives 0.5 and 0.7 % for oxygen contents of 12 and 16 ppm; the square law of the boron-oxygen defect predicts a ratio of 1.78 but 1.40 is observed (computed). The UNSW test of a 23.83 % cell found about 1 point or less after 40 h at 75 °C. LeTID is larger: Chen lists 4.3 to 16 % relative for cells, which is 0.95 to 3.5 points at 22.1 % (computed), and PV Magazine mentions more than 10 % over years. The first values describe the treated boron-oxygen defect and are likely for today’s cells; LeTID is the risk that only the process and the gallium doping can control. Reference: Lohmuller, Greulich, Saint-Cast et al., ‘Front side optimization on boron- and gallium-doped Cz-Si PERC solar cells exceeding 22% conversion efficiency’, 37th EU PVSEC (2020); LONGi, ‘Gallium-doped monocrystalline silicon fully solves the problem of a PERC module’s LID’ (2020 press release); pv magazine Australia, ‘UNSW Sydney: Preventing LID in a 23.83% efficient Longi PERC cell’ (4 February 2020); Chen, ‘Light and Elevated Temperature Induced Degradation’, APVI Solar Research Conference slides (file uploaded 2019/12); pv magazine Australia, ‘Understanding LeTID’ (6 April 2020).

Ques: When did PERC enter mass production: 2012 or 2013?

The pv-manufacturing.org page says the industry began to change to PERC from 2013 and that the concept dates from 1983, with a record of 22.8 % in 1989. Lohmuller et al. write that mass production began in 2012 and that PERC dominated the production in 2018. The statements need not contradict each other: the first can describe the start of the large shift of the lines, the second the first commercial production. I could not read a source with market-share numbers, because the ITRPV pages I fetched give no percentages for PERC. TaiyangNews called PERC the working horse of the industry in the 14th edition, and pv Europe says that TOPCon overtakes PERC in 2024. Therefore 2012 is the more likely year for the first production and 2013 for the start of the ramp; this is my reading. Reference: pv-manufacturing.org, ‘PERC Solar Cells’; Lohmuller, Lohmuller, Saint-Cast, Greulich, Glunz and Preu, ‘Review and Highlights of More Than 30 Years Research on Ever Improving Technology for PERC Solar Cells at Fraunhofer ISE’, 41st EU PVSEC (2024); TaiyangNews, ‘ITRPV’s 14th Edition: PERC Continues To Dominate’; pv Europe, ‘ITRPV: TOPCon technology overcomes PERC in 2024’.

Ques: Is the bifaciality 97 % or 82 %?

The ion-implanted n-PERT cells have 97.3 % (boron) and 97.7 % (BF $_{2}$ ), measured in-house on the front and on the rear of the cell. The press release on the LONGi Hi-MO2 bifacial PERC module gives a record bifaciality of 82.15 %. A cell value and a module value of two structures do not compare directly. A symmetric n-PERT cell with the same texture and passivation on both sides should be near 1, while a PERC cell has a rear with local contacts and a full-area aluminium or grid, so the order is expected. At a rear irradiance of 20 % of the front, the gains are 19.5 % and 16.4 % (computed). The 97 % is more likely for the n-PERT cell and 82 % for the PERC module. Reference: Innovations Report, ‘Ion implanted, co-annealed, screen-printed 21% efficient n-PERT solar cells with a bifaciality >97%’; pv-tech, ‘LONGi hits record 23.6% conversion efficiency for mono PERC solar cells’.

Ques: Is the simulated current gain of 8 % or the measured gain of 3 to 4 % right?

Zanuccoli et al. normalize the short-circuit current to a conventional cell with a fully metallized rear and find 1.080 to 1.087 for rear points, which is 8 to 8.7 %. Lauermann et al. measured 1.4 and 1.0 $mA/c m^{2}$ on 36.4 and 36.7 $mA/c m^{2}$ when they passivated the contacts, which is 3.8 and 2.7 % (computed). Fraunhofer ISE has 40.3 $mA/c m^{2}$ against 38.1 $mA/c m^{2}$ of Werner et al., 5.8 %, but with a better front. The simulation compares with a rear that, as far as I can tell, has $1 0^{5}$ $cm/s$ over the whole area (no back-surface field is mentioned) and a reflectance of 0.65, so it measures more than the usual Al-BSF; the measured 3 to 4 % is more likely for the rear change alone. This is my reading. Reference: Zanuccoli, Guo, Sangiorgi and Fiegna, ‘Three-Dimensional Numerical Simulation of Rear Point Contact Crystalline Silicon Solar Cells’, Renewable Energy and Power Quality Journal 1(9) (2011); Lauermann, Zuschlag, Scholz, Hahn and Terheiden, ‘The Influence of Contact Geometry and Sub-Contact Passivation on the Performance of Screen-Printed Al2O3 Passivated Solar Cells’, 26th EU PVSEC (2011); Lohmuller, Greulich, Saint-Cast et al., ‘Front side optimization on boron- and gallium-doped Cz-Si PERC solar cells exceeding 22% conversion efficiency’, 37th EU PVSEC (2020); Werner, Lohmuller, Maier, Kimmerle, Spribille, Wasmer, Clement and Wolf, ‘Process Optimization for the Front Side of p-Type Silicon Solar Cells’, 29th EU PVSEC, Amsterdam (2014).

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PERC and PERT Silicon Cell