Table 1.

Summary of symbol definitions and units

Symbol	Units	Description	Symbol	Units	Description
β	Angstroms−1	Tunneling constant	Csc	Farads centimeter-2	Differential capacitance of the space-charge layer in the semiconductor
b	—	$\equiv {\gamma }_{\mathit{surf}}\text{/}{\gamma }_{sc}$	Css	Farads centimeter-2	Differential capacitance of surface states
d	Centimeters	Length of the tether	Csurf	Farads centimeter-2	Differential capacitance of the surface layer
ε 0	Farads centimeter−1	Permittivity of free space	Celec	Farads centimeter-2	Differential capacitance of the electrolyte
εsc,b	—	Relative dielectric constant of the bulk semiconductor	Cf	Farads centimeter-2	Differential capacitance of the faradaic reaction
εsc,scl	—	Relative dielectric constant at the edge of the semiconductor space-charge layer	Eapp	Volts	Applied potential relative to the flat-band potential
εsurf	—	Relative dielectric constant of the surface layer	Ecb	Volts	Conduction-band potential for the corresponding value of Eapp
εelec	—	Relative dielectric constant of the electrolyte	Ecb,fb	Volts	Conduction-band potential when Eapp = Efb
ϕsc,b	Volts	Electrostatic potential in the bulk of the semiconductor	Efb	Volts	Flat-band potential ≡ 0
ϕsc,s	Volts	Electrostatic potential at the surface of the semiconductor	E 0 fb	Volts	Standard potential of redox adsorbate when Eapp = Efb
ϕPET	Volts	Electrostatic potential at the plane of electron transfer	Fs	—	Potential-dependent probability function for the integrated charge across the space-charge layer in the semiconductor
ϕsol	Volts	Electrostatic potential at the edge of the diffuse layer in solution	fs	—	Potential-dependent probability function for the integrated charge held in surface states
Γlower(x,y)	—	Lower incomplete Γ function with arguments x and y	j	Amps centimeter−2	Total measured current density
Γupper(x,y)	—	Upper incomplete Γ function with arguments x and y	jf	Amps centimeter−2	Faradaic current density
κ	Centimeters−1	Reciprocal thickness of the double layer	jc	Amps centimeter−2	Charging current density
σsc,s	Coulombs centimeter−2	Charge density at the surface of the semiconductor	kf	Seconds−1	Forward charge-transfer rate constant
σsc,b	Coulombs centimeter−2	Charge density in the semiconductor bulk	kb	Seconds−1	Back charge-transfer rate constant
σPET	Coulombs centimeter−2	Charge density at the plane of electron transfer	ket	Centimeters4 second−1	Electron transfer rate constant from the conduction band
σelec	Coulombs centimeter−2	Charge density in the electrolyte	k 0	Seconds−1	Heterogeneous rate constant when Eapp = E0
σscl	Coulombs centimeter−2	Charge density stored in the semiconductor space-charge layer	kss	Centimeters3 second−1	Rate constant for filling/emptying surface states
σss	Coulombs centimeter−2	Charge density stored in surface states	m	—	Normalized experimental timescale, $m=\frac{k_0{k}_{B}T}{qv{\gamma }_{sc}}$
χA	—	Fraction of oxidized adsorbed redox species	Nd	Centimeters−3	No. of dopants per unit volume
χA-	—	Fraction of reduced adsorbed redox species	nelec	Molecules centimeters−3	Concentration of supporting electrolyte
γsc	—	Fraction of the time-dependent applied potential dropped across the space-charge layer of the semiconductor	ns, 0	Centimeters−3	Majority carrier concentration when Eapp = E0
γsurf	—	Fraction of the time-dependent applied potential dropped across the surface layer	Nss	Centimeters−2	Density of surface states per unit area
γelec	—	Fraction of the time-dependent applied potential dropped across the electrolyte layer	u	—	Normalized applied potential that directly moves the Fermi level
[A]s,0	Molecules centimeter−2	Total surface concentration of redox species	v	Volts second−1	Scan rate (+ and − on cathodic and anodic sweeps, respectively)
q	Coulombs	Unsigned charge of an electron	$w_{E_{\mathit{app}}}$	Centimeters	Potential-dependent width of semiconductor space-charge layer
kB	Joules Kelvin−1	Boltzmann's constant	zA	—	Oxidation state of oxidized form of redox species
T	Kelvin	Temperature	zA-	—	Oxidation state of reduced form of redox species
CT	Farads centimeters-2	Total measured capacitance of the semiconductor electrode	z	—	Type of electrolyte (=1 for a 1:1 electrolyte)
			Z	—	$\equiv e\frac{-q{\gamma }_{\mathit{diff}}}{k_{B}T}\left(E^0-E_{fb}\right)$