Erratum: Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading(Applied Optics (2019) 58(6067–6078) DOI: 10.1364/AO.58.006067)

Equations (8)–(13) of our paper [1] contain a repeated typographical error. The correct versions of these equations are as follows: _J ^J _p ⁿ ₍ ⁽ _z ^z ₎ ⁾ ₌ ⁼ _µ ^µ _p ⁿⁿ _p ⁽ ₍ ^z _z ⁾ ₎ ^dz _dz ^d _{d _} ^E _E ^F _F ⁿ _p ⁽ ₍ ^z _z ⁾ ₎ ^} , z ∈ (L_w, L_d) (8) E_Fn(z)= E_c(z)+ k_BT ln[n(z)/N_c(z)] (9) E_Fp(z)= E_v(z)− k_BT ln[p(z)/N_v(z)] (10) _p n ₍(_z z ₎ ) ₌ = _n n _i(i(_z z ₎ ) _exp exp _{−[ {[E _{E Fn F} (_p z _(z ) ₎ − ₋ E _{E i}(_i z _(z )] ₎ / _]/ k _{k B B} T _T } _} ^} (11) n_i(z)= √ N_c(z)N_v(z)exp[−E_g(z)/k_BT] (12) E_i(z)= (1/2){E_c(z)+ E_v(z)− k_BT ln[N_c(z)/N_v(z)]} (13) The definition of conduction band-edge energy E_c(z)contains the same typographical error. The correct definition is E_c(z)= E₀ − [q_eφ(z)+ χ(z)]. In Eq. (16), N_f(z) should be replaced by N_f(z) + N_D(z), where N_D(z) is the doping density, which is positive for donors and negative for acceptors. The correct version of this equation is as follows: ε_{0 dz} ^{d [} ε_dc(z)_dz ^d φ(z) ] = −q_e [N_f(z) + N_D(z) + p(z) − n(z)]. (16) In Table 1, µ_n(cm⁻² V⁻¹ s⁻¹), µ_p(cm⁻² V⁻¹ s⁻¹), and R_B(cm⁻³ s⁻¹) have to be replaced by µ_n(cm² V⁻¹ s⁻¹), µ_p(cm² V⁻¹ s⁻¹), and R_B(cm⁻³ s⁻¹), respectively. These errors did not affect any numerical result or conclusion provided in the paper. We regret our carelessness.