A simple accurate solution to minority electron injection in the p-type heavily doped emitter region of silicon devices

Abstract

In the p‐type quasi‐neutral and heavily doped emitter region of silicon devices at room temperature, with the aid of our accurate empirical models for the apparent band‐gap narrowing and minority‐electron lifetime, a simple accurate theory of minority‐electron (emitter) saturation current density JEO, and effective minority‐electron transit time, which are expressed as functions of the surface acceptor density Ns, the electron surface recombination velocity S, and the emitter width W, is derived and discussed. It is found that, under transparent emitter region condition, our theoretical values of JEO(Ns) for S = ∞ and 0.19 μm ≦ W ≦ 0.25 μm are in good agreement with the corresponding ones measured by Cuevas et al., with a precision of the order of 22%.

Best Performance of n<sup>+</sup> - p Crystalline Silicon Junction Solar Cells at 300 K, Due to the Effects of Heavy Doping and Impurity Size. I

“…Moreover, Equation (18) indicates that, for a given N and with increasing r * , μ decreases, since ε(r * ) decreases as seen in Table 1, being due to the d-size effect, in good accordance with that observed by Logan et al [9]. Further, from Equations (5,8,9,15,18), we can define the following minority-hole transport parameter F as [22,25]:…”

“…"×&\ un + 3 × 10 .&W × N + 1.83 × 10 .W& × N C . 23Furthermore, Equation (22) indicates that, for a given N and with increasing r , μ decreases, since ε(r ) decreases, as seen in Table 1, in good accordance with that observed by Logan et al [9].…”

“…Then, in P(B)-Si systems at 300 K and for g = 6 , Klaassen et al confirmed, in Figures 1 and 2 of their paper [16], that the expressions (18,22) for minority-hole (electron) mobility μ ( ) are simple and accurate.…”

“…is the "effective doping density" [8] and the ABGN is determined in Equation 9for our ΔE -result or in Equation 15for our approximate ΔE (¢ *.¡ƒ) -one. Furthermore, the minority-hole length, L (N, T, r * , g ) = Áτ × D , τ being the minority-hole lifetime, can be determined by [22,25]:…”

“…I expressed as functions of the open circuit voltage V [4]. Further, it should be noted that, in most fabricated silicon devices, the effective Gaussian donor-density profile ρ x , being proposed in next Equation (24), varies with carrier position x in the emitter region of width W [13,[18][19][20]22], and it decreases with increasing W, being found to be in good agreement with that used by Essa et al [13]. As a result, many other physical quantities, given in this NUHD n(p)-type thin emitter region such as : the band gap narrowing (BGN), ΔE , Fermi energy E , apparent band gap narrowing (ABGN), ΔE , minority-hole (electron) mobility μ , minority-hole (electron) lifetime τ , and minority-hole (electron) diffusion length L , strongly depend on ρ x .…”