### Challenges Related to (V)LWIR InAs/InAsSb T2 SLS Bulk Properties
However, in practice, Sb segregation effects can negate the benefit of higher Sb fraction; see [16] for more detailed discussions. The short hole diffusion length in (V)LWIR InAs/InAsSb T2 SLS can be traced to the large hole conductivity effective mass along the growth direction. From the expressions for diffusion length (\(L=\sqrt{D\tau_{r}}\)), diffusivity (\(D=\mu k_{B}T/e\)), and mobility (\(\mu=e\tau_{c}/m^{**}\)) we can write the diffusion length along the \(i\)th direction as \(L_{i}=\big{[}\big{(}k_{B}T/m_{i}^{**}\big{)}\tau_{r}\tau_{c}\big{)}^{1/2}\), where the roles of the conductivity effective mass \(m_{i}^{**}\), the minority carrier recombination lifetime \(\tau_{r}\), and the collision (momentum relaxation) time \(\tau_{c,i}\) are delineated. It can be seen that larger conductivity effective mass leads to shorter diffusion length. We note that the conductivity effective mass differs from the band-edge curvature effective mass, and we therefore use a \"double-starred\" notation to emphasize the distinction between the conductivity effective mass and the band-edge curvature effective mass (typically with \"single-starred\" notation). The conductivity effective mass is a thermally averaged quantity that accounts for the anisotropy and non-parabolicity in the superlattice band structure, and is given, approximately, by the expression \(m_{i}^{**}\approx k_{B}T/\langle v_{i}^{2}\rangle\), where \(v_{i}\) is the band structure-derived group velocity along the \(i\)th direction. Detailed discussions on the conductivity effective mass are found in [20; 21]. Figure 1b shows the calculated electron conductivity effective masses along the growth direction \(z\) (\(m_{\text{n},\text{z}}\)**) and the in-plane direction \(x\) (\(m_{\text{n},\text{x}}\)**) as functions of cutoff wavelengths for the same sets of superlattices, discussed in Figure 1a; Figure 1c shows the corresponding hole conductivity effective masses \(m_{\text{p},\text{z}}\)** and \(m_{\text{p},\text{x}}\)**. The numerical values of the various conductivity effective masses for a 5.7 \(\upmu\)m cutoff and a 13 \(\upmu\)m cutoff (\(m\),\(n\))-InAs\(/\)InAs\({}_{0.5}\)Sb\({}_{0.5}\) T2 SLS, (\(m/n\)) = 4, are tabulated in Table 1. In general, for the cutoff wavelength range shown in Figure 1, the electron conductivity effective mass \(m_{\text{n},\text{z}}\)** is quite small in InAs/InAsSb T2 SLS with higher (-50%) Sb fraction since the wavefunctions of the lowest conduction sub-bands are only weakly confined in the relative shallow conduction band quantum wells. On the other hand, the hole conductivity effective mass \(m_{\text{p},\text{z}}\)** can be very large in the (V)LWIR superlattices where the InAsSb hole quantum wells are separated by wider InAs layer. Here, a higher Sb fraction reduces the InAs/InAsSb T2 SLS period, and is therefore helpful in reducing the value of \(m_{\text{p},\text{z}}\)**. Nevertheless, for the InAs/InAsSb T2 SLS, \(m_{\text{p},\text{z}}\)** can still be more than two orders of magnitude greater than \(m_{\text{n},\text{z}}\)** in the (V)LWIR, even with 50% Sb (see Table 1). Therefore, we expect the hole diffusion length to be much shorter than the electron diffusion length for (V)LWIR InAs/InAsSb T2 SLS. Another important aspect shown in Figure 1 is superlattice conductivity effective masses anisotropy. Figure 1b shows that while the growth direction and in-plane electron conductivity effective masses, \(m_{\text{n},\text{z}}\)** and \(m_{\text{n},\text{x}}\)**, respectively, are very similar at below 6 \(\upmu\)m \begin{table}
\begin{tabular}{c c c c c} \hline Carrier Type & \(\lambda_{\text{c}}\) (\(\upmu\)m) & \(m_{\text{z}}\)** (\(m_{\text{0}}\)) & \(m_{\text{x}}\)** (\(m_{\text{0}}\)) & \(m_{\text{z}}\)**/\(m_{\text{z}}\)** \\ \hline electron & 5.7 & 0.0201 & 0.0205 & 0.982 \\ electron & 13.0 & 0.0313 & 0.0212 & 1.48 \\ hole & 5.7 & 1.53 & 0.133 & 11.5 \\ hole & 13.0 & 7.89 & 0.0908 & 86.8 \\ \hline \end{tabular}
\end{table}