Low-temperature mobility of holes in $\mathrm{Si}∕\mathrm{Si}\mathrm{Ge}$ $p$-channel heterostructures

We present a theory of the low-temperature mobility of holes in strained SiGe layers of $\mathrm{Si}∕\mathrm{Si}\mathrm{Ge}$ $p$-channel heterostructures. Our theory must not be based on the unclear concept of interface impurity charges assumed in the previous calculations, but takes adequate account of the random deformation potential and random piezoelectric field. These appear as effects arising from both lattice mismatch and interface roughness. It is proved that deformation potential scattering may be predominant over the well-known scattering mechanisms such as background doping, alloy disorder, and surface roughness for a Ge content $x\gtrsim 0.2$, while piezoelectric scattering is comparable thereto for $x\gtrsim 0.4$. Our theory turns out to be successful in providing a good quantitative explanation of recent experimental findings not only about the low value of the hole mobility but also its dependence on carrier density as well as its decrease with Ge content.

Figure 1

Ratio $Q={\mu }^{\mathrm{fin}}∕{\mu }^{\mathrm{infin}}$ between the 2DHG mobilities, calculated with a finite and an infinite potential barrier, vs sheet hole density $p_s$ for various scattering mechanisms: alloy disorder $Q_{\mathrm{AD}}$, surface roughness $Q_{\mathrm{SR}}$, deformation potential $Q_{\mathrm{DP}}$, and piezoelectric charges $Q_{\mathrm{PE}}$. The triangular QW is made from $\mathrm{Si}∕{\mathrm{Si}}_{0.8}{\mathrm{Ge}}_{0.2}$ with a barrier height $V_0=0.148\mathrm{eV}$ and a SiGe layer thickness $L=200\mathrm{\AA }$.

Figure 2

Different 2DHG mobilities of the $\mathrm{Si}∕{\mathrm{Si}}_{0.8}{\mathrm{Ge}}_{0.2}$ QW in Fig. 1 vs hole density $p_s$. The solid lines show the calculated mobilities limited by: alloy disorder ${\mu }_{\mathrm{AD}}$, surface roughness ${\mu }_{\mathrm{SR}}$, deformation potential ${\mu }_{\mathrm{DP}}$, piezoelectric charges ${\mu }_{\mathrm{PE}}$, and overall ${\mu }_{\mathrm{tot}}$. The $4\mathrm{K}$ experimental data reported in Ref. 12 are marked by squares.

Figure 3

Different 2DHG mobilities of the $\mathrm{Si}∕{\mathrm{Si}}_{0.8}{\mathrm{Ge}}_{0.2}$ QW in Fig. 1 vs SiGe thickness $L$. The interpretation is the same as in Fig. 2.

Figure 4

Different 2DHG mobilities of the $\mathrm{Si}∕{\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ triangular QW vs Ge content $x$ under a SiGe layer thickness $L=200\mathrm{\AA }$ and a hole density $p_s=2\times {10}^{11}{\mathrm{cm}}^{-2}$. The interpretation is the same as in Fig. 2. The dashed line refers to the calculation based on alloy disorder alone without screening and with an alloy potential $u_{\mathrm{al}}=0.74\mathrm{eV}$. The $4\mathrm{K}$ experimental data reported in Refs. 3, 8 are marked by filled squares, and in Ref. 11 by open one. [Note the ordinate axis scale is distinct from that in Figs. 2, 3.]