We discuss the choice and implementation of intervalley potentials in the so-called two-band $k·p$ model for the opposite $X, Y$, or $Z$ valleys of silicon. We focus on the description of valley splittings in Si/SiGe heterostructures for spin qubits, with a particular attention to alloy disorder. We demonstrate that the two-band $k·p$ model reproduces the valley splittings of atomistic tight-binding calculations in relevant heterostructures (SiGe spikes, wiggle wells, $\cdots$), yet at a much lower cost. We show that the model also captures the effects of valley-orbit mixing and yields the correct intervalley dipole matrix elements that characterize manipulation, dephasing, and relaxation in spin and valley qubits. We simulate a realistic Si/SiGe spin-qubit device as an illustration, and discuss electron-phonon interactions in the two-band $k·p$ model. Beyond spin qubits, this model enables efficient simulations of SiGe heterostructure devices where spin and valley physics are relevant.

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• Valley degrees of freedom
• Quantum dots
• Qubits
• Semiconductors
• Spin