Spin exchange between a quantum well and the donor layer in ${\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}}_{1-x}{\mathrm{C}}_x$

Electron-spin-resonance (ESR) data from modulation-doped ${\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}}_{1-x}{\mathrm{C}}_x$ heterostructures are reported. The experiments at high ESR frequency (94 GHz) and corresponding high magnetic field (3.5 T) enabled us to separate the ESR of the conduction electrons in the quantum well from the ESR of the phosphorous donors in the doping layer. At temperatures above 20 K a thermally activated electron-exchange process between the quantum well and the donor layer is observed. The effective activation energy of this process is $\approx 19$ meV. The g factors of the conduction electrons and of the P donors were determined with high absolute accuracy.