A novel technique is proposed for controlling the current supplied to a growth-solution by using individual solute components in the liquid-source. One and two liquid-source versions of this method were developed. Criteria were also established for selecting the configuration and characteristic dimensions of the growth cell. In this growth cell liquid-source components are transported to the growth-solution by electromigration, and with minimal influence from other transport mechanisms. A theoretical model for two liquid sources, current-controlled growth was developed for binary and A(3)B(1-x)(5)C(x)(5) ternary compounds. This model describes the composition profile and growth velocity dependence on the growth parameters. In particular, it was shown that depending on the current passed through each of the liquid-sources, layers with increasing, decreasing or uniform compositions could be grown. Numerical simulation results showed a good agreement with the experimental data on the electroepitaxial growth of InAs and InAs1-xPx. The values of the calculated and experimental data for mu(As)rho(ln) and mu(p)rho(ln) were 3.5 x 10(-7) and 8 x 10(-7) cm(3) /s A, respectively. (C) 2002 Elsevier Science B.V. All rights reserved.