We fabricated carbon doped InAs/In(x)Ga(1-x)As/In(x)Al(1-x)As heterostructures, which show p-type and n-type conductivity for different In contents. Two-dimensional hole gas in a structure with x = 0.75 has been prepared in the ternary compound, despite the fact that carbon as an n-type dopant in InAs exhibits electron conductivity in In(x)Ga(1-x)As and In(x)Al(1-x)As compounds with high indium content. A special doping design has been employed to obtain hole conductivity. As a result, the conductivity can be tuned from n-type to p-type with the In content and with different doping profiles in these structures. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3557026]