Radiation hardened chips are made on insulating wafers rather than semiconductors to reduce electronic noise reaching junctions, Silicon dioxide or sapphire are used (these type of devices are called silicon on insulator (SOI) and silicon on sapphire  (SOS)) and the junctions are made with wide band gap materials such as silicon carbide or gallium nitride which gives higher tolerances. The chip is further covered with borophosphosilicate glass for shielding from neutron. For more details please  refer "Handbook of Radiation Effects" (Oxford University Press, England 2002)

Your question is very wide. Actually the material depends on various parameters out of which most important are the type of ionizing radiation, type of materials which is compatible for electronics, temperature concern etc. For gamma and X-ray shielding high Z materials are preferred, for beta perspex or Al may be good choice. For neutron field some hydrogeneous material with Neutron capturing material(like Boron) may be good choice. For HCP shielding is not much concern due to smaller range.But only these material can not be used in semiconductor/electronic devices, where Si or Ge are used.In such situation an outer covering of shielding material with ceramics may be used.

It is the use of SOI and not the ceramic that makes the component radiation hard. Actually borophosphosilicate glass is bad for shielding thermal neutrons as the B-10 isotope gives out highly ionising reaction products that produce single event effects. The only package for reducing total ionising dose effects from electrons utilises a graded shield with layers of low-Z/high-Z/low-Z to minimise and then absorb the bremsstrahlung. This has to be optimised to a particular electron spectrum.

Thanks guys for all your answers.

I'll try to implement your solutions to my device

It depends on the kind of radiation… and if you heave a device that must not be exposed, i.e., it must be shielded. I suggest you be more especific in your question!