The main challenge in dielectric measurements is producing good contacts where good means ohmic. That is absolutely essential and an art. It might be possible that your contacts are not ohmic. It very often happens that people get contacts with some rectification properties. That is a killer for those measurements. The problem is that you will always get some results from your analyzer and start interpreting sample physics which in fact might be dominated by contact physics. This may serve as a start. I am not an expert in giving advice how to prepare the contacts.

I faced the the same problem while measuring dielectric properties of thin films,. Although i don't exactly know the origin of the problem, but as Christian Binek said it may be due to contact problem. I overcame the problem by preparing thin films with lower roughness and measuring CV at lower frequencies.

Hello Zhonghua,

It will help if you elaborate on your problem. Ohmicity of contacts, as already pointed out, is an important factor in measuring impedance of a sample accurately. There are few other important issues. You say that you obtained negative impedance. Are you measuring both resistance and reactance, and both components are negative? Are they negative over the whole range of frequencies of measurement? What is the frequency range? Is your measurement 2-terminal or 4-terminal? Did you calibrate your impedance analyser?

For frequencies above resonance, there is a phase change that could be seen as a change of impedance sign. This could be solved by taking the modulus of impedance, but depending on your application for the dielectric constant, it could be better to be away from the resonance frequency.