I found out the problem in my German recording. I knew I had to open my mouth a bit more when I pronounce an /e/ than in /i/, and I did so. But when I analyzed them in a spectrum, they got all together in the upper-left corner of the vowel chart.
I've also tried to pronounce an [i] when I open my jaw so much as well as in [a] and analyzed it with a normal [i] in spectrum and I found the formants same. And of course, they are perceived the same by ear.
People can pronounce an [a] even if they clench their teeth.