In a recent work, we have shown that speaker verification systems can be built where both features and classifiers are directly learned from the raw speech signal with convolutional neural networks (CNNs). In this framework, the training phase also decides the block processing through cross validation. It was found that the first convolution layer, which processes about 20 ms speech, learns to model fundamental frequency information. In the present paper, inspired from speech recognition studies, we build further on that framework to design a CNN-based system, which models sub-segmental speech (about 2ms speech) in the first convolution layer, with an hypothesis that such a system should learn vocal tract system related speaker discriminative information. Through experimental studies on Voxforge corpus and analysis on American vowel dataset, we show that the proposed system (a) indeed focuses on formant regions, (b) yields competitive speaker verification system and (c) is complementary to the CNN-based system that models fundamental frequency information.