The one-dimensional (1-D) Z-complementary sequence set (ZCSS) has been widely employed in communications engineering. The concept of 1-D ZCSS can be extended to the two-dimensional (2-D) Z-complementary array set (ZCAS) where the 2-D aperiodic autocorrelations of constituent arrays sum to zero for the 2-D certain shifts.2-D ZCASs play an important role in radar, 2-D multi-carrier code-division multiple access (MC-CDMA) systems, multiple-input and multiple-output (MIMO) systems, ultra wideband communication systems, etc.In this paper, we focus on designing new 2-D ZCASs by using Boolean functions and concatenation.We first present a direct construction of (2k,2k,2n,142m,2n,122m)-ZCASs by employing Boolean functions.The constructed ZCASs have the largest known zero correlation zone (ZCZ) width and low peak to-mean envelope power (PMEPR).Next, we provide a class of 2-D ZCASs with ZCZ around the end-shift position by using concatenation, which have new lengths and large ZCZ widths.