Vertical transport in GaAs/Ga1-yAlyAs barrier structures was investigated using current-temperature (I-T) measurements in the dark. The samples studied had 500 A thick GaAs/Ga1-yAlyAs (0 <= y <= 0.26) linearly graded barriers between the n(+)-GaAs contacts and the Ga0.74Al0.26As central barrier containing N-w (= 0, 4, 7 and 10) n-doped GaAs quantum wells of width 35 angstrom. The thickness of Ga0.74Al0.26As barrier between the wells was 310, 135 and 77 angstrom for the samples with N-w = 4, 7 and 10, respectively. The vertical current was measured as a function of temperature (3.5-295 K) at applied voltages in the range 0.01-0.7 V. The total barrier height (Delta U-m) and the space charge density in the sample with N-w = 0, and the effective barrier height (Delta E) for the samples with N-w = 4, 7 and 10 were determined by analysing the experimental I-T characteristics using drift-diffusion theory for thermal current. The variation of Delta U and Delta E with applied voltage was discussed in connection with various dark current mechanisms in barrier structures, including thermionic emission, Fowler-Nordheim, tunnelling and sequential resonant tunnelling. (C) 2008 Elsevier Ltd. All rights reserved.