built-in electric field, and (2) a decrease in backbarrier doping that reduces the 2DEG density while leaving the potential well intact that attracts carriers from surface states. Methods Sample growth. All samples investigated in this study were grown by metal-organic chemical vapour deposition (MOCVD). C-plane sapphire substrates with 4° misorientation towards sapphire-a-plane were used to achieve smooth N-polar (Al,Ga)N films 4. A 1.4 μm thick semi-insulating (S.I.) GaN base layer was first deposited using the procedure reported previously. For all samples, the backbarrier layer consisted of a 20 nm thick graded Al x Ga 1−x N layer with x = 0.05 → 0.38 and a 10 nm thick Al 0.38 Ga 0.62 N film, followed by a 0.7 nm thick AlN interlayer, a GaN channel layer with thickness varying from 9 to 20 nm, a 0 or 2.6 nm thick Al 0.46 Ga 0.54 N cap layer, and a 0 or 5 nm thick in-situ SiN x film. The graded Al x Ga 1−x N layers were doped with Si to achieve n-type doping of 4 × 10 18 cm −2 (1st and 2nd series) or 5 × 10 18 cm −2 (3rd series). The SiN x film was grown at 1,030 °C using disilane and ammonia flows of 4.46 μmol/min and 268 mmol/min, respectively. 2DEG concentration measurements. Van der Pauw Hall measurements with indium contacts were performed at room temperature to determine the carrier concentrations. Contactless electroreflectance measurements. For CER measurements the samples were mounted in a capacitor with a half-transparent top electrode made from a copper-wire mesh. An air gap of ~ 0.5 mm was kept between the sample surface and the top electrode. An alternating voltage of ~ 3 kV provided the band bending modulation. Other relevant details on CER can be found in Refs. 32,33. Calculations. A commercial package nextnano++ was used for band profile and carrier concentration calculations 34 that provides solutions for coupled Schrödinger-Poisson equations.