c-axis resistivity of Bi 2 Sr 2 CaCu 2 O y thin films at various oxygen doping: Phase diagram and scaling law He ´le `ne Raffy * , Valentin Toma, Christopher Murrills, Zhi Zhong Li Laboratoire de Physique des Solides, Ba ˆt.. 510, Universite ´ Paris-Sud, 91405 Orsay, France Available online 4 May 2007 Abstract We compare the temperature-dependence of the in-plane and c-axis resistivity, q ab (T) and q c (T), of Bi 2 Sr 2 CaCu 2 O y . Measurements have been made on a thin film deposited on a vicinal substrate, examined in various doping states by removing oxygen in steps from the overdoped to very underdoped states. q c (T) exhibits a metallic behaviour at high T followed by a semiconducting-like behaviour at lower T, interrupted by the superconducting transition: q c (T) is minimum at T min and maximum at T P , T min is defined as the temper- ature where the pseudogap opens. T min , 1.4 larger than the temperature T * , below which the pseudogap signature is seen in q ab (T), exhib- its the same dependence on hole doping p. A phase diagram (T, p) is established with these characteristic temperatures. Interestingly q c (T) normalized by its value at T min obeys a scaling law vs T/T min . This confirms that T min is the important energy scale in the normal state c-axis transport. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Bi 2 Sr 2 CaCu 2 O y ; Anisotropy; Pseudogap; Phase diagram; Thin films Among the cuprates, Bi 2 Sr 2 CaCu 2 O y (Bi-2212) exhibits the largest anisotropy, in excess of 10 4 , which is a function of temperature and doping. There is a dramatic difference in the T-dependence of the c-axis and ab-plane resistivities, q c and q ab , which is not expected in a Fermi liquid descrip- tion. In particular, the opening of the pseudogap in the underdoped region manifests itself by an increase of q c (T), whereas it leads to a decrease of q ab (T). In order to compare their behaviour directly, we have simulta- neously studied q c (T) and q ab (T), for a large range of hole doping p. This was possible by measuring the transport properties of a Bi-2212 film deposited on a vicinal sub- strate. We will show how these measurements allowed us to determine the characteristic temperatures, (T, p) phase diagram and scaling laws. We have deposited Bi 2 Sr 2 CaCu 2 O 2 thin films by rf mag- netron sputtering onto vicinal SrTiO 3 substrates ([1]). For this study, the vicinal substrate was 4° off toward (1 0 0). The film, 1500 A ˚ thick, with T cmax (R = 0) = 82 K, was patterned by optical lithography and chemical etching with two orthogonal strips, parallel (x direction) and perpendic- ular (y direction) to the substrate steps, respectively. Gold contacts were sputtered for four point measurements on each strip. Since the anisotropy is weak in the ab-plane and very high between the c-axis and ab-plane, we obtain q ab and q c from the expressions: q ab = q x and q c = q y / sin 2 4° where q x and q y are the resistivities measured along the x and y directions, respectively. Measurements have been made on the same film vs doping by removing oxygen, in 17 steps from the overdoped (OD) to the very under- doped (UD) states, by low-temperature annealing treat- ments as in Ref. [2]. Fig. 1 presents q c (T) and q ab (T) curves obtained at an optimal doping. The behaviour of the resistivity q ab (T) at various decreasing doping states is similar to the one we reported previously for Bi-2212 films deposited on classical SrTiO 3 substrates [2]. Briefly, in the OD region, a linear variation is observed at high T while, at lower T, a less rapid decrease, with q ab (T)= q 0 + aT n (1 6 n < 1.3, n being close to 1 at optimal doping) is seen. In the UD region a decrease 0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.04.209 * Corresponding author. E-mail address: raffy@lps.u-psud.fr (H. Raffy). www.elsevier.com/locate/physc Physica C 460–462 (2007) 851–853