A sample carrier (3) for thinning a sample (1) taken from e.g. a semiconductor wafer. The sample carrier comprises a rigid part (5), e.g. made of e.g. copper, with an outer boundary (6), and a supporting film (4), e.g. made of carbon, extending beyond the outer boundary. By placing the sample on the supporting film, the sample can be attached to the rigid structure using e.g. IBID. The supporting film aligns the samples when they are placed onto it. After attaching the sample to the rigid structure the sample can be thinned with e.g. an ion beam, during which thinning the supporting film is locally removed as well. The invention results in better alignment of the sample to the sample carrier, and also in more freedom how the sample is transported from the wafer to the sample carrier, e.g. with the help of an electrically charged glass needle (2). The latter eliminates the attaching/severing steps that are normally associated with the transport of a sample to a sample carrier.