Such was the demand for tickets that police had to intervene to restore order when brawls broke out as fans tried to queue barge as the remaining semi-final tickets went on sale on Tuesday. They were sold out within an hour.
Di Maria says that Real have progressed as a side since their defeat in the group stage.
"We weren't at our best in the two group matches, but that's changed now. Our defence is more compact and we've got more confidence," said the 25-year-old. "Dortmund are very similar to us, they're very good on the counter attack. We've experienced that already."
Jurgen Klopp's Dortmund took four points off Real in the group stages, beating Jose Mourinho's side 2-1 at home last October before drawing 2-2 in Madrid, as the Germans finished top of Group D.
On the huntBorussia are looking for a hat-trick of home victories against Spanish league sides after their dramatic 3-2 quarter-final, second-leg win over Malaga.
Poland striker Robert Lewandowski is reported to be fit, despite bruising his leg in Saturday's 2-0 win over Mainz 05. But both defensive midfielders Sven Bender, inflamed pelvis, and captain Sebastian Kehl, foot ligament, face a race against time.