SYSTEM_USER Always Return The Value NT AUTHORITYNETWORK SERVICE

I use asp.net 2.0 to access a SQL Server Express. I want to record the user who modify the database, so I create a trigger as follows:

BEGIN
 -- SET NOCOUNT ON added to prevent extra result sets from
 -- interfering with SELECT statements.
 SET NOCOUNT ON;

    -- Insert statements for trigger here
 UPDATE Customer
 SET UpdateUser = SYSTEM_USER
 WHERE ID = (SELECT ID FROM inserted)
END

In IIS ,I configed to use Integrated Windows authentication, The problem is when I modify the database, UpdateUser always setting to NT AUTHORITYNETWORK SERVICE.

How to record the user as the format DomainUsername?

 Thanks,

Alvin