Random Password Generator

I needed to create a random password. First I found this short method, which didn't work. Then I found this guy agreed with me. His code works, but not so hot in my test program. The parameterless Random constructor uses a time-based seed value (per millisecond?) so there are duplicates. The code I ended up with reuses a single Random member.

Then there's the holy grail, which was too much for the requirements I was working with, eight alphanumeric digits only. Simplicity is divine.

private Random m_random = new Random();

public string CreateRandomPassword(int length)
{
    char[] chars = new char[length];

    int index = 0;
    while (index < length)
    {
        char c = (char)m_random.Next(48, 122);
        if (Char.IsLetterOrDigit(c))
        {
            chars[index] = c;
            index++;
        }
    }

    return new string(chars);
}