C#中数组中字符串的二进制搜索

好吧，所以我已经在这个错误上呆了大约18个小时，完全迷失了方向。我试图做的是进行二进制搜索，其中搜索从数组的中间开始，然后每次通过将搜索到的项与中间项进行比较来消除一半的数组。到目前为止，我的代码没有产生错误，除非我试图比较搜索到的术语是否大于中间术语。我知道我正在尝试比较两个字符串，所以大于不适用，但我不知道其他方法

public partial class MainWindow : Window
{
    public MainWindow()
    {
        InitializeComponent();
    }
    string[] contacts = new string[20];
    private void button1_Click(object sender, RoutedEventArgs e)
    {
        listBox1.Items.Clear(); //Clears the ListBox of all previous items
        if (!File.Exists("Week3List.txt")) //Verifies that the file exists
        {
            MessageBox.Show("You need to write the file first", "Validation", MessageBoxButton.OK); //Notifies the user if the file does not exist
            return;
        }
        using (StreamReader sr = new StreamReader("Week3List.txt")) //Designates the path to the file that was created
        {
            try
            {
                contacts = File.ReadAllLines("Week3List.txt");
                Array.Sort(contacts);
                foreach (string contact in contacts)
                {
                    listBox1.Items.Add(contact);
                }
                sr.Close(); //Closes the StreamReader
            }
            catch (Exception ex) //A catch to handle access errors
            {
                MessageBox.Show(ex.ToString(), "Exception Handler", MessageBoxButton.OK); //Adds the error message to the ListBox
            }
        }
    }
    private void button2_Click(object sender, RoutedEventArgs e)
    {
        bSearch(contacts);
    }
    private void bSearch(string[] contacts)
    {
        int index = Array.BinarySearch(contacts, textBox1.Text);
    }
    public int BinarySearch(string[] contacts, string searchTerm)
    {
        int first = 0;
        int last = contacts.Length - 1;
        int position = -1;
        bool found = false;
        int compCount = 0;
        searchTerm = textBox1.Text;
        while (found != true && first <= last)
        {
            int middle = (first + last) / 2;
            if (contacts[middle] == searchTerm)
            {
                found = true;
                position = middle;
                compCount++;
                MessageBox.Show("Your search has been found after " + compCount + "comparisons.");
            }
            else if (contacts[middle] > searchTerm)
            {
                last = middle;
                compCount++;
            }
            else
            {
                first = middle;
                compCount++;
            }
        }
        return position;
        return compCount;
    }
}
}

有人看到我哪里错了吗？或者知道一种方法可以将两者进行比较，以获得更大或更小的值吗？我想，因为它是排序的，它可能会比较第一个字母，并根据它来确定，但我错了。