ASP.Net MultiLine TextBox Scroll to Bottom automatically when text is added using JavaScript

HTML

    <asp:TextBox ID="TextBox1" runat="server"></asp:TextBox>
    <asp:Button ID="Button1" runat="server" Text="Button" onclick="Button1_Click" />
    <hr />
    <asp:TextBox ID="TextBox2" runat="server" TextMode = "MultiLine" Height = "100"></asp:TextBox>
    <script type = "text/javascript">
        window.onload = function () {
            var textarea = document.getElementById('<%=TextBox2.ClientID %>');
            textarea.scrollTop = textarea.scrollHeight;
        }
    </script>

Code

    protected void Button1_Click(object sender, EventArgs e)
    {
        TextBox2.Text += TextBox1.Text + "\n";
    }