Why won't my BST get written to a file?

I'm trying to write my BST into a text file but some how it's not working. I would like to know where I messed up at because as of now, nothing is being written into the file. The problem is in the BinaryTree.java. The display() method is where I'm trying to place the items into Student.txt file.

Here's my Node.java:

class Node  {
    Student data;
    Faculty data2;
    Node left;
    Node right;

    public Node(Student data) {
        this.data = data;
        this.left = left;
        this.right = left;
    }

    public Node(Faculty data2) {
        this.data2 = data2;
        this.left = left;
        this.right = right;
    }
}

Here's my BinaryTree.java:

int index = 0;
String[] sa = new String[index];

public void studentArray() {
    studentArray(root,index);
}

public int studentArray(Node root, int index) {     
    if(root.left != null) {
        index = studentArray(root.left, index);
    } 
    sa[++index] = root.data.getLastName().toString();
    if(root.right != null) {
        index = studentArray(root.right,index);
    }
    return index;
}

public void displayStudent(Node root) throws IOException { 
    if(root != null) { // If root isn't empty.
        if(root.left != null) { 
            displayStudent(root.left); // Recursively display left nodes. 
        }
        System.out.println(root.data.toString()); // Print to the console data that's in the root in order.
        if(root.right != null) {
            displayStudent(root.right); // Recursively display right nodes. 
        }
    }

    String file = "Student.txt"; 
    FileWriter fw = new FileWriter(new File(file));

    try {
        for(index = 0; index < sa.length; index++) {
            fw.write(sa[index] + " ");
        }
        fw.close();
    } catch(Exception e) {
        System.out.println("File not found.");
    }
}

Here's my Main.java:

import java.io.IOException;

public class Main {
    public static void main(String[] args) throws IOException {
        Student student1 = new Student("Mike", "Piazza", "S3123456");
        Student student2 = new Student("Jack", "Jill", "S3123456");
        Student student3 = new Student("Alice", "Jones", "S3123456");

        BinaryTree bt = new BinaryTree();
        bt.insertStudent(student1);
        bt.insertStudent(student2);
        bt.insertStudent(student3);
        bt.displayStudent(bt.root);
    }   

Here's my Student.txt file:

*displays nothing*