If you want to get a thicker back then you have to teach yourself how to pull a weight using your back and not your arms. All back movements come from doing a pulling movement but the muscles are all interconnected and it is often difficult to specifically isolate one muscle group in the back.
The complexity of the muscle fiber arrangement in your back means that because the fibers run in several different directions the pulling in only one plane will not build sufficient size and strength in your back. This means that you will need to separate each movement by lifting at every angle that you can to help with your symmetry and size.
Building a solid foundation for your back development comes from always using full range of motion (ROM) and only use your helper muscles like your biceps in the last few reps of a set. Similar to training triceps the position of your elbow is crucial when training your back.
When you flare your elbows outwards you will activate the upper part of your lats like your rhomboids and traps. But if you drop your elbows and tuck them close to your body you will be working the lower portion of your lats and they will grow in length.
It is also a good idea to try using a grip where your wrists are pronated with your palms facing away or down from you as this will help to minimize the use of the biceps in the pulling movement and isolate the lats more effectively.
Full ROM movement is essential when you are doing chin-ups or pull-ups so you need to keep a weary eye out for your lack of full range of motion as you start to fail when doing these movements. If you reach failure and you are training with a partner you could finish off with assisted lifts, or do lat pull-down or use bands.
If your objective is to gain both size and strength in your back then the following workout routine specifically for back that you train twice a week will certainly help you add some serious muscle to your back. Please always be aware of your full range of motion and squeezing your elbows behind you when you pull.
Day 1: Strength
Exercise Sets Reps Rest
Seated Cable Row with a wide grip 4 8 2 min.
Pull-Up 4 8 2 min.
One-Arm Standing Cable Row 4 8 2 min.
Straight-Arm Pull-down 4 12 90 sec.
Day 2: Size
Exercise Sets Reps Rest
Straight-Arm Pull-down 4 12* 90 sec.
Pull-Up 4 12 2 min.
Seated Cable Row wide grip 4 12+ 90 sec.
One-Arm Standing Cable Row 4 8 2 min.
* Straight-arm pull-downs should be done using a second slow contraction on the concentric movement and a 4 second controlled release on the eccentric contraction.
+ You should do 1 or 2 drop sets on the last two sets that you do with this movement.