So you've stepped in a minefield. Reference electrodes have a single function: to provide a stable potential for accurate voltage measurement and control. Depending on the conditions any metal can be a good reference, but generally speaking the best reference materials have known redox couples with controlled relative quantities. Standard reference elctrodes are all of this type: Ag/AgCl, SCE (Hg), Hydrogen electrode (H+ reduction is catalyzed by Pt).
Because a redox couple is necessary to maintain a stable potential, non-reactive metals are not necessarily good. Pt is good because it catalyzes hydrogen reduction, not because it is a good reference itself so it doesn't work very well in aprotic solvents. Ag is good in many solutions because it readily oxidizes with various states (Ag+, AgCl, AgO), which stay on the surface and serve as a good couple. To that end, corroding materials like copper or mild steel (or pure iron) actually serve as good reference electrodes, while non corroding materials like gold, stainless steals, or nickel [alloys] are very poor reference electrodes--a little bit of current and their potentials go all over the place. Keep in mind, however, that if you are sensitive to the products of those corrosion reactions, they may not be a good choice. If you have copper in your system, then copper is a perfectly acceptable reference electrode (there is even a standard copper/copper sulfate reference electrode).
If you are unsure and can't find a reference you can put the Cu electrode in your working solution. First measure it's open circuit which should be stable (after some settling period). Then pass a small amount of current through it (nA to uA depending on size) and see how much it changes--it should be no more than a few mV--and whether it reverts to trend when the current goes away.
Of course all of this becomes irrelevant if you are using copper as the quasi-reference in a 2-electrode setup where the total potential is relevant, but that is another long answer.
A reference electrode must be an electrode which has a stable and well-known electrode potential. If yes. You can use a Cu or Ag metal as a reference electrode.
People have been using different metals (like Pt, Ag (in non-aqueous)) as reference electrode but the metal should not oxidize or reduce in the applied potential range. Cu would be oxidized very easily, so refrain using Cu.
in general, the electrodes are made up of metals but now blends or organics are also in use. To use any metal as electrode, the purity is essential as the electrode either accepts electron (cathode) or releases electrons (anode). So any metal whose electron releasing or acceptance process is not effected then one can definitely use the pure metal as electrode. However, calibration with respect to reference electrode is needed.
Most of electrodes are made up of metals, the reference electrode must be stable during running experiments, the type of electrode is selected with accordance with electrode potential required,
Artur Braun has good advice. Make the experiment himself. The electrode must to hold the potential under current. This is nonpolarisation!!! You must to have nonpolarisation electrode in that degree how many necessary. OK
You give too little information to provide a correct answer. What is the redox- or insertion reaction you are looking at. For example, when you are looking at Li intercalation you need a reference electrode that fixes the Li-activity. This could be pure lithium, but also a two-phase lithium compound. The reference electrode should always be coupled through a reaction path to the active ion/complex. A pure metal electrode in the lithium case would not provide a well defined potential (activity), unless it was lithium.
Cu is not a good choice in aqueous media. A more noble metal should work better, provided that it is not oxidized under the tested experimental conditions.
So you've stepped in a minefield. Reference electrodes have a single function: to provide a stable potential for accurate voltage measurement and control. Depending on the conditions any metal can be a good reference, but generally speaking the best reference materials have known redox couples with controlled relative quantities. Standard reference elctrodes are all of this type: Ag/AgCl, SCE (Hg), Hydrogen electrode (H+ reduction is catalyzed by Pt).
Because a redox couple is necessary to maintain a stable potential, non-reactive metals are not necessarily good. Pt is good because it catalyzes hydrogen reduction, not because it is a good reference itself so it doesn't work very well in aprotic solvents. Ag is good in many solutions because it readily oxidizes with various states (Ag+, AgCl, AgO), which stay on the surface and serve as a good couple. To that end, corroding materials like copper or mild steel (or pure iron) actually serve as good reference electrodes, while non corroding materials like gold, stainless steals, or nickel [alloys] are very poor reference electrodes--a little bit of current and their potentials go all over the place. Keep in mind, however, that if you are sensitive to the products of those corrosion reactions, they may not be a good choice. If you have copper in your system, then copper is a perfectly acceptable reference electrode (there is even a standard copper/copper sulfate reference electrode).
If you are unsure and can't find a reference you can put the Cu electrode in your working solution. First measure it's open circuit which should be stable (after some settling period). Then pass a small amount of current through it (nA to uA depending on size) and see how much it changes--it should be no more than a few mV--and whether it reverts to trend when the current goes away.
Of course all of this becomes irrelevant if you are using copper as the quasi-reference in a 2-electrode setup where the total potential is relevant, but that is another long answer.
You need to tell more about what you intend to measure and how.
If you are going to use a true reference electrode, then yes the copper-copper sulfate ref is well known, and especially useful if you are working in concentrated copper sulfate electrolytes, e.g. studying copper hydrometallurgy, or copper tankhouse processes such as electrowinning and electrorefining, where SSEs might become contaminated.
There are recipes you can follow to build one yourself e.g. http://corrosion-doctors.org/Corrosion-Thermodynamics/Reference-Half-Cells-Copper.htm
it is actually one of the cheapest (inexpensive copper sulfate and copper wire), safest (no mercury), and easiest to construct (no anodising of silver wire needed) to produce in the lab.
In my limited experience the copper sulfate ref. needs a little more maintenance than an SCE or SSE. It's not that much extra work; just make sure to check (calibrate) the copper reference electrode's voltage vs. a commercial ref. electrode e.g. SSE before use. If your test is a long one i.e. more than a couple of hours, it's good practice to check again at the end of your test hat the voltage hasn't drifted.
On the other hand... if you intend just using a copper wire as a pseudo-reference electrode, (without a saturated solution junction), in certain tests that can also work, I believe some people have used Cu/Cu/Cu (working, counter & ref) in measuring copper electrorefining processes, with just the tip of a copper wire covered in heat-shrink sleeve as the ref... but it will not always be suitable for the reasons already discussed.
Ag/AgCl electrodes reference voltages are KCl concentration dependent. I am using 3M KCl solution and thus getting + 0.210 V. If i want to give 1-2 V supply at the gate through Ag/AgCl reference electrode . Can we give it by adding a power supply to the RE and grounding the other end with the source of ISFET device?