How is current produced in semiconductors or metals? I think current is the movement of electrons through the wire or semiconductor, thus when I press the switch of the light bulb the  electrons go from positive part to tungsten and light is produced. Another view point is that the electrons don't move and a wave goes through the device and current is produced, but what is this wave? In this view point electrons don't move at all.
 A: In a semiconductor, current is produced in two different ways. There are the electron current and the hole current. The electron current is produced when electrons are pushed from the negative terminal into the semiconductor.
Holes are positions in the semiconductor atoms that can be but are not occupied by electrons. An atom with a hole can "rob" the electron of an adjacent atom to fill the hole, causing the adjacent atom to lose an electron and get a hole, therefore effectively "conducting" the hole. In a circuit, holes current is produced when electrons in a semiconductor are taken away by the positive terminal.
In both electron current and hole current, electrons travel in the same direction, from the negative terminal to the positive terminal. However, holes can be seen as imaginary particles that bear positive charge and travel in the opposite direction from the positive to the negative terminal.
Note that both kinds of current exist in any given semiconductor with varying significance. These are not two different models of the same phenomenon, but rather two distinct phenomena that both contribute to the total current in a semiconductor. In a nutshell, they can be distinguished by seeing electron current as pushing electrons into the semiconductor and hole current as pulling electrons from the other side. In doped semiconductors, the ratio of free electrons and holes are modified, so doped semiconductors may have a very low hole count and high free electron count or vice versa, making one of the two types of current the "dominant" current in the semiconductor.
A: When the switch is closed the information is communicated to the whole circuit via electromagnetic waves at (less than) the speed of light.  This means that an electric field, which the mobile charge carriers feel, is set up in the wires almost instantaneously.  The movement of the mobile charge carriers is the electric current and that current exists in all parts of the circuit.
A: You should understand that the battery source is not a supplier of electrons. The electrons are inside the metal. The physics of semi-conductors and metal conductors are a little different. Let's start with conductors. A conductor is characterized by the availability of free electrons within the metal if you supply a little energy to liberate it. They have comparably large atomic sizes (like iron) and hence the valence the valence electrons will be less attached to the nucleus. So a little energy is required to liberate the electrons from the atom and make them free. Once they are free, they could move through the crystal lattice in any direction. That's why they are called free electrons. They have zero potential energy. The total energy of a free electron appears as it's kinetic energy. Now this energy to liberate electrons can be given in many ways depending on the material. If you have a good conductor of heat, supplying some heat will free the electrons. Energy from chemical reactions could release electrons from ionic metals. If you have a photosensitive material, irradiating it with a photon of sufficient energy could do the job.
In electric circuits, we use the battery as the supplier of this energy to create the valence electrons in the metal. Not only they free the electrons, but also give some extra energy in order to give energy for the electrons to move. So a battery is an electrical energy source. By some process, this electrical energy is produced within the battery (may be a chemical reaction). The two electrodes of the battery (anode and cathode) are separated by a dielectric or an insulator, to prevent the direct flow of energy from the anode to the cathode.
Now you connect the battery to a bulb through a wire. When you switch on the light bulb, you don't feel anytime lag to push the switch on and the glow of bulb. Both takes place at the same time. This is where you have misunderstood. It's not the electrons from the battery that goes all along the entire wire and finally reach the bulb and make it glow. Of course the electrons in the battery has a job. The electrons produced by some reaction inside the battery carries some energy, call it as it's kinetic energy. This electron interacts with an electron in the metal wire situated next to it. Two electrons come closer creates electric repulsion and one imagine that the two fly off apart. But it's not like that. The electron from the battery cannot go back as there is a continuous supply of energy from that side and the energy has to go from a higher concentration region to a lower concentration region.
So due to repulsion, the second electron moves forward. Yes, the electron electron interaction increases repulsion and this repulsive energy is stored as the system's potential energy. An increase in potential energy constitutes an unstable state. So the electron try to lose that energy by converting it into it's kinetic energy. Thus the electron moves and sees the next electron. They interact and the third electron moves on. There will cause some collisions with the atoms and some of the electrons loses their kinetic energy as the collisions are all inelastic. But in conductors, the possibility of such collisions will be very less. This is the reason why we have no metals as perfect conductors with zero resistance. resistance is created as a result of the lose of energy of the electrons by making collisions with the atoms. In solids, the inter-atomic spaces are very little; so the electrons find themselves a little tougher to move through. The lost energy develops inside the lattice as lattice heat and is irretrievable. This is why resistors become hot after sometime.
Now this process continues all the way along. So the role of electrons here is just carriers of electrical energy from the battery to the load. The load (here the bulb) has some resistance. depending on that resistance, the electrons make collisions inside the material atoms and liberates their energy to the bulb. This heat glows the tungsten filament which we see as light. Te rest of energy is taken towards the cathode.
You have studied that a charge has it's own electric field. When a charge is placed near some external electric field, the charges accelerates. This accelerated charge emit electromagnetic waves and waves are nothing but electromagnetic energy. Every electromagnetic waves travel through a medium as like light travelling through the same medium. The electrons cannot reach from the battery to the bulb within an instant of time. It's because the electron's velocity get averaged due to collisions. So the electron take sufficient time to go from one end of wire to the next. But that's not observed practically. But electromagnetic "news" could travel lakhs of kilometer distances within a very short interval of time which you may feel as an "instantaneous process". Remember that electromagnetic waves travel at the speed of light.
Conventional direction of current flow is opposite to the flow of electrons. It's nothing but so as to keep the direction of a conventional positive charge goes in the direction of the applied field. So we could visualize this whole process as like an electron going from the cathode to the light bulb, dumping it's entire energy there and goes to the anode. We draw a current direction just opposite to it. But the actual process is the wave picture. The other one is just a visualization comfort technique. That's all. It's because we are only concerned with the direction of current flow in electronics rather than the phenomena induced by moving charges (something we deal with in electrodynamics). 
A: The nature of mobile careers  in metals and semiconductors is quite different, as it has been pointed by @busukxuan and @UKH: in the former the mobile electrons are already present, whereas in the latter they are present due to thermal or optical excitation (unless the electric field is so strong that it can excite electrons from the valence band to the conduction - effect rarely observed in actual semiconductors, but easily obtained in periodic semiconductor structure, so-called superlattices).
The transport however can be thought of in both cases as carried out by non-interacting electron-like particles. It is however incorrect to think that an electron travels all the way from the negative to positive pole of the battery: in fact the electrons participate in chaotic thermal motion, being scattered all the time by other electrons and the crystal lattice. This motion is characterized by a thermal velocity $v_{th}$. Due to the electric field generated by the power source the electrons are accelerated somewhat more in the direction of the anode. This excess velocity is however very small compared to the velocity of random motion, so that averaging after many scattering events we have a drift velocity that is much smaller than the thermal one: $$v_{dr} \ll v_{th}.$$ In other words, the electron doesn't go very far from the place where it was before the switch was turned on, but the average displacement of all the electrons is real: some of the are absorbed by the positive pole of the power source, and some are added by the negative one. How do electrons in the middle of the wire know that the switch is turned on? - the know it by the electric field generated due to the displacement of other electrons.
Thus, the true picture is somewhat in between the two alternatives proposed in the question - one could talk about a shock wave of electrons.
