Why silicon has potential barrier of 0.7?

The detailed answer would involve quantum physics, with terms such as the Fermi level, the Fermi statistics, and the band gap.

In short, a band gap forms in a pure semiconductor crystal lattice, such as that of silicon or gallium arsenide, in a wide temperature range (roughly above the absolute zero and below the melting point of the solid). The bandgap just means that carriers, electrons or holes, cannot occupy energy levels within the bandgap. The bandgap for pure silicon at room temperature is about 1.1eV. In perspective, a particle at room temperature has a thermal energy of 0.026eV, so 1.1 eV is a big chunk of energy that an electron has to acquire to jump the gap. Statistics describes how much of the electron population has the probability of acquiring such energy. Above the forbidden band is called the conduction bands for electrons to roam with or without the aid of an electric field. Below the gap is called the valence band, where holes travel like a vacancy (the lack of an electron). Under the influence of an electric field, holes will have a net drift toward the negative electrode and electrons toward the positive.

Introducing impurities into the pure solid will create trap levels within the band gap. That is, impurities always introduce imperfection. These trap levels act like a rest station, allowing electrons to be excited from the valence band to the conduction band (equivalent to holes being excited from the conduction band to the valence band) in two trips instead of one giant leap, from the top of the valence band to the trap, and then from the trap to the bottom of the conduction band. Introducing boron atoms to the silicon solid will create trap levels near the valence band; arsenic or phosphorus atoms will create traps near the conduction band. The introduction of impurities intentionally is called doping. Boron doping is called p-type (p stands for positive) and arsenic or phosphorus doping, n-type (n stands for negative).

At room temperature, trap levels at slightly different energy levels in the bangap exist, but p-type doping creates traps near the top of the valence band and n-doping creates traps near the bottom of the conduction band. The Fermi level is the 50% energy level where half of the electron population can ideally be above and half below. The Fermi level is normally located where the trap levels are. At the absolute zero temperature, all electrons will be below the Fermi level, i.e. the valence band; all holes will be in the conduction band. At room temperature, some electrons acquire enough energy to jump the gap to occupy the bottom of the conduction band. Because of the forbidden gap, the levels that an electron can occupy are not always present in the bandgap.

Technology has allowed p-doping and n-doping to happen consecutively and in adjacent regions in the silicon solid, to form a pn junction or diode junction. On the p-side, there is an excess of holes. Electrons are in abundancy on the n-side. By the theory of diffusion, excess holes like to diffuse to the n-side and excess electrons to the p-side.

Diffusion is evident in real life. For example, human beings treasure a personal space. If everyone stands near the punch bowl at the party, someone will feel uncomfortable and move away from the table. Viola, diffusion ensures. However, nature is such that when too many electrons move to the p-side, the next electrons will have need more and more energy to overcome the repulsion from the electrons that have already migrated. Holes do the same. Eventually (microseconds is a long time in electronics), things will settle down. The phenomenon is called the thermal equilibrium. Equal numbers of electrons are crossing from p to n as from n to p. This reluctance to have more electrons migrating from n to p than from p to n is described as that an energy barrier has formed. This energy barrier is approximately 0.7 eV, which is the origin of the 0.7 V in the question, when converting from energy in [eV] to a voltage in [V] for one electron. The Fermi level plays a role of 0.7 eV here -- the Fermi level on the n-side has to align to the Fermi level on the p-side. Lining up the Fermi level on both p- and n-sides creates the potential barrier. Applying a positive bias to the p-side relative to the n-side will lower the potential barrier, causing a positive current -- electrons flowing from the negative terminal to the positive, while holes do the opposite.

Mathematically, this phenomenon can be written as I = Io * [exp(qV/kT) - 1], the diode equation. In this equation, what is important for understanding is that I is the current the diode will conduct for a certain voltage applied, V. V assumes a positive value when the anode is biased more positive than the cathode or the pn junction is forward biased. Conversely, the diode is reverse biased. At room temperature, the term (kT/q) takes on a value of 0.026 V. The value for Io for silicon at room temperature is, let us say, 1E-12 A. Plugging the known values in the diode equation for an increasing V, we get the following pairs of (V,I) values:

V [volts] I [amperes]

0 1E-12

0.1 4.58E-11

0.2 2.19E-09

0.3 1.03E-07

0.4 4.80E-06

0.5 2.25E-04

0.6 1.05E-02

0.7 4.93E-01

At a forward bias of 0.7V, the diode is basically a short circuit, meaning the electric field intensity is so high that practically any electrons near the pn junction on the n-side are swept across to the p-side. Recall that holes do the opposite. The potential barrier has been practically overcome/breached.