Carrier transport properties and non-equilibrium carriers

Carrier transport properties and non-equilibrium carriers

Carrier transport properties

Under the action of an external electric field and a magnetic field, the movement of electrons and holes in crystalline silicon leads to the transport of electric charges and generates electric current.

At 300K, the resistivity of uncompensated or lightly compensated silicon material versus shallow impurity concentration is shown in Figure 1. For light doping with concentrations less than 1017cm-3, the impurities can be considered fully ionized at room temperature. The resistivity is inversely proportional to the impurity concentration. When the doping concentration increases, since the impurity cannot be fully ionized at room temperature, the mobility decreases significantly with the increase of the impurity concentration, and the resistivity curve deviates from the straight line.

Carrier transport properties and non-equilibrium carriers
Figure 1 – The relationship between resistivity and impurity concentration of silicon single crystal (T=300K)

There are always some impurities and defects in the actual crystalline silicon lattice, and the lattice atoms are thermally vibrating near their equilibrium positions. These factors will cause the lattice potential field to deviate from the periodic potential, so that the carriers continuously transition from one motion state to another motion state, resulting in carrier scattering. Scattering promotes the disorder of the carrier movement and affects the electrical conductivity. At room temperature, the electron mobility of silicon is 1350 cm²/(V s) and the hole mobility is 480 cm²/(V s). Under a strong electric field (on the order of 104V/cm), the average energy of the carriers increases, which is called hot carriers. Collision ionization occurs under stronger electric fields, resulting in a substantial increase in carrier density.

Non-equilibrium carrier

Under thermal equilibrium conditions, holes in N-type semiconductors are minority equilibrium carriers, while electrons in P-type semiconductors are minority equilibrium carriers. Under the external action, new minority carriers will be generated in the semiconductor, these carriers are non-equilibrium minority carriers, referred to as “minority carriers”. When the external effect is eliminated, these non-equilibrium minority carriers will recombine and disappear through various ways, and return to the thermal equilibrium state.

The main methods of injecting minority carriers are optical injection and electrical injection. The non-equilibrium carriers generated by light injection play a particularly important role in silicon solar cells based on the PN junction photovoltaic effect.

In general, the number of non-equilibrium minority carriers decays exponentially with time, i.e.

ΔP(or Δn) ∞e-t/τ

τ is the decay time constant, indicating the average existence time of non-equilibrium carriers from generation to recombination, that is, the lifetime of non-equilibrium minority carriers.

The recombination process of non-equilibrium minority carriers takes many forms. Figure 2(a) shows the band-by-band recombination of electron-hole pairs. Electrons jump from the conduction band to the valence band, emitting a photon at the same time (ie, the radiation process), or transfer energy to other free electrons or holes (ie, the Auger process). The former is the reverse process of phototransition, and the latter is the reverse process of impact ionization.

Carrier transport properties and non-equilibrium carriers
Figure 1 – Recombination process of non-equilibrium minority carriers

Figure 2(b) shows a single-level recombination with only one trap level in the forbidden band; Figure 2(c) shows the multi-level recombination of multiple deep levels or trap levels in the forbidden band. Single-level recombination includes the processes of electron capture, electron emission, hole capture, and hole emission. When the energy level of the recombination center is close to the intrinsic Fermi level at the center of the forbidden band, the recombination rate approaches a maximum value. The most detrimental recombination centers for solar cells are those energy levels located near the center of the forbidden band.

When the number of injected carriers (Δp=Δn) is much lower than the number of majority carriers, that is, under low injection conditions, the recombination rate is

Carrier transport properties and non-equilibrium carriers

In the formula, P0 is the equilibrium minority carrier density; Pn=△P+P0; τp is the minority carrier (hole) lifetime; the unit of recombination rate U is cm-2s-1.

In an N-type semiconductor, when n≈n0 (equilibrium carrier density), n>>ni and pi, the minority carrier lifetime (hole lifetime) is

Carrier transport properties and non-equilibrium carriers

where, σp represents the hole trapping cross section; vth is the thermal velocity of the carrier; Nt is the trap density; ni and pi are the intrinsic carrier density.

Similarly, the electron lifetime in P-type semiconductors is obtained:

Carrier transport properties and non-equilibrium carriers

where σn is the electron capture cross section.

For the multi-level trap recombination process, its qualitative characteristics are similar to the single-level situation.

The carrier recombination process exists in the semiconductor body, and the recombination process also exists in the semiconductor surface layer.

Extending from the body to the surface, the lattice structure is interrupted, and the surface atoms appear dangling bonds; surface damage caused by silicon wafer processing or defects and lattice distortion caused by internal stress will form surface energy levels, and these surface states can become surface recombination centers. In addition, foreign impurities adsorbed and charged by the surface layer will induce an opposite-signal charge in the surface layer, so that an inversion layer is formed on the surface. All these factors make the surface recombination process more complex than in vivo. Taking N-type crystalline silicon as an example, assuming that the total number of recombination centers per unit area in the surface thin layer is Nst, and the non-equilibrium minority carrier concentration in the thin layer is (Δp)s, the surface recombination rate Us is

UspvthNst(Δp)s=s(Δp)s      (1-4)

where s is called the surface recombination velocity, which can be expressed as

      s=σpvthNst           (1-5)

In order to improve the photoelectric conversion efficiency of solar cells, the internal recombination and surface recombination of carriers should be minimized.

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