Construction of internal electric fields (IEFs) is crucial to realize efficient charge separation for charge-induced redox reactions, such as water splitting and CO2 reduction. However, a quantitative understanding of the charge transfer dynamics modulated by IEFs remains elusive. Here, electron microscopy study unveils that the non-equilibrium photo-excited electrons are collectively steered by two contiguous IEFs within binary (001)/(200) facet junctions of BiOBr platelets, and they exhibit characteristic Gaussian distribution profiles on reduction facets by using metal co-catalysts as probes. An analytical model justifies the Gaussian curve and allows us to measure the diffusion length and drift distance of electrons. The charge separation efficiency, as well as photocatalytic performances, are maximized when the platelet size is about twice the drift distance, either by tailoring particle dimensions or tuning IEF-dependent drift distances. The work offers great flexibility for precisely constructing high-performance particulate photocatalysts by understanding charge transfer dynamics. 

/pdf/unveiling-the-charge-transfer-dynamics-steered-by-built-in-iqcmg3bk.pdf

Unveiling the charge transfer dynamics steered by built-in electric fields in BiOBr photocatalysts

The Richardson constants for near-ideal AuGaAs and AlGaAs Schottky diodes have been determined from an analysis of forward current-voltage characteristics. Measurement of capacitance-voltage characteristics at different temperatures shows that the barrier heights of the diodes have very similar temperature dependence for both Au and Al contacts. On taking into account the temperature dependence of the barrier height, the corrected value of the Richardson constant for AuGaAs diode is found to be very close to the predicted theoretical value. The corresponding value for AlGaAs diode is about a factor of five smaller which is explained on the basis of a thin interfacial layer between Al and GaAs.

Measurement of Richardson constant of GaAs Schottky barriers

The J-V characteristics of epitaxial Schottky barrier diodes are analyzed. Based on the assumption of negligible recombination in the epitaxial layer, formal solution from which the J-V characteristics can be calculated is derived. The solution is valid for all injection levels and reduces to the form I = Is[exp (q(V−IR)/kT) − 1], where R is the series resistance of the epitaxial layer, under C12 C12V low-injection conditions. The analysis is justified by very close correspondence with exact numerical calculations using the Finite Element Device Analysis Program (FIELDAY) in which thermionic emission boundary conditions are implemented for both electrons and holes. It is shown that for low barrier Schottky diodes the minority carrier injection is negligible and the expression I = Is[exp (q(V−IR)/kT) − 1] describes the I-V characteristics over large bias range. For high barrier C12 C12 V Schottky diodes the exact solution must be used as minority carriers are injected and the series resistance is decreased due to conductivity modulation effect.

On the current-voltage characteristics of epitaxial Schottky barrier diodes

The high-field transport of electrons in an n -type Schottky barrier diode is analyzed in relation to the existing synthesis of drift-diffusion (DD) and thermionic emission (TE) theories. Energy relaxation is shown to play a significant role in allowing the DDTE theory to encompass as wide an applicability as it does in spite of its underlying assumptions. The transport equations for energy and momentum balance are solved for the electrostatic potential distribution of a Schottky diode while including quasi-ballistic effects of the inertia of the energy and momentum fluxes. Relaxation of both momentum and energy is included through scattering with ionized impurities, acoustic phonons and optical phonons. The model is applied to a silicon Schottky barrier and the results related to the existing theories.

High-field, nonlinear electron transport in lightly doped Schottky-barrier diodes

Assuming the conventional divisions of the semiconductor into depleted and neutral regions, it is shown that for an abrupt p-n junction with nondegenerate carriers a relation exists between the open circuit photovoltage and the PN product at the junction (PN)_{0} , which is valid for all signal levels. In the small-signal case this leads to the standard result. At intermediate levels a new relation V = KT/q (1 \pm m) \log_{e} ([(PN)_{0}]^{1/2}/n_{i}) holds, the upper sign for p+-n junctions, the lower for n+-p junctions; m = (\micro_{e}-\micro_{h})/(\micro_{e}+\micro_{h}) . At very high levels the photovoltage saturates to V = kT/q[log_{e}(M_{p}M_{n}/n_{i^{2}}) + m \log_{e}(\micro_{h}M_{p}/\micro_{e}M_{N})] . Since M p and M N are the doping levels in the p and n regions, the first term is the diffusion potential and the second term will be positive for p+-n junctions and negative for n+-p junctions. These results compare satisfactorily with the available experimental data.

The saturated photovoltage of a p-n junction

Recent evidence indicates that thermionic emission is a more important process than conduction-diffusion for current limitation in many Schottky barriers. By choosing suitable momentum and energy conservation equations an expression for the thermionic-diffusion current is obtained where it is assumed that the carrier temperature in the space charge region of the metal-semiconductor interface does not differ substantially from the equilibrium temperature. When thermionic emission is the dominant process for current limitation it is shown that carrier temperature effects may still be important. A discussion is presented where the above solution is applied to a model Si-type diode. Carrier temperature effects reduce the current below its ‘thermal equilibrium’ value in all cases.

Inclusion of carrier temperature effects in a thermionic-diffusion theory of the schottky barrier

The semiconductor transport equations are reformulated in terms of two new variables one of which measures the departure of the PN product from its equilibrium value and the other the space charge. The electric field is eliminated and the total current becomes the basic independent variable. Boundary conditions are found for these new variables which, being based on thermionic emission at the metal-semiconductor contact, are applicable under all circumstances where tunnelling is insignificant. Using these boundary conditions the terminal voltage is shown to divide into an internal ohmic term, a term dependent on the variation of the PN product and terms dependent on the conditions at the metal semiconductor contacts.

Reformulation of basic semiconductor transport equations—II

The time-dependent coupled linearized diffusion equations for majority and minority carriers in a semiconductor are solved exactly for the situation found in the Haynes-Shockley experiment where a δ-function pulse of electron-hole pairs is injected at an initial time and place. In the recombination regime, where the minority-carrier lifetime τmin is much greater than the dielectric relaxation time τD, the calculations show the expected quasi-neutrality, but in the relaxation regime, where τmin is less than τD, a quite different state of affairs prevails. The majority carriers now move off in the opposite direction to the minority carriers which are accompanied by a region depleted of majority carriers. When τmin is slightly greater than τD, the majority carriers may show a spatial distribution with a double hump.

The theory of majority-carrier motion in the Haynes-Shockley experiment

Carrier temperature effects arising in a p−n junction are discussed by solving a chosen set of conservation equations. An analytic solution is found for the current flow assuming small departures of the carrier temperature from equilibrium, and a numerical solution involving large carrier temperature variations is presented. The reverse bias at which avalanche breakdown is predicted for a germanium diode is in agreement with experiment.

J.E. Parrott

Papers

Inclusion of carrier temperature effects in a thermionic-diffusion theory of the schottky barrier

Reformulation of basic semiconductor transport equations—II

The theory of majority-carrier motion in the Haynes-Shockley experiment

Carrier temperature effects in a p−n junction