Optical cleaning owing to the bulk photovoltaic effect

It is shown within the conventional photovoltaic charge-transport model that photoexcitable electrons, localized at deep impurity levels, can be effectively removed by light from the exposed area at sufficiently high temperatures. This allows to modify strongly the absorption and photoelectric properties of the material and, in particular, to suppress “optical damage” in ${\text{LiNbO}}_3$ and ${\text{LiTaO}}_3$ crystals. This optical cleaning method is applicable to numerous pyro- and piezo-electric optical materials. It employs the photovoltaic drift of electrons and ionic charge compensation at elevated temperatures. The physics of the optical cleaning is very rich; it has strong links to nonlinear dynamics and offers important handles for improvement of the cleaning performance. The use of properly moving light beams leads, e.g., to a strong enhancement of the cleaning rate and allows to reduce the electron concentration by several orders of magnitude. The theoretical predictions are supported by the data of our cleaning experiments with ${\text{LiNbO}}_3$ crystals. In particular, the intensity threshold of optical damage is increased by three orders of magnitude.

Figure 1

Scheme of the electrical equilibrium for a square-wave-shaped light intensity profile $I\left(z\right)$. The electronic current is the sum of the photovoltaic and drift currents, $j_e=j_{pv}+{\sigma }_{ph}E$, while the ionic current is solely due to the drift, $j_i={\sigma }_{i}E$.

Figure 2

(Color online) Dependence $u\left(\widehat{z}\right)$ for $r=v/v_0=0.6$. The dots show the zero points of $u$, while the arrows show the directions of motion of electrons in different regions of $\widehat{z}$.

Figure 3

(Color online) The absolute value of the rate coefficient $\left|{\gamma }_{1,2}\right|$ versus the velocity ratio $v/v_0$ for the Gaussian cleaning beam.

Figure 4

(Color online) The concentration profile for $v=0$ and four values of the normalized time $t/t_0$ within the basic model. The dotted line is the normalized intensity profile $I/I_0$.

Figure 5

(Color online) The normalized profile $N_e\left(\widehat{z}\right)/N_e^0$ for $t/t_0=10$ and $v/v_0=0.6$. For line 1, the impact of the light-induced field is neglected, i.e., parameters $a,b,c$ given by Eq. (18) are set to be zero. Line 2 accounts for the effect of a space-charge field at $a,b,c=0.01$ but ignores diffusion. Line 3 is plotted for $a,b,c=0.01$ and electron diffusion is taken into account. Lines 2 and 3 coincide with line 1 except for the peak region of $N_e$. The dotted line shows the normalized intensity profile.

Figure 6

(Color online) The ratio $N_e^{min}/N_e^0={\rho }_{min}$ versus $v/v_0$ for $t/t_0=10$ within the basic model.

Figure 7

(Color online) Normalized concentration profiles in the standing coordinate frame for $v/v_0=1.2$ and six values of the cleaning time, $t/t_0=2$, 4, 6, 8, 10, and 12.

Figure 8

(Color online) Influence of asymmetry of the cleaning light beam on the cleaning performance. The dotted lines $1^{\prime }$ and $2^{\prime }$ show the symmetric and asymmetric beam profiles, respectively. The width parameter of both trailing edges is $z_0$, $t/t_0=10$, and $v/v_0=0.6$. The solid lines 1 and 2 show the corresponding concentration profiles.

Figure 9

(Color online) Dependence of the ratio ${\rho }_{min}=N_e^{min}/N_e^0$ on the dimensionless parameter $a={\sigma }_{ph}^0/{\sigma }_i^0$ for $t/t_0=10$, $v/v_0=0.6$, and $b=c=0$.

Figure 10

(Color online) Normalized profile $N_e/N_e^0$ for $I_0\approx 10\text{W}/{\text{cm}}^2$ after 24 h cleaning (dots) with a standing light beam (Ref. 15). The solid theoretical line corresponds to $a=0.5$ and $t/t_0=5$.

Figure 11

(Color online) The concentration profile (circles, right scale) and the threshold intensity of optical damage (diamonds, left scale) versus the coordinate $z$ after the long-term cleaning. The errors are given by the heights of the symbols.