Discussion

Valence Band

2.8 Discussion

into the formula for EIlsaturation, we obtain

ll.nlsaturation ex Elisaturation ex _{- -}NXOave _{,'---- ex} N_Fe^{3+ ,}

nO,ave

(2.79)

which is in agreement to the experimental results depicted in Figure 2.9.

To summarize, the simple model based on Equations (2.68) and (2.67) gives us a complete understanding of the physical mechanisms involved in two-step holographic recording with high intensity pulses and helps us understand and explain the exper- imental observations that were not all explained before. Furthermore, it helps us understand the main drawbacks of the method and suggests ways for improving it.

This is explained in Section 2.8.

2.7 Application of the model to two-step record-

Another reason for this large intensity requirement is the weak population mecha- nism of the shallow traps by direct electron transfer from deep traps. The existence of this direct electron transfer mechanism was first proposed by Chen et al. [60]. This mechanism is essential for explaining the experimental observations discussed previ- ously. Without this mechanism, electron transfer from the deep traps to the shallow traps would be performed via the conduction band, and the dark depopulation of the shallow traps would occur due to thermal excitation resulting in an entirely different intensity-dependence of the saturation hologram strength and recording speed from what we observed and explained.

Without direct electron transfer from the shallower traps to the deeper traps (direct depopulation), there would be a partial erasure of the hologram during read- out. This is due to the fact that electrons are transferred from the shallow traps to the deep traps via the conduction band in this case. The electrons can move while they are in the conduction band, and this movement is in the direction of erasing the hologram as in the case of normal holographic recording in LiNb03:Fe crystals.

Such a read-out response is not observed experimentally, confirming the necessity of considering the direct electron transfer between deep and shallow traps in theoretical modeling.

To see the effect of direct depopulation of the shallow traps on the hologram strength, we calculated the recording curve for a non-physical case by neglecting the direct electron transfer from the shallow traps to the deep traps (direct depopulation of shallow traps) while direct electron transfer from the deep traps to the shallow traps is not neglected. In this calculation, we assumed that both recording and sensitization is performed by cw light. The result of this calculation is shown in Figure 2.14, which shows that we could record much stronger holograms (by three orders of magnitude) in the absence of direct depopulation of the shallow traps. This assumption (neglecting direct depopulation of the shallow traps) is of course non-physical as it considers only electron transfer from the deep traps to the shallow traps and not the reverse transfer. However, Figure 2.14 gives us an insight for improving the performance of two-step holographic recording through an increase of the lifetime of electrons in the

300

... ^{...... --_ ...}

-... _-_. __ ........ _---_ ....... _--_ ..... __ . __ ....... __ ._ ... .

-

^{::::I .: /,/} ..-

..!!

200 /

~ /

.~ I

E 100 !

- - With Direct Depopulation

... Without Direct Depopulation

IG = 1 W/cm² I'RO

=

^{1 W/cm} 2

~ I

o

~---~---~

o

⁵

Time (5)

10

Figure 2.14: Theoretical calculation of recording curves for space-charge field of a hologram using two-step holographic recording in a LiNb03:Fe crystal with and without neglecting direct depopulation of the shallow traps (direct electron t.rans- fer from shallow traps to deep traps). The curves are normalized so that the sat- uration space-charge field for the case without neglecting direct depopulation is 1. It is assumed in this calculation that recording is performed by cw light with IG

=

^IIRO

=

^IIRI

=

1 W/cm^2.

shallow traps.

One way to improve the lifetime of electrons in shallow traps is to replace the shallow traps with some long lifetime traps due to doping. In other words, we can use a doubly-doped crystal instead of a singly-doped one. Both deep and shallow traps in a doubly-doped crystal are due to dopands and can be chosen deep enough in the band gap of LiNb03 so that thermal depopulation of either trap is negligible. How- ever, the direct electron transfer between traps is also negligible in this case due to low practical concentrations of both dopands. Therefore, sensitization of the shallow traps is performed via the conduction band. The depopulation of the shallow traps in this case is performed by read-out light during read-out via the conduction band.

The electrons can move while they are in the conduction band, and this movement is in the direction of erasing the hologram as in the case of normal holographic recording in LiNb0₃:Fe crystals. Therefore, there is a partial erasure of the hologram during read-out in this case. In the next chapter, we will see that two-step holographic recording in doubly-doped materials results in much better performance than two- step holographic recording in a singly-doped material. Another way to improve the performance of two-step recording is to increase the lifetime of shallow traps by low- ering the concentration of empty deep traps as well as the concentration of the shal- low traps. This has been done by using nominally pure reduced near-stoichiometric LiNb03 crystals [61, 62] as well as near-stoichiometric LiNb0₃:Pr crystals [63, 64].

The usage of near-stoichiometric crystals is important in reducing the concentration of the shallow polaron levels that are due to the presence of Nb ions on Li sites. The concentration of Nb ions on Li sites in a near-stoichiometric crystal is much smaller than that in a congruent crystal resulting in much smaller polaron concentration in a near-stoichiometric crystal. The crystal is also reduced to lower the concentration of the deep empty traps. Another idea is to use bipolarons instead of remnant Fe centers as deep traps [62]. In all these cases, it is possible to record holograms using cw light with much smaller intensities compared to pulsed experiments. In Chapter 5 we will compare the performance of different two-step recording methods.

Finally, a very interesting point is that both saturation space-charge field and recording time constant depend on energy density per pulse (photon flux) of the recording and sensitizing beams (IGtp and lIRot p) instead of the intensities alone (as proposed in the literature). This can be easily understood by looking at Equa- tions (2.63) and (2.68). In these equations, both intensities (IG and lIRo) always appear in combination with pulse width (t_{p ).} This observation suggests that we can not obtain higher saturation space-charge fields by increasing lG and lIRO and de- creasing the pulse width tp to have constant photon fluxes lGtp and lIRotp, no matter how many pulses we use.