1.10 Domain walls up close

An ideal 180° wall in LiNbO₃ is only one or two unit cells wide P(abs), yet around a freshly written wall the crystal stays strained and slightly birefringent over micrometres, enough to see walls in a polarizing microscope P-comp.

If a wall is tilted away from c, the polarization on its two sides no longer meets it edge-on and leaves a sheet of bound charge; mobile electrons gather to screen it, and the wall conducts (charged wall). In MgO-doped LN such tilted walls conduct more than 10¹³ times better than the surrounding crystal P.

   10 µm      1 µm     100 nm    10 nm      1 nm     0.1 nm     
     +·····-·--+·····-·--+·····-·--+·····-·--+·····-·--+        
     A      B            C         D          E    F            
     ^ s 10.0 µm                                                

  |------| 10.0 µm                                 view 80.0 µm 
A                            [=====]                            
B                               =                               
C                               .                               
D                               .                               
E                               .                               
F                               .                               
  · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 
  P up                                                   P down 
                                |                               
    ^   ^   ^   ^   ^   ^   ^   |   v   v   v   v   v   v   v   
                                |                               
    ^   ^   ^   ^   ^   ^   ^   |   v   v   v   v   v   v   v   
                                |                               
    ^   ^   ^   ^   ^   ^   ^   |   v   v   v   v   v   v   v   
                                |                               
    ^   ^   ^   ^   ^   ^   ^   |   v   v   v   v   v   v   v   
                                |                               
    ^   ^   ^   ^   ^   ^   ^   |   v   v   v   v   v   v   v   
                                |                               

0.14  |                                                         
      |                                         ···········     
      |                              ···········                
0.07  |                  ············                           
      |       ···········                                       
0     | o·····                                                  
      --+---------W---------+---------+---------+---------+     
        0         1         2         3         4         5 deg 
σb C/m², Ps 0.71   o current   W Werner 2017, ~1 deg            

Zoom from 10 µm to 0.1 nm: the micrometre halo that a polarizing microscope sees narrows to the probe-limited PFM width, then to the seam one to two lattice units wide where lithium sits above its oxygen plane on one side and below it on the other. Tilt the wall by 1° and a bound-charge sheet of 0.0248 C/m², 1.55 × 10¹³ electrons per cm² to screen it (P_s = 0.71 C/m²; 1.74 × 10¹³ for 0.80), appears along the wall: one charge per 2.54 nm square. Conductivity enters only as the single Werner et al. 2017 point.

Charged-wall conduction: one sourced example

The numbers below describe one crystal and one writing method; they are a data point, not a material constant (domain-wall conduction).

Why walls are “thick” in congruent crystal. The extended strain and space-charge fields are attributed to defect clusters pinning the wall P-comp P(abs): extrinsic point defects and their clustering control the local wall structure and change macroscopic properties by orders of magnitude. PFM profiles are symmetric across walls in stoichiometric crystal and asymmetric in congruent crystal, read indirectly as a trace of the internal field P-comp. The mechanism remains qualitative.

Measuring walls. Selective etching (the Miller-Savage wall-velocity method), polarizing microscopy of wall birefringence, electro-optic imaging, near-field optics, PFM, SHG microscopy, X-ray topography P-comp. The measured width depends on the probe; the 0.28 nm TEM value is for LiTaO₃, not LiNbO₃ P-comp.

Conduction numbers depend on the assumed wall width. 10 nm gives 0.02 (Ω cm)⁻¹; 1 nm gives about ten times more P. In Schröder et al. 2012, wall transport in undoped crystal was switched by super-bandgap illumination P(abs).

How the figure is computed. Each scale feature is drawn at its sourced full width around the wall; the feature named at a scale is the one whose representative length is nearest the scale bar on a log axis template. The atom strip repeats one octahedral column of the Hsu et al. 1997 cell along a₁, with the refined structure (s = +1) left of the wall and its inversion (s = −1) right of it; Li sits 71.3 pm above or below its O₃ face derived. The bound charge is σ_b = 2P_s sin θ with P_s = 0.71 or 0.80 C/m² conflict derived; the microscope halo and the PFM profile shape are display renderings template template.