Direct current excitation in photoconductive crystal by running intensity pattern
Authors: Dooghin A. V. , Goosev I. V. , Zel’dovich B. Ya. 
Published: February 2023

Techniques of measurement of stationary current [1] and ac photo-electro-motive forces [2] are used for investigations of space charge field amplitude and crystal parameters. We theoretically investigate new method of measurement of crystal parameters through the measurements of de current dependencies on the fringes velocity and the spatial period of interference pattern and carry out experimental measurements. Techniques of measurement of stationary current [1] and ac photo-electro-motive forces [2] are used for investigations of space charge field amplitude and crystal parameters. We theoretically investigate new method of measurement of crystal parameters through the measurements of de current dependencies on the fringes velocity and the spatial period of interference pattern and carry out experimental measurements. The analysis is given for case of small light modulation and restricted by one carrier and one donor level model. ` Let the crystal be illuminated by running intensity pattern where /θ is mean intensity,' |m| is contrast of light modulation,
q
is spatial frequency of interference pattern, □ is oscillation fre- · quency. Moving pattern gives rise to modulation of space charge field inside the crystal. The modulation is shifted with respect, to the intensity pattern due to nonzero response time. Distribution of carriers in conduction band has the form Characteristics used in . expressions C2), C3) are commonly adopted in literature (31. Those distributions is out of phase and therefore there is force acting on the carrier distribution. That force is reason why direct current flows through the 'crystal. Averaging of photocurrent density gives the term
I
that is proportional to contrast squared:
i

2

^~ \tn\
2. for dependence of current density on the fringes velocity we obtain Delay parameter
x
indicates how fast the intensity pattern moves in comparison with the crystal response time. Function
?xΛl + x
2
)
has extreme values ±1 for the delay parameter x = ±l, respectively, as shown on fig.1. Thus we come to the conclusion that the photocurrent readies its maximum value if phase shift between space charge grating and photocarriers distribution is equal to π/4, i.e optimal os- ci llatory frequency coincides with the inverse recording time. For investigation of dependencies of current density on the spatial frequency of intensity pattern we rewrite expression for current in next form The current
j

c
= ε£c|m|2/C4τR) in expression C6) is maximum value of photocurrent which exists in PRC sample for given contrast without external electric field. Here
E

c

= kTq

c

/e
is largest hologram amplitude obtained in crystal under diffusion recording mechanism and
q
= Ce2AL/e£JcT)1/2 is Debye screening spatial frequency. Dependence of photocurrent on normalized spatial grating frequency
q/q

c

-
is shown on fig. 2. It has maximum at a spatial frequency
q

õ
which is determined from the equation C7) where L = 2π/q is Debye screening length and L is diffusion length. The largest current takes place at spatjβi frequency which is somewhat different from the Debye frequency
q.
We see that the characteristics £ç and £µ play role of saturatin field for the photocurrent as field a limiting field for the space charge field amplitude in case of static illumination· The > effect has simple explanation. Photocarriers arv transported at a distance longer then the grating period A when drift field £µ exceeds diffusion field £ö Distribution of carriers in conduction band becomes more smooth and space charge grating amplitude is decreased. Therefore effective interaction between those gratings is diminished. This leads to weakening of the stationary. photocurrent density. ; For experimental measurements we use sample of illuminated by He-Ne laser. Average light powe. inside the crystal is approximately 1 mW. The contrast of light modulation
m
is- equal to 0.2. We obtain the magnitude of direct current through the PRC of IO"13 A at the spatial .of interference pattern.