On the absorption of light by crystals

V 
V 
J ’
an d
r/q = A / ( P + A + B).
Consider first 
r)e, rem em bering t h a t vjA 
10
5.
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387
In fig. 2 tje is p lo tted as a function of te m p eratu re for different values of th e 
ratio W '/W  (the value of v'/v is consistently ta k en to be 
so th a t for high 
tem peratures r/e approaches th e value f). I f W > 
th ere will be a sharp
On 
the absorption of light by crystals
—r
t
=
oo
6
F
ig
. 2. Free electrons produced per absorbed quantum.
F
ig
. 3. Number of quanta re-emitted per quantum absorbed.
drop as the tem perature is lowered; i)e reaches about 1 % of its original value 
for a tem perature Te, given by
exp
and thus by
(v\ 
W
Te = W lkloge(-A 
x 
lO O j-O -
0 6
^ .
(
1
)
Vol. CLXVII. A.
2 5
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388
N. F. Mott
I f W > W ', r]e will fall somewhat less sharply (the drop being caused here 
m ainly by the term
(v' jv)e(W~W)lkT).
We now consider the num ber >jQ of q u an ta reradiated per quantum ab­
sorbed
Vg
[
1
+ * e - W l k T + V' - W ' l k T
A  
J
■T\
rjq will have fallen to about 1 % of its low tem perature value a t one of the 
tem peratures Tq or T q given by
_!L e 
-wikTq
~ 100 and V
—r e~w'lkT'q ~ 100
A
A
and hence by 
J ^ ~
0-14
W/k, ~
0-14
(2)
whichever is th e lower. The form of 
rjq is shown in fig. 
3
.
2. C
omparison
 
with
 
experim ent
(a) Alkali-halides with F centres. As shown by the work of Pohl and his 
co-workers on photoconductivity (Pohl 1937), th e current per absorbed 
quantum in coloured alkali-halides drops sharply by a factor of th e order of 
1000 as the tem perature is lowered below a critical tem perature, — 
150
° C. in 
sodium chloride. Gurney and M ott (1938) have interpreted this on lines 
similar to those of this paper, b u t have tak en A  and B  independent of T, 
so th a t
[
1
+
e W / k T
r
They found fair agreem ent w ith experim ent w ith
W =
0-075
e-volt and {A + B )/v = 
0
-
0033
.
W ith the larger num ber of variables available in the present theory it will 
certainly be possible to obtain a fit, b u t one can no longer deduce a value for 
W, i.e. the work required to remove an electron from an excited F  centre.
(b) Pure alkali-halides. No photoconductivity is observed, probably 
because th e work W necessary to separate an “ ex cito n ” into an electron 
a n d positive hole is too large. Theoretical estim ates of W are m ade below.
(c) 
Silver halides. The work of Lehfeldt (1935) has shown th a t even at 
liquid-air tem peratures rje is greater th a n 0-5. No m easurem ents of the 
prim ary photoelectric current have been made a t lower tem peratures, but 
th e secondary current shows, according to Lehfeldt, a very sharp drop at 
about 
50
° K . for AgCl and 
25
° K. for AgBr. The drop in the secondary 
current is believed to be due to a drop in the prim ary current.
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