CC BY
20
https ://doi.org/10.29013/ESR-19-11.12-74-76
Rasulov Rustam Yavkachovich, Professor of Fergana State University
E-mail: [email protected].
Rayimjonova Umidaxon, Bachelor of Fergana State University Mamatova Muhhayyo Adhamovna, Researcher of Fergana State University Nasirov Mardon Xaldarbekovich, Researcher of Fergana State University
Muminov Islom Arabboyevich, Researcher of Fergana State University
TO THE THEORY OF CURRENT-VOLTAGE CHARACTERISTICS OF THE THREE-LAYER STRUCTURE OF SEMICONDUCTORS IN DIODE SWITCHING
Asbstract. A generalized theory of the current-voltage characteristics of a three-layer semiconductor structure in a diode inclusion is proposed. It was believed that the base of this structure is made of compensated semiconductor.
The obtained results are generalized for structures with different conductivities.
Keywords: current-voltage characteristic, three-layer semiconductor structure, diode, compensated semiconductor.
The current-voltage characteristic of the three-layer structure of semiconductors in a diode inclusion, in which the base is made of a compensated semiconductor, has been considered in a number of works (see, for example, [1-4] and the references therein). In [4], in particular, a number of phenomena are listed that explain the appearance of a section of negative resistance in the current-voltage characteristic in the through direction in p - n - p structures.
In this work, following [2], expressions are obtained for the distribution of current densities and concentrations of current carriers along the length of the base. To determine the relationship between these parameters, the Poisson equations, the conditions of electroneutrality and continuity of flows for current carriers in the stationary case are taken into account [1-3]. Then the distribution of current den-
sities along the length of the base of the three-layer structure is described by the equation (in the one-dimensional approximation, i.e., along the axis Ox): L 2n + Sdp0 + n0 d2 jn _ . + " (1 + bôd)p + 50(p0 + bn0) dx2 jn
b(n + n0 ) (1)
—j=0'
b + — I p + n0b + p0
{ 50/
where is used the notation of[l; 2], j = jn + jp is the density of the total current of electrons and holes. Here it is believed that the base of the structure is made of a semiconductor compensated by impurities that create deep levels in the band gap. Then in the region of strong injection (l) takes the form 2L d L b .
-jn +t-= 0. (2)
b + — 50
1 + b50 dx2
TO THE THEORY OF CURRENT-VOLTAGE CHARACTERISTICS OF THE THREE-LAYER STRUCTURE OF SEMICONDUCTORS IN DIODE SWITCHING
To solve the latter, it is convenient to go to
7 = inH = kj(( + jP). Then rt's easy to get
y(d) = jn (d)/j = m2 we get the expression for j (see table 1) n
d2 y _ böd +l dx
r böd y_
V
böd +l
= 0,
(3)
böQ (m + l)bö9 + ml d - x
- + —--—1 sh-+
jn
j böd +l
whose solution we are looking for in the form
y = —7 + c^hxyfa + c2chxy/a, (4)
(böd + l)sh-
L
where a =
böd +l böQ +l
2
L = .
2L
(m2 + l)böd + m2 x + ~Ä Sh , (bö6 + l)shd L
(6)
böd +1
-. From the condi-
Then, in the diffusion approximation, the elec-
tion y(0) = jn (0Vj = m (electron fraction of the total tron distributi°n atong the length of the base of the current density in x = 0 ) we have
(m2 + l)böd + m2 -[böd(ml -1) - ml]ch-(b§6 + l)shd
structure has the form
-l d
(5)
jLn sh-
n =
L
eDj 2(1 + böd)
[(m2 - l)böd + m2 ]sh--[(ml - l)böd + ml]sh
d - x
(7)
Then, introducing the electron fraction in the total whence the electron concentrations in the contacts current density at x = d ( d is the base length), i.e. are determined by the relations
,(0 ) =
jLn
eDj2(1 + böd) sh-
[(m2 -l)böd + m2]ch--[(ml -l)böd + ml] I,
i(d ) =
[(m2 -l)bö6 + m2]ch--[(ml -l)bö6 + ml]
_L_
(m2 -l)bö6 + m2 -[(ml -l)böö + ml]ch—
Hence the distribution of electrons over the thickness of the base for structures of the type, p+ -n - n+, n+ - n - p+ and n+ - n - n+ is written in the form
jLn
jLn
n(x ) = -
i x i d x ch— + ch
L
L
(8)
(9)
n(x ) = -
eD. 2(1 + bö9)sh-
ch— + böQchd x
L
L
eD 2 (l + böd)sh-
jLn
n(x ) = ■
ch d—x - böOch x LL
eD 2 (l + böd)sh-
The current - voltage characteristic of a three-layer semiconductor structure, determined by the voltage drop at the base of the structure, in the diffusion approximation has the form
d
V = J Edx = V + V2 (10)
w
V =-
IT böQ-1
V. —----
l e böd +1
9r l
■ ln
chd -K. Ll
l - ch—■K. Ll
ere
(m. - \)böQ - m. 1 (m2 -l)bö6 + m2
K =
l -K- exp-
l -K- exp
arctg
l -K- exp
L
l -K- exp
- arctg
l -K - exp ( d \
~ 1
I L )
d
l -K- exp—
cl
d
(m1 - 1)bôd - m1 (m2 - 1)bSO - m2
For example, for the structure, n+ - n - p+ we have
kT 4• shd/
9r 1 =■
kT
4 ■ sh-
L
e a(1 + bôd)
v =---
L
r]1 • bôd
1 + bôd
1 + bôd exp-
1 + bôd exp
(11)
(12)
where
n1 = arctg <
(b56 + ed/L )(b56+ e ~d/L )
X
1 + b56
d
th
2L
Then the electric field strength in the structure has the form
E =
j ■ Ln (m2 - 1)b + m2
eD
2(1 + b)ch-
chx-L
K-ch-
x
L
(13)
and for the minimum value of the voltage drop at
the base
4b d
--sh—
b +1 L
V . =
mm
kT
arctg
F -
1 -K1 • <
c
1/2
1 — K • e— I • ((m2 - 1)b + m1) V L
, ,T 1 — K • chd + — •—ln , L
b +1 e chd —K L
(14)
In conclusion, we note that the discussion of conductor structures in a diode inclusion requires a
our theoretical results on specific three-layer semi- separate consideration.
References:
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3. Baranenkov A. I., Osipov V. V. Current-voltage characteristics of long diodes from compensated semiconductors // FTP. 1969.- T. 3.- P. 39-44.
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