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Section 10. Physics
https ://doi.org/10.29013/ESR-19-11.12-70-73
Rasulov Rustam Yavkachovich, Professor of Fergana State University E-mail: r_rasulov51@mail.ru.
Madgaziev Abdulaziz Abdukarim ogli, Master of Fergana State University
Rayimjonova Umidaxon, Bachelor of Fergana State University
Mamatova Makhliyo, Researcher of Fergana State University Muminov Islomjon Arabboyevich, Researcher of Fergana State University
AGENCY OF SURFACE RECOMBINATION ON VOLT-AMPERE CHARACTERISTIC OF THE DIODE WITH DOUBLE INJECTION
Abstract. The current-voltage characteristic of a three-layer semiconductor structure, base of which is made of a compensated semiconductor vas calculated. Where taken into account the surface recombination of free charge carriers.
Keywords: free charge carriers, compensated semiconductor, the volt-ampere characteristic, surface recombination, S - diode.
The properties of long diodes with injection of space charge in the diode base; d) radiative recom-
minority charge carriers and with double injection, bination of further reabsorption of photons; e) an
as well as multilayer semiconductor structures, have increase in ambipolar and drift mobility; f) a change
been researched in many works [1-6]. in the screening radius of charged impurity centers
The volt - ampere characteristic of the diode, the during carrier injection. base ofwhich is made of a compensated semiconduc- In these works, the effect of surface recombina-
tor, has been considered in a number of works (see, tion on the volt - ampere characteristic is neglect-
for example, [1-3] and the literature cited there). ed. It can be proved that a change in the effective
Below we list a number of phenomena explaining recombination leads to a change in the shape of the
the appearance of a negative resistance (NR) sec- volt - ampere characteristic. In this work, this case
tion in the volt - ampere characteristics of S diodes: is considered for S - diodes.
a) a change in the injection coefficient of the p - n In this report, we show that a change in the effec-
junction; b) an increase in the lifetime of minority tive rate of surface recombination of the emitter and
carriers during injection; c) decompensation of the collector junctions of the diode by double injection
leads to a change in the volt - ampere characteristic. In the stationary case, the distribution of charge carriers in the base of S - diodes, which is made of a semiconductor compensated by impurities that create deep levels in the band gap, are described by the following equations:
dp (1)
Ip = eV p (p + po)E - gDp~x >
In = eVn (n + n0)E - gDndT,
dx
-1 j = P.
2 dx r
Here t , t are the lifetime,
(2) (3)
'f> ~n~................7 Vp , Vn are the m0"
bilities, Dp, Dn are the diffusion coefficients, n0, n and p0, p are the equilibrium and nonequilibrium concentrations of electrons and holes T and J are
pn
hole and electronic components of a full current J
J = Jp +J„. (4)
The dependence between the electron and hole concentrations is determined by the solution of the Poissons equation, and can easily be obtained using the conditions of quasi neutrality
' (5)
s dE
^ n + n
4ne dx
and assuming that the deep levels as sticking level for holes, the relationship between the electron and hole concentrations can be written as [2; 3]:
■p + N . (6)
where
N1 =
n = pp + N2
9Nf0 +9(1 + 5)p0 + (1+ Ô-1 )n0
N - N =
9+1 0N( f0 - f0 ) 0 + 1
(7)
(8)
E = -
2 ■ j ■ b
y [(a +1) -1]
y [1 + b(a +1)] + b y [1 + (a + b)b ] + b
y (a +1) +1
j, = r. . y J - 1.. + 2 . y'
y [1 + b(a +1)] + b y [1 + b(a +1)] + b'
p N - N
There y = —, a =
(9)
(10)
N
, b = ^, J = » p
IL„
2eDnn0
Statement (10) in (3) leads to the following equation at high injection levels for the case y2s » 1
/-2 y ■ y'-y = 0 (11)
At high currents, it is necessary to take into account not only the properties of the transition, but also the properties of the contact, which requires taking into account the recombination process on the surface. If we take into account that the rear contact of the diode is anti-locking, then the spatial distribution along the length of the base of the structure of current carriers is determined as
y = Ae^ + Be-^, (12)
where k12 =J j2 +1 + j, J = j-¡^--, A
1,2 yJ J J2(a +1)[1 + b(a +1)]
and B are integration constants determined from the following boundary conditions
j jp (d) = esp [p(d) - Pn ] « espn0y(d), ( 1 3) [ y '(0) = — • j.
To simplify, jp (d) write in dimensionless form
jp (d ) = K- y (d ),
0 - is the ratio of the capture cross section of electrons and holes to a deep level, 5 is the ratio of minus f0 and zero charged f00 atoms of a deep impurity in an equilibrium state. From equations (1-4), taking into account (5), (6), we obtain dimension-less expressions for E and Jp t a high level of injection. Then it is easy to obtain a system of equations which can be calculate the volt - ampere characteristic of the structure under consideration
es L
where ^ =_LJL
eD
s;=.
e(Vm ±Vk ) kT
+ -
D
i '
eV (x) kT
(14)
(15)
dx
is the velocity of the surface distribution, Vm is the drop in the external voltage at the contact with the metal, ±Vk is the contact potential difference, "+" and "-" refer to the barrier and anti-blocking layers, respectively.
According to (13), (13) and (12) we have
n
0
S
p
p
e
Y +
K
m ■ e
-k,d
A = -
vi
K
— + G
k
V 2 J
kd , ■ e 2 +
K
1
Vkid k
/V-,
a =
a +1 eDpno _ 1 ' Lp
1
1 + b(a +1) Ln
-, Y_
eDpn0 1 + b(a +1)
--a
V k1 J
Y +
a +
K
At K = 0
A = ^
■ m ■ e
„-k,d
B =
2
K
— + a
k
V 2 7
ekd +
K
--a
V k1 7
-V k1
(16)
where
y (x ) =
Y / k2
K
— + G
k
V 2 y
ek2d +
K
--G
V k1 y
-k,d
A / 1 +
(17)
^ + m • e^ 1 ^ + m • eM 1
e^!—^ ■ y2> B = ^7"' k (18) If m = 1 (18) and (19) correspond to the results [2; 3].
Substituting (16) and (17) into (12) we obtain the expressions for the distribution of current along the length of the base of the structure
K
A
G
VV
m
-k1d
x2 y
e
Yy
ek2X +
( r 1 +
VV
K
G+
k
A
m
-k1d
2y
e
Yy
-k2x
(19)
Taking into account j (0) = j we obtain the expression for the maximum current value determined by
dy
the relation j = -/ —
dx
y o =-
1 +
G
K
2 y
m
Y
exp(-k1d )
+ k
1 +
\
K
— + G
k
V 2 y
k2d
k1 ' k2
\
K
— + G
k
V 2 y
ek2d +
K
k1
A
— G
-hd
(20)
7 o(1 + a) - -
where ft = —-. Then the voltage drop in the p - n junction is determined by the expression
b [y o(1 + a) +1]
Vp = ln
pn
Yk1
1 +
G -
K
m -k1d e1
2 y
+k
1 +
G+
K
m k d
_ek2d
2y
YnK ■ k2
K
— + G
k
V 2 y
ekd +
K
--G
V k1 y
-k.d
where it is taken into account that
pn
y (a) = yne kT , Yn = —y (a )e
kT
(22)
U
VT = V1 + V2 =j Edx
(21)
(23)
and substituting (22) in (26) and performing inte The voltage drop in the thickness is determined gration, we obtain by the formula
' k ek-d + k2ekld + mG(k2 - k1 )e(kl-k-)d _Y
V = 1 - b(a +1) |n
1 1 + b(a +1)
k + k2 + jG(k1e-k<d + k2 ek2d ) + Y(ek2d- e-kd )
(24)
and V2 (for long diodes) takes the form:
1 - b(a +1) 1 n
V2 =
1 + b(a +1) B k1 + k
A
2 V B J
k1+k2 nk
■ cos ec-—
k + k
(25)
1
k
k
If the surface recombination rate is too low Thus, taking into account the surface recombina-
(sp ^ 1), then expressions (20), (24), (25) will go tion of current carriers can greatly change both the
over to the results obtained in [3; 4]. nature of the change in the volt - ampere charac-
At an infinitely high rate of surface recombina- teristic of the structure and the current distribution
tion V and V2, it tends to zero, but Vpn has the form (also of current carriers) along the length of the base
m(eM _ e-v) of a three-layer structure, in a diode switch, the base
Vpn =ln (k ek2d + k -k1d) ( ) of which is made of a compensated semiconductor.
yn (k1e + k2e )
References:
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3. Osipov V. V., Kholodnov V. A. Negative resistance in diodes of compensated semiconductors during double injection.- Physics and technology of semiconductors. 1971.- Vol. 5.- Issue 7.- P. 1387-1399.
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