Transition regions in epilayer structures

7bin SolM kTbns, 57 (1979) L9 L I 0 "(" EIse',ier Sequoia SA.. Lausanne

Printed in the Netherlands

L9

Letter

Transition regions in epilayer structures ZBIGNIEW 1 . KUZNICKI

Section I ~ oJ "l~'chnical Sciences, Polish .4cademy o]'Sciences, Palac Kultury i Nauki. 00-901 Warsaw ( Pohmd~ (Recei'.ed No,,ember 6, 1978: accepted No',ember 20. 1978)

A very interesting paper of Aleksandrov concerning the transition regions in epilayer structures has been published recently in T h i n Solid F i l m s 1. The importance of an analytical description of the electrical structure of these regions was emphasized. The problem is related to a description of the electrical structure of an abrupt lightly doped heavily doped (I h)junction in an equilibrium state which has been resolved on the basis of the recently discovered I..h junction electrostatic law "-5. This can be expressed as follows: (1)

(b = N = L

where 4) =

4,,- 4,~ 4,,

N

nl --tlmO

.....

tim( ) --

n2

L = --/,

(2) (3)

(4)

and for n-type semiconductors q56

=

k- T I n n, • e

kT

4) = - .

C

(5)

172

n,

In---.

(6)

nmo

where n~ is the clectron concentration in the heavily doped section, n 2 is the electron concentration in the lightly doped section, nmo is the electron concentration at the interface,/~ is the thickness of the space-charge layer in the heavily doped section and 12 is the thickness of the space-charge layer in the lightly doped section, lfnt and n 2 are given it is very simple to lind nmo and q5 from eqns. 11), (2) and (3). The distribution function of the statistical electrostatic potential of the electrons in the transition region has the following shape:

LIO

LETTERS

1 4>~(x) = ( 4 ) . - ~

. , e x p ( x l, l - e x p ( - x " l l ) ) ' - .......... " hexp(x."ll)+exp(-xl~)

-4> * e x p ( x . . . / , * ) - e x p ( - x ' / l * ) " expi - x 1, *) - h exp(x.i~-ii + ~h, x~
B - 4)~)*

exp(x;/2.) - exp( - x.'l 2.) ..... + exp(x..I 2.) + b exp( - x.'l 2.)

(7)

+ l(4)R-qS~)-(~bn-4),l*} e x p ( x " / z l - e x p ( - x 1 2 l +¢,b, exp(x.12) - b exp( - x 1 2 1 x />0 where b is an abrupt parameter'*, l~*, 12" are the abrupt region thicknesses in the heavily doped and lightly doped sections respectively, qS,* is the barrier height parameter at the interface in the heavily doped section and (~/5~)- <,t~l* is the barrier height parameter at the interface in the lightly' doped section. O n differentiating eqn. (7) once we obtain the internal electric field distribution. and on differentiating eqn. (71 twice we can lind the charge density and electron concentration distributions. I 2 3 4 5

L.N. Aleksandro',, Thin Solid l"ihns, 50 ( 19781 13, Z T. Kuznicki. Prm. 7th Int. I"ucuum (_'on,~r. and3rdlnt. ( o n L on SolidSu~Jaces. I'icnna, September 1977, Vol. 2, Berger, Vienna, 1977, p. 1975. Z T. Ku/nicki. Bull. Acad. Pol. Sci. Sbr. Sci. lech., 26 (1978) 3. Z.T. Kuvnicki, IFPTRep. ( Prate I t ' P T P A . ' % , in Polish, to be pubhshed. Z.T. Kuznicki, Electron 7k,chmd., Nos. 2 and 3 (1979).