86

60 6 5 70 75 ao a5 90 95 100 FREQUENCY I G H Z I

Fig. 3. VSWR of mica pressure window.

0 9

08

07

- 0 5

; 0 5

2 04

03

0 2

01

0 0 MI 63 10 75 80 8 5 SO 95 I O 0

F R E O U E N C Y I G H Z I

Fig. 4. Insertion loss of mica pressure window.

Fig. 5. Millimeter-wave pressure window.

Electrical tests for insertion loss were made using the substitution method, and VSWR was measured using a precision slotted line with a choke flange against the window. Single-frequency tests were made at 5-GHz intervals from 60 to 95 GHz. Though no sweep generator was available, a search was made for absorptive resonances by manually varying signal frequency; none was observed. Window thicknesses from 0.1 to 3 milliinches were tested experimentally. The selection of 0.00075-inch mica was based on a compromise between insertion loss and mechanical rigidity. Mechanical rigidity was based on the total flexure at a pressure differential of 1 atmosphere, whereas acceptable maximum insertion loss was 0.4 dB over the entire band. The VSWR and insertion loss of the window is shown in Figs. 3 and 4 as a function of frequency for various thicknesses. The VSWR was under

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1.5 as shown in Fig. 3, and the insertion loss under 0.4 dB from 60 to 95 GHz as shown in Fig. 4 for the selected window. The window, which was designed for use in a broad-band low-loss plasma waveguide switch, is illus- trated in Fig. 5. Twelve windows were fabricated and all remained leaktight after several temperature cyclings from 25 to 350°C.

1%'. D. CHERRY M. A. GOLDMAN R. Ross HARRY GOLDIE Westinghouse Defense and Space Center Baltimore, Md.

Photoelectric Fields in Semicon- ductors Under Strong Excitation

Abstracf-Photoelectric fields induced in semiconductors with nonuniform impurity profiles cancel the built-in electric field. In the case of strong photoexcitation, the maxi- mum open-circuit voltage approaches the internal built-in potential difference due to the impurity gradient between the ohmic contact probes on the semiconductor slice.

INTRODUCTION Under strong photoexcitation, the in-

duced carrier concentrations are much greater than the equilibrium carrier concen- tration, and as a result the drift field vanishes leaving the diffusion potential un- compensated. For simple, experimentally verified considerations [ l ] in the case of strong photoexcitation (An, Ap>>no, PO), the potential barrier of the p-n junction almost vanishes and the photo-EMF approaches the contact potential difference [2 ] . Re- cently, Shachar [3] confirmed the existence of the photovoltaic effects due to lifetime gradient (impurity gradient). Holonyak et al. [4] investigated the maximum photo- EMF of p-n junction. However, the analyses of the resulting photoelectric fields in semi- conductors and the open-circuit voltage between the contact probes on the semi- conductor have not been adequately dis- cussed.

The total internal electric field can be analytically determined from the total cur- rent, whole current, and electron current relations for semiconductors. This field consists of three terms: a conduction term, a built-in field, and an induced field. The built-in field Ed, which is due to the impurity gradient alone, is usually considered to be balanced by, or more appropriately bal- ances, the diffusion potential. Therefore, Ed can be written as

Ed = (Dpdpo/dx - D,dno/dx)/u, (1)

where

u = PO + AP) f pn(no f An),

Manuscript received May 9, 1969.

ELECTRON DEVICES, JANUARY 1970

D,is the holediffusionconstant, D, the elec- tron diffusion constant, po the equilibrium hole concentration (due to the impurity concentration), no the electron equilibrium concentration, pLp the electron mobility, and p p the hole mobility. An and A p are, respec- tively, the excess electron and hole concen- trations which are induced by photoex- citation.

For a p-type semiconductor, (1) reduces to

Ed (DpdPo/dx)/(ppPo f A%% f APUp) = (DpdPo/dx)/(Anun + APup) (2)

for An, Ap >> PO. Under very strong photoexcitation con-

ditions, the carrier recombination rate can be written as

R = ran2, (3) where R is the recombination rate, r is the appropriate recombination constant, and An the excess electron concentration for p- type material.

The drift field terms (2) vanish under strong photoexcitation. Therefore the con- tinuity equation for p-type material has the form

dn/dt = G - rAn2 f Dd2An/dx2, (4)

where D = (crnDp+upDn)/(un+crp), G is the generation rate, Dm the electron diffusion constant, and D, the hole diffusion constant. un and up represent the electron and hole conductivity under external excitation, respectively. Obviously, (4) is nonlinear.

In steady state, (4) can be solved by using Runge-Kutta integration with ap- propriate boundary conditions. If, a t some distance from the surface into the material, the diffusion term is sufficiently small, the excess electrons An are proportional to the square root of G while An is linearly de- pendent upon G in low excitation region.

If ideal ohmic contacts are assumed (Le., infinite surface recombination) on the sur- faces of the diffused semiconductor, then the boundary condition can be expressed as

An(A) = 0 and An(@ = 0, (5)

where A and B are the contact surfaces on the semiconductor.

Using these boundary conditions, the internal electric field, which is generated by the photoinduced carriers, can be deter- mined from the following equation under intense excitation:

Ei = (- D,dAn/dx f DpdAp/dx)

/ ( A w ~ f APPP f PO/+). (6)

If one assumes that An = Ap, the value of A p can be obtained from Ei and Poisson's equation. A more accurate value of Ei can then be obtained from ( 6 ) , and this itera- tion procedure pursued further until an exact value of Ei is obtained. The assump- tion An = A p is a reasonable approximation.

This high photoelectric field Ei does exist in the semiconductor under strong photo- excitation. However, the integral of this field from one surface to the other becomes vanishingly small compared wtih the con- tact potential difference, which is the change in the equilibrium chemical potential across the material.

CORRESPONDENCE 87

Fig. 1. The energy diagram of a diffused p-on-p

excitation. ( c ) Strong photoexcitation. semiconductor. (a) No excitation. (h) With photo-

To assist the explanation of the open- circuit voltage in this case, the energy dia- grams for a diffused semiconductor with and without external photoexcitation are shown in Fig. 1.

In the nondegenerate diffused p-on-p semiconductor, the relation between the carrier concentration and the Fermi energy is

Thus, the potential difference #'between the conduction band or valence band edges a t the two contact points is due to the impurity gradient. The potential #'d, which is due to the original built-in field, is

/(P& + A w , + A P d d X , where po is a function of position but not excitation.

The open-circuit voltage is the difference between these two potentials,

voc = #'A - +B - #'d. (10)

Without photoexcitation, +d is equal to ++, and Vo,,,=O.

Under strong photoexcitation, the drift field vanishes, the value of @(A) and p ( B ) remain constant under our boundary condi- tion, and the open-circuit voltage is simply equal to the contact potential equivalent between the opposite ends of the material.

voo #'A - #'B = + ( k T / e ) 1n [P(A)/P(B)~ = 6.

(11)

I t can then be summarized that in a diffused semiconductor slice under external excitation, an excess carrier concentration

A p and An will be produced. Then we find that the value of built-in field decreases and the total open-circuit voltage approaches the equivalent distributed contact potential dif- ference due to impurity gradient. The quasi- Fermi levels split away from the Fermi energy, however, return to the same level a t the ohmic contacts. Thus the open-circuit voltage depends solely upon the internal material contact potential difference. This agrees with the discussion by Esposito et al. (5). Although high induced photo- electric fields may exist in a semiconductor, ohmic contact probes can only detect the Fermi energy difference between the con- tact points.

W. B. BERRY H. Y. Yu1 University of Notre Dame Notre Dame, Ind.

REFERENCES [I] P. N. Keaiing, "Photovoltaic effect in photo-

conductors, J . A5al. Phys.. vol. 36, p. 564, 1965.

[2] L. M. Blinvo, V. S. Vavilov, and G. N. Galki,

semiconductor, J E T P Letters, vol. 3, p. 234 Photo-emf of p,;n junctions in a strongly excited

._

[3] G. Shachar, "The generation of lifetime-gradient 1966.

photovoltages in photoconductors, J . Appl . Phys.. vol. 38, p. 5412, 1967.

[41 N. Holonyak, Jr.. J. A. Rossi, R. D. Burnham,

mental investigatioy of the maximum photo-emf B. G. Streetman, and M. R. Johnson, "An experi-

of a p-n junctions, J . Appl. Phys.. vol. 38, p.

[5] R. M. Esposito, J. J. Loferski, and H. Flicker, 5422, 1967.

gradient and dember photovo!tages in semicon- "Concerning the possibility of observing lifetime-

ductors," J . App l . Phys., vol. 38, p. 825, 1967.

University of New Mexico, Albuquerque, N. Mex. 1 Now with the Bureau of Engineering Research,