Current transport in metal-semiconductor barriers
Abstract
A theory for calculating the magnitude of majority carrier current flow in metal-semiconductor barriers is developed which incorporates Schottky's diffusion (D) theory and Bethe's thermionic emission (T) theory into a single T-D emission theory, and which includes the effects of the image force. A low electric field limit for application of this theory is estimated from consideration of phonon-induced backscattering near the potential energy maximum. A high electric field limit associated with the transition to T-F emission is estimated from calculations of the quantum-mechanical transmission of a Maxwellian distribution of electrons incident on the barrier. The theory predicts a wide range of electric field ≈ 2 × 102 to 4 × 105 V/cm over which the T-D theory may be applied to metal-n-type Si barriers at 300°K. The corresponding range for metal-n-type GaAs barriers is 9 × 103 to 8 × 104V/ at 300°K. The decreased upper limit is due mainly to the smaller electron effective mass in GaAs, the increased lower limit to a small optical-phonon energy and a shorter electron-optical-phonon mean-free path. The theory predicts Richardson constants of 96 and 4.4 A/cm2/°K2 for metal-n-type Si and metal-n-type GaAs barriers respectively. Experimental measurements on both metal-Si and metal-GaAs barriers are in general agreement with the theory. Values of the barrier n[(q/kT)(dV/d ln J)] appreciably greater than unity are predicted for the field-dependent barrier height which occurs when an interface layer of the order of atomic thickness exists between the metal and the semi-conductor. A field dependence of the barrier height is shown to have no first order effect on the derivative of the 1/C2 vs. V relationship for the barrier. The intercept of a 1/C2 vs. V plot is shown to yield the barrier height extrapolated linearly to zero field in the semiconductor. Experimental evidence for the existence of interface layers in near-ideal Schottky barriers is also presented.
Résumé
On développe une théorie pour calculer la grandeur du courant porteur majoritaire dans les barrières métal-semiconducteur qui comprend la théorie de diffusion de Schottky (D) et la théorie d'émission thermionique de Bethe (T) combinées dans une seule; cette théorie d'émission T-D comprend les effets de la force d'image. Une faible limite de champ électrique pour l'application de cette théorie est estimée en considérant les éparpillements arrières induits par des phonons près du maximum d'énergie potentielle. Une forte limite de champ électrique associée à la transition de l'émission TF est estimée par des calculs de transmission quanta-mécaniques d'une distribution maxwellienne d'électrons incidents à la barrière. La théorie prédit une large gamme de champs électriques le long de laquelle la théorie TD peut être appliquée aux barrières métal-Si de type n à 300°K. La gamme correspondante pour les barrières métal-AsGa de type n est de 9 × 103 à 8 × 104 V/cm à 300°K. La réduction de la limite supérieure est due principalement à la masse d'électrons effectivement plus petite dans l'AsGa et la réduction de la limite inférieure à une plus petite énergie phonon-optique et un plus petit parcours moyen libre électron-optique-phonon. La théorie prédit des constantes de Richardson de 96 et de 4,4 A/cm2/°K2 pour les barrières métal-Si de type n et métal-AsGa de type n respectivement. Des mesures expérimentales sur ces deux barrières sont en accord général avec la théorie. Des valeurs de barrière n[(q/kT)(dV/d ln J)] beaucoup plus grandes que l'unité ont été prédites pour la hauteur de barrière à dépendance de champ qui se produit quand une couche d'interface ayant des épaisseurs d'ordre atomiques existe entre le métal et le semiconducteur. On démontre que la dépendance de champ de la hauteur de la barrière ne possède pas d'effets de premier ordre sur la relation-derivée de 1/C2 en fonction de V-de la barrière. On démontre que l'interception de l'axe dans le graphique 1/C2 en fonction de V donne la hauteur de barrière extrapolée linéairement au champ zéro dans le semi-conducteur. On présente aussi des preuves expérimentales pour l'existence de couches d'interface dans les barrières Schottky quasi-idéales.
Zusammenfassung
Eine Theorie für die Berechnung des Majoritätsträgerstromes in Metall-Halbleiter-Übergängen wird entwickelt, welche Schottkys Diffusionstheorie (D) und Bethes thermionische Emissionstheorie (T) zu einer TD-Theorie kombiniert und die Auswirkungen der Bildkraft Berücksichtigt. Die Anwendbarkeit der Theorie ist durch eine untere und eine obere Grenze für das elektrische Feld beschränkt. Die untere Feldgrenze wird aus der Rückstreuung der Elektronen infolge Elektron-Phonon-Wechselwirkung in der Nähe des Maximums der potentiellen Energie abgeschätzt. Die obere Grenze für das elektrische Feld ist durch den Einsatz der thermionischen Feldemission (TF) gegeben und wird über die Tunnelwahrscheinlichkeit einer Maxwellschen Elektronenverteilung abgeschätzt. Für Metall-nSi-Übergänge bei 300°K ergibt sich ein grosser Feldstärkenbereich, in dem die TD-Theorie anwendbar sein sollte, nämlich 2 × 102 bis 4 × 105 V/cm. Der entsprechende Bereich für Metall-nGaAs-Übergänge bei 300°K erstreckt sich dagegen nur von 9 × 103 bis 8 × 104 V/cm. Die Abnahme der oberan Feldgrenze ist hier hauptsächlich auf die geringere effektive Masse von GaAs gegenüber Si zurückzuführen und die Zunahme der unteren Grenze auf die kleinere Anregungsenergie für optische Phononen sowei die kürzere mittlere freie Weglänge der Elektronen bei Wechselwirkung mit optischen Phononen. Die Theorie sagt Richardsonkonstanten von 96 und 4,4 A/cm2/°K für Metall-nSi bzw. Metall-nGaAs-Übergänge voraus. Experimentelle Ergebnisse sowohl an Metall-Si als auch an Metall-GaAs-Übergängen stimmen im allgemeinen mit der Theorie überein. Eine monoatomare Grenzschicht zwischen Halbleiter und Metall hat eine felstärkenabhängige Potentialschwelle zur Folge. In diesem Fall liefert die Rechnung für die Kennzahl n[(q/kT)(dV/d ln J)] erheblich grössere Werte als 1. Es wird gezeigt, dass sich eine feldabhängige Potentialstufe in erster Näherung nicht auf die Kurve 1/C2 gegen V auswirkt. Der auf äussere Spannung Null extrapolierte Achsenabschnitt einer Kurve 1/C2 gegen V steht im Zusammenhang mit der Potentialstufe des betreffenden Überganges. Experimentelle Hinweise für die Existenz von Grenzschichten in nahezu idealen Schottky-Übergängen werden ebenfalls gebracht.
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Present address: E.E. Dept., Univ. of Southern California, Los Angeles, California, U.S.A.