Semiconductor Device Physics Lecture 11 Dr Ing Erwin

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Semiconductor Device Physics Lecture 11 Dr. -Ing. Erwin Sitompul President University http: //zitompul. wordpress.

Semiconductor Device Physics Lecture 11 Dr. -Ing. Erwin Sitompul President University http: //zitompul. wordpress. com 2 President University 0 1 3 Erwin Sitompul SDP 11/1

Semiconductor Device Physics Chapter 14 MS Contacts and Schottky Diodes President University Erwin Sitompul

Semiconductor Device Physics Chapter 14 MS Contacts and Schottky Diodes President University Erwin Sitompul SDP 11/2

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes MS Contact n The metal-semiconductor (MS) contact

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes MS Contact n The metal-semiconductor (MS) contact plays a very important role in solid-state devices. n When in the form of a rectifying contact, the MS contact is referred to as the Schottky. n When in the from of a non-rectifying or ohmic contact, the MS contact is the critical link between the semiconductor and the outside. n The reverse-bias saturation current IS of a Schottky diode is 103 to 108 times larger than that of a pnjunction diode, depending on the type of material. n Schottky diodes are proffered rectifiers for low-voltage highcurrent applications. President University Erwin Sitompul pn-junction diode I VA Schottky diode SDP 11/3

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes MS Contact n A vacuum energy level,

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes MS Contact n A vacuum energy level, E 0, is defined as the minimum energy an electron must possess to completely free itself from the material. n The energy difference between E 0 and EF is known as the workfunction (Φ). President University Erwin Sitompul SDP 11/4

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Workfunction E 0: vacuum energy level c.

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Workfunction E 0: vacuum energy level c. Si = 4. 03 e. V FM: Metal workfunction EFM: Fermi level in metal President University FS: Semiconductor workfunction EFS: Fermi level in semiconductor c: electron affinity Erwin Sitompul SDP 11/5

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Ideal MS Contact: FM > FS, n-type

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Ideal MS Contact: FM > FS, n-type n E 0 is continuous n Band diagram instantly after contact formation n Band diagram under equilibrium condition n Surface potential -energy barrier President University Erwin Sitompul SDP 11/6

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Ideal MS Contact: FM < FS, n-type

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Ideal MS Contact: FM < FS, n-type n E 0 is continuous n Band diagram instantly after contact formation n Band diagram under equilibrium condition President University Erwin Sitompul SDP 11/7

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes n-type MS Contact Forward Bias n Current

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes n-type MS Contact Forward Bias n Current is determined by majoritycarrier flow across the MS junction. n Under forward bias, majoritycarrier diffusion from the semiconductor into the metal dominates. n Under reverse bias, majoritycarrier diffusion from the metal into the semiconductor dominates. Forward bias Reverse Bias President University Reverse bias Erwin Sitompul SDP 11/8

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Metal-Semiconductor Contacts n There are 2 kinds

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Metal-Semiconductor Contacts n There are 2 kinds of metal-semiconductor (MS) contact: I n Rectifying (“Schottky diode”) I VA n Non-rectifying (“Ohmic contact”) President University Erwin Sitompul VA SDP 11/9

Metal-Semiconductor Contacts EF Ev EF Ec Ev President University Ec Ec EF Ev Erwin

Metal-Semiconductor Contacts EF Ev EF Ec Ev President University Ec Ec EF Ev Erwin Sitompul SDP 11/10

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes The Depletion Approximation n The semiconductor is

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes The Depletion Approximation n The semiconductor is depleted to a depth W: n In the depleted region (0 x W ): n Beyond the depleted region (x > W ): Vbi : “built-in” voltage President University Erwin Sitompul SDP 11/11

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Poisson’s Equation n According to Gauss’s Law:

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Poisson’s Equation n According to Gauss’s Law: Area A E(x) n Or: E(x+Dx) Dx n E : electric field intensity (V/m) n S : relative permittivity (F/cm) n : charge density (C/cm 3) n S = KS 0 n 0 = 8. 854 × 10– 14 F/cm n For Si, KS = 11. 8 President University Erwin Sitompul SDP 11/12

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes MS Contact Electrostatics n Poisson’s equation: +

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes MS Contact Electrostatics n Poisson’s equation: + – n The solution is: n Furthermore: President University Erwin Sitompul SDP 11/13

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Depletion Layer Width W + n The

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Depletion Layer Width W + n The potential in the semiconductor side is chosen to be the zero reference. n At x = 0, V = –Vbi n The depletion width is given by – n W decreases as ND increases President University Erwin Sitompul SDP 11/14

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Depletion Layer Width W for VA 0

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Depletion Layer Width W for VA 0 n Previously, + – n At x = 0, now V = – (Vbi – VA) n W decreases as ND increases n W increases as –VA increases – (Vbi – VA) President University Erwin Sitompul SDP 11/15

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Thermionic Emission Current n Thermionic emission current

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Thermionic Emission Current n Thermionic emission current results from majority carrier injection over the potential barrier. n Electrons can cross the junction into the metal if: n The current for electrons at a certain velocity is: n Or: n The total current over the potential barrier is: President University Erwin Sitompul SDP 11/16

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes I –V Characteristics n For a non-degenerate

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes I –V Characteristics n For a non-degenerate semiconductor, it can be shown that: n We can then obtain n Where n And President University Erwin Sitompul SDP 11/17

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes I –V Characteristics n In the reverse

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes I –V Characteristics n In the reverse direction and equilibrium condition, the electrons always see the same barrier FB, so n Therefore –IS : reverse bias saturation current n Finally, combining the total current at an arbitrary VA, n Where President University Erwin Sitompul SDP 11/18

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Small-Signal Capacitance n In an MS contact,

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Small-Signal Capacitance n In an MS contact, charge is stored on either side of the MS junction. n The applied bias VA affects this charge and varies the depletion width. n If an a. c. voltage va is applied in series with the d. c. bias VA, the charge stored in the MS contact will be modulated at the frequency of the a. c. voltage. n Displacement current will flow. President University Erwin Sitompul SDP 11/19

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Small-Signal Capacitance n Since in general n

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Small-Signal Capacitance n Since in general n Then n Or President University Erwin Sitompul SDP 11/20

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Practical Ohmic Contact n In practice, most

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Practical Ohmic Contact n In practice, most MS-contacts are rectifying. n In order to achieve a contact that can conduct easily in both directions, the semiconductor is to be doped very heavily. n Depletion width W becomes so narrow that the carriers can tunnel directly through the barrier. President University Erwin Sitompul SDP 11/21

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Voltage Drop Across the MS Contact n

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Voltage Drop Across the MS Contact n Under equilibrium conditions (VA = 0), the voltage drop across the semiconductor depletion region is the built-in voltage Vbi. n If VA 0, the voltage drop across the semiconductor depletion region is Vbi – VA. q. Vbi q(Vbi–VA) President University Erwin Sitompul SDP 11/22

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes MS Contact with p-type Semiconductor n If

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes MS Contact with p-type Semiconductor n If p-type semiconductor is used, the depletion layer width W of the MS contact for VA 0 is given by ? n At x = 0, V = Vbi + VA, n W increases as VA increases n W decrease as NA increases President University ? Erwin Sitompul ? SDP 11/23

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Homework 9 n 1. (Nea. EC. 10.

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes Homework 9 n 1. (Nea. EC. 10. 27) An MS-junction is formed between a metal with a work function of 4. 3 e. V and p-type Si with an electron affinity of 4 e. V. The doping concentration in semiconductor is 5× 1016 cm– 3. Assume T = 300 K. (a) Sketch thermal equilibrium energy band diagram; (b) Determine the height of the Schottky barrier; (c) Sketch the energy band diagram with an applied reverse-bias voltage of VA = – 3 V; (d) Sketch the energy band diagram with an applied forward-bias voltage of VA = 0. 25 V. n Due: 12. 2013. President University Erwin Sitompul SDP 11/24