PHYSICAL ELECTRONICS(ECE3540) CHAPTER 9 –METAL AND SEMICONDUCTOR HETEROHETERO-JUNCTIONS-JUNCTIONS

Tennessee Technological University Monday, November 11, 2013 1 Introduction . Chapter 4: we considered the semiconductor in equilibrium and determined and hole concentrations in the conduction and valence bands, respectively. . The net flow of the and holes in a semiconductor generates current. The process by which these charged particles move is called transport. . Chapter 5: we considered the two basic transport mechanisms in a semiconductor crystal: drift: the movement of charge due to electric fields, and diffusion: the flow of charge due to density gradients.

Tennessee Technological University Monday, November 11, 2013 2 Introduction . Chapter 6: we discussed the behavior of non- equilibrium electron and hole concentrations as functions of time and space. . We developed the ambi-polar transport equation which describes the behavior of the excess electrons and holes. . Chapter 7: We considered the situation in which a p-type and an n-type semiconductor are brought into contact with one another to form a PN junction.

Tennessee Technological University Monday, November 11, 2013 3 Introduction . Chapter 8: We considered the PN junction with a forward-bias applied voltage and determined the current-voltage characteristics. . When holes flow from the p region across the region into the n region, they become excess minority carrier holes and are subject to excess minority carrier diffusion, drift, and recombination. . When electrons from the n region flow across the space charge region into the p region, they become excess minority carrier electrons and are subject to these same processes.

Tennessee Technological University Monday, November 11, 2013 4 Introduction . When a sufficiently large reverse-bias voltage is applied across a PN junction, breakdown can occur, producing a large reverse-bias current in the junction, which can cause heating effects and catastrophic failure of the . . Zener are designed to operate in the breakdown region. Breakdown puts limits on the amount of voltage that can be applied across a PN junction.

Tennessee Technological University Monday, November 11, 2013 5 Introduction . Chapter 9: we will consider the metal- semiconductor junction and the semiconductor hetero-junction, in which the material on each side ofthejunctionisnotthesame.Thesejunctionscan also produce diodes. . An is a low-resistance junction providing current conduction in both directions. We will examine the conditions that yield metal- semiconductor Ohmic contacts.

Tennessee Technological University Monday, November 11, 2013 6 Metal-Semiconductor Junction . There are two kinds of metal-semiconductor contacts:

 Rectifying Schottky diodes: metal on lightly doped .

 Low-resistance Ohmic contacts: metal on heavily doped Silicon.

Tennessee Technological University Monday, November 11, 2013 7 The Diode . Rectifying contacts are mostly made of n-type ; for this reason we will concentrate on this type of diode. . In the ideal energy- for a particular metal and n- type semiconductor, the level is used as a reference.

. The parameter M is the metal work function (in volts), s is the semiconductor work function,and is known as the . . Before contact, the in the semiconductor was above that in the metal. In order for the Fermi level to become a constant through the system in thermal equilibrium, electrons from the semiconductor flow into the lower energy states in the metal.

Tennessee Technological University Monday, November 11, 2013 8 The Schottky Barrier Diode

. The parameter B0 is the ideal barrier height of the semiconductor contact, the potential barrier seen by electrons in the metal trying to move into the semiconductor. . The barrier is known as the Schottky barrier and is given as:

B0  (M  ) . On the semiconductor side, is the built-in potential barrier. This barrier, similar to the case of the PN Junction, is the barrier seen by electrons in the conduction band trying to

move into the metal Vbi is given as:

Vbi  (B0 n )

Tennessee Technological University Monday, November 11, 2013 9 The Schottky Barrier Diode

Bn Increases with Increasing Metal Work Function

Vacuum level, E0  = 4.05 eV  Si M : Work Function q M of metal

 Si : Electron Affinity of Si qBn Ec

Ef Theoretically,

Bn= M – Si

Ev

x = 0 x = xn Fig. 9.1: Ideal energy-band diagram of a metal-semiconductor junction

Tennessee Technological University Monday, November 11, 2013 10 The Schottky Barrier Diode

Depletion Metal layer Neutral region

qBn Ec • Schottky barrier height, B , Ef N-Si is a function of the metal material. Ev •  is the most important Ec B parameter. The sum of q P-Si Bn and qBp is equal to Eg . Ef

qBp Ev

Fig. 9.2: Energy Band Diagram of Schottky Contact

Tennessee Technological University Monday, November 11, 2013 11 The Schottky Barrier Diode Schottky barrier heights for electrons and holes

Metal Mg Ti Cr W Mo Pd Au Pt

Bn (V) 0.4 0.5 0.61 0.67 0.68 0.77 0.8 0.9

Bp (V) 0.61 0.5 0.42 0.3 Work Function 3.7 4.3 4.5 4.6 4.6 5.1 5.1 5.7

m (V)

Bn + Bp  Eg

Bn increases with increasing metal work function

Tennessee Technological University Monday, November 11, 2013 12 The Schottky Barrier Diode

• A high density of energy Vacuum level, E0 states in the band gap at  = 4.05 eV Si the metal-semiconductor  q M interface pins Ef to a narrow range and Bn is qBn E c typically 0.4 to 0.9 V +  E f • Question: What is the

typical range of Bp?

Ev

Fig. 9.3: Fermi Level Pinning

Tennessee Technological University Monday, November 11, 2013 13 The Schottky Barrier Diode Schottky Contacts of Metal Silicide on Si

Silicide: A Silicon and metal compound. It is conductive similar to a metal.

Silicide-Si interfaces are more stable than metal-silicon interfaces. After metal is deposited on Si, an annealing step is applied to form a Silicide-Si contact. The term metal-silicon contact includes and almost always means Silicide-Si contacts.

Silicide ErSi1.7 HfSi MoSi2 ZrSi2 TiSi2 CoSi2 WSi2 NiSi2 Pd2Si PtSi f Bn (V)0.280.450.550.550.610.650.670.670.750.87 f Bp (V) 0.55 0.49 0.45 0.45 0.43 0.43 0.35 0.23 Table. 9.1: Schottky Contacts of Metal Silicide on Si

Tennessee Technological University Monday, November 11, 2013 14 The Schottky Barrier Diode 

qVbi  qBn (Ec  Ef ) qbi qBn Ec N E c f  q BnkT ln Nd

2 s (Vbi VR ) Ev  Wdep  xn  qNd q Bn q(bi + V) eN x C  s A | E | d n W max  qV dep s Ec Question: Ef How should we plot the CV

data to extract bi? Ev

Fig. 9.4: Using C-V Data to Determine B

Tennessee Technological University Monday, November 11, 2013 15 Exercise 1. Consider a contact between and an n-type 16 -3 Silicon doped to Nd =10 cm at T = 300K. Calculate the theoretical barrier height, built-in potential barrier and maximum in the metal-semiconductor diode for a zero applied bias.

Use the metal work function for Tungsten as M = 4.55V and electron affinity for Silicon  = 4.01V. V  (  ) B0  (M  ) bi B0 n eN x 2s (Vbi VR ) d n W  x  | Emax | dep n  qNd s

Tennessee Technological University Monday, November 11, 2013 16 Solution B0 is the ideal Schottky barrier height.

B0  (M  )  4.554.01 0.54V The space charge width at a zero bias is: kT  N   2.8x1019    ln c   0.0259ln   0.206V n    16  e  Nd   10 

Vbi  (B0 n )  0.540.206 0.33V

 14 2 s (V bi  V R ) 2 (11 .7 )( 8 .85 * 10 )( 0 .33 ) - 4 W dep  x n   19 16  0.207 * 10 cm qN d (1 .6 * 10 )(10 )

19 16 4 eNd xn (1.6*10 )(10 )(0.207*10 ) 4 | Emax |  14  3.2*10 V / cm  s (11.7)(8.85*10 )

Tennessee Technological University Monday, November 11, 2013 17 The Schottky Barrier Diode Using CV Data to Determine B

1 2(bi V ) 2  2 C qNd s A 1/C2

qbi qBn Ec

Ef

V E bi v

Fig. 9.5: Using C-V Data to Determine C

Tennessee Technological University Monday, November 11, 2013 18 The Schottky Barrier Diode

v thx- E q( B  V) c q N-type B E qV Efn V Metal Silicon fm 

E v x 3/ 2  2 m kT  Richardson's Constant n  N eq( B V )/ kT  2 n eq( B V )/ kT c  h2  4qm k 2   A*  n h3 vth  3kT / mn vthx   2kT / mn

1 4qm k 2   J   qnv  n T 2eq B / kT eqV / kT SM 2 thx h3

qV / kT qB / kT 2  J sT e , where J sT 100e A/cm Tennessee Technological University Monday, November 11, 2013 19 The Schottky Barrier Diode Schottky Diodes

Forward biased V = 0

I

V Reverse Reverse bias Forward bias biased

Tennessee Technological University Monday, November 11, 2013 20 The Schottky Barrier Diode Schottky Diodes

* 2 qB / kT Richardson's Constant I0  A KT e 2 2 * 4qmnk * 4qmnk 2 2 A  3 A  3 100 A/(cm K ) h h qV / kT qV / kT I  ISM  IM S  IsT e  IsT  IsT (e 1) Tennessee Technological University Monday, November 11, 2013 21 The Schottky Barrier Diode Applications of Schottky Diodes

I Schottky diode qV / kT I I  IsT (e 1)

2 qB / kT IsT  AKT e

 BB PN junction diode

V

3 8 • IsT of a Schottky diode is 10 to 10 times larger than a PN junction diode, depending on B .AlargerI0 means a smaller forward drop V. • A Schottky diode is the preferred rectifier in low voltage, high current applications.

Tennessee Technological University Monday, November 11, 2013 22 Exercise 2. Consider a Tungsten-Silicon diode with a barrier -5 2 height of BN = 0.67V and JsT =6*10 A/cm . Calculate the effective Richardson constant.

* 2 qBn / kT JsT  A T e

Richardson's Constant 4qm k 2 A*  n h3

Tennessee Technological University Monday, November 11, 2013 23 Solution 1. Using the relation for the reverse saturation :

* 2 qBn / kT JsT  A T e

J A A*  sT eqBn / kT 114 T 2 K 2cm2

Tennessee Technological University Monday, November 11, 2013 24 The Schottky Barrier Diode

PN Junction Schottky rectifier Transformer rectifier 100kHz 110V/220V Hi-voltage Hi-voltage Lo-voltage 50A DC AC AC 1V DC AC MOSFET utility inverter power

= 1V feedback to modulate the pulse width to keep Vout

Fig. 9.6: Switching Power Supply

Tennessee Technological University Monday, November 11, 2013 25 Applications of Schottky Barrier Diode . Synchronous Rectifier: For an even lower forward drop, replace the diode with a wide-W MOSFET which is not bound by the tradeoff between diode V and leakage current. . There is no minority carrier injection at the Schottky junction. Therefore, Schottky diodes can operate at higher frequencies than PN junction diodes.

Tennessee Technological University Monday, November 11, 2013 26 Comparison of Schottky Barrier Diode and the PN Junction Diode . The ideal current-voltage relationship of the Schottky barrier diode are of the same form as the PN Junction Diode, there is only a magnitude difference in the reverse-saturation current densities and the switching characteristics. . The current in a PN Junction is determined by the diffusion of minority carriers while the current in a Schottky barrier diode is determined by of majority carriers over a potential barrier. . The effective turn-on voltage of the Schottky diode is less than the PN Junction diode. . TheSchottkydiodeisahigh-frequency device than the PN Junction diode, therefore can be used in fast-switching application in pico-second time.

Tennessee Technological University Monday, November 11, 2013 27 Metal-Semiconductor Ohmic Contacts . Ohmic Contacts: metal-to-semiconductor contacts providing conduction in both directions, and having the current throught the ohmic contact as a linear function of applied voltage. . Ohmic contacts can be classified as ideal (non-rectifying barrier) or tunnel barrier. . A) Ideal (Non-rectifying) Barrier

. Check the Energy band Diagram (the case where m < s)

Tennessee Technological University Monday, November 11, 2013 28 Metal-Semiconductor Ohmic Contacts . Now, if a positive voltage is applied into the metal, there is no barrier to electrons flowing from the semiconductor into the metal. . If a positive voltage is applied to the semiconductor, the effective barrier height for electrons flowing from the metal into the

semiconductor will be Bn = n which is fairly small for a moderately doped semiconductor therefore electrons can easily flow from the metal into the semiconductor.

Tennessee Technological University Monday, November 11, 2013 29 Metal-Semiconductor Ohmic Contacts . B) Tunneling Barrier . In a metal to semiconductor contact, the space charge width is inversely proportional to the square root of the semiconductor . . As the doping concentration in the semiconductor increases, the probability of tunneling through the barrier increases.

Tennessee Technological University Monday, November 11, 2013 30 Semiconductor . Semiconductor Heterojunctions are formed between two semiconductor materials with different bandgap energies. . Such a junction is useful because it can create a potential well at the interface where electrons are confined to in the direction perpendicular to the interface but are free to move in the other direction. . In order to have a useful , the latice constants of the two materials must be well-matched. . Examples of Heterojunctions: GaAs - AlGaAs

Tennessee Technological University Monday, November 11, 2013 31 Exercise 18 -3 3. Consider Silicon at T = 300K doped at Nd =7*10 cm . Assume a rectifying Schottky barrier with Bn =0.67V. Consider the density of energy states for Silicon NcSi = 2.8*1019cm-3. Calculate the space charge width for the Schottky rectifying diode.

1 2 2 sVbi  xn     qNd 

Tennessee Technological University Monday, November 11, 2013 32 Solution 1. Using the relation for the reverse saturation current density:

* 2 qBn / kT JsT  A T e

J A A*  sT eqBn / kT 114 T 2 K 2cm2

Tennessee Technological University Monday, November 11, 2013 33 Picture Credits . Semiconductor Physics and Devices, Donald Neaman, 4th Edition, McGraw Hill Publications. . Modern Semiconductor Devices for Integrated Circuits, Prof. Chenming Calvin Hu, UC Berkeley (Free e-Book Download) . http://www.eecs.berkeley.edu/~hu/Book-Chapters-and-Lecture-Slides-download.html

Tennessee Technological University Monday, November 11, 2013 34