Avalanche breakdown

Impact ionization causes an avalanche of current

Occurs at low doping Zener tunneling

Electrons tunnel from valence band to conduction band

Occurs at high doping Tunneling

wave decays exponentially in the classically forbidden region

e1>e2

Tunneling is a wave phenomena. Tunneling and total internal reflection are used in a beam splitter. http://lampx.tugraz.at/~hadley/physikm/apps/snell/snell.en.php Zener tunneling

Breakdown voltage is typically much lower than the of an avalanche and can be tuned by adjusting the width of the depletion layer.

Used to provide a reference voltage. Avalanche breakdown

Tunneling Institute of Solid State Physics Technische Universität Graz metal - contacts

Photoelectric effect Workfunction Electron affinity Interface states Schottky barriers Schottky Ohmic contacts Thermionic emission Tunnel contacts Photoelectric effect current hf0 = ef at threshold workfunction f

threshold frequency f0 There is a dipole field at the surface of a metal. This electric field must be overcome for an electron to escape.

Singh work function - electron affinity

If fs < fm, the semiconductor bands bend down.

If fs > fm, the semiconductor bands bend up. work function - electron affinity

Electrons flow from a low work function material to high work function material. The high work function material becomes negatively charged. You have to push the electrons uphill into the low work function material. This determines the band bending.

If fs < fm, the semiconductor bands bend down.

If fs > fm, the semiconductor bands bend up. Singh

p-type Walter Schottky Schottky contact / ohmic contact

EF,m E metal F,s Schottky contact

EF,s EF,m metal Ohmic contact: linear resistance

1 J  2 Rc    -cm specific contact resistance: V  n-type Schottky contact / ohmic contact

Schottky contact EF,s

EF,m metal

EF,m metal EF,s

Ohmic contact: linear resistance

1 J  2 specific contact resistance: Rc    -cm V  Interface states http://www.springermaterials.com/navigation/#n_240905_Silicon+%2528Si%2529 Schottky barrier

Vbif s  f m eN 2 D 2e Vbi  V  eND x  E xx  n  W x  V  xx 0  xx e e n n  n r 0 eND e 2 

Like a one sided junction, the metal side is heavily doped. CV measurements

2e Vbi  V  xp  eN A

e ee N C   A F m-2 xp2 VV bi   2 C 1/

1 2Vbi  V  2  C eNe A V

GaAs has larger Eg and Vbi Thermionic emission

1901 Richardson Owen Willans Richardson Current from a heated is:

2 ef  J ATR exp   kB T 

Some electrons have a thermal energy that exceeds the work function and escape from the wire. Vacuum diodes

diode Thermionic emission

eV bi  V  Fermi function

EF

EE   E E   E f( E ) expF   exp  F exp  exp  kTB   kT BB kT  kT B E  The density of electrons with enough energy to go over the barriers  exp  kB T  Thermionic emission

eV  nth  exp  kB T 

eV  Ism n th  exp  kB T 

Ims IV sm (  0)

eV  II I I ekB T  1  sm ms s     Schottky barrier

Ism ~ 0 Ism > Ims Ims constant Thermionic emission

eV  II I I ekB T  1  sm ms s    

Nonideality factor = 1 Thermionic emission

* 2 efb  Is AAT R exp  kB T 

A = Area * AR = Richardson constant

* -2 -2 n-Si AR = 110 A K cm * -2 -2 p-Si AR = 32 A K cm * -2 -2 n-GaAs AR = 8 A K cm * -2 -2 p-GaAs AR = 74 A K cm

Thermionic emission dominates over diffusion current in a . Schottky diodes

Majority carrier current dominates. nonideality factor = 1.

Fast response, no recombination of electron-hole pairs required.

Used as rf mixers.

Low turn on voltage - high reverse bias current eV  I I ekB T  1  s     Tunnel contacts

For high doping, the Schottky barrier is so thin that electrons can tunnel through it.

metal p+ p

Degenerate doping at a tunnel contact

metal n+ n

Tunnel contacts have a linear resistance. Contacts Transport mechanisms

Drift Diffusion Thermionic emission Tunneling

All mechanisms are always present.

One or two transport mechanisms can dominate depending on the device and the bias conditions.

In a forward biased pn-junction, diffusion dominates.

In a tunnel contact, tunneling dominates.

In a Schottky diode, thermionic emission dominates. Institute of Solid State Physics Technische Universität Graz - MESFETs - MODFETs

Junction Field Effect (JFET) Metal-Semiconductor Field Effect Transistors (MESFET) Modulation Doped Field Effect Transistors (MODFET)

n JFET n-channel JFET

n

For NA >> ND

2(e Vbi  V ) xn  eND

2eV bi conducting at Vg = 0 Depletion mode h xn  eND

2eV bi nonconducting at V = 0 Enhancement mode h xn  g eND Power SiC JFET

p

p n n-channel (power) JFET

depletion zone n-channel JFET

drain n+ p+ depletion region

p n p gate

n+ JFETs are often discrete devices source MESFET

Metal-Semiconductor Field Effect Transistors

n

Depletion layer created by Schottky barrier

2(e Vbi  V ) xn  eND

Fast transistors can be realized in n-channel GaAs, however GaAs has a low hole mobility making p-channel devices slower. JFET

n

D n-channel JFET D G 2(e V V ) G S x  bi n-channel JFET n eN S D p-channel JFET

eN h2 Pinch-off at h = xn V  D V = pinch-off voltage p 2e p

At Pinch-off, Vp = Vbi -V. JFET

The drain is the side of the that gets pinched off.