Outline Chap. 1 Introduction Chap. 2 Basics of Semiconductor Physics Chap. 3 P-N Junctions Chap. 4 Metal-Semiconductor Junctions Chap. 5 Semiconductor Heterojunctions Chap. 6 Semiconductor solar cells & Photodiodes Chap. 7 Light Emitting Diodes & Semiconductor Lasers Chap. 8 Quantum Dots for Biological Fluorescent Probes

Chapter 3 P-N Junctions

3.1 Junction Formation Junction: metallurgical contacts (or atomic contacts) of any two materials (except insulators). p-n junction: metallurgical contacts of a p-type and an n-type semiconductors. The elementary units of almost all of the semiconductor devices. Isotype homojunction: p-Si and p-Si. Isotype heterojunction: p-Si and p-Ge Anisotype homojunction: p-Si and n-Si Anisotype heterojunction: p-Si and n-Ge Common techniques of junction formation: ion implantation, diffusion, epitaxial growth, lithography, vacuum deposition, oxidization, testing and packaging technology.

Fabrication process of a p-n junction with Si single crystals

Fabrication process of a p-n junction with Si single crystals

linearly graded junction one-sided abrupt junction 3.1 Junction Formation The most common technique of junction formation is impurity diffusion. In practice, diffusion junctions can be approximately described by abrupt junctions and linearly graded junctions. P+N 低表面浓度的深扩散结 高表面浓度的浅扩散结 NA ND linearly graded junction diffusion junction one-sided abrupt junction

p  n 3.2 p-n junctions under equilibrium conditions p n + Space Charge When a p- and n-type semiconductors are joined, the large concentration gradient of holes from the p- to the n-side and vice versa for electrons results in the diffusion of free carriers. Immobile positively ionized donor atoms and negatively ionized acceptor atoms are left behind in the n- and p- region respectively. --------- space charge p n _ + Built-in electric field p  n

3.2 p-n junctions under equilibrium conditions Band Diagram P N When junction is formed, electrons transfer from n-region (high EF) to p-region (low EF), vice versa for holes. EF increases in p-region and decreases in n-region, until they are equal on both sides. Space-charge region is also called barrier region. qVD=EFn - EFp

3.2 p-n junctions under equilibrium conditions Built-in field generates drift currents in opposite direction of diffusion currents. At thermal equilibrium, drift current = diffusion current.  no net current flow. VD + - Neutral zone: p- and n-regions far from the space-charge region. No space charge, high density of carriers, low resistance. Depletion region: space-charge region. Immobile charges, no free carriers, high resistance. Boundary zone: area between neutral and depletion regions.

3.3 p-n junctions under bias Forward Bias Forward bias reduce the built-in electric field, equivalent to reducing space charges  barrier region width reduces and potential barrier lowers. Drift current is reduced and diffusion current is favorable  large current. Low-resistance current path is created by applied forward bias. VD

3.3 p-n junctions under bias Reverse Bias Barrier region width increases and potential barrier increases. Diffusion current is reduced and drift current dominates. Very low current passing through the junction  high resistance. A p–n junction only allows current in one direction. rectification.  VD

3.3 p-n junctions under bias Electrical injection of non-equilibrium carriers Forward bias generates net diffusion current, electrons moving from N to P, holes from P to N, leading to non-equilibrium minority carriers in N and P. Electrical injection of non-equilibrium carriers The majority carrier densities are hardly affected. The density of non-equilibrium minority is very high in the boundary zone, decreases as recombination happens, and finally drops to zero. In LEDs or laser, injected minority carriers recombine with the background majority carriers and produce photons. nn=nn0 pp=pp0

3.3 p-n junctions under bias Quasi-Fermi level under electrical injection Under forward bias, quasi Fermi levels are present in the areas where non-equilibrium minorities exist. In hole diffusion region, the Fermi level of electrons is unchanged. Large change in the hole density  Quasi-Fermi level is a diagonal line and approaching the Fermi level when hole injection is zero. Changes of quasi-Fermi levels at the barrier region can be ignored. Electron Diffusion Region Hole Diffusion Region Barrier Region V + - P N

3.3 p-n junctions under bias Extraction of minority carriers Under reverse bias, the holes in the boundary region of N side are forced to move to the P side, introducing hole diffusion current in the neutral region of N side. ------- Extraction of minority carriers

3.4 I-V characteristics for ideal diodes Diode: a two terminal rectifier. One p-n junction for one diode. DC current-voltage relation of p-n junctions ---- I-V characteristic Basic assumptions for ideal p-n junctions: （1）Ignore the bulk and contact resistances in the neutral region. The applied voltage completely drops across the depletion region; （2）Homogeneous doping; （3）Small injection; （4）No recombination and generation currents in the depletion region; （5）Degenerate semiconductor (low doping).

3.4 I-V characteristics for ideal diodes Under forward bias, the injected minority carriers recombine with the majority carriers. The hole (electron) current dissipates exponentially in the p (N) side. Since current continuity requires total current unchanged, the majority current increases exponentially. Ip In P N P N Ip In In Ip

3.4 I-V characteristics for ideal diodes Under reverse bias, the strengthened electric field in the barrier region could sweep away any minority carrier diffused into the barrier region. Reverse current: generated in the vicinity of the space charge region and related to the diffusion of minority carriers to the space charge region. Since the minority carrier densities are very low, the reverse current is small and will be saturated. P N N P |In| |Ip|

3.4 I-V characteristics for ideal diodes Unidirectional conduction of an ideal p-n junction: forward current increases exponentially with applied voltage, and reverse current is very low and will be saturated. I0 I Shockley equation: I0 : Saturated current.

3.5 Recombination and generation current in the depletion region In real diodes, the I-V characteristics deviate from the Shockley equation, due to the recombination and generation of carriers in the depletion region and external contact resistance. The injected carriers by forward bias move across the depletion region, pn>ni2 ----- recombination of non-equilibrium carriers. Under reverse bias, due to thermal excitation, in the depletion region, pn<ni2 ----- generation of non-equilibrium carriers. Recombination and generation currents will be generated by the recombination and generation of non-equilibrium carriers.

3.5 Recombination and generation current in the depletion region Recombination current under forward bias Recombination of non-equilibrium carriers at the recombination centers in the depletion region. h+ e- ABCD: injected electron current; A’B’C’D’: injected hole current. EFGH：recombination current at the recombination center.

3.5 Recombination and generation current in the depletion region Recombination current under forward bias （Maximum recombination） For P+N (one-side injection), diffusion current due to injection V. S. recombination current in the depletion region: For semiconductors with larger band gap, ni is smaller, so Irec is larger. Eg., Irec in Si is larger than that in Ge, for small injection. For light doped region with higher impurity density, Irec is larger. For smaller forward bias, Irec is larger.

Id Irec I-V characteristics of a Si diffusion junction Effect of series resistance I-V characteristics of a Si diffusion junction For a low forward bias, recombination current in the depletion region dominates. As the forward bias increases, the slope also goes up, indicating larger diffusion current. For a higher current, the series resistance causes a large Ohm voltage drop. Experimental data Id Slope = q/KBT Irec Slope = q/2KBT

3.5 Recombination and generation current in the depletion region Generation current under reverse bias h+ e- Due to thermal excitation CBAD: reverse electron diffusion current; C’B’A’D’: reverse hole diffusion current. EFGH：generation current due to the recombination centers in the depletion region.

3.5 Recombination and generation current in the depletion region Generation current under reverse bias I0 Ideal Non-ideal A: cross section of the junction. W: depletion region width. 1/0: capture probability in the combination center. As W increases with reverse bias, Ig also gets higher with increasing reverse bias. Thus, the reverse current of a real diode can not be saturated.

3.6 Breakdown in a p-n junction One of the most important problems that should be considered in device designing. Junction breakdown：Sudden increasing of reverse current when the reverse bias exceeds a certain value. Breakdown bias VBR. VBR I V Breakdown Mechanisms Thermal Avalanche Zener

3.6 Breakdown in a p-n junction Zener Breakdown (tunnel breakdown) Earlieat model. Under the high E field, covalent bonds break in the depletion region and generate e-h pairs (tunneling effect)  Reverse tunnel current. Non-destructively reversible breakdown. Dominated in heavily doped diodes. Zener breakdown is applicable for low voltages. Eg., Si p-n junction, VBR< 4.5 V. Avalanche breakdown is applicable for high voltages. Eg., Si p-n junction, VBR > 6.7 V.

3.6 Breakdown in a p-n junction Avalanche Breakdown High reverse bias  Carriers gains energy from the electric field  Carriers collide with the lattice in the depletion region  For high enough energy, electrons will be excited from VB to CB, leading to e-h pairs  E-h pairs are accelerated by the E field, and collisions give rise to more e-h pairs  The carriers multiply. The electric field for avalanche breakdown in a Si based p-n junction is 105-106 V/cm N P Non-destructive breakdown.

Localized Temperature Rise 3.6 Breakdown in a p-n junction Thermal Breakdown Very important for narrow-band-gap Ge p-n diodes at room temperature. Heat Loss Localized Temperature Rise Current Increasing Destructive breakdown !

Outline Chap. 1 Introduction Chap. 2 Basics of Semiconductor Physics Chap. 3 P-N Junctions Chap. 4 Metal-Semiconductor Junctions Chap. 5 Semiconductor Heterojunctions Chap. 6 Semiconductor solar cells & Photodiodes Chap. 7 Light Emitting Diodes & Semiconductor Lasers Chap. 8 Quantum Dots for Biological Fluorescent Probes

Metal-Semiconductor (M-S) Junctions Chapter 4 Metal-Semiconductor (M-S) Junctions

Introduction M-S Junction: metallurgical contacts of metals and semiconductors. Point-contact: pressing metal pins on the semiconductor crystals. Surface-contact: evaporation of metal films on the semiconductors. Schottky contacts: rectification effect, rectifying junction Ohm contacts: Ohm effect, non-rectifying junction Properties of ideal M-S contacts: 1. Atomic contacts between metal and semiconductor, no layers in between. 2. No mutual diffusion or mixing between metal and semiconductor. 3. No impurities or charges on the interface of metal and semiconductor.

Introduction In 1970s, the devices based on M-S junctions were developing promptly, due to the reproducibility in making M-S contacts by using semiconductor planar process and vacuum technology. Schottky diodes are unipolar devices, where the current is predominantly due to the thermionic emission of carriers over the potential barrier. Non-rectifying diodes (Ohm contacts): equal and large currents flow in both forward and reverse bias directions with small resistance. All of the devices need Ohm contacts to connect to other devices. Primary M-S devices: Schottky diodes, Schottky field effect transistors.

4.1 Schottky Barriers 4.1.1 Formation of Schottky Barriers Assume no surface states  flat band till the surface of semiconductor E0：vacuum level After contacts, electrons in the semiconductor transfer to the metal, to flatten out the Fermi levels.  Positive space charges on the surface of semiconductor, and negative space charges on the surface of metal. －work function of semiconductor - work function of metal - electron affinity of semiconductor

4.1 Schottky Barriers 4.1.1 Formation of Schottky Barriers The space charge region is very thin on the surface of metal (~0.5nm), and much thicker on the semiconductor side. Under thermal equilibrium, the band of semiconductor bends upwardly —— built in potential Metal Semiconductor Schottky barrier: or Where,

4.1 Schottky Barriers 4.1.2 Under forward bias Forward bias: negative voltage applied on the semiconductor. The barrier reduces to , and changed to The space charge is very thin in the depletion region, b unchanged. The Fermi level of metal is lower than that of semiconductor, by qV. As the barrier is lowered, it is easier for the electrons in the semiconductor to move to the metal. large current. 金属 半导体 金属 半导体 No Bias Forward Bias

Schottky barrier has rectification property. 4.1 Schottky Barriers 4.1.3 Under reverse bias Reverse bias: positive voltage applied on the semiconductor The barrier increases to , is changed to . The space charge layer is very narrow on the metal sizeb is unchanged. The Fermi level of metal is higher than that of semiconductor, by ~qVR. The electron current from metal to semiconductor dominates, while the barrier is so high that the reverse current is small and can be saturated. Schottky barrier has rectification property. Metal Semiconductor metal Semiconductor No Bias Reverse Bias

4.2 Effect of Interface States on the Barrier Height For a given semiconductor,  is fixed. Based on , the height of Schottky barrier will change with the work function of metal. But actual measurements reveal that the work function of metal does not affect the barrier height, due to the presence of surface states on the surface of semiconductor.

4.2 Effect of Interface States on the Barrier Height What are interface states? - + - + In real Schottky diodes, the break of crystal lattice of semiconductor at the interface introduces a large amount energy states in the forbidden band, so called interface states or surface states. Properties of surface states. The interface states have a distribution in the forbidden band, which can be characterized by a neutral level , below which, all the interface states are filled by electrons and the interface is electrical neutrality. If , the interface is positively charged, similar to the donors. If , the interface is negatively charged, similar to the acceptors. If , the interface is electrical neutrality. No net charges.

4.2 Effect of Interface States on the Barrier Height If , The interface is positively charged, similar to the donors. W Potential forms in the tiny gap between metal and semiconductor, due to the charges on the surface of metal and semiconductor. LESS ionized donors are needed in the depletion region to reach equilibrium. Built-in potential is greatly reduced, and b also lowers. Ef is closer to E0 .

4.2 Effect of Interface States on the Barrier Height If , The interface is negatively charged, similar to the acceptors. MORE ionized donors are needed in the depletion region to reach equilibrium. Built-in potential increases, and b also greatly increases. Ef is closer to E0 .

4.2 Effect of Interface States on the Barrier Height Interface charges has inverse feedback effect, which makes close to . If density of interface states is very high, the Fermi level will be pinned at , so called Pinning Effect of Fermi level. And is not related to the work functions of metal and semiconductor. In most of the real Schottky diodes, the interface states predominantly decide , and the barrier height has nothing to do with the work functions and the doping density in semiconductors.

4.3 I-V Charateristics of Schottky Diodes The current in the Schottky barrier is dominated by the carrier flow from the edge of the depletion region of semiconductor to the metal. The forward bias reduces the E field and potential in the depletion region, leading to electron diffusion current across the depletion region, and the emission of electrons to the metal. At room temperature, the carrier transport is limited by the electron emission process in most real Schottky diodes, and the electron diffusion effect can be ignored. Metal Semiconductor Forward Bias

4.3 I-V Charateristics of Schottky Diodes Hot electrons and hot carrier diodes When electrons on the top of the barrier emit to the metal, their energy is higher (by ~ ) than that of the electrons in the metal.  Hot electrons. After entering the metal, the hot electrons will collide with other electrons and release the excess energy. The Schottky diodes are also called hot carrier diodes. The equilibrium will be shortly (< 0.1 ns) reached between the hot electrons and other electrons in the metal. Metal Semiconductor Forward Bias

W-Si和W-GaAs肖特基二极管正向电流密度与电压的对应关系 4.3 I-V Charateristics of Schottky Diodes I-V characteristics Richardson-dushman equation: n=1.02 where, n=1.04 Effective Richardon constant n is ideality factor, induced by non-ideal effects. For ideal Shnokky diodes, n=1. W-Si和W-GaAs肖特基二极管正向电流密度与电压的对应关系

4.3 I-V Charateristics of Schottky Diodes The thermionic emission corresponds to the majority carrier current. Minority carrier current: electron current from the top of the valence band of the semiconductor to the empty states below EF of the metal, and can be considered as hole current from the metal to the semiconductor. where, The current of the Schottky diodes is primarily conveyed by the majority carriers, and the minority carrier current can be ignored. Metal Semiconductor Forward Bias

4.4 M-I-S Schottky Diodes Basic Structures M I S In reality, there has been always a thin layer (0.5-1.5 nm) of oxides between the metal and semiconductor, forming a M-I-S structure. In MIS Schottky diodes, the current is generated by the tunneling effect of carriers across the oxide layer. If applied voltage is unchanged, the oxide layer (<2nm) only reduces majority carrier current and does not affect the minority carrier current.  Increasing ratio of minority to majority carrier current.  Increasing injection ratio of minority carriers, good for solar cells and LEDs. M I S

4.5 Schottky Diodes V.S. P-N Diodes Schottky diodes: thermionic emission current, majority carrier devices; P-N diodes: diffusion current, minority carrier devices. Forward bias converts abruptly to reverse bias  Switching speed of p-n diodes are limited by the storage effect of minority carriers, but Schottky diodes do not have minority carrier storage. Schottky diodes is applicable to high-frequency and fast-switching devices. Al-Si(N) Si The saturated current of a Schottky diode is much higher than that for a p-n diode. And under the same current, forward voltage drop and threshold voltage are much lower than those for a p-n diodes.

4.5 Schottky Diodes V.S. P-N Diodes Schottky diodes are more stable at different temperatures. Schottky diodes have lower noises. Schottky diodes are easier to fabricate.

4.6 Ohm Contact：Non-Rectifying M－S Junction Ohm contact: no large spurious impedance which cannot change the equilibrium carrier density and affect the performance of devices. Before contact After contact Almost no barriers in the junction and currents can flow freely in both directions.

4.6 Ohm Contact：Non-Rectifying M－S Junction Schottky contact and Ohm contact Metal－n-type semiconductor: : Schottky contact, rectifying junction : Ohm contact, non-rectifying junction Metal－ p-type semiconductor: Due to the charge effect in the interface states, M-S junctions are usually not Ohm contacts, especially for low doping.

4.6 Ohm Contact：Non-Rectifying M－S Junction For heavy-doping (>1019 cm-3), the space charge region is so narrow that carriers can penetrate the barrier due to tunneling effect. Symmetric I-V curve for forward and reverse biases  Ohm contacts, non-rectifying barrier, low resistance. In practice, heavily doped substrates are used to realize ohm contacts to the metal electrodes.