Development of an electrochemical capacitance-voltage profiler for highly doped silicon wafers

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UNIVERSIDADE DE LISBOA FACULDADE DE CIÊNCIAS

DEPARTAMENTO DE ENGENHARIA GEOGRÁFICA, GEOFÍSICA E ENERGIA

Development of an Electrochemical

Capacitance-Voltage profiler for highly doped silicon wafers

Eduardo Jerónimo dos Santos

Mestrado Integrado em Engenharia de Energia e Ambiente

Dissertação orientada por:

Professor Doutor Killian Lobato, PhD

Doutor Guilherme Gaspar, PhD

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.

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Agradecimentos

Primeiramente, aos meus orientadores Professor Doutor Killian Lobato e Doutor Guilherme Gaspar, pela incrível oportunidade, conança, dedicação e disponibilidade, sem os quais esta dissertação não seria possível.

A todos os membros do projeto de investigação S-LoTTuSS, por todo o tempo e apoio, em especial Doutor Filipe Serra, cuja ajuda foi inestimável.

Ao Doutor Hadi Esmeailsabzali, Doutor Ivo Costa e Barrel Technologies, pelas informações disponi- bilizadas.

À minha família, em especial aos meus pais e irmãs, por todo o apoio nos últimos 24 anos.

Um grande obrigado à minha Inês por todo o apoio e amor.

A todos os meus amigos que compartilharam comigo a aventura da educação universitária, Francisco Bolrão, José Grosso, André Pereira, André Nunes, Miguel da Fonte, Ricardo Duarte, Rita Maçorano por tudo, seja nos bons ou maus momentos.

Por último, mas não menos importante, a toda a comunidade UL.

Esta dissertação foi apoiada pelo projeto S-LoTTuSS através do contrato de subvenção PTDC/CTM- CTM/28962/2017, nanciado pelos fundos nacionais FCT/MCTES (PIDDAC).

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Abstract

As the solar energy production industry evolves it becomes more and more necessary to study with good denition the doping of solar cells in a laboratory. Today it is possible to acquire the equipment to do so, but all the options are costly. The measurements can be done using a Secondary Ion Mass Spectroscopy (SIMS), Glow Discharge Optical Emission Spectroscopy (GD-OES) and Electrochemical Capacitance-Voltage (ECV). The rst option oers results with great resolution, however it is a very expensive option. The GD-OES also emits results with good resolution but with low depth. The latter, the ECV, is easier to use and has great resolution, yet the commercial version of the equipment values 100 000¿.

The motivation of this work is to reproduce ECV equipment, in a way that produces results with the same great resolution but at a lower price point. This work was done by researching and studying papers that used an ECV system and learning about all the physics behind the process.

After compiling all the information, a rst sketch was made for each component in AutoCAD, taking into account all the needs and safety measures until all the conditions were satised. In the end, all the components were designed and assembled in SolidWorks and then analyzed as a whole.

To our knowledge this is the rst study achieving a much cheaper ECV system with the same theoretical precision and little manual work. This method is more accessible to smaller laboratories with less resources, making it possible to study more doping proles than ever before, thus accelerating the rate of solar energy investigation and related elds.

Keywords: Electrochemical Capacitance-Voltage, Tunnel Junctions, SolidWorks, pumps, Doping

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Resumo

À medida que a indústria de produção de energia solar evolui torna-se cada vez mais necessário estudar com boa denição a dopagem de células solares em laboratório. Hoje é possível adquirir o equipamento para tal efeito, mas todas as opções são bastante dispendiosas. As medições podem ser feitas usando uma Espectroscopia de Massa de Íons Secundários (SIMS) que oferece resultados com ótima resolução, mas é bastante caro e com uso muito exclusivo do equipamento, o Glow Discharge Optical Spectroscopy (GD-OES) em que os resultados são emitidos com grande resolução porém a baixa profundidade, ou a Capacitância-Tensão Eletroquímica (ECV) que apesar de ter uma fácil utilização e uma boa resolução, a versão comercial do equipamento tem um custo de cerca de 100 000 ¿.

A motivação deste trabalho é reproduzir um equipamento ECV, de forma que produza os mesmos resultados com a mesma grande resolução, mas a um preço mais acessível. Tal é feito através do estudo de artigos que usaram uma versão antiquada, no caso de artigos mais antigos, ou uma versão comercial, em livros que explicam como as medições são feitas, e nalmente aplicar engenharia reversa dessa informação, obtendo um design que, embora mais simples e menos automatizado, possa funcionar como um ECV comercial.

Os primeiros modelos dos componentes foram feitos em AutoCAD, tendo em atenção todas as medidas de segurança necessárias. Posteriormente, os componentes foram desenhados em SolidWorks e montados em conjunto.

A técnica ECV mede os portadores de cargas eletricamente ativas à superfície da amostra de silício, alternando entre medição e dissolução da superfície da amostra, de modo a serem feitas medições em profundidade maiores.

O ECV desenhado trata-se de uma célula eletroquímica, composta por 3 grupos principais de componentes. O reservatório de onde é introduzido o eletrólito, os componentes de translação onde a célula é transportada e posicionada, e o conjunto de elétrodos pelos quais são feitas as medições.

O material pelo qual é constituído o reservatório é uma das suas principais características. Dado que o eletrólito que nele é introduzido é de natureza nociva para a saúde humana e altamente corrosivo para a maioria dos materiais, foi então decidido a utilização de PTFE. Este polímero é inerte a ácido uorídrico (HF) mesmo em altas concentrações.

A célula contruída tem diversos orifícios, cada um deles com um propósito único, sendo eles, posicionamento de elétrodos, introdução de eletrólito, remoção do mesmo e ejetor de eletrólito, estando estes presentes na tampa da célula. Na face frontal e traseira, encontra-se a zona de contacto com amostra e o orifício para a entrada de iluminação, respetivamente.

A tampa foi desenhada com duas camadas, em que, na camada inferior estão presentes o-rings em cada orifício de maneira que, quando ambas as camadas são apertadas uma contra a outra, o o-ring expande horizontalmente apertando assim os elétrodos. Este pormenor foi pensado com o propósito de impedir que os gases e salpicos provenientes do eletrólito alcancem o utilizador, dado que ambos são altamente nocivos.

O orifício de iluminação tem como propósito a entrada de um feixe de luz para iluminação de amostras do tipo N, devido à necessidade de cargas positivas para a dissolução química da amostra.

O material da janela de iluminação tem como propriedades a transparência para os comprimentos de onda de interesse e ser inerte ou quase inerte ao eletrólito, dado que existe a possibilidade de substituição da janela quando necessário. O equipamento de iluminação não está presente na discussão desta dissertação, sendo, no entanto, possível de descrever as propriedades esperadas do mesmo. É necessário para uma dissolução uniforme da amostra, tal é atingido com a utilização de um feixe de luz horizontal uniforme e controlado na superfície da amostra. Para essa nalidade é utilizado um reetor parabólico.

Na técnica de ECV são necessários três elétrodos, o elétrodo de carbono, o elétrodo calomelano saturado e o elétrodo de platina. Ao controlar a corrente DC que passa entre o semicondutor e o elétrodo de carbono, é possível controlar a taxa de dissolução e as condições de medição. Esta corrente DC é em referência ao elétrodo calomelano saturado. Esse processo garante que nenhuma corrente passe para o outro lado da célula e, portanto, esta não seja polarizada. A corrente AC é medida em relação ao elétrodo de platina que está localizado próximo à amostra para reduzir a resistência em série devido ao eletrólito.

O ejetor de eletrólito tem como função a remoção das bolhas de hidrogénio formadas na superfície

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da amostra durante a dissolução química. O ejetor de eletrólito desenhado utiliza uma tetina para fazer a sucção de eletrólito e ejeção do mesmo, sendo assim possível regular a intensidade do uxo do eletrólito ejetado.

O contacto entre o eletrólito presente no reservatório e a amostra é feito a partir de um adaptador que é inserido na célula eletroquímica. Foram desenhados três adaptadores diferentes, em que o fator diferencial entre eles é a área de contacto com a amostra. No primeiro adaptador foi dada como prioridade a segurança, em que o contacto com a amostra é feito com um o-ring de Viton®, também inerte ao eletrólito, e uma margem de segurança. O segundo adaptador é idêntico ao primeiro, mas sem a margem de segurança. Por m, o terceiro adaptador sem o-ring, em que é abdicado o fator de segurança, mas com a compensação de oferecer melhores resultados devido à menor área de contacto com a amostra.

O sistema de introdução e remoção do eletrólito no reservatório é feito através de tubos de Viton®, com o auxílio de uma bomba peristáltica. Esta bomba não tem qualquer contacto com o eletrólito, uma vez que a sucção é feita através do massageamento do tubo onde o eletrólito é transportado.

Nos componentes de translação está presente a plataforma de vácuo. Esta tem como propósito o posicionamento e xação da amostra. O sistema de vácuo foi desenhado de maneira que seja pos- sível fazer o transporte de qualquer amostra independentemente do tamanho. Esta permite que o semicondutor seja posicionado na horizontal e posteriormente transposto em segurança para a posição vertical onde é encostado ao adaptador do reservatório. Na plataforma de vácuo também está presente o contacto elétrico traseiro, sendo desta maneira possível de fechar o circuito elétrico com os elétrodos.

A força com que a amostra é pressionada contra o adaptador é controlada por um sistema manual.

O sistema consiste num pistão onde numa extremidade está presente a plataforma de vácuo e na outra uma mola. É possível regular com precisão a intensidade da força investida pela mola através do aperto de um parafuso.

Todo o componente de translação está suportado por pés ajustáveis, em que é possível o ajuste de altura caso exista alguma discrepância e também seja facilitado a montagem e desmontagem do equipamento.

Por m, três grupos principais de componentes estão xos numa bacia de acrílico, onde qualquer vazamento do eletrólito será capturado em segurança.

Foi concluído que é possível construir um ECV funcional a um preço bastante mais acessível, abdicando de elementos de automação e substituindo-os por componentes de manuseamento manual de alta precisão.

Uma vez atingido o objetivo deste trabalho será possível aumentar o alcance de laboratórios com menores possibilidades de adquirir equipamentos dispendiosos, permitindo estudar mais pers de dopagem onde antes não era possível, acelerando a velocidade de investigação solar e outras.

Palavras-chave: Capacitância-tensão Electroquímica, Junções de Túnel, SolidWorks, Semicondu- tores, Dopagem

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List of Figures

1 Electric circuit diagram of the C-V method for doping determination . . . 2 2 Electric circuit diagram of the ECV method for doping prole determination . . . 3 3 First design of an ECV proler, taken from Ambridge et al. (1973) . . . 4 4 Still the rst design of an ECV proler, taken from Ambridge and Faktor (1975), but with

less information available . . . 4 5 Most common diagram of ECV components, taken from Blood (1986) . . . 5 6 Most common diagram of ECV components, taken from Saraei et al. (2018) . . . 5 7 Water pipe swing valve analogy, where is possible to see the direction of water ow opens

the swing valve, and opposite direction closes it. . . 6 8 (a) Atoms of a conductive material were is possible to see the conduction band overlapping

the valence shell allowing electron to leave the atom and conduct electricity, (b) Atom of a isolation material where the valence shell is far from the conduction band not allowing the ow of electrons . . . 7 9 Silicon lattice doped with phosphorus and aluminium atoms . . . 7 10 Silicon PN junction, where the green dots represent free charge carrier electrons and the

black dots the free charge carrier holes . . . 9 11 PN junction when reverse bias is applied and no current can ow, and the diode acts as an

isolator . . . 9 12 Charge transfer until the equilibrium is reached . . . 10 13 Depletion region of a n-type pump . . . 10 14 Energy Band diagram for a pump showing the lower edge of the conduction band (E_c), the

donor and the acceptor level within the forbidden gap (Eg), the Fermi level (EF) and the top of the valence band (E_v) . . . 11 15 Band bending diagram of a pump/electrolyte interface in the dark, at the left is represented

before contact, and at the right, after contact and at a state of electrostatic equilibrium when E_F =E_redox . . . 12 16 Diagram of the double layer in the pump/electrolyte interface at the equilibrium condition.V_s

is the potential drop across the scr and VH the potential drop across the Helmholtz layer from Zhang (2007) . . . 12 17 P-type sample in contact with the electrolyte which is connected to a potential source ,

where Qe is the charge applied to the electrolyte and the Qs the charge in the depletion region . . . 13 18 On the Y axis we can see acceptor type impurities,N_A andp the hole density. And on the

X axis is the distance from the surface to the interior of the pump. . . 14 19 Comparison between plots of a p-type sample example that increases doping concentration

with depth , (a)using C−V and (b) C⁻² , taken from Liu et al. (2020) . . . 15 20 Current density-Potencial curves for illuminated and dark n- and p-type pump samples, in

a 2.5wt%HF solution, from Lehmann and Föll (1988) . . . 16 21 Schematic illustration of the three major etching systems . . . 17 22 Possible reaction pathways resulting in the dissolution of Silicon in HF. Monk et al. (1993) 18 23 Etching of n-type materials takes place under conditions of reverse bias, as illustrated

above. b) Forward biasing the n-type sample would deposit ions from solution. The holes created by illumination give rise to an appreciable leakage current through the depleted region. This current is a function of the density of the minority carriers and is therefore only controlled by the level of illumination . . . 19 24 I-V curve of a typical implanted sample . . . 20 25 Excess area of a "blue slice" sample . . . 22

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26 Dissolution rate for silicon oxides for dierent concentrations ofN H₄F solution from Zhang

(2007) . . . 23

27 Ternary phase diagram of HF, N H₄F and H₂O. The dots correspond to some mixtures commonly used as silicon dioxide etchants. The percentages are given in weight percent, from Bühler et al. (1997) . . . 23

28 ECV diagram with the most important components, where 1 is the illumination window, 2 graphite electrode, 3 SCE, 4 Ejector, 5 platinum electrode, 6 Sample, 7 Translation Component, 8 Back contact, 9 electrolyte exit, 10 Electrolyte, 11 Teon®container, 12 Pump/valve equipment and Cleaning containers, 13 Illumination . . . 25

29 Electric circuit diagram of the ECV method for doping prole determination . . . 26

30 Diagram of the ECV electrolyte and deionized water circuit, pumped by an peristaltic pump.All the blue lling represents the electrolyte contaminated space. . . 27

31 Basic information about Threads taken from Thr (2021) . . . 28

32 Tapered thread diagram taken from Tap (2021) . . . 28

33 O-ring diagram . . . 29

34 Side view of the total ECV assembly . . . 30

35 Section view of the total assembly, where 1 is Spring adjusting screw, 2 Piston Spring, 3 Spring guide, 4 Removable Piston, 5 Main Piston, 6 Piston Guide, 7 Platform grabber, 8 Platform holder, 9 vacuum platform, 10 Sample Adapter, 11 Electrochemical cell interior, 12 platin wire, 13 electrolyte ejector, 14 SCE, 15 Graphite electrode, 16 Illumination window, 17 Viton tubing adapter, 18 Translaction legs, 19 Piston guide holder, acrylic tub, 20 Acrylic tub, 21 Electrochemical cell leg . . . 30

36 Trimetric view of the top cover of the ECV . . . 31

37 Side by side diagrams of the two positions expected for the back contact, (a) When no sample is being examined, (b) When the sample is placed on the vacuum platform and applies force to the contact pin, completing the electric circuit . . . 32

38 Contact pin assembly, where 1 is Spring adjusting screw, 2 Spring, 3 Contact pin and 4 Metal cover with a rubber sleeve . . . 33

39 In the diagram (a) is possible to see the how the silicon teat is supposed to work, by applying force ans squeezing the electrolyte inside the ejector body is pushed, and its intensity is proportional to the force applied . . . 34

40 Electrolyte ejector and Silicone teat . . . 34

41 Optical properties of PVDF is represented by the letter c) from Aziz et al. (2020) . . . 35

42 Design for the sample adapter. . . 36

43 Comparison between Diagrammatic cross section of the contact between the sealing ring and the pump sample, showing the outer excess area due to leakage of electrolyte and area not exposed to illumination . . . 36

44 First sample adapter design, with low risk of leakage . . . 37

45 Second sample adapter design, with higher risk of leakage and better area denition . . . . 37

46 Third sample adapter design, with increased probability of leakage but even better area denition . . . 37

47 Trimetric view of the 3 platforms that constitute as vacuum platform . . . 38

48 Two views of the same component, by comparing both images above is possible to compre- hend the vacuum path and how it is applied to the sample uniformly . . . 39

49 Two views of the same component, where is possible to see that the set of hole coincide with a second set of grooves done on the middle component . . . 40

50 Top and middle platforms, (a) Top component with the vacuum holes that coincide with the vacuum groove, (b) Middle platform with both vacuum and o-ring grooves . . . 40

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51 Side view of the positioning platform rst design, (a) on the vertical position the sample is ready to be squeezed against the ECV o-ring, (b) on the horizontal position is possible to

place the sample and select the area which will be analysed . . . 41

52 Side view of the positioning platform nal design, (a) on the vertical position the sample is ready to be squeezed against the ECV o-ring, (b) on the horizontal position is possible to place the sample and select the area which will be analysed . . . 41

53 Close view of the Thrust ball bearing system . . . 42

54 Top view of the Sample positioning platform . . . 42

55 Sample translational Support . . . 42

56 Trimetric view of the translation piston guide holder . . . 43

57 Side by side diagrams at dierent possible heights using the blue screws to lock the inner legs at the desired position . . . 44

58 Trimetric view of the piston guide legs, where the left leg is transparent so is possible to see the inner and outer cylinders . . . 44

59 Hardness chart taken from Rub (2019) . . . 45

60 Compressive load force necessary to seal the for the specic rubber used in our o-ring taken from Com (2021) . . . 46

61 Diagram section view of an o-ring where 5mm of compression results on a 16% squeeze . 46 62 Side view of the spring guide and stopper on both side of the spring . . . 47

63 Side view of the spring guide and stopper when applied no compression and at the maximum value . . . 48

64 Side view of removable piston, highlighted in blue . . . 48

65 Side view without the removable piston . . . 48

66 Trimetric view of the guiding rod . . . 49

67 Comparison between replicated model . . . 49

68 Sample catcher assembled to the vacuum platform . . . 50

69 Flowchart with all the assembly steps needed to correctly assemble the ECV setup . . . . 51

70 Blueprint of the ECV Box with all needed dimensions . . . 53

71 Blueprint of store bought rubber teat with all needed dimensions . . . 54

72 Blueprint of the acrylic tub with all needed dimensions . . . 54

73 Blueprint of the Back contact pin with all needed dimensions . . . 55

74 Blueprint of the back contact spring's adjusting screw with all needed dimensions . . . 55

75 Blueprint of the back contact tube with all needed dimensions . . . 56

76 Blueprint of the Carbon electrode with all needed dimensions . . . 56

77 Blueprint of the ECV Box cover oring with all needed dimensions . . . 57

78 Blueprint of the ECV box legs with all needed dimensions . . . 57

79 Blueprint of the lower cover of ECV Box with all needed dimensions . . . 58

80 Blueprint of the top cover of ECV Box with all needed dimensions . . . 58

81 Blueprint of the Ejector Body with all needed dimensions . . . 59

82 Blueprint of the ejector cover with teat adapter with all needed dimensions . . . 59

83 Blueprint of the rst sample adapter with all needed dimensions . . . 60

84 Blueprint of the Guiding bolt with all needed dimensions . . . 60

85 Blueprint of the guiding rod with all needed dimensions . . . 61

86 Blueprint of the oring with 10mm if inside diameter with all needed dimensions . . . 61

87 Blueprint of the inner leg of the translations piston with all needed dimensions . . . 62

88 Blueprint of the left Viton®tube guide with all needed dimensions . . . 62

89 Blueprint of the lower part of the vaccum platform with all needed dimensions . . . 63

90 Blueprint of a M4 bolt with all needed dimensions . . . 63

91 Blueprint of a M4 nut with all needed dimensions . . . 64

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92 Blueprint of a M6 bolt with all needed dimensions . . . 64

93 Blueprint of the main piston guide with all needed dimensions . . . 65

94 Blueprint of the main translation piston with all needed dimensions . . . 65

95 Blueprint of a outer leg of the translation piston with all needed dimensions . . . 66

96 Blueprint of the positioning platform with all needed dimensions . . . 66

97 Blueprint of the positioning platform's screw with all needed dimensions . . . 67

98 Blueprint of the ejector's pump adapter with all needed dimensions . . . 67

99 Blueprint of the removable piston with all needed dimensions . . . 68

100 Blueprint of the removable piston pin with all needed dimensions . . . 68

101 Blueprint of the right Viton®tube guide with all needed dimensions . . . 69

102 Blueprint of the rotational support with all needed dimensions . . . 69

103 Blueprint of the sample catcher with all needed dimensions . . . 70

104 Blueprint of the second sample adapter with all needed dimensions . . . 70

105 Blueprint of a M4 set screw with all needed dimensions . . . 71

106 Blueprint of the spring adjusting screw with all needed dimensions . . . 71

107 Blueprint of the main spring guide and support with all needed dimensions . . . 72

108 Blueprint of the third sample adapter with all needed dimensions . . . 72

109 Blueprint of thrust ball bearing with all needed dimensions . . . 73

110 Blueprint of the top vacuum platform with all needed dimensions . . . 73

111 Blueprint of the translation piston guide holder with all needed dimensions . . . 74

112 Blueprint of the V13-32 spring model from Polimold with all needed dimensions . . . 74

113 Blueprint of transparent window material with all needed dimensions . . . 75

114 Blueprint of the needed adapter to connect the vacuum tubes with all needed dimensions . 75 115 Blueprint of the window sealing ring with all needed dimensions . . . 76

116 Image corresponding the step 1 of the owchart . . . 77

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150 ECV setup totally assembled . . . 102

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List of Tables

1 Optical properties and mechanical strength of conventional PVDF lm and GT-PVDF-3 lm from Qui (2020) . . . 35 2 O-ring properties in inches used to calculate the Force needed to squeeze 16% of the CS for

both designs of Sample adapters with o-rings . . . 46 3 O-ring properties in millimeters used to calculate the Force needed to squeeze 16% of the

CS for both designs of Sample adapters with o-rings . . . 47

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1 Abbreviations and Acronyms

AC Alternating Current.

DC Direct Current

ECV Electrochemical Capacitance-Voltage GaAs Gallium arsenide

HF Hydrouoric acid InP Indium phosphide IR Infra-Red

Pt Platinum

PTFE Polytetrauoroethylene SCE Saturated Calomel Electrode SIMS Secondary Ion Mass Spectroscopy UV Ultraviolet

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2 List of Symbols

.

A Area (cm²) C Capacitance (F) D Molecular density

E_c Energy of the conduction band (eV) E_F Fermi level (eV)

Er Etch Rate (nm/s)

E_v Energy of the valence band (eV) εRelative Permittivity of the pump ε0 Permittivity of free space

F Faraday's constant (9.64∗10⁴C) I Current (A)

M Molecular weight (g)

N Charge carriers density (cm⁻³) n Free charge electrons density (cm⁻³) p Free charge holes density (cm⁻³) q Electronic charge (C)

Qm Charge applied to the metal contact Q_s Charge applied in the depletion region T Temperature

Vi Contact potencial dierence (V) V_s Band bending of the pump V_{f b} Flat band potential

Wd Width of the depletion layer (nm)

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W_r Thickness of the material removed by dissolution (nm) ρ Density of the pump (g/cm³)

σ Conductivity of electronsS/m µ Mobility of electrons (m²/V.s) x_m Crater depth

z Eective valence number

z_r predened Eective valence number

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3 Introduction

The conversion of solar light into electric energy from the photovoltaic eect is believed to be the most promising source of renewable energy Delucchi and Jacobson (2011). The solar photovoltaic energy industry is growing at a radical rate, evolving from a niche market into a large-scale low-cost renewable energy technology. A clear indicator of this great evolution is that 80% of the worldwide PV installa- tions have been deployed during the last 5 years Tsanakas et al. (2020). But to be possible for further sustainable development of solar technology, permanent improvement of the material properties and conversion eciencies are needed. There are various ways to increase eciency, one of them being learning more about dierent combinations of doping and pumps (SC), so it's possible to study more methods of doping and create correlations from the dierent pump parameters. The precise control over the carrier concentration prole is a paramount subject for device fabrication since it has an inuence on carrier transport properties as well as on the conversion eciency between carriers and photons Da Silva Filho and Frateschi (1999). The study of the pump properties does not only apply to the photovoltaic industry but also to the eciency of all pump devices such as diodes, present in almost all electronics. Even though silicon is the most known pump material associated with solar cells, other SC materials such as Indium Phosphide would also benet from optimum performance and reliability research, gained from the accurate knowledge of doping proles.

The most used methods for doping prole measurements are Electrochemical Capacitance-Voltage Proling (ECV), Secondary Ion Mass Spectroscopy (SIMS), and Glow Discharge Optical Emission Spec- troscopy (GD-OES), the rst one being the discussed method in this dissertation. The SIMS method is a widely employed material characterization technique with high sensitivity and high depth resolution. It consists of using an ion beam to bombard the surface of the material in study, so those ions composing the surface are ejected. Those are then analyzed giving all the information about the composition of the sample surface. This technique was rst observed in 1910 but only became available in the mid 1960s.

The most popular commercial dedicated SIMS instrument had a cost of between 400 000 and 1 million US$(1993)Schwarz (2001).

The second method GD-OES, consists of applying a potential between the sample and the electrode, emitting an electrical discharge heating the sample surface to thousands of degrees. The heated surface will then vaporize, and those vapors consiste of element characteristic emission lines that can be analyzed by a spectrometer. The spectrometer will then separate them into element-specic wavelengths whose intensity is proportional to their concentration. This method requires expensive equipment and can only determine proles at low depth.

Given such a high price for the usage of these methods, another way to determine doping proles was needed, and that became the principal motivation for ECV development.

Currently most research where the determination of doping proles is implied, the technology used is SIMS, where its usage has to be justied because of the high cost of usage. There is a clear need for a more economical solution, but still with high denition method like the ECV.

Today, even though ECV devices exist on the market, their price is still too high, varying between 90 000 and 110 000¿. Given that most of the materials present in an ECV system are not expensive, mostly being Teon®and steel, it is believed to be possible to assemble a working ECV with the same accuracy and depth denition at much lower prices of construction.

Since the biggest justication for such a high price is the automation of all measurement processes, it's possible to design a mostly manual design where automation is replaced with careful and precise handling, with help of thoughtfully chosen materials.

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4 State of the Art

Since the mid 20th century big investments have been made to create tools that can describe how doped a wafer sample is. The rst big incentive was the discovery of photovoltaic energy, where the unknown amount of dopants present in the sample would increase the eciency or decrease without knowing why.

One of the rst methods to determine the dopant concentration prole was the Capacitance-Voltage technique. The C-V technique was very similar to the ECV, which is the main subject of this dissertation, the main dierence is how the contact is made between the sample and the source of bias. As shown in the gure below, the CV method uses a metal contact as the interface with the pump sample, and then by applying bias it's possible to calculate the dopant density.

Figure 1: Electric circuit diagram of the C-V method for doping determination

The doping determination is done by applying a bias to an electric circuit from the front to the back of the sample. This will create a polarized volume inside of the sample known as the depletion region. By varying the bias applied, the polarized volume will also vary, permitting the acquisition of a Capacitance value, which is used to calculate the doping prole of the sample and will be further discussed later in this dissertation.

Although with the metal contact it is fairly easy to determine the area of contact, which is a very important parameter, there is also a major step back associated with this metal interface, which is the limited depth of doping determination. Because the depletion width is measured from the surface to the interior of the pump, and because this method preserves the sample surface, there is no way to determine at further depth.

Later was invented by Ambridge and his co-workers the ECV technique, with an electrolyte instead of a metal contact. This liquid contact by being transparent, allows the observation of the radiation spectra being absorbed, that way providing the extra capability of band-gap proling but also solves the depth limitation problem discussed before.

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Figure 2: Electric circuit diagram of the ECV method for doping prole determination

After comparing the C-V method with the ECV it is easily noticed that instead of a metal front contact, it is instead used a liquid to make contact with the sample. This liquid is an electrolyte and is used to complete the electric circuit and etch the surface of the sample.

Also, it can be noticed that it is used 2 dierent electric circuits, one to apply DC bias, from the graphite electrode to the sample and the other much closer to the sample from the platinum wire to the sample to apply AC bias.

The depth problem is solved by the etching process, which dissolves the surface of the sample when a certain bias is applied, allowing deeper measurements.

As it will be later explained, there are 2 types of doped pumps, n-type and p-type. For an n-type sample, ething must be done under illumination, that is why a transparent window has also been added.

The addition of the liquid interface caused the most change to the setup design. Because of the dangers associated with this liquid, a lot of security measures had to be added, since the most used electrolyte is a dangerous acid. Also with a liquid interface, electrodes are needed for the measurements to be done, so their placement had to be carefully thought out.

The most used electrolyte for this purpose are HF solutions with varying concentrations but are always dangerous since they can dissolve most common materials including most of the known polymers, ceramics, metals, esh, and bone.

So engineers had to design structures that could contain the electrolyte and have other features that will be talked over.

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Figure 3: First design of an ECV proler, taken from Ambridge et al. (1973)

Figure 4: Still the rst design of an ECV proler, taken from Ambridge and Faktor (1975), but with less information available

This rst documented design already used Teon®. as the main body compound but all the other components are from disposable materials. The mounting ring, where the sample is being placed, is made of PVC which is not inert to HF and swells over time when exposed to high concentrations. Also because illumination is needed to etch the surface of an n-type pump most of the early designs did not use inert materials to construct the illumination window.

The usage of these disposable materials was justied because at the time the biggest concern was not to construct an expensive inert design, but to learn about what works, and carefully adapt, since is such a dangerous electrolyte.

As we can see by comparing both gures 3 and 4, illustrations became more and more just illustrative,

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giving less detail of the actual construction.

Today most of the papers related to ECV have the same diagram as below, where is possible to see that it was added a pump to eject electrolytes against the sample, but there is no description of how it is installed.

Figure 5: Most common diagram of ECV components, taken from Blood (1986)

Figure 6: Most common diagram of ECV components, taken from Saraei et al. (2018)

Today most of the published studies using this technique, have references of using a commercial version of the ECV, meaning that there is little to no information about the inner working of the ECV system.

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4.1 Conductor, Isolator and Semi-conductor

Typically a diode is composed of a black cylindrical body with a wire coming out of it from each side.

The diode has a particularity of only letting current pass from one direction. It's easier to imagine this like a water pipe with a swing valve installed. So when the water is passing in one direction the pressure is going to open the valve, but the moment the direction of the ow changes the swing valve automatically shuts.

Figure 7: Water pipe swing valve analogy, where is possible to see the direction of water ow opens the swing valve, and opposite direction closes it.

This is very similar to a diode, and we use it to control the direction of current ow in the circuit.

Since the electrons ow from the negative to the positive pole of the circuit, is necessary to have the diode installed the correct way to assure the diode is acting as a conductor and not an isolator by not letting pass electrons. If the current is owing, we call this the Forward Bias. Otherwise, if the diode is acting as an insulator we call that current the Reverse Bias.

As we know electricity is the ow of free electrons between atoms. Normally cooper wire is used to conduct, since copper has a lot of free electrons, which makes it very easy to pass electricity through.

Additionally, it's used rubber on the outside of the wire to make it safe since rubber's electrons are held very tightly and they can not, therefore, move between atoms.

If we look at a metal atom, we can see a nucleus at the center and it is surrounded by several orbital shells, which hold the electrons.

Each shell holds a maximum number of electrons, and an electron has to have a certain amount of energy to be accepted into each shell. The electron located further from the nucleus holds the most energy. The outermost shell is known as the valence shell, a conductor material that has between 1 to 3 electrons in it. Electrons are held in place by the nucleus but if an electron on the valence band reaches the conduction band it can break free from the atom and move to another. In the case of metal atom, the valence band, and the conduction band overlap. So is very easy for the electron to move.

For an insulator, the outermost shell is packed and there is very little to no room for an electron to join, the nucleus has a strong grip on its electrons and the conduction band is far away.

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(a) Atom of an conductive material (b) Atom of an isolator material

Figure 8: (a) Atoms of a conductive material were is possible to see the conduction band overlapping the valence shell allowing electron to leave the atom and conduct electricity, (b) Atom of a isolation material where the valence shell is far from the conduction band not allowing the ow of electrons

So electrons can not reach it to escape, therefore electricity cannot ow through this material.

Silicon is an example of a pump, there are one too many electrons in the outermost shell for it to be a conductor, so it acts as an insulator, but because the conduction band is quite close, if provided enough external energy, some electrons will make the jump to the conduction band to become free.

The energy needed to make the jump can be given by thermal energy if the conduction band is quite close.Therefore this material can act as both an insulator and a conductor.

Pure silicon has almost no free electrons, so what engineers do is dope the silicon with a small amount of another material to change electrical properties. We call this p-type and n-type doping or impurities, and we combine these two doped materials to form a diode.

Imagining an undoped silicon material, this lattice is composed of silicon atoms surrounded by four silicon atoms. Each atom wants eight electrons in its valence shell, but each silicon atom only has four electrons, so they share an electron with their neighboring atom to get the eight, this is called covalent bonding.

Figure 9: Silicon lattice doped with phosphorus and aluminium atoms

When we add in an n-type doping atom it will take the position of some of the silicon atoms. Since the phosphorus atom has 5 electrons in its valence shell, as the silicon atoms are sharing electrons to get

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their desired eight, they do not need this extra one, so now there are extra electrons in the material and these, therefore, are free to move.

With the p-type doping, we add in a material such as aluminum. This atom has only three electrons in its valence shell, so it can not provide its four neighbors with an electron to share, so one of them will have to go without, there is, therefore, a hole created where an electron can sit and occupy, so now we have two pieces of silicon, one with too many electrons and one with not enough electrons.

Because impurities have such a big impact on the electrical properties of the pump, it's necessary to keep these materials in sterile conditions.

Shallow dopants are those with an energy level very close to the conduction band, for a n-type dopant or the valence band for an p-type. Since shallow dopants are easily ionized, the concentration of the dopant atoms will be almost the same as the concentration of the free charges.

Because the typical donor density N_d and acceptor density N_a concentration is around 10¹⁴ to 10¹⁸ and the intrinsic carrier concentration, n_i or p_i around 10⁵ to 10¹¹, their value can be considered as insignicant.

N_d≫n_i

n=ni+ND ∼=ND

So the value of the free charge carriers nor p, can be assumed as the same as the donor density ND

or N_A.

NA≫pi

p=p_i+N_A∼=N_A

Assuming that we can control the number of charge carriers present in the pump, it's intuitive to think that, the more doped the material is, the more conductive will be the pump.

σ=qnµ_n+qpµ_p [σ] =S/m [µ] =m²/V.s

v_d=µE [v_d] =cm/s [E] =V /cm

As we can see, conductivity σ is closely dependent on the mobility µ, which denes how well the electron or hole can move in an electric eld. Holes and electrons have dierent mobilities, the electron tends to have superior mobility and it does not depend on the charge, this means that the mobility is not aected by the positive charge of the hole or the negative charge of the electron.

We can join an n-type material with a p-type to form a PN junction, and at this junction, we get what is known as Depletion region, where some of the excess electrons from the n-type side will move over to occupy the holes in the p-type side.

This migration will form a barrier with a buildup of electrons and holes on opposite sides. The electrons are negatively charged so therefore the holes are considered positively charged, so the build-up is considered slightly negatively/positively charged.

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(a) PN juntion before equilibrium is reached (b) PN junction in equilibrium

Figure 10: Silicon PN junction, where the green dots represent free charge carrier electrons and the black dots the free charge carrier holes

This creates an electric eld and prevents more electrons from moving across, the potential dierence across this region is about 0.7 Volts in typical diodes. When we connect a voltage source across the diode with the positive side connected to the p-type and the negative side connected to the n-type, this will create a forward bias and allow the current to ow. For this to happen the voltage source has to be bigger than 0.7 V, otherwise, the electrons can't make the jump.

If we inverse the power supply so that the positive side is connected to the n-type material and the negative side is connected to the p-type material, the holes are going to be pulled to the negative side and the electrons pulled to the positive side, that way increasing the depletion region and not letting pass current, acting like an insulator.

Figure 11: PN junction when reverse bias is applied and no current can ow, and the diode acts as an isolator

Almost the same phenomenon happens when a p-type or n-type material makes contact with a solution electrically active.

Since both sides of the interface have dierent potentials, the free charges are immediately going to pass to the solution side until equilibrium is reached. Equilibrium means that the Fermi level and the redox level are the same. The charges are passed to the electrolyte and not the other way around because the electrolyte behaves like a buer solution, this means that the electrolyte is a very diluted solution, so

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the number of available states per unit of energy is greatly over the pump's, so generally is assumed that the electrochemical potential (or redox fermi level) does not move.

(a) For the p-type pump (b) For the n-type pump

Figure 12: Charge transfer until the equilibrium is reached

For an n-type pump, although the equilibrium of the fermi level is reached, every electron that is transferred to the electrolyte side leaves a hole in its place creating a non-equilibrium zone called a depletion region or a space charged region, scr, which has a width of W.

The greater the potential dierence across the interface the greater theW will be.

(a) PN juntion after equilibrium is reached (b) PN junction in equilibrium Figure 13: Depletion region of a n-type pump

4.2 Band Bending

For ideal crystals, the energy spectrum consists of two dierent types of energy bands, those with lled energy levels (allowed bands) and those with no energy levels (band gaps).

The energy levels in a pump are characterized by the conduction and valence band edges,Ecand Ev, in relation to the Fermi level EF. The Fermi level describes the distribution of the carriers in the bands in equilibrium and is the chemical potential of the electrons in the pump. Also, the distance that the two bands are from each other depends on the strength of the chemical bonds, E_g =E_v−E_c.

For silicon, at the normal temperature value of 26 degrees Celsius, the band gap is1.12eV. A reduction of more than 100meV is associated with a dopant concentration of 10¹⁹/cm³, for an eective band gap reduction, the doping has to be as high as 10¹⁸/cm³.

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The electronic conductivity of the pump depends on the intrinsic properties of the basic substance in the crystal, and on the extrinsic properties of the impurity atoms used to dope the pump.

In intrinsic pumps, at a temperature superior toT >> 0K, is the thermal excitation, allowing some electrons from the valence to the conduction band, that generates the current carriers. At the same time, an equal amount of positively charged holes are created in the valence band. These holes possess the same charge as an electron but their value is positive. We can join an n-type material with a p-type to form a PN junction, and at this junction, we get what is known as Depletion region, where some of the excess electrons from the n-type side will move over to occupy the holes in the p-type side.

This migration will form a barrier with a buildup of electrons and holes on opposite sides. The electrons are negatively charged so therefore the holes are considered positively charged, so the build-up is considered slightly negatively/positively charged.

Figure 14: Energy Band diagram for a pump showing the lower edge of the conduction band (E_c), the donor and the acceptor level within the forbidden gap (Eg), the Fermi level (EF) and the top of the valence band (Ev)

In the same way that the pump has the Fermi level that describes the equilibrium distribution of carriers, in the bands, there is a chemical potential of the pump's electrons that when in contact with the electrolyte forms a redox potential, E_redox. This redox potential describes the tendency of the species to give up or accept electrons and can be considered the eective Fermi level of the solution.

When contact between electrolyte and pump is made, equilibrium is attained,EF =Eredox, and the two levels become equal.

For an n-type pump, where E_F is higher than E_redox, electrons will ow from the pump to the electrolyte. The excess charge in the solid sample will not reside at its surface but instead will be distributed in a region near the surface called, the space charge region (scr). So the resulting electric eld in the scr can be shown by a band bending diagram.

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Figure 15: Band bending diagram of a pump/electrolyte interface in the dark, at the left is represented before contact, and at the right, after contact and at a state of electrostatic equilibrium whenEF =Eredox

There exists other parameters that determine the energy levels on the electrolyte side. The Helmholtz layer is formed by ions attracted to the electrode surface by the excess of charge in the space charge layer and the polar water molecules. The GouyChapman layer, is a region of solution with excess ions of one sign and its thickness depends on the electrolyte concentration. For concentrated electrolytes (<0.1M) the contribution of the GouyChapman layer is negligible and the potential drop on the electrolyte side can be expressed by the potential drop in the Helmholtz layer, VH.

Figure 16: Diagram of the double layer in the pump/electrolyte interface at the equilibrium condition.Vs

is the potential drop across the scr and V_H the potential drop across the Helmholtz layer from Zhang (2007)

The typical thickness of each of these layers is indicated in gure 16, but their value can change depending, as said previously, on the doping level of the pump, electrolyte concentration, and the bias condition.

The magnitude of the Helmholtz potential is determined by the adsorption/desorption processes, which in many cases depend on the pH of the electrolyte. It's possible to reach V_H = 0by adjusting the pH of the solution, and this is called the point of zero charge (pzc).

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4.3 Practical context

The electrochemical capacitance-voltage (ECV) technique is used to obtain a prole of the doping concentration over any arbitrary thickness, by repeating two processes, the measurement of C-V which is the dopant prole, and the etching of the surface that is chemically dissolving micron thick layers by feeding electrical energy to the chemical process. This etching can be controlled by choosing the amount of current that is being injected.

The electrolyte has to be carefully chosen by their properties, this acid has to be inert to silicon by itself, or the etching can not be controlled. It has to be one that, when the ejected current reacts with the sample, it dissolves it. Unlike in the case of III-V pumps InP and GaAs, silicon forms a non-soluble oxide SiOx (x= 1.7−1.9)at the surface during anodic oxidation. By purely chemical reaction, uoride ions dissolve this oxide in the electrolyte. Even though the rate of formation of the oxide is proportional to the rate of the current density, the dissolution is going to depend on the composition of the electrolyte and the silicon properties Mika and Grmanov (2002).

One of the properties of silicon that is very troublesome is the formation of silicon-on-insulator structures by oxidation of buried porous silicon layers Peiner and Schlachetzki (1992). The main manifested problem comes from the uncertainty of the eective dissolution valence number of z (the number of electronic charges transferred per atom of silicon dissolved) and consequently the reduced accuracy of depth calibration. This is a problem that is going to be solved by calibrating the algorithm controlling the electronic components, like the current feeder, and comparing the results with a certied electrochemical prole plotter or comparing the proles obtained by ECV with the results from a Talystep proler, which is an electromechanical method for measuring roughness and thin lm thickness, measuring surface roughness down to 4 Angstroms using a 0.1-micron probe tip.

4.4 pump-Electrolyte interface 4.4.1 Dierential Capacitance Method

The Dierential Capacitance is the method used with the etching process to determine the carrier concentration at a determined depth.

To explain what the Dierential Capacitance method is, it's easier to use a p-type sample as an example and explain step by step what is happening.

Figure 17: P-type sample in contact with the electrolyte which is connected to a potential source , where Qe is the charge applied to the electrolyte and the Qs the charge in the depletion region

The width of a reverse-biased space-charge region of a pump junction device depends on the applied

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voltage. As we can see in the gure 17, we have a p-type pump with its surface connected to a bias source that provides a potential V to the sample.

This potential creates a electric eld, since the sample is a p-type pump that will have holes that move around as free charge carriers and this holes will be pushed away from the positive electric eld created, to the interior part of the pump, leaving only unmovable intrinsic negative ions, from the doping, in its place, creating a negative region with the width of W.

Applying DC Bias,V, will determineW, and adding to it a AC bias,v, will result in a small uctuation of W, since the width of space charged region, scr, and the potential applied are directly related, and that small variation isdW, and its value will vary, being 0at the lowest value of the bias and peak at the maximum applied bias.

Capacitance is equal to the variation of the charge in function of the applied voltage. Since it's a p-type pump its free charge carrier holes, are pushed to the interior of the sample past the depletion region, leaving a region negatively charged with the same module value of the holes that were pushed, that's why dQe =−dQ_s.

Figure 18: On the Y axis we can see acceptor type impurities,N_A and pthe hole density. And on the X axis is the distance from the surface to the interior of the pump.

As we can see in the gure 18, in the scr, the hole density is zero since all the holes have been pushed to the interior of the sample, but the acceptor-type impurities remain at the same energy level since they are unmovable intrinsic carriers. Past the scr, both NA and p remain almost at the same level since is a neutral region that hasn't been aected.

In gure 18 we have p₁(x)(V = V) and p₂(x)(V = V +v) where, p₁ represents the hole density at corresponded DC bias applied through the graphite electrode andp2 the DC plus AC bias applied at the platinum wire electrode. So because of the alternating current being applied, the amount of charge at the depletion region keeps on changing in function of the bias applied, and the change in function of the applied voltage determines the capacitance.

C= dQe

dV =−dQs

dV (1)

The amount of change of charge in response to the applied bias depends on the carrier concentration, the bigger the carrier concentration the smaller change of the charge dQs .

Qs=qA Z W

0

(p−n+N_D⁺−N_A⁻)dx (2) Whereq represents the charge of an ion,Athe area of contact, limited by the o-ring, where the charge Q_e is being applied,p−nthe dierence between the free charge carriers densities,N_D⁺ andN_A⁻the Donor and acceptor type impurities or the doping concentration.

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In our example, the pump is p-type meaning that it only has acceptor type impurities. We can also ignore the dierence between free charge carrier densities since they have been pushed to the interior of the pump, past the scr.

Qs≈ −qA Z W

0

N_A⁻dx (3)

Since we know that charge in the depletion region is intimately related to the bias applied as Eq.1, we can add the change in bias (dV) to the Capacitance equation

C =−dQs

dV (4)

There is a very know equation known as the MottSchottky equation that relates Capacitance, that can be measured, with the potential applied.

1 C_sc² =

2

eεε₀N_a V_s−kT e

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C_sc² = 2

eεε0Na

V_m−V_{f b}−kT e

(6) or

C_sc =

e²N_aεε₀/(2kT)1/2

exp[−eV_s/(2kT)] (7) Two important parameters can be determined by plotting _C¹2

sc versusV_app, the atband potentialV_{f b} when C⁻² = 0 (where Vs = 0) and the density of charge in the space charge layer, that is, the doping concentration N_a.

Csc =

e²Naεε0/(2kT)1/2

exp[−eV_s/(2kT)] (8) 1

C_sc² = 2

eεε₀N_a Vs−kT e

(9) Here both equations can be used to plot and both will give you information about the sample, but as we are going to see , the equation 5 is a lot more informative than just capacitance versus the bias applied.

Figure 19: Comparison between plots of a p-type sample example that increases doping concentration with depth , (a)using C−V and (b) C⁻² , taken from Liu et al. (2020)

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As we can see in the gure 19, capacitance in the function of the bias applied appears linear even if the sample in the gure 19 is more heavily doped at a deeper depth, but when plotting using C⁻² we can see a decrease in slope value, indicating, in this case, an increase on the doping concentration and that change in slope represents a doping density increase at that depth.

N_A= 2 qεε0A²^d(C_dV⁻²⁾

= 2

qεε0∗slope N_A= 1

qεε0A² ∗ C³

dC/dV (10)

Another advantage of using C⁻² is that a highly doped layer is going to appear as a linear function, as described by the red line, that linear function, decreases greatly the error associated with the measurement of doping concentration for eachV value.

4.4.2 Etching

The etching process wasn't always associated with the C-V measurement. It became apparent that the advantage of using an electrolyte as the interface with the pump when combining capacitance measurement with the etching technique, since it allows the doping measurement to be done at any wanted depth.

Etch is the dissolution process that uniformly or preferentially removes material from the pump crystals immersed in a solution, and it depends on the presence of holes. For a p-type material, holes are very abundant, and the dissolution is ready to be achieved by forward biasing of the pump/electrolyte junction.

For an n-type pump the behavior becomes identical if the sample is illuminated at a suciently high light intensity.

Figure 20: Current density-Potencial curves for illuminated and dark n- and p-type pump samples, in a 2.5wt%HF solution, from Lehmann and Föll (1988)

The anodic polarization curves are typically characterized by two peak currents J₁and J₂ and two plateau currents J3 andJ4.

Until the potential peak ofJ1, the electrode behavior is characterized by an exponential dependence of current on potential, and by the uneven dissolution of silicon surface leading to the formation of porous silicon. At potentials more positive than J1 the curve is characterized by the formation and dissolution of a surface oxide lm, resulting in a smooth surface. Also, the current at potentials more positive than that J₁ is not constant, indicating that the oxide formed at dierent potentials has dierent properties.

The values of the characteristic currentsJ1 to J4, which may occur at dierent potentials for p-type and

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n-type silicon, and are a function of the electrolyte composition but are largely independent of doping since they are determined by the properties of the anodic oxide.

The potential corresponding to the maximum slope of the i-V curve is about the upper limit for the formation of a uniform porous silicon layer. At potentials between the maximum slope and the current peak, the porous layer may still form but its surface coverage is not uniform.

The etching process can be used for various reasons. The etching can be isotropic, so the etching happens in all directions, anisotropic etching when etching happens in only one direction and defect etching, a way of using etching to nd dislocations and small cracks on the sample.

Figure 21: Schematic illustration of the three major etching systems

In HF based solutions, the over all reaction involving the dissolution of silicon oxide can be expressed as

SiO₂+ 6HF ⇔2H⁺+SiF₆²⁻+ 2H₂O (11) As we can see from the equation 11, one of the products will be hydrogen ions which will result in hydrogen gas. Meaning that hydrogen bubbles will form on the surface of the sample, which could result in bad etching conditions. So later it will be discussed a way to blow those bubbles away.

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Figure 22: Possible reaction pathways resulting in the dissolution of Silicon in HF. Monk et al. (1993)

The path I shows the case when HF reacts directly with the surface leading to breaking of SiO bonds.

Path II and III show the case of absorption of hydrogen on the oxygen to form hydroxyl groups as the rst step.

Then one path where the formation of the hydroxyl group causes polarization and weakening of the underlying Si-O bond, thus facilitating the attack by a uoride species(II), and another path where the hydroxyl group is replaced by the uoride ion, which results in weakening and breaking of the underlying SiO bond(III). Zhang (2007)

For n-type materials, in which electrons are the majority charge carriers, holes have to be created for dissolution to take place. This is done by illuminating the pump/electrolyte interface with the light of a short enough wavelength (550nm).

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(a) P-type pump Forward Bias (b) N-type pump Reverse Bias under illumination Figure 23: Etching of n-type materials takes place under conditions of reverse bias, as illustrated above.

b) Forward biasing the n-type sample would deposit ions from solution. The holes created by illumination give rise to an appreciable leakage current through the depleted region. This current is a function of the density of the minority carriers and is therefore only controlled by the level of illumination

Electrons can be promoted from the valence band to the conduction band leaving holes behind. For this to happen the wavelength, λ, must obey the condition:

λ≤ h_c

Eg (12)

The etching of silicon oxides has been the most investigated in HF-based solutions. Various salts, acids, and other substances can be added to the HF solution to obtain better control of the etch rate, sensitivity, uniformity, and stability of the solution composition. The wide variety of silicon oxides produced by dierent processes may have dierent etch rates. In a given etch solution, a given oxide has a specic etch rate and dierent oxides may etch very dierently in dierent etching solutions. So given a large number of oxide/etchant combinations, it's dicult to generalize the etching characteristics of silicon oxides. But in most cases it's safe to assume that the oxidation of the silicon is the rate-controlling step in silicon etching with SiO₂ being removed as fast as it is formed. Hu and Kerr (1967)

Given that our experiment utilizes etching to reach a deeper surface of the pump, the etching system that we are going to use is isotropic, since the wanted result is a uniformly etched surface.

As said, silicon forms a non-soluble oxideSiO_x during anodic oxidation, if under a constant potential or a constant current density, and by purely chemical reaction, uoride ions dissolve this oxide in the electrolyte. Although the rate of formation of the oxide is proportional to the current density, the rate of dissolution depends mainly on the composition of the electrolyte and the properties of silicon.

The main problem is the uncertainty associated with the eective dissolution valence number z (number of electronic charges transferred per atom of silicon dissolved) and consequently the reduced accuracy of depth calibration. The eective valence dissolution valence number may vary within the range from 2 to 4 from Arita (1978).

According to work Mika and Grmanov (2002), for p-type silicon z = 3.72 at an anodic dissolution process with a0.1M solution ofN H4F.HF, while for implantation layers in epitaxial substrate isz= 3.3.

Development of an electrochemical capacitance-voltage profiler for highly doped silicon wafers